Finite Group Databasebeta

← #28293265

Subgroups — #28293265

Order 13568.

7082 conjugacy classes of subgroups.

The subgroup lattice has 2026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288826C211yesmaximal, characteristic, complemented
2#20288824C211yesmaximal, characteristic, complemented
3#20288801C211yesmaximal, characteristic, complemented
4#20288791C211yesmaximal, characteristic, complemented
5#20288788C213yesmaximal, complemented
6#20288782C213yesmaximal, complemented
7#20288762C213yesmaximal, complemented
8#20288759C213yesmaximal, complemented
9#20288726C211yesmaximal, characteristic, complemented
10#20288709C211yesmaximal, characteristic, complemented
11#20288701C211yesmaximal, characteristic, complemented
12#20288679C213yesmaximal, complemented
13#20288672C213yesmaximal, complemented
14#20288661C213yesmaximal, complemented
15#20288659C213yesmaximal, complemented
16#20288619C213yesmaximal, complemented
17#20288605C213yesmaximal, complemented
18#20288533C211yesmaximal, characteristic, complemented
19#20288506C211yesmaximal, characteristic, complemented
20#20288460C213yesmaximal, complemented
21#20288449C213yesmaximal, complemented
22#20288392C211yesmaximal, characteristic, complemented
23#20288381C211yesmaximal, characteristic, complemented
24#20288146C213yesmaximal, complemented
25#20288135C213yesmaximal, complemented
26#20288098C213yesmaximal, complemented
27#542×D53C213yesmaximal, complemented
28#20287924C211yesmaximal, characteristic, complemented
29C4×#13133263C211yesmaximal, characteristic, complemented
30#20287917C211yesmaximal, characteristic, complemented
31C53×#3518C211yesmaximal, characteristic, complemented
32C2×#13133265C2211yescharacteristic
33C2×#13133263C2211yescharacteristic
34C22×#11719949C2211yescharacteristic
35#16811358C2213yescomplemented
36#16811358C2213yescomplemented
37#16811356C2213yescomplemented
38#16811355C2213yescomplemented
39Q8×Dic106C2211yescharacteristic, complemented
40#16811349C2211yescharacteristic, complemented
41#16811349C2211yescharacteristic, complemented
42#16811347C2213yescomplemented
43#16811346C2213yescomplemented
44#16811345C2213yescomplemented
45#16811342C2213yescomplemented
46#16811341C2213yescomplemented
47#16811336C2213yescomplemented
48#16811336C2213yescomplemented
49#16811336C2213yescomplemented
50#16811334C2213yescomplemented
51#16811334C2213yescomplemented
52#16811333C2213yescomplemented
53#16811331C2213yescomplemented
54#16811331C2213yescomplemented
55#16811331C2213yescomplemented
56#16811324C2216yescomplemented
57#16811324C2216yescomplemented
58#16811323C2213yescomplemented
59#16811320C2213yescomplemented
60#16811319C2213yescomplemented
61#16811317C2213yescomplemented
62#16811314C2213yescomplemented
63#16811314C2216yescomplemented
64#16811313C2213yescomplemented
65#16811312C2213yescomplemented
66#16811309C2216yescomplemented
67#16811307C2213yescomplemented
68#16811303C2216yescomplemented
69#16811303C2216yescomplemented
70#16811300C2216yescomplemented
71#16811298C2216yescomplemented
72#16811298C2216yescomplemented
73#16811298C2216yescomplemented
74#16811297C2216yescomplemented
75#16811297C2216yescomplemented
76#16811295C2211yescharacteristic
77#16811292C2211yescharacteristic
78#16811288C2213yescomplemented
79#16811288C2213yescomplemented
80Q8×C22⋊D53C2211yescharacteristic, complemented
81#16811285C2211yescharacteristic, complemented
82#16811285C2211yescharacteristic, complemented
83#16811285C2216yescomplemented
84#16811284C2211yescharacteristic
85#16811284C2211yescharacteristic, complemented
86#16811284C2211yescharacteristic, complemented
87#16811281C2216yescomplemented
88#16811280C2211yescharacteristic, complemented
89#16811277C2213yescomplemented
90#16811276C2213yescomplemented
91#16811276C2213yescomplemented
92#16811276C2213yescomplemented
93#16811275C2213yescomplemented
94#16811273C2213yescomplemented
95#16811270C2213yescomplemented
96#16811269C2213yescomplemented
97#16811269C2213yescomplemented
98#16811266C2213yes—
99#16811266C2213yescomplemented
100#16811266C2216yescomplemented
101#16811264C2213yes—
102#16811264C2213yescomplemented
103#16811264C2213yescomplemented
104#16811262C2216yescomplemented
105D4×D212C2213yes—
106#16811257C2213yes—
107#16811250C2213yescomplemented
108#16811250C2213yescomplemented
109#16811247C2213yescomplemented
110#16811247C2213yescomplemented
111#16811246C2213yescomplemented
112#16811246C2213yescomplemented
113#16811245C2213yescomplemented
114#16811245C2213yescomplemented
115#16811244C2213yescomplemented
116#16811243C2216yescomplemented
117#16811243C2213yescomplemented
118#16811242C2213yescomplemented
119#16811241C2213yescomplemented
120#16811240C2213yescomplemented
121#16811239C2216yescomplemented
122#16811239C2213yescomplemented
123#16811238C2213yescomplemented
124#16811237C2216yescomplemented
125#16811237C2211yescharacteristic, complemented
126#16811234C2213yescomplemented
127#16811233C2213yescomplemented
128#16811232C2213yescomplemented
129#16811230C2213yescomplemented
130#16811228C2213yescomplemented
131#16811225C2213yescomplemented
132#16811224C2213yescomplemented
133#16811223C2213yescomplemented
134#16811221C2213yescomplemented
135#16811221C2216yescomplemented
136#16811219C2213yescomplemented
137#16811219C2216yescomplemented
138#16811216C2213yescomplemented
139#16811214C2213yescomplemented
140#16811212C2216yescomplemented
141#16811212C2213yescomplemented
142#16811209C2213yescomplemented
143#16811207C2216yescomplemented
144#16811207C2213yescomplemented
145#16811205C2213yescomplemented
146#16811203C2213yes—
147#16811203C2213yescomplemented
148#16811198C2213yescomplemented
149#16811196C2213yescomplemented
150#16811191C2213yes—
151#16811189C2213yescomplemented
152#16811177C2213yescomplemented
153#16811177C2216yescomplemented
154#16811177C2213yescomplemented
155#16811174C2213yescomplemented
156#16811172C2216yescomplemented
157#16811170C2213yescomplemented
158#16811168C2213yescomplemented
159C4⋊Q8×D53C2213yescomplemented
160#16811160C2213yescomplemented
161#16811160C2216yescomplemented
162#16811160C2213yescomplemented
163#16811159C2213yescomplemented
164#16811157C2213yescomplemented
165#16811157C2213yescomplemented
166#16811156C2216yescomplemented
167#16811155C2213yescomplemented
168#16811153C2213yescomplemented
169#16811153C2213yescomplemented
170#16811152C2213yescomplemented
171#16811151C2216yescomplemented
172#16811151C2213yescomplemented
173#16811151C2216yescomplemented
174#16811151C2213yescomplemented
175#126×D53C2216yescomplemented
176#124×D53C2213yescomplemented
177#124×D53C2216yescomplemented
178#16811136C2216yescomplemented
179#16811132C2213yes—
180#16811132C2213yescomplemented
181#16811131C2216yescomplemented
182#123×D53C2216yescomplemented
183C22⋊Q8×D53C2213yescomplemented
184C22⋊Q8×D53C2216yescomplemented
185#121×D53C2213yes—
186#16811106C2211yescharacteristic, complemented
187#16811105C2211yescharacteristic
188#16811105C2211yescharacteristic
189#16811105C2213yescomplemented
190#16811105C2211yescharacteristic, complemented
191#16811105C2211yescharacteristic, complemented
192#16811105C2211yescharacteristic, complemented
193#16811105C2213yescomplemented
194#16811105C2213yescomplemented
195#16811103C2213yescomplemented
196#16811103C2213yescomplemented
197#16811103C2213yescomplemented
198#16811101C2211yescharacteristic, complemented
199#16811099C2211yescharacteristic, complemented
200#16811099C2213yescomplemented
201#16811097C2213yescomplemented
202#16811097C2213yescomplemented
203#16811097C2213yescomplemented
204#16811095C2213yescomplemented
205#16811095C2213yescomplemented
206C4×#11719949C2211yescharacteristic
207C4×#11719949C2211yescharacteristic
208C4×#11719949C2213yescomplemented
209C4×#11719949C2211yescharacteristic, complemented
210C4×#11719949C2213yescomplemented
211C4×#11719949C2213yescomplemented
212C4×#11719945C2213yescomplemented
213#16811091C2213yescomplemented
214#16811091C2213yescomplemented
215C2×Q8×Dic53C2211yescharacteristic, complemented
216C4×Q8×D53C2211yescharacteristic, complemented
217C4×Q8×D53C2213yescomplemented
218C2×C4×D212C2213yescomplemented
219C4×D4×D53C2213yescomplemented
220C4×D4×D53C2213yescomplemented
221#117×D53C2213yescomplemented
222#117×D53C2213yescomplemented
223Q82×C53C2211yescharacteristic, complemented
224C53×#556C2213yescomplemented
225C53×#556C2213yescomplemented
226C53×#556C2213yescomplemented
227C53×#555C2213yescomplemented
228D4×Q8×C53C2211yescharacteristic, complemented
229C53×#548C2211yescharacteristic
230C53×#548C2211yescharacteristic, complemented
231C53×#542C2213yescomplemented
232C53×#542C2213yescomplemented
233C53×#533C2213yescomplemented
234C53×#529C2213yescomplemented
235C53×#519C2211yescharacteristic, complemented
236C53×#519C2211yescharacteristic, complemented
237C4×#41×C53C2211yescharacteristic, complemented
238#13133265—28no—
239#13133263—28no—
240C2×#11719949—28no—
241C2×#11719949C2313yes—
242C2×#11719949C2313yes—
243C2×#11719949C2311yescharacteristic
244C2×#11719949C2311yescharacteristic
245C2×#11719949C2313yes—
246C2×#11719949C2316yes—
247C2×#11719949C2311yescharacteristic
248C2×#11719945C2313yes—
249C2×#11719945C2313yes—
250C2×#11719945C2313yes—
251C2×#11719947C2316yes—
252C2×Q8×D53C2311yescharacteristic
253C2×Q8×D53C2313yes—
254C2×Q8×D53C2316yes—
255C22×D212C2313yes—
256C22×D212C2313yes—
257C2×D4×D53C2313yes—
258C2×D4×D53C2313yes—
259C2×D4×D53C2316yes—
260C22×C4×D53C2313yes—
261C22×C4×D53C2316yes—
262#13133217C2313yes—
263#13133216C2313yes—
264#13133216C2313yes—
265#13133216C2313yes—
266#13133216C2313yes—
267#13133216C2313yes—
268#13133216C2313yes—
269#13133215C2313yes—
270#13133215C2316yes—
271#13133215C2311yescharacteristic
272#13133214C2313yes—
273#13133213C2313yes—
274#13133213C2313yes—
275#13133212C2313yes—
276#13133212C2316yes—
277#13133212C2316yes—
278#13133212C2313yes—
279#13133212C2313yes—
280#13133212C2316yes—
281#13133212C2313yes—
282#13133212C2313yes—
283#13133212C2313yes—
284#13133211C2316yes—
285#13133211C2316yes—
286#13133211C2313yes—
287#13133211C2311yescharacteristic
288#13133210C2313yes—
289#13133210C2313yes—
290#13133210C2316yes—
291#13133210C2313yes—
292#13133210C2313yes—
293#13133210C2316yes—
294#13133210C2313yes—
295#13133210C2316yes—
296#13133210C2311yescharacteristic
297#13133209C2313yes—
298#13133209C2313yes—
299#13133209C2313yes—
300#13133208C2313yes—
301#13133208C2313yes—
302#13133208C2313yes—
303#13133208C2313yes—
304#13133207C2316yes—
305#13133207C2313yes—
306#13133207C2316yes—
307#13133207C2313yes—
308#13133207C2313yes—
309#13133207C2313yes—
310#13133207C2313yes—
311#13133207C2313yes—
312#13133206C2313yes—
313#13133206C2313yes—
314#13133206C2313yes—
315#13133206C2313yes—
316#13133206C2316yes—
317#13133205C2313yes—
318#13133205C2313yes—
319#13133205C2313yes—
320#13133205C2316yes—
321#13133205C2316yes—
322#13133204C2313yes—
323#13133204C2313yes—
324#13133203C2313yes—
325#13133203C2316yes—
326#13133203C2313yes—
327#13133203C2316yes—
328#13133203C2313yes—
329#13133203C2313yes—
330#13133203C2316yes—
331#13133203C2316yes—
332#13133203C2311yescharacteristic
333#13133203C2311yescharacteristic
334#13133202C2313yes—
335#13133202C2316yes—
336#13133202C2316yes—
337#13133202C2316yes—
338#13133202C2313yes—
339#13133202C2313yes—
340#13133202C2313yes—
341#13133202C2316yes—
342#13133202C2316yes—
343#13133202C2313yes—
344#13133202C2316yes—
345#13133202C2316yes—
346#13133202C2313yes—
347#13133201C2313yes—
348#13133201C2316yes—
349#13133201C2313yes—
350#13133200C2313yes—
351#13133200C2313yes—
352#13133200C2316yes—
353#13133199C2313yes—
354#13133199C2316yes—
355#13133199C2316yes—
356#13133199C2316yes—
357#13133199C2313yes—
358#13133199C2316yes—
359#13133199C2313yes—
360#13133199C2313yes—
361#13133199C2313yes—
362#13133199C2311yescharacteristic
363#13133198C2313yes—
364#13133198C2316yes—
365#13133198C2311yescharacteristic
366#13133197C2313yes—
367#13133197C2313yes—
368#13133197C2316yes—
369#13133197C2313yes—
370#13133197C2316yes—
371#13133197C2313yes—
372#13133196C2313yes—
373#13133196C2313yes—
374#13133196C2313yes—
375#13133195C2313yes—
376#13133195C2313yes—
377#13133195C2316yes—
378#13133195C2316yes—
379#13133195C2313yes—
380#13133195C2313yes—
381#13133195C2316yes—
382#13133195C2316yes—
383#13133195C2313yes—
384#13133195C2313yes—
385#13133194C2316yes—
386#13133194C2313yes—
387#13133194C2316yes—
388#13133194C2313yes—
389#13133194C2311yescharacteristic
390#13133194C2311yescharacteristic
391#13133193C2313yes—
392#13133193C2313yes—
393#13133193C2316yes—
394#13133193C2316yes—
395#13133193C2313yes—
396#13133193C2313yes—
397#13133193C2316yes—
398#13133193C2316yes—
399#13133193C2313yes—
400#13133193C2311yescharacteristic
401#13133192C2313yes—
402#13133192C2316yes—
403#13133192C2313yes—
404#13133192C2316yes—
405#13133192C2313yes—
406#13133192C2313yes—
407#13133192C2313yes—
408#13133192C2313yes—
409#13133191C2313yes—
410#13133191C2313yes—
411#13133191C2313yes—
412#13133191C2313yes—
413#13133191C2313yes—
414#13133190C2316yes—
415#13133190C2313yes—
416#13133190C2313yes—
417#13133190C2316yes—
418#13133190C2313yes—
419#13133190C2316yes—
420#13133190C2316yes—
421#13133190C2316yes—
422#13133190C2313yes—
423#13133190C2313yes—
424#13133190C2313yes—
425#13133189C2313yes—
426#13133189C2313yes—
427#13133189C2311yescharacteristic
428#13133189C2313yes—
429#13133188C2313yes—
430#13133188C2313yes—
431#13133188C2313yes—
432#13133188C2313yes—
433#13133187C2316yes—
434#13133187C2313yes—
435#13133187C2316yes—
436#13133187C2316yes—
437#13133187C2313yes—
438#13133185C2313yes—
439#13133185C2316yes—
440#13133185C2313yes—
441Q8×Dic53C2311yescharacteristic
442Q8×Dic53C2311yescharacteristic
443Q8×Dic53C2311yescharacteristic
444Q8×Dic53C2313yes—
445Q8×Dic53C2313yes—
446Q8×Dic53C2311yescharacteristic
447Q8×Dic53C2313yes—
448Q8×Dic53C2313yes—
449C4×Dic106C2316yes—
450C4×Dic106C2313yes—
451C4×Dic106C2313yes—
452C4×Dic106C2313yes—
453C4×Dic106C2313yes—
454C4×Dic106C2316yes—
455C4×Dic106C2313yes—
456C4×Dic106C2311yescharacteristic
457C4×Dic106C2313yes—
458#13133182C2313yes—
459#13133182C2313yes—
460#13133182C2313yes—
461#13133182C2313yes—
462C4×D212C2313yes—
463C4×D212C2313yes—
464C4×D212C2313yes—
465C4×D212C2313yes—
466C4×D212C2316yes—
467C4×D212C2316yes—
468C4×D212C2313yes—
469C4×D212C2313yes—
470C4×D212C2313yes—
471C4×D212C2313yes—
472C4×D212C2316yes—
473C4×D212C2316yes—
474C4×D212C2313yes—
475C4×D212C2313yes—
476C4×D212C2313yes—
477C4×D212C2313yes—
478C4×D212C2316yes—
479C4×D212C2313yes—
480D4×Dic53C2313yes—
481D4×Dic53C2313yes—
482#13133179C2313yes—
483#13133179C2313yes—
484#13133179C2313yes—
485#13133179C2316yes—
486#13133179C2316yes—
487#13133179C2313yes—
488#13133179C2313yes—
489#13133179C2313yes—
490#13133179C2313yes—
491#13133179C2313yes—
492#13133179C2313yes—
493#13133179C2316yes—
494#13133179C2313yes—
495C4×C22⋊D53C2313yes—
496C4×C22⋊D53C2313yes—
497C4×C22⋊D53C2313yes—
498C4×C22⋊D53C2313yes—
499C4×C22⋊D53C2313yes—
500C4×C22⋊D53C2313yes—
501C4×C22⋊D53C2316yes—
502C4×C22⋊D53C2313yes—
503C4×C22⋊D53C2313yes—
504C4×C22⋊D53C2313yes—
505C4×C22⋊D53C2313yes—
506#13133177C2316yes—
507#13133177C2316yes—
508#13133177C2316yes—
509#13133177C2316yes—
510#13133177C2316yes—
511#13133177C2316yes—
512#13133177C2313yes—
513#13133177C2311yescharacteristic
514#13133177C2313yes—
515#13133177C2313yes—
516#13133176C2313yes—
517#13133176C2313yes—
518#13133176C2313yes—
519#13133175C2316yes—
520#13133175C2316yes—
521#13133175C2313yes—
522#13133175C2313yes—
523#13133175C2313yes—
524#13133175C2313yes—
525#13133175C2313yes—
526#13133175C2313yes—
527#13133174C2316yes—
528#13133174C2316yes—
529#13133174C2316yes—
530#13133174C2316yes—
531#13133174C2316yes—
532#13133174C2313yes—
533#13133174C2313yes—
534#13133174C2313yes—
535#13133174C2313yes—
536#13133174C2313yes—
537#13133174C2313yes—
538#13133173C2316yes—
539#13133173C2313yes—
540#13133173C2311yescharacteristic
541C2×C4⋊Dic53C2313yes—
542C2×C4⋊Dic53C2313yes—
543C4⋊C4×D53C2313yes—
544C4⋊C4×D53C2316yes—
545C4⋊C4×D53C2313yes—
546C4⋊C4×D53C2313yes—
547C4⋊C4×D53C2313yes—
548C4⋊C4×D53C2316yes—
549C4⋊C4×D53C2313yes—
550C4⋊C4×D53C2313yes—
551C4⋊C4×D53C2313yes—
552C4⋊C4×D53C2313yes—
553C4⋊C4×D53C2316yes—
554C2×#11719921C2316yes—
555C22⋊C4×D53C2316yes—
556C22⋊C4×D53C2316yes—
557C22⋊C4×D53C2316yes—
558C22⋊C4×D53C2316yes—
559C22⋊C4×D53C2316yes—
560C22⋊C4×D53C2316yes—
561C22⋊C4×D53C2313yes—
562C22⋊C4×D53C2313yes—
563C22⋊C4×D53C2316yes—
564C2×C4×Dic53C2313yes—
565C42×D53C2313yes—
566C42×D53C2313yes—
567C42×D53C2316yes—
568C42×D53C2313yes—
569C42×D53C2316yes—
570C42×D53C2313yes—
571C2×#41×C53C2311yescharacteristic
572C22×Q8×C53C2311yescharacteristic
573C22×Q8×C53C2311yescharacteristic
574C4⋊Q8×C53C2313yes—
575C4⋊Q8×C53C2313yes—
576C4⋊Q8×C53C2313yes—
577C4⋊Q8×C53C2313yes—
578#126×C53C2313yes—
579#126×C53C2316yes—
580#126×C53C2316yes—
581#126×C53C2313yes—
582#125×C53C2313yes—
583#124×C53C2313yes—
584#124×C53C2316yes—
585#124×C53C2313yes—
586#124×C53C2316yes—
587#124×C53C2311yescharacteristic
588#123×C53C2313yes—
589#123×C53C2313yes—
590C22⋊Q8×C53C2313yes—
591C22⋊Q8×C53C2313yes—
592C22⋊Q8×C53C2313yes—
593C22⋊Q8×C53C2313yes—
594C22⋊Q8×C53C2313yes—
595C22⋊Q8×C53C2316yes—
596#121×C53C2313yes—
597#121×C53C2313yes—
598#121×C53C2313yes—
599C4×Q8×C53C2311yescharacteristic
600C4×Q8×C53C2311yescharacteristic
601C4×Q8×C53C2316yes—
602C4×Q8×C53C2311yescharacteristic
603C4×Q8×C53C2311yescharacteristic
604C4×Q8×C53C2313yes—
605C4×Q8×C53C2313yes—
606C4×Q8×C53C2313yes—
607C4×Q8×C53C2313yes—
608C4×Q8×C53C2313yes—
609C4×D4×C53C2313yes—
610C4×D4×C53C2313yes—
611C4×D4×C53C2313yes—
612C4×D4×C53C2313yes—
613C4×D4×C53C2313yes—
614#117×C53C2313yes—
615#117×C53C2316yes—
616#117×C53C2313yes—
617#117×C53C2313yes—
618#117×C53C2313yes—
619#117×C53C2313yes—
620C2×C42×C53C2313yes—
621C23×D53C2413yes—
622C23×D53C2416yes—
623#41×C53—24no—
624C2×Q8×C53—24no—
625C2×Q8×C53—24no—
626C2×Q8×C53C2413yes—
627C2×Q8×C53C2413yes—
628C2×Q8×C53C2411yescharacteristic
629C2×Q8×C53C2416yes—
630C2×Q8×C53C2411yescharacteristic
631C2×D4×C53C2413yes—
632C2×D4×C53C2411yescharacteristic
633C2×D4×C53C2413yes—
634C2×D4×C53C2413yes—
635C22×C4×C53C2413yes—
636C22×C4×C53C2413yes—
637C22×C4×C53C2413yes—
638C22×C4×C53C2413yes—
639C22×C4×C53C2413yes—
640C2×C22⋊D53C2413yes—
641C2×C22⋊D53C2411yescharacteristic
642C2×C22⋊D53C2413yes—
643C2×C22⋊D53C2413yes—
644C2×C22⋊D53C2413yes—
645C2×C22⋊D53C2413yes—
646C2×C22⋊D53C2413yes—
647C2×C22⋊D53C2411yescharacteristic
648C2×C22⋊D53C2413yes—
649C2×C22⋊D53C2416yes—
650C2×C22⋊D53C2413yes—
651C22×Dic53C2411yescharacteristic
652C22×Dic53C2411yescharacteristic
653C22×Dic53C2413yes—
654C22×Dic53C2416yes—
655#11719949—24no—
656#11719949—24no—
657#11719949—212no—
658#11719949—212no—
659#11719949—212no—
660#11719949—86no—
661#11719949#4118yescomplemented
662Q8×D53—24no—
663Q8×D53—212no—
664Q8×D53—86no—
665#11719947—86no—
666D4×D53—212no—
667D4×D53—212no—
668D4×D53—86no—
669#11719945—212no—
670#11719945—212no—
671#11719945—212no—
672C2×D212—212no—
673C2×D212—212no—
674C2×D212C2413yes—
675C2×D212C2416yes—
676C2×D212C2413yes—
677C2×D212C2413yes—
678C2×D212C2413yes—
679C2×D212C2413yes—
680C2×D212C2413yes—
681C2×D212C2413yes—
682C2×D212C2416yes—
683C2×D212C2413yes—
684C2×C4×D53—212no—
685C2×C4×D53—86no—
686C2×C4×D53C2413yes—
687C2×C4×D53C2416yes—
688C2×C4×D53C2413yes—
689C2×C4×D53C2413yes—
690C2×C4×D53C2413yes—
691C2×C4×D53C2413yes—
692C2×C4×D53C2413yes—
693C2×C4×D53C2411yescharacteristic
694C2×C4×D53C2413yes—
695C2×C4×D53C2413yes—
696C2×C4×D53C2413yes—
697C2×C4×D53C2413yes—
698C2×C4×D53C2416yes—
699C2×C4×D53C2416yes—
700C2×C4×D53C2416yes—
701C2×C4×D53C2413yes—
702C2×C4×D53C2413yes—
703C2×C4×D53C2416yes—
704C2×C4×D53C2416yes—
705C2×C4×D53C2413yes—
706C2×Dic106C2413yes—
707C2×Dic106C2413yes—
708C2×Dic106C2411yescharacteristic
709C2×Dic106C2411yescharacteristic
710C2×Dic106C2413yes—
711C2×Dic106C2416yes—
712C2×Dic106C2413yes—
713C4⋊C4×C53C2413yes—
714C4⋊C4×C53C2413yes—
715C4⋊C4×C53C2413yes—
716C4⋊C4×C53C2413yes—
717C4⋊C4×C53C2413yes—
718C4⋊C4×C53C2413yes—
719C4⋊C4×C53C2413yes—
720C4⋊C4×C53C2413yes—
721C4⋊C4×C53C2413yes—
722C4⋊C4×C53C2413yes—
723C4⋊C4×C53C2413yes—
724C4⋊C4×C53C2413yes—
725C4⋊C4×C53C2416yes—
726C4⋊C4×C53C2413yes—
727C4⋊C4×C53C2413yes—
728C22⋊C4×C53C2413yes—
729C22⋊C4×C53C2413yes—
730C22⋊C4×C53C2411yescharacteristic
731C22⋊C4×C53C2411yescharacteristic
732C22⋊C4×C53C2416yes—
733C22⋊C4×C53C2416yes—
734C22⋊C4×C53C2416yes—
735C22⋊C4×C53C2411yescharacteristic
736C22⋊C4×C53C2411yescharacteristic
737C22⋊C4×C53C2413yes—
738C22⋊C4×C53C2413yes—
739C22⋊C4×C53C2413yes—
740C22⋊C4×C53C2413yes—
741C42×C53C2411yescharacteristic
742C42×C53C2413yes—
743C42×C53C2413yes—
744C42×C53C2413yes—
745C42×C53C2416yes—
746C42×C53C2416yes—
747C42×C53C2413yes—
748C42×C53C2413yes—
749C22⋊Dic53C2413yes—
750C22⋊Dic53C2411yescharacteristic
751C22⋊Dic53C2413yes—
752C22⋊Dic53C2413yes—
753C22⋊Dic53C2413yes—
754C22⋊Dic53C2413yes—
755C22⋊Dic53C2413yes—
756C22⋊Dic53C2416yes—
757C22⋊Dic53C2411yescharacteristic
758C22⋊Dic53C2411yescharacteristic
759C22⋊Dic53C2411yescharacteristic
760#11719921C2416yes—
761#11719921C2413yes—
762#11719921C2413yes—
763#11719921C2413yes—
764#11719921C2413yes—
765#11719921C2413yes—
766#11719921C2416yes—
767#11719921C2416yes—
768#11719921C2413yes—
769#11719921C2413yes—
770#11719921C2413yes—
771#11719921C2413yes—
772#11719921C2416yes—
773#11719921C2416yes—
774#11719921C2416yes—
775#11719921C2416yes—
776#11719921C2416yes—
777#11719921C2413yes—
778#11719921C2413yes—
779#11719921C2413yes—
780#11719921C2411yescharacteristic
781#11719921C2413yes—
782#11719921C2413yes—
783#11719921C2413yes—
784#11719921C2413yes—
785#11719921C2413yes—
786#11719921C2413yes—
787#11719921C2411yescharacteristic
788#11719921C2413yes—
789#11719921C2413yes—
790#11719921C2411yescharacteristic
791#11719921C2411yescharacteristic
792C4⋊Dic53C2413yes—
793C4⋊Dic53C2413yes—
794C4⋊Dic53C2413yes—
795C4⋊Dic53C2413yes—
796C4⋊Dic53C2413yes—
797C4⋊Dic53C2416yes—
798C4⋊Dic53C2413yes—
799C4⋊Dic53C2413yes—
800C4⋊Dic53C2413yes—
801C4⋊Dic53C2413yes—
802C4⋊Dic53C2413yes—
803C4⋊Dic53C2411yescharacteristic
804C4⋊Dic53C2411yescharacteristic
805C4⋊Dic53C2413yes—
806C4⋊Dic53C2413yes—
807#11719919C2413yes—
808#11719919C2411yescharacteristic
809#11719919C2411yescharacteristic
810#11719919C2413yes—
811#11719919C2413yes—
812#11719919C2413yes—
813#11719919C2413yes—
814#11719919C2416yes—
815#11719919C2413yes—
816#11719919C2413yes—
817#11719919C2416yes—
818#11719919C2416yes—
819#11719919C2416yes—
820#11719919C2413yes—
821#11719919C2411yescharacteristic
822#11719919C2413yes—
823#11719919C2411yescharacteristic
824#11719919C2411yescharacteristic
825#11719919C2413yes—
826#11719919C2413yes—
827#11719919C2413yes—
828#11719919C2413yes—
829#11719919C2413yes—
830#11719919C2411yescharacteristic
831#11719919C2413yes—
832#11719919C2413yes—
833#11719919C2411yescharacteristic
834#11719919C2411yescharacteristic
835C4×Dic53C2413yes—
836C4×Dic53C2411yescharacteristic
837C4×Dic53C2411yescharacteristic
838C4×Dic53C2413yes—
839C4×Dic53C2413yes—
840C4×Dic53C2411yescharacteristic
841C4×Dic53C2413yes—
842C4×Dic53C2413yes—
843C4×Dic53C2413yes—
844C4×Dic53C2416yes—
845C4×Dic53C2413yes—
846C4×Dic53C2416yes—
847C4×Dic53C2413yes—
848C4×Dic53C2413yes—
849C4×Dic53C2413yes—
850C4×Dic53C2413yes—
851C23×C53C2511yescharacteristic
852C23×C53C2513yes—
853C23×C53C2511yescharacteristic
854C22×D53—26no—
855C22×D53—212no—
856C22×D53—46no—
857C22×D53—43no—
858C22×D53—43no—
859C22×D53—46no—
860C22×D53C2511yescharacteristic
861C22×D53C2513yes—
862C22×D53C2513yes—
863C22×D53C2513yes—
864Q8×C53—26no—
865Q8×C53—26no—
866Q8×C53—46no—
867Q8×C53—41no—
868Q8×C53C2×#4114yes—
869D4×C53—26no—
870D4×C53—43no—
871D4×C53—43no—
872D4×C53—41no—
873C2×C4×C53—26no—
874C2×C4×C53—26no—
875C2×C4×C53—26no—
876C2×C4×C53—43no—
877C2×C4×C53—43no—
878C2×C4×C53C2513yes—
879C2×C4×C53C2513yes—
880C2×C4×C53C2513yes—
881C2×C4×C53C2511yescharacteristic
882C2×C4×C53C2513yes—
883C2×C4×C53C2511yescharacteristic
884C2×C4×C53C2511yescharacteristic
885C2×C4×C53C2513yes—
886C2×C4×C53C2513yes—
887C2×C4×C53C2511yescharacteristic
888C2×C4×C53C2511yescharacteristic
889C2×C4×C53C2513yes—
890C22⋊D53—26no—
891C22⋊D53—26no—
892C22⋊D53—22no—
893C22⋊D53—26no—
894C22⋊D53—43no—
895C22⋊D53—46no—
896C22⋊D53—43no—
897C22⋊D53—41no—
898C22⋊D53—43no—
899C22⋊D53—43no—
900C22⋊D53—43no—
901C2×Dic53—22no—
902C2×Dic53—46no—
903C2×Dic53—43no—
904C2×Dic53—41no—
905C2×Dic53C2511yescharacteristic
906C2×Dic53C2513yes—
907C2×Dic53C2513yes—
908C2×Dic53C2513yes—
909C2×Dic53C2511yescharacteristic
910C2×Dic53C2511yescharacteristic
911C2×Dic53C2511yescharacteristic
912C2×Dic53C2513yes—
913C2×Dic53C2511yescharacteristic
914C2×Dic53C2511yescharacteristic
915C2×Dic53C2513yes—
916C2×Dic53C2511yescharacteristic
917D212—26no—
918D212—212no—
919D212—26no—
920D212—26no—
921D212—26no—
922D212—43no—
923D212—46no—
924D212—43no—
925D212—43no—
926D212C2×#41112yes—
927C4×D53—26no—
928C4×D53—212no—
929C4×D53—26no—
930C4×D53—26no—
931C4×D53—26no—
932C4×D53—26no—
933C4×D53—43no—
934C4×D53—43no—
935C4×D53—46no—
936C4×D53—46no—
937C4×D53—43no—
938C4×D53—43no—
939C4×D53—41no—
940C4×D53—43no—
941C4×D53—46no—
942C4×D53—46no—
943C4×D53—46no—
944C4×D53—43no—
945C4×D53—43no—
946C4×D53C2×#41112yes—
947Dic106—26no—
948Dic106—22no—
949Dic106—26no—
950Dic106—41no—
951Dic106—46no—
952Dic106—43no—
953Dic106—43no—
954#62857—531nomaximal, Sylow
955C22×C53—21no—
956C22×C53—21no—
957C22×C53—23no—
958C22×C53—21no—
959C22×C53—23no—
960C22×C53—21no—
961C22×C53—21no—
962C22×C53—23no—
963C22×C53—21no—
964C22×C53C2611yescharacteristic
965C2×D53—23no—
966C2×D53—23no—
967C2×D53—21no—
968C2×D53—23no—
969C2×D53—23no—
970C2×D53—21no—
971C2×D53—23no—
972C2×D53—23no—
973C2×D53—23no—
974C2×D53—23no—
975C2×D53—21no—
976C2×D53—86no—
977C2×D53—812no—
978C2×D53C22×#4116yes—
979C4×C53—23no—
980C4×C53—21no—
981C4×C53—23no—
982C4×C53—23no—
983C4×C53—23no—
984C4×C53—23no—
985C4×C53—21no—
986C4×C53—21no—
987C4×C53—23no—
988C4×C53—21no—
989C4×C53—21no—
990C4×C53C22×#4116yes—
991Dic53—23no—
992Dic53—21no—
993Dic53—21no—
994Dic53—21no—
995Dic53—23no—
996Dic53—23no—
997Dic53—23no—
998Dic53—21no—
999Dic53—21no—
1000Dic53—21no—
1001Dic53—23no—
1002Dic53C22×#4112yes—
1003#3524—531no—
1004#3524—531no—
1005#3522—531no—
1006#3522—531no—
1007#3521—533no—
1008#3521—533no—
1009#3520—533no—
1010#3520—533no—
1011#3518—531no—
1012#3518D5311yescharacteristic, complemented
1013#3516—531no—
1014#3516—531no—
1015#3514—533no—
1016#3514—533no—
1017#3513—533no—
1018#3513—533no—
1019#3511—533no—
1020#3510—533no—
1021#3503—531no—
1022#3500—531no—
1023#3495—533no—
1024#3494—533no—
1025#3489—531no—
1026#3488—531no—
1027#3461—533no—
1028#3460—533no—
1029#3455—533no—
1030C2×#542—533no—
1031C4×2−1+4—531no—
1032C4×H(5,𝔽2)—531no—
1033#3428—531no—
1034C2×C53—41no—
1035C2×C53—43no—
1036C2×C53—41no—
1037C2×C53C23×#4111yescharacteristic
1038C2×C53H(7,𝔽2)11yescharacteristic
1039C2×C532−1+611yescharacteristic
1040D53—26no—
1041D53—41no—
1042D53—43no—
1043D53—43no—
1044C2×2−1+4—531no—
1045C2×H(5,𝔽2)—531no—
1046C22×#41—531no—
1047#559—533no—
1048#559—533no—
1049#559—533no—
1050#559—533no—
1051Q82—531no—
1052Q82C2×D5311yescharacteristic, complemented
1053#557—531no—
1054#557—531no—
1055#556—533no—
1056#556—533no—
1057#556—533no—
1058#556—533no—
1059#556—533no—
1060#556C2×D5313yescomplemented
1061#556C2×D5313yescomplemented
1062#556C2×D5313yescomplemented
1063#555—533no—
1064#555—533no—
1065#555—533no—
1066#555C2×D5313yescomplemented
1067#554—533no—
1068#554—533no—
1069#554—533no—
1070#554—533no—
1071#554—533no—
1072#554—533no—
1073#553—536no—
1074#553—536no—
1075#553—533no—
1076#553—533no—
1077#553—533no—
1078#553—533no—
1079#552—536no—
1080#552—533no—
1081#552—536no—
1082#552—533no—
1083#552—533no—
1084#552—533no—
1085#551—536no—
1086#551—536no—
1087#551—536no—
1088#551—536no—
1089#551—536no—
1090#551—536no—
1091#551—536no—
1092#551—536no—
1093#550—531no—
1094#550—531no—
1095D4×Q8—531no—
1096D4×Q8—533no—
1097D4×Q8—533no—
1098D4×Q8C2×D5311yescharacteristic, complemented
1099#548—531no—
1100#548—531no—
1101#548—531no—
1102#548—531no—
1103#548—536no—
1104#548—531no—
1105#548—531no—
1106#548—536no—
1107#548C2×D5311yescharacteristic
1108#548C2×D5311yescharacteristic, complemented
1109#547—533no—
1110#547—533no—
1111#547—533no—
1112#547—533no—
1113#547—533no—
1114#547—533no—
1115#546—533no—
1116#546—536no—
1117#546—533no—
1118#546—533no—
1119#546—533no—
1120#546—533no—
1121#546—533no—
1122#546—536no—
1123#546—533no—
1124#546—533no—
1125D42—533no—
1126D42—533no—
1127#544—533no—
1128#544—533no—
1129#542—533no—
1130#542—533no—
1131#542—536no—
1132#542—533no—
1133#542—536no—
1134#542—533no—
1135#542—531no—
1136#542—533no—
1137#542—536no—
1138#542—533no—
1139#542—533no—
1140#542—533no—
1141#542—533no—
1142#542—533no—
1143#542—533no—
1144#542—533no—
1145#542—533no—
1146#542C2×D5313yescomplemented
1147#542C2×D5313yescomplemented
1148#541—533no—
1149#541—533no—
1150#541—533no—
1151#541—533no—
1152#540—533no—
1153#540—533no—
1154#540—533no—
1155#540—533no—
1156#539—533no—
1157#539—533no—
1158#539—536no—
1159#539—533no—
1160#539—533no—
1161#539—536no—
1162#538—533no—
1163#538—536no—
1164#538—533no—
1165#538—536no—
1166#538—533no—
1167#538—533no—
1168#537—533no—
1169#537—533no—
1170#536—533no—
1171#536—533no—
1172#535—533no—
1173#535—533no—
1174#533—533no—
1175#533—536no—
1176#533—533no—
1177#533C2×D5313yescomplemented
1178#532—533no—
1179#532—536no—
1180#532—533no—
1181#532—533no—
1182C2×C4⋊Q8—533no—
1183#529—536no—
1184#529—533no—
1185#529—533no—
1186#529—533no—
1187#529—533no—
1188#529—536no—
1189#529—533no—
1190#529—533no—
1191#529—533no—
1192#529—533no—
1193#529—533no—
1194#529—536no—
1195#529—536no—
1196#529—533no—
1197#529—533no—
1198#529C2×D5313yescomplemented
1199C2×#126—536no—
1200C2×#124—533no—
1201C2×#124—536no—
1202#525—536no—
1203#525—536no—
1204#525—533no—
1205#525—533no—
1206C2×#123—536no—
1207C2×C22⋊Q8—533no—
1208C2×C22⋊Q8—536no—
1209C2×#121—533no—
1210#520—531no—
1211#520—531no—
1212#520—531no—
1213#520—533no—
1214#520—533no—
1215#520—531no—
1216#520—531no—
1217#520—531no—
1218#520—533no—
1219#520—533no—
1220#520—533no—
1221#520—533no—
1222#519—531no—
1223#519—533no—
1224#519—531no—
1225#519C2×D5311yescharacteristic, complemented
1226#519C2×D5311yescharacteristic, complemented
1227#518—533no—
1228#518—533no—
1229#518—533no—
1230#518—533no—
1231#518—533no—
1232C4×#41—531no—
1233C4×#41—531no—
1234C4×#41—533no—
1235C4×#41—533no—
1236C4×#41—531no—
1237C4×#41—533no—
1238C4×#41—533no—
1239C4×#41—533no—
1240C4×#41—533no—
1241C4×#41C2×D5311yescharacteristic, complemented
1242C2×C4×Q8—531no—
1243C2×C4×Q8—533no—
1244C2×C4×Q8—531no—
1245C2×C4×D4—533no—
1246C2×C4×D4—533no—
1247C2×C4×D4—533no—
1248C2×#117—533no—
1249C2×#117—533no—
1250C53#6285711yescharacteristic, complemented, Sylow
12512−1+4—1068no—
1252H(5,𝔽2)—1068no—
1253C2×#41—531no—
1254C2×#41—533no—
1255C2×#41—533no—
1256C2×#41—531no—
1257C2×#41—533no—
1258C2×#41—531no—
1259C2×#41—536no—
1260C2×#41—536no—
1261C2×#41—533no—
1262C2×#41—533no—
1263C2×#41—533no—
1264C2×#41—1068no—
1265C2×#41C22×D5311yescharacteristic
1266C22×Q8—533no—
1267C22×Q8—531no—
1268C22×Q8—536no—
1269C22×Q8C22×D5311yescharacteristic
1270C22×Q8C22×D5311yescharacteristic
1271C22×D4—533no—
1272C22×D4—533no—
1273C22×D4—536no—
1274C22×D4—533no—
1275C22×D4—533no—
1276C23×C4—533no—
1277C23×C4—536no—
1278C4⋊Q8—536no—
1279C4⋊Q8—531no—
1280C4⋊Q8—533no—
1281C4⋊Q8—533no—
1282C4⋊Q8—533no—
1283C4⋊Q8—533no—
1284C4⋊Q8—533no—
1285C4⋊Q8—533no—
1286C4⋊Q8—533no—
1287C4⋊Q8—533no—
1288C4⋊Q8C22×D5313yes—
1289C4⋊Q8C22×D5313yes—
1290C4⋊Q8C22×D5313yes—
1291C4⋊Q8C22×D5313yes—
1292#127—533no—
1293#127—533no—
1294#127—533no—
1295#126—533no—
1296#126—536no—
1297#126—536no—
1298#126—533no—
1299#126—533no—
1300#126—533no—
1301#126—536no—
1302#126—533no—
1303#126—533no—
1304#126—533no—
1305#126—536no—
1306#126—536no—
1307#126—531no—
1308#126—533no—
1309#126—533no—
1310#126—533no—
1311#126—536no—
1312#126—533no—
1313#126—536no—
1314#126—533no—
1315#126—531no—
1316#126—536no—
1317#126C22×D5316yes—
1318#126C22×D5316yes—
1319#126C22×D5313yes—
1320#126C22×D5313yes—
1321#125—533no—
1322#125—533no—
1323#125—533no—
1324#125—533no—
1325#125—533no—
1326#125—533no—
1327#125—533no—
1328#125—533no—
1329#125—533no—
1330#125—533no—
1331#125—536no—
1332#125—536no—
1333#125—533no—
1334#125—533no—
1335#125—533no—
1336#125C22×D5313yes—
1337#124—536no—
1338#124—533no—
1339#124—533no—
1340#124—533no—
1341#124—533no—
1342#124—533no—
1343#124—533no—
1344#124—533no—
1345#124—533no—
1346#124—536no—
1347#124—536no—
1348#124—536no—
1349#124—536no—
1350#124—531no—
1351#124—533no—
1352#124—533no—
1353#124—531no—
1354#124—533no—
1355#124—536no—
1356#124—533no—
1357#124—533no—
1358#124—536no—
1359#124C22×D5313yes—
1360#124C22×D5316yes—
1361#124C22×D5313yes—
1362#124C22×D5311yescharacteristic
1363#124C22×D5316yes—
1364#123—536no—
1365#123—531no—
1366#123—533no—
1367#123—536no—
1368#123—533no—
1369#123—533no—
1370#123—536no—
1371#123—536no—
1372#123—533no—
1373#123—533no—
1374#123—533no—
1375#123—536no—
1376#123—536no—
1377#123—536no—
1378#123—536no—
1379#123—533no—
1380#123—533no—
1381#123—533no—
1382#123—536no—
1383#123—533no—
1384#123—536no—
1385#123—536no—
1386#123—533no—
1387#123—533no—
1388#123—531no—
1389#123—533no—
1390#123—533no—
1391#123—536no—
1392#123—536no—
1393#123—533no—
1394#123—533no—
1395#123—536no—
1396#123C22×D5313yes—
1397#123C22×D5313yes—
1398C22⋊Q8—533no—
1399C22⋊Q8—536no—
1400C22⋊Q8—536no—
1401C22⋊Q8—531no—
1402C22⋊Q8—533no—
1403C22⋊Q8—533no—
1404C22⋊Q8—536no—
1405C22⋊Q8—533no—
1406C22⋊Q8—533no—
1407C22⋊Q8—536no—
1408C22⋊Q8—533no—
1409C22⋊Q8—533no—
1410C22⋊Q8—533no—
1411C22⋊Q8—533no—
1412C22⋊Q8—536no—
1413C22⋊Q8—536no—
1414C22⋊Q8—533no—
1415C22⋊Q8—536no—
1416C22⋊Q8—533no—
1417C22⋊Q8—533no—
1418C22⋊Q8—536no—
1419C22⋊Q8—533no—
1420C22⋊Q8—533no—
1421C22⋊Q8—536no—
1422C22⋊Q8—533no—
1423C22⋊Q8—533no—
1424C22⋊Q8—533no—
1425C22⋊Q8—533no—
1426C22⋊Q8—536no—
1427C22⋊Q8—533no—
1428C22⋊Q8—536no—
1429C22⋊Q8—536no—
1430C22⋊Q8—531no—
1431C22⋊Q8—531no—
1432C22⋊Q8—533no—
1433C22⋊Q8C22×D5316yes—
1434C22⋊Q8C22×D5313yes—
1435C22⋊Q8C22×D5313yes—
1436C22⋊Q8C22×D5313yes—
1437C22⋊Q8C22×D5313yes—
1438C22⋊Q8C22×D5313yes—
1439#121—533no—
1440#121—533no—
1441#121—531no—
1442#121—533no—
1443#121—533no—
1444#121—533no—
1445#121—533no—
1446#121—533no—
1447#121—533no—
1448#121—533no—
1449#121—533no—
1450#121—533no—
1451#121—533no—
1452#121—533no—
1453#121—536no—
1454#121—533no—
1455#121—536no—
1456#121—533no—
1457#121—533no—
1458#121—533no—
1459#121—533no—
1460#121—536no—
1461#121—533no—
1462#121—533no—
1463#121—533no—
1464#121—536no—
1465#121—536no—
1466#121—533no—
1467#121—533no—
1468#121—533no—
1469#121—536no—
1470#121—536no—
1471#121C22×D5313yes—
1472#121C22×D5313yes—
1473#121C22×D5313yes—
1474#120—536no—
1475#120—533no—
1476#120—533no—
1477#120—536no—
1478#120—536no—
1479#120—536no—
1480#120—533no—
1481#120—533no—
1482C4×Q8—531no—
1483C4×Q8—533no—
1484C4×Q8—531no—
1485C4×Q8—533no—
1486C4×Q8—533no—
1487C4×Q8—531no—
1488C4×Q8—533no—
1489C4×Q8—531no—
1490C4×Q8—533no—
1491C4×Q8—533no—
1492C4×Q8—533no—
1493C4×Q8—533no—
1494C4×Q8—536no—
1495C4×Q8—533no—
1496C4×Q8—533no—
1497C4×Q8—531no—
1498C4×Q8—533no—
1499C4×Q8—533no—
1500C4×Q8—533no—
1501C4×Q8—533no—
1502C4×Q8—536no—
1503C4×Q8C22×D5313yes—
1504C4×Q8C22×D5311yescharacteristic
1505C4×Q8C22×D5311yescharacteristic
1506C4×Q8C22×D5313yes—
1507C4×Q8C22×D5313yes—
1508C4×Q8C22×D5311yescharacteristic
1509C4×Q8C22×D5313yes—
1510C4×Q8C22×D5311yescharacteristic
1511C4×Q8C22×D5313yes—
1512C4×Q8C22×D5316yes—
1513C4×D4—533no—
1514C4×D4—533no—
1515C4×D4—533no—
1516C4×D4—533no—
1517C4×D4—533no—
1518C4×D4—533no—
1519C4×D4—533no—
1520C4×D4—533no—
1521C4×D4—533no—
1522C4×D4—533no—
1523C4×D4—536no—
1524C4×D4—533no—
1525C4×D4—533no—
1526C4×D4—533no—
1527C4×D4—533no—
1528C4×D4—533no—
1529C4×D4—533no—
1530C4×D4—533no—
1531C4×D4—536no—
1532C4×D4—533no—
1533C4×D4—533no—
1534C4×D4—536no—
1535C4×D4—533no—
1536C4×D4—533no—
1537C4×D4—533no—
1538C4×D4—536no—
1539C4×D4—536no—
1540C4×D4—536no—
1541C4×D4—533no—
1542C4×D4—531no—
1543C4×D4—533no—
1544C4×D4—533no—
1545C4×D4—536no—
1546C4×D4—536no—
1547C4×D4—536no—
1548C4×D4—536no—
1549C4×D4—533no—
1550C4×D4—533no—
1551C4×D4—533no—
1552C4×D4—533no—
1553C4×D4—533no—
1554C4×D4—536no—
1555C4×D4—533no—
1556C4×D4—536no—
1557C4×D4—533no—
1558C4×D4—533no—
1559C4×D4—533no—
1560C4×D4—536no—
1561C4×D4—533no—
1562C4×D4—536no—
1563C4×D4—533no—
1564C4×D4—533no—
1565C4×D4—536no—
1566C4×D4—533no—
1567C4×D4C22×D5313yes—
1568C4×D4C22×D5313yes—
1569C4×D4C22×D5313yes—
1570C4×D4C22×D5313yes—
1571C4×D4C22×D5313yes—
1572#117—533no—
1573#117—533no—
1574#117—533no—
1575#117—533no—
1576#117—533no—
1577#117—533no—
1578#117—533no—
1579#117—533no—
1580#117—536no—
1581#117—533no—
1582#117—536no—
1583#117—533no—
1584#117—531no—
1585#117—536no—
1586#117—533no—
1587#117—533no—
1588#117—536no—
1589#117—533no—
1590#117—533no—
1591#117—533no—
1592#117—533no—
1593#117—536no—
1594#117—536no—
1595#117—536no—
1596#117—536no—
1597#117C22×D5313yes—
1598#117C22×D5313yes—
1599#117C22×D5313yes—
1600#117C22×D5313yes—
1601#117C22×D5313yes—
1602#117C22×D5316yes—
1603C2×C4⋊C4—533no—
1604C2×C4⋊C4—533no—
1605C2×C4⋊C4—533no—
1606C2×C4⋊C4—533no—
1607C2×C4⋊C4—533no—
1608C2×C4⋊C4—533no—
1609C2×C4⋊C4—533no—
1610C2×C4⋊C4—533no—
1611C2×C4⋊C4—533no—
1612C2×C4⋊C4—536no—
1613C2×C4⋊C4—533no—
1614C2×C4⋊C4—536no—
1615C2×C4⋊C4—536no—
1616C2×C22⋊C4—536no—
1617C2×C22⋊C4—533no—
1618C2×C22⋊C4—533no—
1619C2×C22⋊C4—536no—
1620C2×C22⋊C4—536no—
1621C2×C22⋊C4—536no—
1622C2×C22⋊C4—536no—
1623C2×C22⋊C4—536no—
1624C2×C22⋊C4—536no—
1625C2×C22⋊C4—536no—
1626C2×C42—533no—
1627C2×C42—533no—
1628C2×C42—533no—
1629C2×C42—536no—
1630C2×C42—533no—
1631C2×C42—536no—
1632C2×C42—533no—
1633C2×C42C22×D5313yes—
1634C24—536no—
1635C24—533no—
1636#41—24no—
1637#41—538no—
1638#41—10612no—
1639#41—10612no—
1640#41—10612no—
1641#41—10612no—
1642#41—10612no—
1643#41—10612no—
1644#41—1064no—
1645#41—1064no—
1646#41—4246no—
1647#41—4246no—
1648C2×Q8—24no—
1649C2×Q8—24no—
1650C2×Q8—533no—
1651C2×Q8—533no—
1652C2×Q8—531no—
1653C2×Q8—531no—
1654C2×Q8—533no—
1655C2×Q8—533no—
1656C2×Q8—536no—
1657C2×Q8—10612no—
1658C2×Q8—1064no—
1659C2×Q8—4246no—
1660C2×Q8C23×D5313yes—
1661C2×Q8C23×D5313yes—
1662C2×Q8C23×D5311yescharacteristic
1663C2×Q8C23×D5316yes—
1664C2×Q8C23×D5311yescharacteristic
1665C2×D4—533no—
1666C2×D4—533no—
1667C2×D4—533no—
1668C2×D4—531no—
1669C2×D4—531no—
1670C2×D4—533no—
1671C2×D4—533no—
1672C2×D4—533no—
1673C2×D4—533no—
1674C2×D4—533no—
1675C2×D4—536no—
1676C2×D4—533no—
1677C2×D4—533no—
1678C2×D4—536no—
1679C2×D4—533no—
1680C2×D4—533no—
1681C2×D4—533no—
1682C2×D4—533no—
1683C2×D4—533no—
1684C2×D4—533no—
1685C2×D4—536no—
1686C2×D4—10612no—
1687C2×D4—10612no—
1688C2×D4—10612no—
1689C2×D4—10612no—
1690C2×D4—4246no—
1691C2×D4C23×D5313yes—
1692C2×D4C23×D5311yescharacteristic
1693C2×D4C23×D5313yes—
1694C2×D4C23×D5313yes—
1695C22×C4—533no—
1696C22×C4—531no—
1697C22×C4—531no—
1698C22×C4—533no—
1699C22×C4—536no—
1700C22×C4—533no—
1701C22×C4—536no—
1702C22×C4—533no—
1703C22×C4—533no—
1704C22×C4—533no—
1705C22×C4—533no—
1706C22×C4—533no—
1707C22×C4—531no—
1708C22×C4—533no—
1709C22×C4—533no—
1710C22×C4—533no—
1711C22×C4—533no—
1712C22×C4—536no—
1713C22×C4—536no—
1714C22×C4—536no—
1715C22×C4—533no—
1716C22×C4—533no—
1717C22×C4—536no—
1718C22×C4—536no—
1719C22×C4—10612no—
1720C22×C4—4246no—
1721C22×C4C23×D5313yes—
1722C22×C4C23×D5313yes—
1723C22×C4C23×D5313yes—
1724C22×C4C23×D5313yes—
1725C22×C4C23×D5313yes—
1726C4⋊C4—533no—
1727C4⋊C4—531no—
1728C4⋊C4—533no—
1729C4⋊C4—531no—
1730C4⋊C4—533no—
1731C4⋊C4—533no—
1732C4⋊C4—533no—
1733C4⋊C4—533no—
1734C4⋊C4—533no—
1735C4⋊C4—533no—
1736C4⋊C4—533no—
1737C4⋊C4—536no—
1738C4⋊C4—533no—
1739C4⋊C4—536no—
1740C4⋊C4—533no—
1741C4⋊C4—533no—
1742C4⋊C4—533no—
1743C4⋊C4—533no—
1744C4⋊C4—533no—
1745C4⋊C4—533no—
1746C4⋊C4—536no—
1747C4⋊C4—536no—
1748C4⋊C4—536no—
1749C4⋊C4—531no—
1750C4⋊C4—531no—
1751C4⋊C4—531no—
1752C4⋊C4—531no—
1753C4⋊C4—533no—
1754C4⋊C4—533no—
1755C4⋊C4—533no—
1756C4⋊C4—533no—
1757C4⋊C4—533no—
1758C4⋊C4—533no—
1759C4⋊C4—533no—
1760C4⋊C4—531no—
1761C4⋊C4—531no—
1762C4⋊C4—533no—
1763C4⋊C4—533no—
1764C4⋊C4—533no—
1765C4⋊C4—533no—
1766C4⋊C4—533no—
1767C4⋊C4—531no—
1768C4⋊C4—531no—
1769C4⋊C4C23×D5313yes—
1770C4⋊C4C23×D5313yes—
1771C4⋊C4C23×D5313yes—
1772C4⋊C4C23×D5313yes—
1773C4⋊C4C23×D5313yes—
1774C4⋊C4C23×D5313yes—
1775C4⋊C4C23×D5313yes—
1776C4⋊C4C23×D5313yes—
1777C4⋊C4C23×D5316yes—
1778C4⋊C4C23×D5313yes—
1779C4⋊C4C23×D5313yes—
1780C4⋊C4C23×D5313yes—
1781C4⋊C4C23×D5313yes—
1782C4⋊C4C23×D5313yes—
1783C4⋊C4C23×D5313yes—
1784C22⋊C4—533no—
1785C22⋊C4—531no—
1786C22⋊C4—533no—
1787C22⋊C4—533no—
1788C22⋊C4—533no—
1789C22⋊C4—533no—
1790C22⋊C4—533no—
1791C22⋊C4—536no—
1792C22⋊C4—531no—
1793C22⋊C4—531no—
1794C22⋊C4—531no—
1795C22⋊C4—536no—
1796C22⋊C4—533no—
1797C22⋊C4—533no—
1798C22⋊C4—533no—
1799C22⋊C4—533no—
1800C22⋊C4—536no—
1801C22⋊C4—533no—
1802C22⋊C4—533no—
1803C22⋊C4—533no—
1804C22⋊C4—536no—
1805C22⋊C4—533no—
1806C22⋊C4—533no—
1807C22⋊C4—533no—
1808C22⋊C4—533no—
1809C22⋊C4—536no—
1810C22⋊C4—536no—
1811C22⋊C4—536no—
1812C22⋊C4—536no—
1813C22⋊C4—536no—
1814C22⋊C4—533no—
1815C22⋊C4—533no—
1816C22⋊C4—531no—
1817C22⋊C4—533no—
1818C22⋊C4—533no—
1819C22⋊C4—533no—
1820C22⋊C4—533no—
1821C22⋊C4—533no—
1822C22⋊C4—533no—
1823C22⋊C4—533no—
1824C22⋊C4—531no—
1825C22⋊C4—531no—
1826C22⋊C4—531no—
1827C22⋊C4C23×D5313yes—
1828C22⋊C4C23×D5311yescharacteristic
1829C22⋊C4C23×D5316yes—
1830C22⋊C4C23×D5313yes—
1831C22⋊C4C23×D5313yes—
1832C22⋊C4C23×D5316yes—
1833C22⋊C4C23×D5316yes—
1834C22⋊C4C23×D5313yes—
1835C22⋊C4C23×D5311yescharacteristic
1836C22⋊C4C23×D5313yes—
1837C22⋊C4C23×D5313yes—
1838C22⋊C4C23×D5311yescharacteristic
1839C22⋊C4C23×D5311yescharacteristic
1840C42—531no—
1841C42—533no—
1842C42—533no—
1843C42—531no—
1844C42—533no—
1845C42—531no—
1846C42—533no—
1847C42—533no—
1848C42—536no—
1849C42—533no—
1850C42—533no—
1851C42—533no—
1852C42—536no—
1853C42—533no—
1854C42—533no—
1855C42—533no—
1856C42C23×D5313yes—
1857C42C23×D5316yes—
1858C42C23×D5316yes—
1859C42C23×D5313yes—
1860C42C23×D5313yes—
1861C42C23×D5311yescharacteristic
1862C42C23×D5313yes—
1863C42C23×D5313yes—
1864C23—533no—
1865C23—533no—
1866C23—533no—
1867C23—531no—
1868C23—1066no—
1869C23—10612no—
1870C23—2126no—
1871C23—2123no—
1872C23—2126no—
1873C23—2123no—
1874C23C24×D5311yescharacteristic
1875C23C24×D5313yes—
1876C23C24×D5311yescharacteristic
1877Q8—26no—
1878Q8—26no—
1879Q8—46no—
1880Q8—41no—
1881Q8—1066no—
1882Q8—1062no—
1883Q8—1066no—
1884Q8—2121no—
1885Q8—2123no—
1886Q8—2123no—
1887Q8—2126no—
1888Q8#41×D5314yes—
1889D4—26no—
1890D4—43no—
1891D4—41no—
1892D4—43no—
1893D4—5312no—
1894D4—1066no—
1895D4—10612no—
1896D4—1066no—
1897D4—1066no—
1898D4—1062no—
1899D4—1066no—
1900D4—1066no—
1901D4—1066no—
1902D4—1066no—
1903D4—2123no—
1904D4—2126no—
1905D4—2123no—
1906D4—2123no—
1907D4—2123no—
1908D4—2123no—
1909D4—2121no—
1910D4—2123no—
1911D4—2123no—
1912D4—2126no—
1913D4—2123no—
1914C2×C4—26no—
1915C2×C4—26no—
1916C2×C4—26no—
1917C2×C4—43no—
1918C2×C4—43no—
1919C2×C4—531no—
1920C2×C4—5312no—
1921C2×C4—531no—
1922C2×C4—531no—
1923C2×C4—533no—
1924C2×C4—531no—
1925C2×C4—531no—
1926C2×C4—533no—
1927C2×C4—533no—
1928C2×C4—531no—
1929C2×C4—533no—
1930C2×C4—533no—
1931C2×C4—531no—
1932C2×C4—1066no—
1933C2×C4—1066no—
1934C2×C4—10612no—
1935C2×C4—1062no—
1936C2×C4—1066no—
1937C2×C4—1066no—
1938C2×C4—1066no—
1939C2×C4—2123no—
1940C2×C4—2126no—
1941C2×C4—2123no—
1942C2×C4—2123no—
1943C2×C4—2121no—
1944C2×C4—2123no—
1945C2×C4—2123no—
1946C2×C4—2126no—
1947C2×C4—2126no—
1948C2×C4—2126no—
1949C2×C4—2123no—
1950C2×C4—2123no—
1951C2×C4—2126no—
1952C2×C4—2121no—
1953C2×C4—2126no—
1954C2×C4—2123no—
1955C2×C4C24×D5313yes—
1956C2×C4C24×D5311yescharacteristic
1957C2×C4C24×D5311yescharacteristic
1958C2×C4C24×D5313yes—
1959C2×C4C24×D5313yes—
1960C2×C4C24×D5311yescharacteristic
1961C2×C4C24×D5313yes—
1962C2×C4C24×D5313yes—
1963C2×C4C24×D5311yescharacteristic
1964C2×C4C24×D5311yescharacteristic
1965C2×C4C24×D5313yes—
1966C2×C4C24×D5313yes—
1967C22—21no—
1968C22—21no—
1969C22—23no—
1970C22—23no—
1971C22—21no—
1972C22—21no—
1973C22—23no—
1974C22—21no—
1975C22—21no—
1976C22—536no—
1977C22—1063no—
1978C22—1063no—
1979C22—1061no—
1980C22—1063no—
1981C22—1063no—
1982C22—1061no—
1983C22—1063no—
1984C22—1063no—
1985C22—1063no—
1986C22—1061no—
1987C22—1063no—
1988C22—4246no—
1989C22—42412no—
1990C22C25×D5311yescharacteristic
1991C4—21no—
1992C4—23no—
1993C4—23no—
1994C4—21no—
1995C4—23no—
1996C4—23no—
1997C4—23no—
1998C4—21no—
1999C4—23no—
2000C4—21no—
2001C4—21no—
2002C4—532no—
2003C4—1061no—
2004C4—1061no—
2005C4—1063no—
2006C4—1063no—
2007C4—1063no—
2008C4—1063no—
2009C4—1061no—
2010C4—1061no—
2011C4—1063no—
2012C4—1061no—
2013C4—1061no—
2014C4C2×#41×D5316yes—
2015C2—41no—
2016C2—43no—
2017C2—41no—
2018C2—1066no—
2019C2—2123no—
2020C2—2123no—
2021C2—2121no—
2022C2C22×#41×D5311yescharacteristic
2023C2#2028952611yescharacteristic
2024C2#2028952711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3518C2
hypercenter#3518D53
hypocenterC53#62857
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3518

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20288826C2semidirect
2. #20288824C2semidirect
3. #20288801C2semidirect
4. #20288791C2semidirect
5. #20288788C2semidirect
6. #20288782C2semidirect
7. #20288762C2semidirect
8. #20288759C2semidirect
9. #20288726C2semidirect
10. #20288709C2semidirect
11. #20288701C2semidirect
12. #20288679C2semidirect
13. #20288672C2semidirect
14. #20288661C2semidirect
15. #20288659C2semidirect
16. #20288619C2semidirect
17. #20288605C2semidirect
18. #20288533C2semidirect
19. #20288506C2semidirect
20. #20288460C2semidirect
21. #20288449C2semidirect
22. #20288392C2semidirect
23. #20288381C2semidirect
24. #20288146C2semidirect
25. #20288135C2semidirect
26. #20288098C2semidirect
27. #542×D53C2semidirect
28. #20287924C2semidirect
29. C4×#13133263C2semidirect
30. #20287917C2semidirect
31. C53×#3518C2semidirect
35. #16811358C22semidirect
36. #16811358C22semidirect
37. #16811356C22semidirect
38. #16811355C22semidirect
39. Q8×Dic106C22semidirect
40. #16811349C22semidirect
41. #16811349C22semidirect
42. #16811347C22semidirect
43. #16811346C22semidirect
44. #16811345C22semidirect
45. #16811342C22semidirect
46. #16811341C22semidirect
47. #16811336C22semidirect
48. #16811336C22semidirect
49. #16811336C22semidirect
50. #16811334C22semidirect
51. #16811334C22semidirect
52. #16811333C22semidirect
53. #16811331C22semidirect
54. #16811331C22semidirect
55. #16811331C22semidirect
56. #16811324C22semidirect
57. #16811324C22semidirect
58. #16811323C22semidirect
59. #16811320C22semidirect
60. #16811319C22semidirect
61. #16811317C22semidirect
62. #16811314C22semidirect
63. #16811314C22semidirect
64. #16811313C22semidirect
65. #16811312C22semidirect
66. #16811309C22semidirect
67. #16811307C22semidirect
68. #16811303C22semidirect
69. #16811303C22semidirect
70. #16811300C22semidirect
71. #16811298C22semidirect
72. #16811298C22semidirect
73. #16811298C22semidirect
74. #16811297C22semidirect
75. #16811297C22semidirect
78. #16811288C22semidirect
79. #16811288C22semidirect
80. Q8×C22⋊D53C22semidirect
81. #16811285C22semidirect
82. #16811285C22semidirect
83. #16811285C22semidirect
85. #16811284C22semidirect
86. #16811284C22semidirect
87. #16811281C22semidirect
88. #16811280C22semidirect
89. #16811277C22semidirect
90. #16811276C22semidirect
91. #16811276C22semidirect
92. #16811276C22semidirect
93. #16811275C22semidirect
94. #16811273C22semidirect
95. #16811270C22semidirect
96. #16811269C22semidirect
97. #16811269C22semidirect
99. #16811266C22semidirect
100. #16811266C22semidirect
102. #16811264C22semidirect
103. #16811264C22semidirect
104. #16811262C22semidirect
107. #16811250C22semidirect
108. #16811250C22semidirect
109. #16811247C22semidirect
110. #16811247C22semidirect
111. #16811246C22semidirect
112. #16811246C22semidirect
113. #16811245C22semidirect
114. #16811245C22semidirect
115. #16811244C22semidirect
116. #16811243C22semidirect
117. #16811243C22semidirect
118. #16811242C22semidirect
119. #16811241C22semidirect
120. #16811240C22semidirect
121. #16811239C22semidirect
122. #16811239C22semidirect
123. #16811238C22semidirect
124. #16811237C22semidirect
125. #16811237C22semidirect
126. #16811234C22semidirect
127. #16811233C22semidirect
128. #16811232C22semidirect
129. #16811230C22semidirect
130. #16811228C22semidirect
131. #16811225C22semidirect
132. #16811224C22semidirect
133. #16811223C22semidirect
134. #16811221C22semidirect
135. #16811221C22semidirect
136. #16811219C22semidirect
137. #16811219C22semidirect
138. #16811216C22semidirect
139. #16811214C22semidirect
140. #16811212C22semidirect
141. #16811212C22semidirect
142. #16811209C22semidirect
143. #16811207C22semidirect
144. #16811207C22semidirect
145. #16811205C22semidirect
147. #16811203C22semidirect
148. #16811198C22semidirect
149. #16811196C22semidirect
151. #16811189C22semidirect
152. #16811177C22semidirect
153. #16811177C22semidirect
154. #16811177C22semidirect
155. #16811174C22semidirect
156. #16811172C22semidirect
157. #16811170C22semidirect
158. #16811168C22semidirect
159. C4⋊Q8×D53C22semidirect
160. #16811160C22semidirect
161. #16811160C22semidirect
162. #16811160C22semidirect
163. #16811159C22semidirect
164. #16811157C22semidirect
165. #16811157C22semidirect
166. #16811156C22semidirect
167. #16811155C22semidirect
168. #16811153C22semidirect
169. #16811153C22semidirect
170. #16811152C22semidirect
171. #16811151C22semidirect
172. #16811151C22semidirect
173. #16811151C22semidirect
174. #16811151C22semidirect
175. #126×D53C22semidirect
176. #124×D53C22semidirect
177. #124×D53C22semidirect
178. #16811136C22semidirect
180. #16811132C22semidirect
181. #16811131C22semidirect
182. #123×D53C22semidirect
183. C22⋊Q8×D53C22semidirect
184. C22⋊Q8×D53C22semidirect
186. #16811106C22semidirect
189. #16811105C22semidirect
190. #16811105C22semidirect
191. #16811105C22semidirect
192. #16811105C22semidirect
193. #16811105C22semidirect
194. #16811105C22semidirect
195. #16811103C22semidirect
196. #16811103C22semidirect
197. #16811103C22semidirect
198. #16811101C22semidirect
199. #16811099C22semidirect
200. #16811099C22semidirect
201. #16811097C22semidirect
202. #16811097C22semidirect
203. #16811097C22semidirect
204. #16811095C22semidirect
205. #16811095C22semidirect
208. C4×#11719949C22semidirect
209. C4×#11719949C22semidirect
210. C4×#11719949C22semidirect
211. C4×#11719949C22semidirect
212. C4×#11719945C22semidirect
213. #16811091C22semidirect
214. #16811091C22semidirect
215. C2×Q8×Dic53C22semidirect
216. C4×Q8×D53C22semidirect
217. C4×Q8×D53C22semidirect
218. C2×C4×D212C22semidirect
219. C4×D4×D53C22semidirect
220. C4×D4×D53C22semidirect
221. #117×D53C22semidirect
222. #117×D53C22semidirect
223. Q82×C53C22semidirect
224. C53×#556C22semidirect
225. C53×#556C22semidirect
226. C53×#556C22semidirect
227. C53×#555C22semidirect
228. D4×Q8×C53C22semidirect
230. C53×#548C22semidirect
231. C53×#542C22semidirect
232. C53×#542C22semidirect
233. C53×#533C22semidirect
234. C53×#529C22semidirect
235. C53×#519C22semidirect
236. C53×#519C22semidirect
237. C4×#41×C53C22semidirect
661. #11719949#41semidirect
1012. #3518D53semidirect
1052. Q82C2×D53semidirect
1060. #556C2×D53semidirect
1061. #556C2×D53semidirect
1062. #556C2×D53semidirect
1066. #555C2×D53semidirect
1098. D4×Q8C2×D53semidirect
1108. #548C2×D53semidirect
1146. #542C2×D53semidirect
1147. #542C2×D53semidirect
1177. #533C2×D53semidirect
1198. #529C2×D53semidirect
1225. #519C2×D53semidirect
1226. #519C2×D53semidirect
1241. C4×#41C2×D53semidirect
1250. C53#62857semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202888262
#202888242
#202888012
#202887912
#202887882
#202887822
#202887622
#202887592
#202887262
#202887092
#202887012
#202886792
#202886722
#202886612
#202886592
#202886192
#202886052
#202885332
#202885062
#202884602
#202884492
#202883922
#202883812
#202881462
#202881352
#202880982
#542×D532
#202879242
C4×#131332632
#202879172
C53×#35182
#6285753