Finite Group Databasebeta

← #28293186

Subgroups — #28293186

Order 13568.

7066 conjugacy classes of subgroups.

The subgroup lattice has 2024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288826C211yesmaximal, characteristic, complemented
2#20288821C213yesmaximal, complemented
3#20288817C211yesmaximal, characteristic, complemented
4#20288814C213yesmaximal, complemented
5#20288800C211yesmaximal, characteristic, complemented
6#20288799C213yesmaximal, complemented
7#20288796C213yesmaximal, complemented
8#20288791C211yesmaximal, characteristic, complemented
9#20288722C211yesmaximal, characteristic, complemented
10#20288719C213yesmaximal, complemented
11#20288715C211yesmaximal, characteristic, complemented
12#20288714C213yesmaximal, complemented
13#20288709C211yesmaximal, characteristic, complemented
14#20288706C213yesmaximal, complemented
15#20288703C213yesmaximal, complemented
16#20288568C213yesmaximal, complemented
17#20288561C213yesmaximal, complemented
18#20288522C211yesmaximal, characteristic, complemented
19#20288485C211yesmaximal, characteristic, complemented
20#20288423C213yesmaximal, complemented
21#20288415C213yesmaximal, complemented
22#20288372C211yesmaximal, characteristic, complemented
23#20288372C211yesmaximal, characteristic, complemented
24#20288136C213yesmaximal, complemented
25#20288135C213yesmaximal, complemented
26#20288106C213yesmaximal, complemented
27#20288098C213yesmaximal, complemented
28C4×#13133265C211yesmaximal, characteristic, complemented
29#20287924C211yesmaximal, characteristic, complemented
30#520×D53C211yesmaximal, characteristic, complemented
31C53×#3516C211yesmaximal, characteristic, complemented
32C2×#13133265C2211yescharacteristic
33C2×#13133265C2211yescharacteristic
34C2×#41×D53C2211yescharacteristic
35#16811358C2213yescomplemented
36#16811358C2213yescomplemented
37#16811357C2216yescomplemented
38#16811356C2216yescomplemented
39#16811355C2213yescomplemented
40#16811355C2213yescomplemented
41Q8×Dic106C2211yescharacteristic, complemented
42#16811353C2213yescomplemented
43#16811351C2213yescomplemented
44#16811350C2213yescomplemented
45#16811350C2213yescomplemented
46#16811349C2211yescharacteristic, complemented
47#16811349C2211yescharacteristic, complemented
48#16811347C2213yescomplemented
49#16811340C2216yescomplemented
50#16811337C2213yescomplemented
51#16811336C2216yescomplemented
52#16811336C2213yescomplemented
53#16811333C2213yescomplemented
54#16811331C2213yescomplemented
55#16811331C2213yescomplemented
56#16811329C2216yescomplemented
57#16811327C2216yescomplemented
58#16811326C2213yescomplemented
59#16811326C2213yescomplemented
60#16811324C2216yescomplemented
61#16811324C2216yescomplemented
62#16811324C2216yescomplemented
63#16811323C2213yescomplemented
64#16811322C2216yescomplemented
65#16811321C2213yescomplemented
66#16811319C2213yescomplemented
67#16811319C2213yescomplemented
68#16811317C2213yescomplemented
69#16811315C2213yescomplemented
70#16811314C2213yescomplemented
71#16811307C2213yescomplemented
72#16811306C2216yescomplemented
73#16811305C2216yescomplemented
74#16811295C2211yescharacteristic
75#16811295C2211yescharacteristic
76#16811295C2213yescomplemented
77#16811295C2211yescharacteristic, complemented
78#16811294C2213yes—
79#16811294C2213yes—
80#16811294C2213yescomplemented
81#16811294C2213yescomplemented
82#16811292C2211yescharacteristic
83#16811292C2211yescharacteristic
84#16811291C2213yes—
85#16811291C2213yes—
86#16811291C2216yescomplemented
87#16811288C2213yescomplemented
88#16811284C2211yescharacteristic
89#16811284C2211yescharacteristic
90#16811284C2211yescharacteristic, complemented
91#16811284C2211yescharacteristic, complemented
92#16811283C2213yes—
93#16811283C2213yes—
94#16811283C2213yescomplemented
95#16811283C2213yescomplemented
96#16811281C2213yes—
97#16811281C2213yes—
98#16811277C2213yescomplemented
99#16811276C2213yescomplemented
100#16811275C2216yescomplemented
101#16811275C2216yescomplemented
102#16811274C2213yescomplemented
103#16811274C2213yescomplemented
104#16811274C2213yescomplemented
105#16811273C2213yescomplemented
106#16811271C2216yescomplemented
107#16811253C2213yes—
108#16811250C2213yes—
109#16811246C2213yescomplemented
110#16811246C2213yescomplemented
111#16811246C2213yescomplemented
112#16811245C2213yescomplemented
113#16811245C2213yescomplemented
114#16811245C2213yescomplemented
115#16811243C2213yescomplemented
116#16811243C2216yescomplemented
117#16811242C2213yescomplemented
118#16811241C2213yescomplemented
119#16811239C2216yescomplemented
120#16811239C2213yescomplemented
121#16811237C2213yescomplemented
122#16811234C2213yescomplemented
123#16811232C2213yescomplemented
124#16811230C2213yescomplemented
125#16811229C2213yescomplemented
126#16811229C2213yescomplemented
127#16811228C2213yescomplemented
128#16811228C2213yescomplemented
129#16811226C2213yescomplemented
130#16811225C2216yescomplemented
131#16811225C2216yescomplemented
132#16811225C2213yescomplemented
133#16811224C2213yescomplemented
134#16811223C2213yescomplemented
135#16811221C2213yes—
136#16811221C2216yes—
137#16811219C2213yes—
138#16811216C2211yescharacteristic
139#16811214C2213yes—
140#16811212C2216yes—
141#16811212C2213yes—
142#16811212C2216yes—
143#16811209C2213yes—
144#16811207C2213yes—
145#16811205C2213yes—
146#16811203C2213yes—
147#16811203C2213yes—
148#16811191C2213yes—
149#16811191C2213yes—
150#16811189C2213yes—
151#16811189C2213yes—
152#16811179C2213yes—
153#16811177C2213yes—
154#16811174C2213yes—
155#16811174C2213yescomplemented
156#16811173C2213yescomplemented
157#16811172C2216yescomplemented
158#16811170C2213yes—
159#16811170C2213yescomplemented
160#16811170C2216yescomplemented
161#16811168C2213yescomplemented
162#16811160C2213yescomplemented
163#16811160C2213yescomplemented
164#16811159C2213yescomplemented
165#16811158C2216yescomplemented
166#16811158C2216yescomplemented
167#16811157C2213yescomplemented
168#16811156C2216yescomplemented
169#16811156C2216yescomplemented
170#16811156C2216yescomplemented
171#16811155C2213yescomplemented
172#16811153C2213yescomplemented
173#16811153C2213yescomplemented
174#16811152C2213yescomplemented
175#16811151C2213yescomplemented
176#16811151C2216yescomplemented
177#16811151C2213yescomplemented
178#16811136C2216yes—
179#16811136C2213yes—
180#16811136C2213yes—
181#16811135C2216yes—
182#16811132C2216yes—
183#16811132C2213yes—
184#16811132C2213yes—
185#16811131C2216yes—
186#16811106C2211yescharacteristic
187#16811105C2211yescharacteristic
188#16811105C2213yes—
189#16811105C2213yes—
190#16811105C2211yescharacteristic
191#16811105C2211yescharacteristic, complemented
192#16811105C2211yescharacteristic, complemented
193#16811104C2213yes—
194#16811104C2213yes—
195#16811104C2213yescomplemented
196#16811103C2213yes—
197#16811103C2213yes—
198#16811103C2213yescomplemented
199#16811102C2213yes—
200#16811102C2213yes—
201#16811101C2211yescharacteristic, complemented
202#16811099C2211yescharacteristic
203#16811099C2211yescharacteristic
204#16811099C2213yescomplemented
205#16811099C2213yescomplemented
206C4×#11719949C2213yes—
207C4×#11719949C2213yes—
208C4×#11719949C2211yescharacteristic, complemented
209C4×#11719949C2211yescharacteristic, complemented
210C4×#11719945C2213yes—
211C4×#11719945C2213yescomplemented
212#16811091C2213yes—
213#16811091C2213yescomplemented
214C2×Q8×Dic53C2211yescharacteristic, complemented
215C4×Q8×D53C2211yescharacteristic
216C4×Q8×D53C2211yescharacteristic
217C4×Q8×D53C2213yescomplemented
218C4×Q8×D53C2213yescomplemented
219C4×D4×D53C2213yes—
220C4×D4×D53C2213yes—
221#117×D53C2213yes—
222C2×C4⋊C4×D53C2213yes—
223C53×#557C2211yescharacteristic, complemented
224C53×#556C2213yescomplemented
225C53×#554C2213yescomplemented
226C53×#553C2213yescomplemented
227C53×#552C2213yescomplemented
228D4×Q8×C53C2211yescharacteristic, complemented
229C53×#548C2211yescharacteristic
230C53×#548C2211yescharacteristic
231C53×#542C2213yescomplemented
232C53×#541C2213yescomplemented
233C53×#529C2213yescomplemented
234C53×#529C2213yescomplemented
235C53×#520C2211yescharacteristic
236C53×#519C2211yescharacteristic, complemented
237C2×C4×Q8×C53C2211yescharacteristic, complemented
238#13133265—28no—
239#13133265—28no—
240C2×#11719949C2311yescharacteristic
241C2×#11719949C2311yescharacteristic
242C2×#11719949C2311yescharacteristic
243C2×#11719949C2313yes—
244C2×#11719949C2313yes—
245C2×#11719949C2316yes—
246C2×#11719945C2313yes—
247C2×#11719945C2313yes—
248C2×#11719945C2313yes—
249C2×#11719945C2313yes—
250C2×#11719945C2313yes—
251C2×#11719945C2316yes—
252C2×#11719945C2316yes—
253C2×#11719947C2313yes—
254C2×#11719947C2316yes—
255#41×D53—28no—
256C2×Q8×D53C2313yes—
257C2×Q8×D53C2313yes—
258C2×Q8×D53C2311yescharacteristic
259C2×D4×D53C2313yes—
260C22×C4×D53C2313yes—
261C22×C4×D53C2316yes—
262#13133217C2313yes—
263#13133216C2316yes—
264#13133216C2313yes—
265#13133216C2313yes—
266#13133216C2313yes—
267#13133216C2313yes—
268#13133216C2313yes—
269#13133216C2313yes—
270#13133215C2313yes—
271#13133215C2316yes—
272#13133214C2313yes—
273#13133214C2313yes—
274#13133214C2313yes—
275#13133213C2316yes—
276#13133213C2316yes—
277#13133213C2313yes—
278#13133213C2313yes—
279#13133213C2313yes—
280#13133212C2313yes—
281#13133212C2316yes—
282#13133212C2313yes—
283#13133212C2316yes—
284#13133212C2313yes—
285#13133212C2313yes—
286#13133212C2316yes—
287#13133212C2313yes—
288#13133212C2313yes—
289#13133211C2316yes—
290#13133211C2313yes—
291#13133211C2313yes—
292#13133210C2313yes—
293#13133210C2313yes—
294#13133210C2311yescharacteristic
295#13133210C2313yes—
296#13133210C2313yes—
297#13133210C2311yescharacteristic
298#13133209C2313yes—
299#13133209C2313yes—
300#13133209C2313yes—
301#13133208C2313yes—
302#13133208C2313yes—
303#13133208C2313yes—
304#13133208C2311yescharacteristic
305#13133207C2313yes—
306#13133207C2316yes—
307#13133207C2316yes—
308#13133207C2316yes—
309#13133207C2313yes—
310#13133207C2313yes—
311#13133207C2313yes—
312#13133207C2311yescharacteristic
313#13133207C2313yes—
314#13133206C2313yes—
315#13133206C2313yes—
316#13133206C2313yes—
317#13133206C2313yes—
318#13133206C2313yes—
319#13133205C2316yes—
320#13133205C2313yes—
321#13133205C2316yes—
322#13133204C2313yes—
323#13133203C2316yes—
324#13133203C2316yes—
325#13133203C2313yes—
326#13133203C2313yes—
327#13133203C2313yes—
328#13133203C2313yes—
329#13133203C2316yes—
330#13133203C2313yes—
331#13133203C2313yes—
332#13133203C2316yes—
333#13133202C2316yes—
334#13133202C2316yes—
335#13133202C2316yes—
336#13133202C2316yes—
337#13133202C2313yes—
338#13133202C2316yes—
339#13133202C2316yes—
340#13133202C2313yes—
341#13133202C2313yes—
342#13133202C2313yes—
343#13133202C2313yes—
344#13133202C2313yes—
345#13133202C2316yes—
346#13133201C2316yes—
347#13133201C2313yes—
348#13133201C2316yes—
349#13133201C2313yes—
350#13133200C2313yes—
351#13133200C2313yes—
352#13133200C2316yes—
353#13133199C2313yes—
354#13133199C2316yes—
355#13133199C2313yes—
356#13133199C2313yes—
357#13133199C2316yes—
358#13133199C2311yescharacteristic
359#13133199C2311yescharacteristic
360#13133199C2316yes—
361#13133199C2313yes—
362#13133198C2313yes—
363#13133198C2311yescharacteristic
364#13133197C2316yes—
365#13133197C2316yes—
366#13133197C2313yes—
367#13133197C2313yes—
368#13133196C2311yescharacteristic
369#13133195C2316yes—
370#13133195C2313yes—
371#13133195C2316yes—
372#13133195C2313yes—
373#13133195C2313yes—
374#13133195C2316yes—
375#13133195C2316yes—
376#13133195C2316yes—
377#13133195C2313yes—
378#13133195C2311yescharacteristic
379#13133195C2313yes—
380#13133194C2313yes—
381#13133194C2316yes—
382#13133194C2313yes—
383#13133194C2313yes—
384#13133194C2311yescharacteristic
385#13133193C2313yes—
386#13133193C2313yes—
387#13133193C2313yes—
388#13133193C2313yes—
389#13133193C2313yes—
390#13133193C2313yes—
391#13133192C2313yes—
392#13133192C2313yes—
393#13133192C2313yes—
394#13133192C2313yes—
395#13133192C2313yes—
396#13133192C2313yes—
397#13133192C2316yes—
398#13133192C2313yes—
399#13133192C2316yes—
400#13133192C2316yes—
401#13133192C2316yes—
402#13133192C2313yes—
403#13133191C2313yes—
404#13133191C2313yes—
405#13133191C2313yes—
406#13133191C2313yes—
407#13133191C2313yes—
408#13133191C2313yes—
409#13133191C2316yes—
410#13133191C2313yes—
411#13133190C2316yes—
412#13133190C2313yes—
413#13133190C2316yes—
414#13133190C2316yes—
415#13133190C2316yes—
416#13133190C2316yes—
417#13133190C2316yes—
418#13133190C2316yes—
419#13133190C2316yes—
420#13133190C2313yes—
421#13133190C2313yes—
422#13133190C2313yes—
423#13133190C2313yes—
424#13133190C2313yes—
425#13133190C2316yes—
426#13133189C2313yes—
427#13133189C2313yes—
428#13133189C2313yes—
429#13133189C2316yes—
430#13133189C2313yes—
431#13133188C2313yes—
432#13133188C2313yes—
433#13133188C2313yes—
434#13133188C2311yescharacteristic
435#13133187C2316yes—
436#13133187C2313yes—
437#13133187C2316yes—
438#13133187C2313yes—
439#13133185C2313yes—
440#13133185C2313yes—
441Q8×Dic53C2311yescharacteristic
442Q8×Dic53C2311yescharacteristic
443Q8×Dic53C2311yescharacteristic
444Q8×Dic53C2313yes—
445Q8×Dic53C2313yes—
446Q8×Dic53C2311yescharacteristic
447Q8×Dic53C2313yes—
448Q8×Dic53C2313yes—
449C4×Dic106C2313yes—
450C4×Dic106C2313yes—
451C4×Dic106C2313yes—
452C4×Dic106C2313yes—
453C4×Dic106C2316yes—
454C4×Dic106C2313yes—
455C4×Dic106C2313yes—
456C4×Dic106C2313yes—
457C4×Dic106C2313yes—
458C4×Dic106C2313yes—
459#13133182C2313yes—
460#13133182C2313yes—
461#13133182C2313yes—
462#13133182C2316yes—
463#13133182C2316yes—
464#13133182C2313yes—
465#13133182C2313yes—
466#13133182C2313yes—
467#13133182C2316yes—
468C4×D212C2313yes—
469C4×D212C2313yes—
470C4×D212C2313yes—
471C4×D212C2313yes—
472C4×D212C2313yes—
473C4×D212C2313yes—
474C4×D212C2316yes—
475C4×D212C2316yes—
476C4×D212C2313yes—
477C4×D212C2313yes—
478C4×D212C2313yes—
479C4×D212C2313yes—
480C4×D212C2316yes—
481C4×D212C2313yes—
482D4×Dic53C2313yes—
483D4×Dic53C2313yes—
484#13133179C2313yes—
485#13133179C2313yes—
486#13133179C2313yes—
487#13133179C2316yes—
488#13133179C2316yes—
489#13133179C2316yes—
490#13133179C2316yes—
491#13133179C2316yes—
492#13133179C2313yes—
493#13133179C2313yes—
494#13133179C2313yes—
495#13133179C2313yes—
496#13133179C2316yes—
497#13133179C2313yes—
498C4×C22⋊D53C2313yes—
499C4×C22⋊D53C2313yes—
500C4×C22⋊D53C2313yes—
501C4×C22⋊D53C2313yes—
502C4×C22⋊D53C2316yes—
503C4×C22⋊D53C2316yes—
504C4×C22⋊D53C2313yes—
505C4×C22⋊D53C2313yes—
506C4×C22⋊D53C2316yes—
507C4×C22⋊D53C2316yes—
508C4×C22⋊D53C2311yescharacteristic
509C4×C22⋊D53C2313yes—
510C4×C22⋊D53C2313yes—
511C4×C22⋊D53C2313yes—
512#13133177C2316yes—
513#13133177C2316yes—
514#13133177C2316yes—
515#13133177C2316yes—
516#13133177C2316yes—
517#13133177C2316yes—
518#13133177C2316yes—
519#13133177C2316yes—
520#13133177C2311yescharacteristic
521#13133177C2313yes—
522#13133177C2313yes—
523#13133177C2313yes—
524#13133176C2313yes—
525#13133176C2313yes—
526#13133176C2313yes—
527#13133175C2316yes—
528#13133175C2313yes—
529#13133175C2313yes—
530#13133175C2313yes—
531#13133175C2313yes—
532#13133175C2313yes—
533#13133175C2313yes—
534#13133175C2316yes—
535#13133175C2316yes—
536#13133174C2316yes—
537#13133174C2316yes—
538#13133174C2316yes—
539#13133174C2313yes—
540#13133174C2313yes—
541#13133174C2313yes—
542#13133174C2313yes—
543#13133174C2313yes—
544#13133174C2313yes—
545#13133173C2316yes—
546#13133173C2313yes—
547#13133173C2313yes—
548C2×C4⋊Dic53C2313yes—
549C2×C4⋊Dic53C2313yes—
550C2×#11719919C2316yes—
551C4⋊C4×D53C2316yes—
552C4⋊C4×D53C2313yes—
553C4⋊C4×D53C2313yes—
554C4⋊C4×D53C2313yes—
555C4⋊C4×D53C2316yes—
556C4⋊C4×D53C2316yes—
557C4⋊C4×D53C2313yes—
558C4⋊C4×D53C2313yes—
559C4⋊C4×D53C2313yes—
560C4⋊C4×D53C2313yes—
561C4⋊C4×D53C2311yescharacteristic
562C22⋊C4×D53C2313yes—
563C22⋊C4×D53C2313yes—
564C2×C4×Dic53C2313yes—
565C42×D53C2313yes—
566C42×D53C2313yes—
567C42×D53C2313yes—
568C42×D53C2316yes—
569C42×D53C2313yes—
570C42×D53C2316yes—
571C2×#41×C53C2311yescharacteristic
572C22×Q8×C53C2311yescharacteristic
573C22×Q8×C53C2311yescharacteristic
574C4⋊Q8×C53C2313yes—
575C4⋊Q8×C53C2313yes—
576#126×C53C2316yes—
577#126×C53C2313yes—
578#126×C53C2313yes—
579#126×C53C2316yes—
580#125×C53C2316yes—
581#125×C53C2313yes—
582#125×C53C2313yes—
583#125×C53C2313yes—
584#124×C53C2313yes—
585#124×C53C2313yes—
586#124×C53C2313yes—
587#123×C53C2316yes—
588#123×C53C2313yes—
589#123×C53C2311yescharacteristic
590C22⋊Q8×C53C2313yes—
591C22⋊Q8×C53C2316yes—
592C22⋊Q8×C53C2313yes—
593C22⋊Q8×C53C2313yes—
594C22⋊Q8×C53C2313yes—
595C22⋊Q8×C53C2313yes—
596#121×C53C2313yes—
597#121×C53C2313yes—
598#121×C53C2313yes—
599C4×Q8×C53C2311yescharacteristic
600C4×Q8×C53C2311yescharacteristic
601C4×Q8×C53C2313yes—
602C4×Q8×C53C2313yes—
603C4×Q8×C53C2311yescharacteristic
604C4×Q8×C53C2311yescharacteristic
605C4×Q8×C53C2313yes—
606C4×Q8×C53C2313yes—
607C4×Q8×C53C2313yes—
608C4×D4×C53C2313yes—
609C4×D4×C53C2313yes—
610C4×D4×C53C2313yes—
611C4×D4×C53C2313yes—
612C4×D4×C53C2313yes—
613C4×D4×C53C2316yes—
614#117×C53C2313yes—
615#117×C53C2313yes—
616#117×C53C2313yes—
617#117×C53C2316yes—
618C2×C4⋊C4×C53C2313yes—
619C2×C4⋊C4×C53C2313yes—
620C2×C42×C53C2313yes—
621C23×D53C2413yes—
622#41×C53—24no—
623C2×Q8×C53—24no—
624C2×Q8×C53—24no—
625C2×Q8×C53C2413yes—
626C2×Q8×C53C2413yes—
627C2×Q8×C53C2413yes—
628C2×Q8×C53C2411yescharacteristic
629C2×D4×C53C2413yes—
630C2×D4×C53C2413yes—
631C2×D4×C53C2411yescharacteristic
632C2×D4×C53C2413yes—
633C22×C4×C53C2413yes—
634C22×C4×C53C2413yes—
635C22×C4×C53C2413yes—
636C22×C4×C53C2411yescharacteristic
637C22×C4×C53C2413yes—
638C22×C4×C53C2416yes—
639C2×C22⋊D53C2411yescharacteristic
640C2×C22⋊D53C2413yes—
641C2×C22⋊D53C2416yes—
642C2×C22⋊D53C2411yescharacteristic
643C2×C22⋊D53C2413yes—
644C2×C22⋊D53C2413yes—
645C2×C22⋊D53C2416yes—
646C2×C22⋊D53C2413yes—
647C2×C22⋊D53C2416yes—
648C2×C22⋊D53C2413yes—
649C2×C22⋊D53C2413yes—
650C2×C22⋊D53C2413yes—
651C2×C22⋊D53C2413yes—
652C22×Dic53C2413yes—
653C22×Dic53C2411yescharacteristic
654C22×Dic53C2413yes—
655C22×Dic53C2416yes—
656#11719949—24no—
657#11719949—24no—
658#11719949—24no—
659#11719949—212no—
660#11719949—212no—
661#11719949—86no—
662Q8×D53—212no—
663Q8×D53—212no—
664Q8×D53#4118yescomplemented
665#11719947—212no—
666#11719947—86no—
667D4×D53—212no—
668#11719945—212no—
669#11719945—212no—
670#11719945—212no—
671#11719945—212no—
672#11719945—212no—
673#11719945—86no—
674#11719945—86no—
675C2×D212C2413yes—
676C2×D212C2413yes—
677C2×D212C2413yes—
678C2×D212C2413yes—
679C2×D212C2413yes—
680C2×D212C2416yes—
681C2×D212C2413yes—
682C2×D212C2416yes—
683C2×D212C2416yes—
684C2×D212C2413yes—
685C2×D212C2413yes—
686C2×C4×D53—212no—
687C2×C4×D53—86no—
688C2×C4×D53C2416yes—
689C2×C4×D53C2416yes—
690C2×C4×D53C2413yes—
691C2×C4×D53C2413yes—
692C2×C4×D53C2411yescharacteristic
693C2×C4×D53C2413yes—
694C2×C4×D53C2413yes—
695C2×C4×D53C2411yescharacteristic
696C2×C4×D53C2411yescharacteristic
697C2×C4×D53C2413yes—
698C2×C4×D53C2413yes—
699C2×C4×D53C2413yes—
700C2×C4×D53C2413yes—
701C2×C4×D53C2413yes—
702C2×C4×D53C2416yes—
703C2×C4×D53C2416yes—
704C2×C4×D53C2413yes—
705C2×C4×D53C2416yes—
706C2×C4×D53C2416yes—
707C2×C4×D53C2413yes—
708C2×Dic106C2413yes—
709C2×Dic106C2413yes—
710C2×Dic106C2413yes—
711C2×Dic106C2416yes—
712C2×Dic106C2411yescharacteristic
713C2×Dic106C2413yes—
714C2×Dic106C2413yes—
715C4⋊C4×C53C2413yes—
716C4⋊C4×C53C2413yes—
717C4⋊C4×C53C2413yes—
718C4⋊C4×C53C2413yes—
719C4⋊C4×C53C2416yes—
720C4⋊C4×C53C2411yescharacteristic
721C4⋊C4×C53C2413yes—
722C4⋊C4×C53C2413yes—
723C4⋊C4×C53C2413yes—
724C4⋊C4×C53C2413yes—
725C4⋊C4×C53C2416yes—
726C4⋊C4×C53C2413yes—
727C4⋊C4×C53C2413yes—
728C4⋊C4×C53C2416yes—
729C4⋊C4×C53C2413yes—
730C4⋊C4×C53C2411yescharacteristic
731C4⋊C4×C53C2413yes—
732C22⋊C4×C53C2413yes—
733C22⋊C4×C53C2411yescharacteristic
734C22⋊C4×C53C2413yes—
735C22⋊C4×C53C2413yes—
736C22⋊C4×C53C2413yes—
737C22⋊C4×C53C2416yes—
738C22⋊C4×C53C2411yescharacteristic
739C22⋊C4×C53C2413yes—
740C22⋊C4×C53C2411yescharacteristic
741C22⋊C4×C53C2416yes—
742C22⋊C4×C53C2413yes—
743C22⋊C4×C53C2413yes—
744C42×C53C2413yes—
745C42×C53C2413yes—
746C42×C53C2413yes—
747C42×C53C2413yes—
748C42×C53C2416yes—
749C42×C53C2413yes—
750C42×C53C2413yes—
751C22⋊Dic53C2413yes—
752C22⋊Dic53C2413yes—
753C22⋊Dic53C2413yes—
754C22⋊Dic53C2411yescharacteristic
755C22⋊Dic53C2413yes—
756C22⋊Dic53C2413yes—
757C22⋊Dic53C2411yescharacteristic
758C22⋊Dic53C2411yescharacteristic
759C22⋊Dic53C2411yescharacteristic
760C22⋊Dic53C2411yescharacteristic
761#11719921C2413yes—
762#11719921C2413yes—
763#11719921C2413yes—
764#11719921C2413yes—
765#11719921C2411yescharacteristic
766#11719921C2413yes—
767#11719921C2411yescharacteristic
768#11719921C2413yes—
769#11719921C2413yes—
770#11719921C2413yes—
771#11719921C2416yes—
772#11719921C2413yes—
773#11719921C2413yes—
774#11719921C2413yes—
775#11719921C2416yes—
776#11719921C2416yes—
777#11719921C2413yes—
778#11719921C2413yes—
779#11719921C2413yes—
780#11719921C2416yes—
781#11719921C2416yes—
782#11719921C2416yes—
783#11719921C2413yes—
784#11719921C2413yes—
785#11719921C2413yes—
786#11719921C2413yes—
787#11719921C2413yes—
788#11719921C2413yes—
789#11719921C2413yes—
790#11719921C2413yes—
791C4⋊Dic53C2413yes—
792C4⋊Dic53C2413yes—
793C4⋊Dic53C2413yes—
794C4⋊Dic53C2413yes—
795C4⋊Dic53C2413yes—
796C4⋊Dic53C2416yes—
797C4⋊Dic53C2411yescharacteristic
798C4⋊Dic53C2413yes—
799C4⋊Dic53C2413yes—
800C4⋊Dic53C2413yes—
801C4⋊Dic53C2411yescharacteristic
802C4⋊Dic53C2411yescharacteristic
803C4⋊Dic53C2411yescharacteristic
804C4⋊Dic53C2413yes—
805C4⋊Dic53C2413yes—
806#11719919C2416yes—
807#11719919C2413yes—
808#11719919C2413yes—
809#11719919C2416yes—
810#11719919C2413yes—
811#11719919C2413yes—
812#11719919C2413yes—
813#11719919C2413yes—
814#11719919C2411yescharacteristic
815#11719919C2411yescharacteristic
816#11719919C2413yes—
817#11719919C2416yes—
818#11719919C2413yes—
819#11719919C2411yescharacteristic
820#11719919C2413yes—
821#11719919C2411yescharacteristic
822#11719919C2413yes—
823#11719919C2413yes—
824#11719919C2413yes—
825#11719919C2413yes—
826#11719919C2413yes—
827#11719919C2416yes—
828#11719919C2411yescharacteristic
829#11719919C2411yescharacteristic
830#11719919C2413yes—
831#11719919C2413yes—
832#11719919C2411yescharacteristic
833#11719919C2411yescharacteristic
834C4×Dic53C2413yes—
835C4×Dic53C2413yes—
836C4×Dic53C2411yescharacteristic
837C4×Dic53C2411yescharacteristic
838C4×Dic53C2413yes—
839C4×Dic53C2413yes—
840C4×Dic53C2413yes—
841C4×Dic53C2416yes—
842C4×Dic53C2413yes—
843C4×Dic53C2413yes—
844C4×Dic53C2413yes—
845C4×Dic53C2413yes—
846C4×Dic53C2413yes—
847C4×Dic53C2416yes—
848C4×Dic53C2416yes—
849C4×Dic53C2413yes—
850C4×Dic53C2413yes—
851C23×C53C2511yescharacteristic
852C23×C53C2513yes—
853C23×C53C2511yescharacteristic
854C22×D53—26no—
855C22×D53—43no—
856C22×D53—43no—
857C22×D53C2513yes—
858C22×D53C2513yes—
859C22×D53C2513yes—
860C22×D53C2511yescharacteristic
861Q8×C53—26no—
862Q8×C53—26no—
863Q8×C53—43no—
864Q8×C53C2×#4114yes—
865D4×C53—26no—
866D4×C53—43no—
867D4×C53—43no—
868D4×C53—41no—
869C2×C4×C53—26no—
870C2×C4×C53—26no—
871C2×C4×C53—26no—
872C2×C4×C53—46no—
873C2×C4×C53—43no—
874C2×C4×C53—41no—
875C2×C4×C53C2513yes—
876C2×C4×C53C2513yes—
877C2×C4×C53C2513yes—
878C2×C4×C53C2513yes—
879C2×C4×C53C2513yes—
880C2×C4×C53C2511yescharacteristic
881C2×C4×C53C2513yes—
882C2×C4×C53C2511yescharacteristic
883C2×C4×C53C2511yescharacteristic
884C2×C4×C53C2511yescharacteristic
885C2×C4×C53C2511yescharacteristic
886C2×C4×C53C2513yes—
887C22⋊D53—22no—
888C22⋊D53—22no—
889C22⋊D53—26no—
890C22⋊D53—26no—
891C22⋊D53—212no—
892C22⋊D53—43no—
893C22⋊D53—43no—
894C22⋊D53—43no—
895C22⋊D53—46no—
896C22⋊D53—43no—
897C22⋊D53—46no—
898C22⋊D53—43no—
899C22⋊D53—43no—
900C2×Dic53—26no—
901C2×Dic53—46no—
902C2×Dic53—43no—
903C2×Dic53—41no—
904C2×Dic53C2511yescharacteristic
905C2×Dic53C2511yescharacteristic
906C2×Dic53C2511yescharacteristic
907C2×Dic53C2511yescharacteristic
908C2×Dic53C2513yes—
909C2×Dic53C2513yes—
910C2×Dic53C2513yes—
911C2×Dic53C2511yescharacteristic
912C2×Dic53C2513yes—
913C2×Dic53C2511yescharacteristic
914C2×Dic53C2511yescharacteristic
915C2×Dic53C2513yes—
916D212—26no—
917D212—26no—
918D212—26no—
919D212—26no—
920D212—26no—
921D212—46no—
922D212—43no—
923D212—43no—
924D212—46no—
925D212—46no—
926D212—43no—
927C4×D53—22no—
928C4×D53—26no—
929C4×D53—26no—
930C4×D53—26no—
931C4×D53—26no—
932C4×D53—212no—
933C4×D53—212no—
934C4×D53—43no—
935C4×D53—43no—
936C4×D53—46no—
937C4×D53—46no—
938C4×D53—41no—
939C4×D53—43no—
940C4×D53—43no—
941C4×D53—41no—
942C4×D53—43no—
943C4×D53—46no—
944C4×D53—46no—
945C4×D53—43no—
946C4×D53C2×#41112yes—
947Dic106—26no—
948Dic106—26no—
949Dic106—43no—
950Dic106—41no—
951Dic106—43no—
952Dic106—46no—
953Dic106C2×#41112yes—
954#62851—531nomaximal, Sylow
955C22×C53—23no—
956C22×C53—21no—
957C22×C53—21no—
958C22×C53—21no—
959C22×C53—23no—
960C22×C53—21no—
961C22×C53—21no—
962C22×C53—23no—
963C22×C53—21no—
964C22×C53C2611yescharacteristic
965C2×D53—21no—
966C2×D53—21no—
967C2×D53—23no—
968C2×D53—23no—
969C2×D53—23no—
970C2×D53—23no—
971C2×D53—23no—
972C2×D53—23no—
973C2×D53—23no—
974C2×D53—23no—
975C2×D53—23no—
976C2×D53—412no—
977C2×D53C22×#4112yes—
978C4×C53—23no—
979C4×C53—23no—
980C4×C53—21no—
981C4×C53—23no—
982C4×C53—23no—
983C4×C53—23no—
984C4×C53—21no—
985C4×C53—23no—
986C4×C53—21no—
987C4×C53—21no—
988C4×C53—21no—
989C4×C53C22×#4116yes—
990Dic53—21no—
991Dic53—21no—
992Dic53—21no—
993Dic53—21no—
994Dic53—23no—
995Dic53—23no—
996Dic53—23no—
997Dic53—21no—
998Dic53—23no—
999Dic53—21no—
1000Dic53—21no—
1001Dic53C22×#4116yes—
1002#3524—533no—
1003#3524—531no—
1004#3524—533no—
1005#3524—531no—
1006#3522—533no—
1007#3522—531no—
1008#3522—533no—
1009#3522—531no—
1010#3517—531no—
1011#3517—533no—
1012#3517—533no—
1013#3517—531no—
1014#3516—533no—
1015#3516—531no—
1016#3516—533no—
1017#3516D5311yescharacteristic, complemented
1018#3506—533no—
1019#3506—533no—
1020#3502—531no—
1021#3497—531no—
1022#3492—533no—
1023#3492—533no—
1024#3487—531no—
1025#3487—531no—
1026#3460—533no—
1027#3460—533no—
1028#3455—533no—
1029#3455—533no—
1030C4×2−1+4—531no—
1031C4×2−1+4—531no—
1032C2×#520—531no—
1033C2×C53—43no—
1034C2×C53—41no—
1035C2×C53—41no—
1036C2×C53C23×#4111yescharacteristic
1037C2×C53H(7,𝔽2)11yescharacteristic
1038C2×C532−1+611yescharacteristic
1039D53—22no—
1040D53—43no—
1041D53—43no—
1042D53—43no—
1043C2×2−1+4—531no—
1044C2×2−1+4—531no—
1045C22×#41—531no—
1046#559—533no—
1047#559—533no—
1048#559—536no—
1049#559—533no—
1050#559—533no—
1051#559—536no—
1052Q82—533no—
1053Q82—531no—
1054#557—533no—
1055#557—533no—
1056#557—531no—
1057#557—531no—
1058#557—533no—
1059#557C2×D5311yescharacteristic, complemented
1060#556—533no—
1061#556—536no—
1062#556C2×D5313yescomplemented
1063#555—533no—
1064#555—533no—
1065#555—536no—
1066#554—536no—
1067#554—536no—
1068#554—533no—
1069#554—533no—
1070#554—533no—
1071#554C2×D5313yescomplemented
1072#553—536no—
1073#553—536no—
1074#553—536no—
1075#553—533no—
1076#553—533no—
1077#553—533no—
1078#553—533no—
1079#553—536no—
1080#553—533no—
1081#553—533no—
1082#553—533no—
1083#553C2×D5313yescomplemented
1084#552—536no—
1085#552—533no—
1086#552—533no—
1087#552—533no—
1088#552—536no—
1089#552C2×D5313yescomplemented
1090#550—531no—
1091#550—531no—
1092#550—533no—
1093#550—533no—
1094#550—536no—
1095#550—531no—
1096#550—531no—
1097#550—531no—
1098#550—533no—
1099#550—533no—
1100#550—533no—
1101#550—533no—
1102#550—533no—
1103D4×Q8—533no—
1104D4×Q8C2×D5311yescharacteristic, complemented
1105#548—531no—
1106#548—531no—
1107#548—531no—
1108#548—531no—
1109#548—533no—
1110#548—533no—
1111#548—533no—
1112#548—533no—
1113#548—533no—
1114#548—533no—
1115#548C2×D5311yescharacteristic
1116#548C2×D5311yescharacteristic
1117#547—533no—
1118#547—536no—
1119#547—536no—
1120#547—536no—
1121#547—533no—
1122#547—533no—
1123#547—533no—
1124#547—533no—
1125#547—533no—
1126#544—533no—
1127#544—533no—
1128#542—533no—
1129#542—536no—
1130#542—533no—
1131#542—533no—
1132#542—533no—
1133#542—533no—
1134#542—533no—
1135#542—533no—
1136#542—536no—
1137#542—533no—
1138#542—533no—
1139#542—533no—
1140#542—533no—
1141#542C2×D5313yescomplemented
1142#541—533no—
1143#541—533no—
1144#541—533no—
1145#541C2×D5313yescomplemented
1146#540—533no—
1147#540—533no—
1148#540—533no—
1149#540—536no—
1150#540—536no—
1151#540—533no—
1152#540—533no—
1153#540—533no—
1154#540—533no—
1155#540—533no—
1156#539—533no—
1157#539—533no—
1158#539—536no—
1159#539—531no—
1160#539—533no—
1161#538—536no—
1162#538—536no—
1163#538—533no—
1164#538—533no—
1165#538—533no—
1166#538—533no—
1167#537—533no—
1168#537—533no—
1169#535—533no—
1170#535—533no—
1171#535—533no—
1172#535—533no—
1173#533—533no—
1174#533—533no—
1175#532—533no—
1176#532—533no—
1177#532—536no—
1178#532—533no—
1179#532—533no—
1180#532—536no—
1181#532—533no—
1182#532—533no—
1183#529—536no—
1184#529—536no—
1185#529—536no—
1186#529—536no—
1187#529—536no—
1188#529—533no—
1189#529—533no—
1190#529—533no—
1191#529—533no—
1192#529—533no—
1193#529—533no—
1194#529—533no—
1195#529—533no—
1196#529—533no—
1197#529—536no—
1198#529—533no—
1199#529C2×D5313yescomplemented
1200#529C2×D5313yescomplemented
1201#525—536no—
1202#525—533no—
1203#525—533no—
1204#525—536no—
1205#525—533no—
1206#525—533no—
1207#525—536no—
1208#525—536no—
1209#520—531no—
1210#520—531no—
1211#520—531no—
1212#520—533no—
1213#520—533no—
1214#520—531no—
1215#520—531no—
1216#520—533no—
1217#520—533no—
1218#520—533no—
1219#520—533no—
1220#520—533no—
1221#520—533no—
1222#520—533no—
1223#520—533no—
1224#520C2×D5311yescharacteristic
1225#519—531no—
1226#519—531no—
1227#519—531no—
1228#519—533no—
1229#519—533no—
1230#519C2×D5311yescharacteristic, complemented
1231C4×#41—533no—
1232C4×#41—533no—
1233C4×#41—531no—
1234C4×#41—531no—
1235C4×#41—533no—
1236C4×#41—533no—
1237C4×#41—533no—
1238C4×#41—533no—
1239C2×C4×Q8—531no—
1240C2×C4×Q8—531no—
1241C2×C4×Q8—531no—
1242C2×C4×Q8—533no—
1243C2×C4×Q8—533no—
1244C2×C4×Q8C2×D5311yescharacteristic, complemented
1245C2×C4×D4—533no—
1246C2×C4×D4—533no—
1247C2×#117—533no—
1248C22×C4⋊C4—533no—
1249C53#6285111yescharacteristic, complemented, Sylow
12502−1+4—1068no—
12512−1+4—1068no—
1252C2×#41—533no—
1253C2×#41—533no—
1254C2×#41—531no—
1255C2×#41—531no—
1256C2×#41—531no—
1257C2×#41—536no—
1258C2×#41—533no—
1259C2×#41—536no—
1260C2×#41—533no—
1261C2×#41—533no—
1262C2×#41—533no—
1263C2×#41—533no—
1264C2×#41—533no—
1265C2×#41—536no—
1266C2×#41—536no—
1267C2×#41—1068no—
1268C2×#41C22×D5311yescharacteristic
1269C22×Q8—531no—
1270C22×Q8—533no—
1271C22×Q8—533no—
1272C22×Q8C22×D5311yescharacteristic
1273C22×Q8C22×D5311yescharacteristic
1274C22×D4—533no—
1275C23×C4—533no—
1276C23×C4—536no—
1277C4⋊Q8—536no—
1278C4⋊Q8—533no—
1279C4⋊Q8—533no—
1280C4⋊Q8—536no—
1281C4⋊Q8—533no—
1282C4⋊Q8—533no—
1283C4⋊Q8—533no—
1284C4⋊Q8—533no—
1285C4⋊Q8—533no—
1286C4⋊Q8—533no—
1287C4⋊Q8C22×D5313yes—
1288C4⋊Q8C22×D5313yes—
1289#127—536no—
1290#127—536no—
1291#127—533no—
1292#127—533no—
1293#127—533no—
1294#127—533no—
1295#127—533no—
1296#127—533no—
1297#126—536no—
1298#126—533no—
1299#126—533no—
1300#126—533no—
1301#126—536no—
1302#126—533no—
1303#126—533no—
1304#126—536no—
1305#126—533no—
1306#126—533no—
1307#126—533no—
1308#126—531no—
1309#126—531no—
1310#126—533no—
1311#126—533no—
1312#126—533no—
1313#126—533no—
1314#126—536no—
1315#126C22×D5316yes—
1316#126C22×D5316yes—
1317#126C22×D5313yes—
1318#126C22×D5313yes—
1319#125—533no—
1320#125—531no—
1321#125—531no—
1322#125—536no—
1323#125—533no—
1324#125—533no—
1325#125—533no—
1326#125—536no—
1327#125—536no—
1328#125—533no—
1329#125—533no—
1330#125—533no—
1331#125—533no—
1332#125—533no—
1333#125—533no—
1334#125—533no—
1335#125C22×D5313yes—
1336#125C22×D5316yes—
1337#125C22×D5313yes—
1338#125C22×D5313yes—
1339#124—533no—
1340#124—533no—
1341#124—533no—
1342#124—533no—
1343#124—533no—
1344#124—533no—
1345#124—536no—
1346#124—533no—
1347#124—533no—
1348#124—536no—
1349#124—536no—
1350#124—536no—
1351#124—533no—
1352#124—533no—
1353#124—533no—
1354#124—533no—
1355#124—536no—
1356#124—536no—
1357#124—533no—
1358#124C22×D5313yes—
1359#124C22×D5313yes—
1360#124C22×D5313yes—
1361#123—531no—
1362#123—533no—
1363#123—536no—
1364#123—533no—
1365#123—533no—
1366#123—533no—
1367#123—533no—
1368#123—536no—
1369#123—536no—
1370#123—536no—
1371#123—533no—
1372#123—536no—
1373#123—533no—
1374#123—533no—
1375#123—533no—
1376#123—536no—
1377#123—536no—
1378#123—536no—
1379#123—531no—
1380#123—531no—
1381#123—536no—
1382#123—536no—
1383#123—536no—
1384#123—536no—
1385#123—533no—
1386#123—533no—
1387#123—533no—
1388#123—536no—
1389#123—533no—
1390#123—533no—
1391#123—533no—
1392#123C22×D5316yes—
1393#123C22×D5313yes—
1394#123C22×D5311yescharacteristic
1395C22⋊Q8—533no—
1396C22⋊Q8—533no—
1397C22⋊Q8—533no—
1398C22⋊Q8—533no—
1399C22⋊Q8—533no—
1400C22⋊Q8—533no—
1401C22⋊Q8—531no—
1402C22⋊Q8—536no—
1403C22⋊Q8—533no—
1404C22⋊Q8—533no—
1405C22⋊Q8—533no—
1406C22⋊Q8—536no—
1407C22⋊Q8—536no—
1408C22⋊Q8—533no—
1409C22⋊Q8—533no—
1410C22⋊Q8—536no—
1411C22⋊Q8—536no—
1412C22⋊Q8—536no—
1413C22⋊Q8—533no—
1414C22⋊Q8—536no—
1415C22⋊Q8—533no—
1416C22⋊Q8—531no—
1417C22⋊Q8—533no—
1418C22⋊Q8—533no—
1419C22⋊Q8—536no—
1420C22⋊Q8—531no—
1421C22⋊Q8—533no—
1422C22⋊Q8C22×D5313yes—
1423C22⋊Q8C22×D5313yes—
1424C22⋊Q8C22×D5316yes—
1425C22⋊Q8C22×D5313yes—
1426C22⋊Q8C22×D5313yes—
1427C22⋊Q8C22×D5313yes—
1428#121—536no—
1429#121—533no—
1430#121—533no—
1431#121—533no—
1432#121—533no—
1433#121—533no—
1434#121—533no—
1435#121—531no—
1436#121—533no—
1437#121—536no—
1438#121—533no—
1439#121—533no—
1440#121—533no—
1441#121—533no—
1442#121—533no—
1443#121—533no—
1444#121—533no—
1445#121—536no—
1446#121—536no—
1447#121—533no—
1448#121—533no—
1449#121—536no—
1450#121—533no—
1451#121—536no—
1452#121—533no—
1453#121—533no—
1454#121—533no—
1455#121—533no—
1456#121—533no—
1457#121—533no—
1458#121—533no—
1459#121—536no—
1460#121—533no—
1461#121—533no—
1462#121—533no—
1463#121—536no—
1464#121—536no—
1465#121—536no—
1466#121—536no—
1467#121—533no—
1468#121—536no—
1469#121—536no—
1470#121—536no—
1471#121—536no—
1472#121C22×D5313yes—
1473#121C22×D5313yes—
1474#121C22×D5313yes—
1475#120—533no—
1476#120—533no—
1477#120—533no—
1478#120—536no—
1479#120—536no—
1480#120—533no—
1481C4×Q8—531no—
1482C4×Q8—533no—
1483C4×Q8—531no—
1484C4×Q8—533no—
1485C4×Q8—533no—
1486C4×Q8—531no—
1487C4×Q8—533no—
1488C4×Q8—531no—
1489C4×Q8—533no—
1490C4×Q8—533no—
1491C4×Q8—533no—
1492C4×Q8—536no—
1493C4×Q8—533no—
1494C4×Q8—533no—
1495C4×Q8—533no—
1496C4×Q8—536no—
1497C4×Q8—536no—
1498C4×Q8—533no—
1499C4×Q8—533no—
1500C4×Q8—533no—
1501C4×Q8—536no—
1502C4×Q8—533no—
1503C4×Q8—533no—
1504C4×Q8—533no—
1505C4×Q8—533no—
1506C4×Q8—533no—
1507C4×Q8—533no—
1508C4×Q8C22×D5311yescharacteristic
1509C4×Q8C22×D5313yes—
1510C4×Q8C22×D5313yes—
1511C4×Q8C22×D5311yescharacteristic
1512C4×Q8C22×D5311yescharacteristic
1513C4×Q8C22×D5313yes—
1514C4×Q8C22×D5313yes—
1515C4×Q8C22×D5311yescharacteristic
1516C4×Q8C22×D5313yes—
1517C4×D4—533no—
1518C4×D4—533no—
1519C4×D4—536no—
1520C4×D4—536no—
1521C4×D4—531no—
1522C4×D4—533no—
1523C4×D4—533no—
1524C4×D4—533no—
1525C4×D4—536no—
1526C4×D4—533no—
1527C4×D4—533no—
1528C4×D4—533no—
1529C4×D4—533no—
1530C4×D4—536no—
1531C4×D4—533no—
1532C4×D4—533no—
1533C4×D4—533no—
1534C4×D4—533no—
1535C4×D4—533no—
1536C4×D4—533no—
1537C4×D4—533no—
1538C4×D4—536no—
1539C4×D4—533no—
1540C4×D4—533no—
1541C4×D4—533no—
1542C4×D4—536no—
1543C4×D4—536no—
1544C4×D4—536no—
1545C4×D4—536no—
1546C4×D4—536no—
1547C4×D4—536no—
1548C4×D4—536no—
1549C4×D4—531no—
1550C4×D4—533no—
1551C4×D4—533no—
1552C4×D4—533no—
1553C4×D4—536no—
1554C4×D4—536no—
1555C4×D4—536no—
1556C4×D4—536no—
1557C4×D4—536no—
1558C4×D4—536no—
1559C4×D4—533no—
1560C4×D4—533no—
1561C4×D4—533no—
1562C4×D4—533no—
1563C4×D4—536no—
1564C4×D4—533no—
1565C4×D4—533no—
1566C4×D4—533no—
1567C4×D4—533no—
1568C4×D4—533no—
1569C4×D4—533no—
1570C4×D4—536no—
1571C4×D4—536no—
1572C4×D4—533no—
1573C4×D4C22×D5313yes—
1574C4×D4C22×D5313yes—
1575C4×D4C22×D5313yes—
1576C4×D4C22×D5313yes—
1577C4×D4C22×D5316yes—
1578C4×D4C22×D5313yes—
1579#117—533no—
1580#117—533no—
1581#117—533no—
1582#117—533no—
1583#117—533no—
1584#117—533no—
1585#117—533no—
1586#117—536no—
1587#117—536no—
1588#117—533no—
1589#117—533no—
1590#117—536no—
1591#117—533no—
1592#117—533no—
1593#117—536no—
1594#117—533no—
1595#117—533no—
1596#117—533no—
1597#117—533no—
1598#117—533no—
1599#117—533no—
1600#117—536no—
1601#117—536no—
1602#117—536no—
1603#117C22×D5313yes—
1604#117C22×D5313yes—
1605#117C22×D5313yes—
1606#117C22×D5316yes—
1607C2×C4⋊C4—536no—
1608C2×C4⋊C4—533no—
1609C2×C4⋊C4—533no—
1610C2×C4⋊C4—533no—
1611C2×C4⋊C4—533no—
1612C2×C4⋊C4—533no—
1613C2×C4⋊C4—536no—
1614C2×C4⋊C4—533no—
1615C2×C4⋊C4—533no—
1616C2×C4⋊C4—531no—
1617C2×C4⋊C4—536no—
1618C2×C4⋊C4—536no—
1619C2×C4⋊C4—533no—
1620C2×C4⋊C4—533no—
1621C2×C4⋊C4C22×D5313yes—
1622C2×C4⋊C4C22×D5313yes—
1623C2×C22⋊C4—533no—
1624C2×C22⋊C4—533no—
1625C2×C42—533no—
1626C2×C42—533no—
1627C2×C42—533no—
1628C2×C42—533no—
1629C2×C42—536no—
1630C2×C42—536no—
1631C2×C42—533no—
1632C2×C42C22×D5313yes—
1633C24—533no—
1634#41—24no—
1635#41—10612no—
1636#41—10612no—
1637#41—10612no—
1638#41—10612no—
1639#41—10612no—
1640#41—10612no—
1641#41—10612no—
1642#41—10612no—
1643#41—1064no—
1644#41—1064no—
1645#41—1064no—
1646#41—4246no—
1647#41—4246no—
1648#41—4246no—
1649#41—4246no—
1650C2×Q8—24no—
1651C2×Q8—24no—
1652C2×Q8—538no—
1653C2×Q8—533no—
1654C2×Q8—533no—
1655C2×Q8—533no—
1656C2×Q8—533no—
1657C2×Q8—531no—
1658C2×Q8—533no—
1659C2×Q8—536no—
1660C2×Q8—10612no—
1661C2×Q8—10612no—
1662C2×Q8C23×D5313yes—
1663C2×Q8C23×D5313yes—
1664C2×Q8C23×D5313yes—
1665C2×Q8C23×D5311yescharacteristic
1666C2×D4—531no—
1667C2×D4—531no—
1668C2×D4—536no—
1669C2×D4—533no—
1670C2×D4—533no—
1671C2×D4—533no—
1672C2×D4—536no—
1673C2×D4—533no—
1674C2×D4—533no—
1675C2×D4—536no—
1676C2×D4—533no—
1677C2×D4—533no—
1678C2×D4—533no—
1679C2×D4—533no—
1680C2×D4—533no—
1681C2×D4—533no—
1682C2×D4—533no—
1683C2×D4—533no—
1684C2×D4—536no—
1685C2×D4—533no—
1686C2×D4—533no—
1687C2×D4—536no—
1688C2×D4—533no—
1689C2×D4—536no—
1690C2×D4—10612no—
1691C2×D4C23×D5313yes—
1692C2×D4C23×D5313yes—
1693C2×D4C23×D5311yescharacteristic
1694C2×D4C23×D5313yes—
1695C22×C4—533no—
1696C22×C4—533no—
1697C22×C4—531no—
1698C22×C4—533no—
1699C22×C4—536no—
1700C22×C4—536no—
1701C22×C4—536no—
1702C22×C4—533no—
1703C22×C4—533no—
1704C22×C4—531no—
1705C22×C4—533no—
1706C22×C4—533no—
1707C22×C4—531no—
1708C22×C4—531no—
1709C22×C4—533no—
1710C22×C4—533no—
1711C22×C4—533no—
1712C22×C4—533no—
1713C22×C4—536no—
1714C22×C4—533no—
1715C22×C4—536no—
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×D5311yescharacteristic
1725C22×C4C23×D5313yes—
1726C22×C4C23×D5316yes—
1727C4⋊C4—536no—
1728C4⋊C4—533no—
1729C4⋊C4—533no—
1730C4⋊C4—533no—
1731C4⋊C4—533no—
1732C4⋊C4—536no—
1733C4⋊C4—533no—
1734C4⋊C4—533no—
1735C4⋊C4—533no—
1736C4⋊C4—533no—
1737C4⋊C4—533no—
1738C4⋊C4—533no—
1739C4⋊C4—536no—
1740C4⋊C4—533no—
1741C4⋊C4—531no—
1742C4⋊C4—531no—
1743C4⋊C4—531no—
1744C4⋊C4—533no—
1745C4⋊C4—533no—
1746C4⋊C4—533no—
1747C4⋊C4—531no—
1748C4⋊C4—531no—
1749C4⋊C4—533no—
1750C4⋊C4—533no—
1751C4⋊C4—533no—
1752C4⋊C4—536no—
1753C4⋊C4—533no—
1754C4⋊C4—531no—
1755C4⋊C4—531no—
1756C4⋊C4—533no—
1757C4⋊C4—531no—
1758C4⋊C4—531no—
1759C4⋊C4—533no—
1760C4⋊C4—531no—
1761C4⋊C4—536no—
1762C4⋊C4—533no—
1763C4⋊C4—533no—
1764C4⋊C4—533no—
1765C4⋊C4—533no—
1766C4⋊C4—533no—
1767C4⋊C4—531no—
1768C4⋊C4—533no—
1769C4⋊C4—531no—
1770C4⋊C4C23×D5313yes—
1771C4⋊C4C23×D5313yes—
1772C4⋊C4C23×D5313yes—
1773C4⋊C4C23×D5313yes—
1774C4⋊C4C23×D5313yes—
1775C4⋊C4C23×D5316yes—
1776C4⋊C4C23×D5311yescharacteristic
1777C4⋊C4C23×D5313yes—
1778C4⋊C4C23×D5313yes—
1779C4⋊C4C23×D5316yes—
1780C4⋊C4C23×D5313yes—
1781C4⋊C4C23×D5313yes—
1782C4⋊C4C23×D5313yes—
1783C4⋊C4C23×D5313yes—
1784C4⋊C4C23×D5316yes—
1785C4⋊C4C23×D5313yes—
1786C4⋊C4C23×D5311yescharacteristic
1787C22⋊C4—533no—
1788C22⋊C4—533no—
1789C22⋊C4—533no—
1790C22⋊C4—531no—
1791C22⋊C4—533no—
1792C22⋊C4—533no—
1793C22⋊C4—531no—
1794C22⋊C4—531no—
1795C22⋊C4—531no—
1796C22⋊C4—531no—
1797C22⋊C4—533no—
1798C22⋊C4—533no—
1799C22⋊C4—533no—
1800C22⋊C4—533no—
1801C22⋊C4—533no—
1802C22⋊C4—531no—
1803C22⋊C4—533no—
1804C22⋊C4—531no—
1805C22⋊C4—536no—
1806C22⋊C4—533no—
1807C22⋊C4—536no—
1808C22⋊C4—533no—
1809C22⋊C4—533no—
1810C22⋊C4—533no—
1811C22⋊C4—533no—
1812C22⋊C4—536no—
1813C22⋊C4—533no—
1814C22⋊C4—533no—
1815C22⋊C4—533no—
1816C22⋊C4—536no—
1817C22⋊C4—533no—
1818C22⋊C4—533no—
1819C22⋊C4—533no—
1820C22⋊C4—533no—
1821C22⋊C4—536no—
1822C22⋊C4—536no—
1823C22⋊C4—533no—
1824C22⋊C4—533no—
1825C22⋊C4—533no—
1826C22⋊C4—533no—
1827C22⋊C4C23×D5313yes—
1828C22⋊C4C23×D5313yes—
1829C22⋊C4C23×D5316yes—
1830C22⋊C4C23×D5311yescharacteristic
1831C22⋊C4C23×D5313yes—
1832C22⋊C4C23×D5313yes—
1833C22⋊C4C23×D5313yes—
1834C22⋊C4C23×D5316yes—
1835C22⋊C4C23×D5313yes—
1836C22⋊C4C23×D5311yescharacteristic
1837C22⋊C4C23×D5311yescharacteristic
1838C22⋊C4C23×D5313yes—
1839C42—533no—
1840C42—533no—
1841C42—533no—
1842C42—531no—
1843C42—533no—
1844C42—531no—
1845C42—533no—
1846C42—536no—
1847C42—533no—
1848C42—533no—
1849C42—533no—
1850C42—533no—
1851C42—533no—
1852C42—536no—
1853C42—536no—
1854C42—533no—
1855C42—533no—
1856C42C23×D5313yes—
1857C42C23×D5313yes—
1858C42C23×D5316yes—
1859C42C23×D5313yes—
1860C42C23×D5313yes—
1861C42C23×D5313yes—
1862C42C23×D5313yes—
1863C23—531no—
1864C23—533no—
1865C23—533no—
1866C23—533no—
1867C23—1066no—
1868C23—2123no—
1869C23—2123no—
1870C23C24×D5311yescharacteristic
1871C23C24×D5313yes—
1872C23C24×D5311yescharacteristic
1873Q8—26no—
1874Q8—26no—
1875Q8—43no—
1876Q8—5312no—
1877Q8—1066no—
1878Q8—1066no—
1879Q8—2121no—
1880Q8—2123no—
1881Q8—2123no—
1882Q8—2126no—
1883Q8#41×D5314yes—
1884D4—26no—
1885D4—41no—
1886D4—43no—
1887D4—43no—
1888D4—1066no—
1889D4—1066no—
1890D4—10612no—
1891D4—1066no—
1892D4—1066no—
1893D4—1062no—
1894D4—1062no—
1895D4—1066no—
1896D4—1066no—
1897D4—1066no—
1898D4—2123no—
1899D4—2123no—
1900D4—2126no—
1901D4—2126no—
1902D4—2126no—
1903D4—2123no—
1904D4—2123no—
1905D4—2126no—
1906D4—2123no—
1907D4—2123no—
1908D4—2123no—
1909D4—2123no—
1910D4—2123no—
1911D4—2126no—
1912C2×C4—26no—
1913C2×C4—26no—
1914C2×C4—26no—
1915C2×C4—46no—
1916C2×C4—41no—
1917C2×C4—43no—
1918C2×C4—533no—
1919C2×C4—5312no—
1920C2×C4—531no—
1921C2×C4—531no—
1922C2×C4—533no—
1923C2×C4—531no—
1924C2×C4—533no—
1925C2×C4—531no—
1926C2×C4—531no—
1927C2×C4—531no—
1928C2×C4—533no—
1929C2×C4—533no—
1930C2×C4—531no—
1931C2×C4—1066no—
1932C2×C4—10612no—
1933C2×C4—10612no—
1934C2×C4—1062no—
1935C2×C4—1066no—
1936C2×C4—1066no—
1937C2×C4—1066no—
1938C2×C4—1066no—
1939C2×C4—2121no—
1940C2×C4—2123no—
1941C2×C4—2121no—
1942C2×C4—2123no—
1943C2×C4—2123no—
1944C2×C4—2123no—
1945C2×C4—2126no—
1946C2×C4—2126no—
1947C2×C4—2123no—
1948C2×C4—2126no—
1949C2×C4—2126no—
1950C2×C4—2123no—
1951C2×C4—2121no—
1952C2×C4—2126no—
1953C2×C4—2123no—
1954C2×C4C24×D5311yescharacteristic
1955C2×C4C24×D5313yes—
1956C2×C4C24×D5311yescharacteristic
1957C2×C4C24×D5313yes—
1958C2×C4C24×D5313yes—
1959C2×C4C24×D5313yes—
1960C2×C4C24×D5313yes—
1961C2×C4C24×D5311yescharacteristic
1962C2×C4C24×D5313yes—
1963C2×C4C24×D5311yescharacteristic
1964C2×C4C24×D5311yescharacteristic
1965C2×C4C24×D5313yes—
1966C22—21no—
1967C22—21no—
1968C22—23no—
1969C22—21no—
1970C22—23no—
1971C22—21no—
1972C22—21no—
1973C22—21no—
1974C22—23no—
1975C22—532no—
1976C22—1061no—
1977C22—1061no—
1978C22—1063no—
1979C22—1063no—
1980C22—1063no—
1981C22—1063no—
1982C22—1063no—
1983C22—1063no—
1984C22—1063no—
1985C22—1063no—
1986C22—1063no—
1987C22—21212no—
1988C22C25×D5311yescharacteristic
1989C4—21no—
1990C4—23no—
1991C4—23no—
1992C4—23no—
1993C4—23no—
1994C4—23no—
1995C4—21no—
1996C4—21no—
1997C4—21no—
1998C4—21no—
1999C4—23no—
2000C4—536no—
2001C4—1061no—
2002C4—1061no—
2003C4—1061no—
2004C4—1063no—
2005C4—1063no—
2006C4—1061no—
2007C4—1063no—
2008C4—1061no—
2009C4—1063no—
2010C4—1061no—
2011C4—1061no—
2012C4C2×#41×D5316yes—
2013C2—43no—
2014C2—41no—
2015C2—41no—
2016C2—1062no—
2017C2—2123no—
2018C2—2123no—
2019C2—2123no—
2020C2C22×#41×D5311yescharacteristic
2021C2#2028952611yescharacteristic
2022C2#2028952711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3516C2
hypercenter#3516D53
hypocenterC53#62851
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3516

Complements

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

NH ≅ G/Ntype
1. #20288826C2semidirect
2. #20288821C2semidirect
3. #20288817C2semidirect
4. #20288814C2semidirect
5. #20288800C2semidirect
6. #20288799C2semidirect
7. #20288796C2semidirect
8. #20288791C2semidirect
9. #20288722C2semidirect
10. #20288719C2semidirect
11. #20288715C2semidirect
12. #20288714C2semidirect
13. #20288709C2semidirect
14. #20288706C2semidirect
15. #20288703C2semidirect
16. #20288568C2semidirect
17. #20288561C2semidirect
18. #20288522C2semidirect
19. #20288485C2semidirect
20. #20288423C2semidirect
21. #20288415C2semidirect
22. #20288372C2semidirect
23. #20288372C2semidirect
24. #20288136C2semidirect
25. #20288135C2semidirect
26. #20288106C2semidirect
27. #20288098C2semidirect
28. C4×#13133265C2semidirect
29. #20287924C2semidirect
30. #520×D53C2semidirect
31. C53×#3516C2semidirect
35. #16811358C22semidirect
36. #16811358C22semidirect
37. #16811357C22semidirect
38. #16811356C22semidirect
39. #16811355C22semidirect
40. #16811355C22semidirect
41. Q8×Dic106C22semidirect
42. #16811353C22semidirect
43. #16811351C22semidirect
44. #16811350C22semidirect
45. #16811350C22semidirect
46. #16811349C22semidirect
47. #16811349C22semidirect
48. #16811347C22semidirect
49. #16811340C22semidirect
50. #16811337C22semidirect
51. #16811336C22semidirect
52. #16811336C22semidirect
53. #16811333C22semidirect
54. #16811331C22semidirect
55. #16811331C22semidirect
56. #16811329C22semidirect
57. #16811327C22semidirect
58. #16811326C22semidirect
59. #16811326C22semidirect
60. #16811324C22semidirect
61. #16811324C22semidirect
62. #16811324C22semidirect
63. #16811323C22semidirect
64. #16811322C22semidirect
65. #16811321C22semidirect
66. #16811319C22semidirect
67. #16811319C22semidirect
68. #16811317C22semidirect
69. #16811315C22semidirect
70. #16811314C22semidirect
71. #16811307C22semidirect
72. #16811306C22semidirect
73. #16811305C22semidirect
76. #16811295C22semidirect
77. #16811295C22semidirect
80. #16811294C22semidirect
81. #16811294C22semidirect
86. #16811291C22semidirect
87. #16811288C22semidirect
90. #16811284C22semidirect
91. #16811284C22semidirect
94. #16811283C22semidirect
95. #16811283C22semidirect
98. #16811277C22semidirect
99. #16811276C22semidirect
100. #16811275C22semidirect
101. #16811275C22semidirect
102. #16811274C22semidirect
103. #16811274C22semidirect
104. #16811274C22semidirect
105. #16811273C22semidirect
106. #16811271C22semidirect
109. #16811246C22semidirect
110. #16811246C22semidirect
111. #16811246C22semidirect
112. #16811245C22semidirect
113. #16811245C22semidirect
114. #16811245C22semidirect
115. #16811243C22semidirect
116. #16811243C22semidirect
117. #16811242C22semidirect
118. #16811241C22semidirect
119. #16811239C22semidirect
120. #16811239C22semidirect
121. #16811237C22semidirect
122. #16811234C22semidirect
123. #16811232C22semidirect
124. #16811230C22semidirect
125. #16811229C22semidirect
126. #16811229C22semidirect
127. #16811228C22semidirect
128. #16811228C22semidirect
129. #16811226C22semidirect
130. #16811225C22semidirect
131. #16811225C22semidirect
132. #16811225C22semidirect
133. #16811224C22semidirect
134. #16811223C22semidirect
155. #16811174C22semidirect
156. #16811173C22semidirect
157. #16811172C22semidirect
159. #16811170C22semidirect
160. #16811170C22semidirect
161. #16811168C22semidirect
162. #16811160C22semidirect
163. #16811160C22semidirect
164. #16811159C22semidirect
165. #16811158C22semidirect
166. #16811158C22semidirect
167. #16811157C22semidirect
168. #16811156C22semidirect
169. #16811156C22semidirect
170. #16811156C22semidirect
171. #16811155C22semidirect
172. #16811153C22semidirect
173. #16811153C22semidirect
174. #16811152C22semidirect
175. #16811151C22semidirect
176. #16811151C22semidirect
177. #16811151C22semidirect
191. #16811105C22semidirect
192. #16811105C22semidirect
195. #16811104C22semidirect
198. #16811103C22semidirect
201. #16811101C22semidirect
204. #16811099C22semidirect
205. #16811099C22semidirect
208. C4×#11719949C22semidirect
209. C4×#11719949C22semidirect
211. C4×#11719945C22semidirect
213. #16811091C22semidirect
214. C2×Q8×Dic53C22semidirect
217. C4×Q8×D53C22semidirect
218. C4×Q8×D53C22semidirect
223. C53×#557C22semidirect
224. C53×#556C22semidirect
225. C53×#554C22semidirect
226. C53×#553C22semidirect
227. C53×#552C22semidirect
228. D4×Q8×C53C22semidirect
231. C53×#542C22semidirect
232. C53×#541C22semidirect
233. C53×#529C22semidirect
234. C53×#529C22semidirect
236. C53×#519C22semidirect
237. C2×C4×Q8×C53C22semidirect
664. Q8×D53#41semidirect
1017. #3516D53semidirect
1059. #557C2×D53semidirect
1062. #556C2×D53semidirect
1071. #554C2×D53semidirect
1083. #553C2×D53semidirect
1089. #552C2×D53semidirect
1104. D4×Q8C2×D53semidirect
1141. #542C2×D53semidirect
1145. #541C2×D53semidirect
1199. #529C2×D53semidirect
1200. #529C2×D53semidirect
1230. #519C2×D53semidirect
1244. C2×C4×Q8C2×D53semidirect
1249. C53#62851semidirect

Maximal subgroups

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

subgroupindex
#202888262
#202888212
#202888172
#202888142
#202888002
#202887992
#202887962
#202887912
#202887222
#202887192
#202887152
#202887142
#202887092
#202887062
#202887032
#202885682
#202885612
#202885222
#202884852
#202884232
#202884152
#202883722
#202881362
#202881352
#202881062
#202880982
C4×#131332652
#202879242
#520×D532
C53×#35162
#6285153