Finite Group Databasebeta

← #28293175

Subgroups — #28293175

Order 13568.

6846 conjugacy classes of subgroups.

The subgroup lattice has 1998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288827C211yesmaximal, characteristic, complemented
2#20288826C211yesmaximal, characteristic, complemented
3#20288821C213yesmaximal, complemented
4#20288820C213yesmaximal, complemented
5#20288808C213yesmaximal, complemented
6#20288807C213yesmaximal, complemented
7#20288802C211yesmaximal, characteristic, complemented
8#20288727C211yesmaximal, characteristic, complemented
9#20288726C211yesmaximal, characteristic, complemented
10#20288725C213yesmaximal, complemented
11#20288724C213yesmaximal, complemented
12#20288709C211yesmaximal, characteristic, complemented
13#20288708C211yesmaximal, characteristic, complemented
14#20288707C213yesmaximal, complemented
15#20288706C213yesmaximal, complemented
16#20288581C213yesmaximal, complemented
17#20288574C213yesmaximal, complemented
18#20288522C211yesmaximal, characteristic, complemented
19#20288485C211yesmaximal, characteristic, complemented
20#20288433C213yesmaximal, complemented
21#20288429C213yesmaximal, complemented
22#20288365C211yesmaximal, characteristic, complemented
23#20288365C211yesmaximal, characteristic, complemented
24#20288147C213yesmaximal, complemented
25#20288146C213yesmaximal, complemented
26#20288106C213yesmaximal, complemented
27#20288098C213yesmaximal, complemented
28C4×#13133265C211yesmaximal, characteristic, complemented
29#20287924C211yesmaximal, characteristic, complemented
30#519×D53C211yesmaximal, characteristic, complemented
31C53×#3523C211yesmaximal, characteristic, complemented
32C2×#13133265C2211yescharacteristic
33C2×#13133265C2211yescharacteristic
34C22×Q8×D53C2211yescharacteristic
35#16811358C2213yescomplemented
36#16811358C2213yescomplemented
37#16811357C2216yescomplemented
38Q8×Dic106C2211yescharacteristic, complemented
39#16811353C2213yescomplemented
40#16811351C2213yescomplemented
41#16811350C2213yescomplemented
42#16811350C2213yescomplemented
43#16811350C2216yescomplemented
44#16811349C2211yescharacteristic, complemented
45#16811349C2211yescharacteristic, complemented
46#16811348C2213yescomplemented
47#16811347C2213yescomplemented
48#16811347C2213yescomplemented
49#16811346C2213yes—
50#16811345C2216yes—
51#16811345C2213yescomplemented
52#16811345C2213yescomplemented
53#16811345C2216yescomplemented
54#16811344C2213yes—
55#16811344C2213yes—
56#16811344C2213yescomplemented
57#16811341C2216yescomplemented
58#16811341C2213yescomplemented
59#16811340C2216yes—
60#16811340C2216yescomplemented
61#16811339C2213yes—
62#16811338C2213yes—
63#16811336C2213yes—
64#16811336C2216yes—
65#16811336C2213yes—
66#16811335C2216yes—
67#16811331C2213yescomplemented
68#16811329C2216yescomplemented
69#16811328C2213yescomplemented
70#16811326C2213yes—
71#16811324C2216yes—
72#16811321C2213yes—
73#16811319C2213yes—
74#16811318C2216yes—
75#16811317C2213yes—
76#16811315C2213yes—
77#16811314C2213yes—
78#16811314C2213yescomplemented
79#16811313C2213yescomplemented
80#16811311C2213yescomplemented
81#16811309C2216yes—
82#16811307C2213yes—
83#16811305C2216yes—
84#16811305C2216yescomplemented
85#16811305C2216yescomplemented
86#16811295C2211yescharacteristic, complemented
87#16811294C2213yescomplemented
88#16811288C2213yes—
89#16811288C2213yes—
90#16811288C2213yescomplemented
91Q8×C22⋊D53C2211yescharacteristic
92Q8×C22⋊D53C2211yescharacteristic
93#16811286C2213yes—
94#16811286C2213yes—
95#16811285C2211yescharacteristic
96#16811285C2211yescharacteristic
97#16811284C2211yescharacteristic
98#16811284C2211yescharacteristic
99#16811284C2211yescharacteristic, complemented
100#16811284C2211yescharacteristic, complemented
101#16811283C2213yes—
102#16811283C2213yes—
103#16811283C2213yescomplemented
104#16811283C2213yescomplemented
105#16811282C2213yes—
106#16811282C2213yes—
107#16811253C2213yes—
108#16811250C2213yes—
109#16811247C2213yescomplemented
110#16811246C2213yes—
111#16811246C2213yes—
112#16811246C2213yescomplemented
113#16811245C2213yes—
114#16811245C2213yes—
115#16811245C2213yescomplemented
116#16811244C2213yescomplemented
117#16811243C2213yes—
118#16811243C2216yescomplemented
119#16811241C2213yes—
120#16811239C2213yes—
121#16811239C2216yescomplemented
122#16811237C2213yes—
123#16811234C2213yes—
124#16811234C2213yescomplemented
125#16811233C2213yescomplemented
126#16811232C2213yes—
127#16811232C2216yescomplemented
128#16811232C2216yescomplemented
129#16811231C2213yescomplemented
130#16811230C2213yes—
131#16811229C2213yes—
132#16811228C2213yes—
133#16811225C2213yes—
134#16811223C2213yes—
135#16811221C2216yes—
136#16811221C2213yes—
137#16811221C2216yes—
138#16811219C2213yes—
139#16811216C2213yes—
140#16811214C2213yes—
141#16811212C2213yes—
142#16811212C2216yes—
143#16811209C2213yes—
144#16811207C2213yes—
145#16811205C2211yescharacteristic
146#16811203C2213yes—
147#16811203C2213yes—
148#16811198C2213yes—
149#16811198C2213yes—
150#16811196C2213yes—
151#16811196C2213yes—
152#16811179C2213yes—
153#16811179C2216yescomplemented
154#16811178C2213yescomplemented
155#16811177C2213yes—
156#16811177C2213yescomplemented
157#16811177C2216yescomplemented
158#16811175C2213yescomplemented
159#16811174C2213yes—
160#16811170C2213yes—
161#16811160C2213yes—
162#16811160C2216yes—
163#16811160C2213yescomplemented
164#16811159C2213yescomplemented
165#16811158C2216yes—
166#16811158C2216yes—
167#16811158C2216yes—
168#16811158C2213yescomplemented
169#16811157C2213yes—
170#16811157C2213yescomplemented
171#16811156C2216yes—
172#16811156C2216yes—
173#16811156C2216yes—
174#16811156C2216yescomplemented
175#16811155C2213yes—
176#16811153C2213yes—
177#16811153C2213yes—
178#16811151C2213yes—
179#16811151C2216yes—
180#16811151C2213yes—
181#16811151C2216yescomplemented
182#16811136C2213yes—
183#16811136C2213yes—
184#16811132C2213yes—
185#16811132C2213yes—
186#16811105C2213yes—
187#16811105C2213yes—
188#16811105C2211yescharacteristic, complemented
189#16811105C2211yescharacteristic, complemented
190#16811104C2213yes—
191#16811104C2213yescomplemented
192#16811103C2213yes—
193#16811103C2213yescomplemented
194#16811101C2211yescharacteristic
195#16811101C2211yescharacteristic, complemented
196#16811100C2213yes—
197#16811100C2213yes—
198#16811099C2211yescharacteristic
199#16811099C2211yescharacteristic
200#16811099C2211yescharacteristic
201#16811099C2213yes—
202#16811099C2213yes—
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×D53C2213yes—
217C4×Q8×D53C2213yes—
218C4×Q8×D53C2211yescharacteristic
219C4×Q8×D53C2213yescomplemented
220C4×Q8×D53C2213yescomplemented
221#117×D53C2213yes—
222#117×D53C2213yes—
223C53×#557C2211yescharacteristic, complemented
224C53×#557C2213yescomplemented
225C53×#556C2213yes—
226C53×#552C2213yes—
227C53×#552C2213yescomplemented
228D4×Q8×C53C2211yescharacteristic
229D4×Q8×C53C2211yescharacteristic
230D4×Q8×C53C2211yescharacteristic, complemented
231C53×#541C2213yes—
232C53×#541C2213yescomplemented
233C53×#533C2213yescomplemented
234C53×#529C2213yes—
235C53×#519C2211yescharacteristic
236C53×#519C2211yescharacteristic, complemented
237C2×C4×Q8×C53C2211yescharacteristic, complemented
238#13133265—28no—
239#13133265—28no—
240C2×#11719949C2311yescharacteristic
241C2×#11719949C2311yescharacteristic
242C2×#11719949C2313yes—
243C2×#11719949C2313yes—
244C2×#11719945C2313yes—
245C2×#11719945C2313yes—
246C2×#11719945C2313yes—
247C2×#11719945C2313yes—
248C22×Dic106C2313yes—
249C2×Q8×D53—28no—
250C2×Q8×D53C2313yes—
251C2×Q8×D53C2313yes—
252C2×Q8×D53C2313yes—
253C2×Q8×D53C2311yescharacteristic
254C2×Q8×D53C2313yes—
255C2×Q8×D53C2311yescharacteristic
256C22×C4×D53C2313yes—
257#13133217C2313yes—
258#13133216C2316yes—
259#13133216C2316yes—
260#13133216C2313yes—
261#13133216C2313yes—
262#13133216C2313yes—
263#13133216C2316yes—
264#13133216C2313yes—
265#13133216C2313yes—
266#13133216C2313yes—
267#13133215C2313yes—
268#13133215C2313yes—
269#13133215C2316yes—
270#13133215C2313yes—
271#13133214C2313yes—
272#13133213C2313yes—
273#13133212C2313yes—
274#13133212C2316yes—
275#13133212C2316yes—
276#13133212C2316yes—
277#13133212C2316yes—
278#13133212C2316yes—
279#13133212C2316yes—
280#13133212C2316yes—
281#13133212C2313yes—
282#13133212C2313yes—
283#13133212C2316yes—
284#13133212C2313yes—
285#13133212C2313yes—
286#13133212C2311yescharacteristic
287#13133211C2313yes—
288#13133211C2316yes—
289#13133211C2316yes—
290#13133211C2313yes—
291#13133211C2316yes—
292#13133210C2313yes—
293#13133210C2313yes—
294#13133210C2316yes—
295#13133210C2313yes—
296#13133210C2313yes—
297#13133210C2311yescharacteristic
298#13133210C2313yes—
299#13133209C2313yes—
300#13133209C2313yes—
301#13133209C2313yes—
302#13133208C2313yes—
303#13133208C2316yes—
304#13133208C2313yes—
305#13133208C2313yes—
306#13133208C2313yes—
307#13133207C2316yes—
308#13133207C2316yes—
309#13133207C2313yes—
310#13133207C2313yes—
311#13133207C2313yes—
312#13133207C2316yes—
313#13133207C2316yes—
314#13133207C2316yes—
315#13133207C2313yes—
316#13133207C2313yes—
317#13133207C2313yes—
318#13133207C2316yes—
319#13133206C2313yes—
320#13133206C2313yes—
321#13133206C2313yes—
322#13133206C2313yes—
323#13133206C2316yes—
324#13133206C2313yes—
325#13133205C2313yes—
326#13133205C2313yes—
327#13133205C2316yes—
328#13133205C2316yes—
329#13133205C2313yes—
330#13133204C2311yescharacteristic
331#13133203C2316yes—
332#13133203C2316yes—
333#13133203C2313yes—
334#13133203C2313yes—
335#13133203C2316yes—
336#13133203C2316yes—
337#13133203C2313yes—
338#13133203C2313yes—
339#13133203C2316yes—
340#13133203C2311yescharacteristic
341#13133203C2313yes—
342#13133202C2313yes—
343#13133202C2316yes—
344#13133202C2313yes—
345#13133202C2313yes—
346#13133202C2316yes—
347#13133202C2316yes—
348#13133202C2313yes—
349#13133202C2313yes—
350#13133202C2316yes—
351#13133202C2316yes—
352#13133202C2313yes—
353#13133202C2316yes—
354#13133202C2316yes—
355#13133201C2313yes—
356#13133201C2313yes—
357#13133200C2311yescharacteristic
358#13133200C2313yes—
359#13133199C2316yes—
360#13133199C2313yes—
361#13133199C2313yes—
362#13133199C2313yes—
363#13133199C2313yes—
364#13133199C2313yes—
365#13133199C2313yes—
366#13133198C2313yes—
367#13133198C2311yescharacteristic
368#13133197C2313yes—
369#13133197C2313yes—
370#13133197C2313yes—
371#13133197C2316yes—
372#13133197C2313yes—
373#13133197C2316yes—
374#13133196C2313yes—
375#13133196C2313yes—
376#13133196C2313yes—
377#13133195C2316yes—
378#13133195C2316yes—
379#13133195C2316yes—
380#13133195C2316yes—
381#13133195C2316yes—
382#13133195C2316yes—
383#13133195C2313yes—
384#13133195C2313yes—
385#13133195C2316yes—
386#13133195C2313yes—
387#13133195C2316yes—
388#13133195C2313yes—
389#13133195C2316yes—
390#13133195C2311yescharacteristic
391#13133195C2313yes—
392#13133194C2313yes—
393#13133194C2313yes—
394#13133194C2313yes—
395#13133194C2313yes—
396#13133193C2313yes—
397#13133193C2313yes—
398#13133193C2313yes—
399#13133193C2313yes—
400#13133193C2313yes—
401#13133193C2313yes—
402#13133193C2313yes—
403#13133193C2313yes—
404#13133192C2313yes—
405#13133192C2313yes—
406#13133192C2313yes—
407#13133192C2313yes—
408#13133192C2316yes—
409#13133192C2313yes—
410#13133192C2316yes—
411#13133192C2313yes—
412#13133191C2313yes—
413#13133191C2313yes—
414#13133191C2313yes—
415#13133191C2313yes—
416#13133191C2313yes—
417#13133190C2313yes—
418#13133190C2313yes—
419#13133190C2316yes—
420#13133190C2316yes—
421#13133190C2316yes—
422#13133190C2313yes—
423#13133190C2313yes—
424#13133190C2313yes—
425#13133190C2313yes—
426#13133189C2313yes—
427#13133189C2313yes—
428#13133189C2313yes—
429#13133189C2311yescharacteristic
430#13133188C2313yes—
431#13133188C2311yescharacteristic
432#13133187C2313yes—
433#13133187C2313yes—
434#13133185C2311yescharacteristic
435#13133185C2311yescharacteristic
436Q8×Dic53C2311yescharacteristic
437Q8×Dic53C2311yescharacteristic
438Q8×Dic53C2311yescharacteristic
439Q8×Dic53C2313yes—
440Q8×Dic53C2313yes—
441Q8×Dic53C2313yes—
442Q8×Dic53C2311yescharacteristic
443Q8×Dic53C2313yes—
444Q8×Dic53C2313yes—
445Q8×Dic53C2313yes—
446C4×Dic106C2313yes—
447C4×Dic106C2313yes—
448C4×Dic106C2313yes—
449C4×Dic106C2316yes—
450C4×Dic106C2313yes—
451C4×Dic106C2316yes—
452C4×Dic106C2316yes—
453C4×Dic106C2313yes—
454C4×Dic106C2316yes—
455C4×Dic106C2313yes—
456C4×Dic106C2313yes—
457C4×Dic106C2313yes—
458C4×Dic106C2313yes—
459C4×Dic106C2313yes—
460C4×Dic106C2313yes—
461#13133182C2313yes—
462#13133182C2313yes—
463#13133182C2313yes—
464#13133182C2316yes—
465#13133182C2316yes—
466#13133182C2313yes—
467#13133182C2316yes—
468#13133182C2316yes—
469#13133182C2313yes—
470#13133182C2316yes—
471#13133182C2313yes—
472#13133182C2313yes—
473#13133182C2316yes—
474#13133182C2313yes—
475#13133182C2316yes—
476C4×D212C2313yes—
477C4×D212C2313yes—
478C4×D212C2313yes—
479C4×D212C2316yes—
480C4×D212C2313yes—
481C4×D212C2313yes—
482C4×D212C2313yes—
483C4×D212C2313yes—
484C4×D212C2313yes—
485C4×D212C2316yes—
486C4×D212C2313yes—
487#13133179C2316yes—
488#13133179C2316yes—
489#13133179C2316yes—
490#13133179C2316yes—
491#13133179C2313yes—
492#13133179C2316yes—
493#13133179C2313yes—
494#13133179C2313yes—
495#13133179C2313yes—
496#13133179C2313yes—
497#13133179C2316yes—
498#13133179C2313yes—
499C4×C22⋊D53C2313yes—
500C4×C22⋊D53C2313yes—
501C4×C22⋊D53C2313yes—
502C4×C22⋊D53C2313yes—
503C4×C22⋊D53C2313yes—
504C4×C22⋊D53C2313yes—
505C4×C22⋊D53C2316yes—
506C4×C22⋊D53C2316yes—
507C4×C22⋊D53C2311yescharacteristic
508C4×C22⋊D53C2313yes—
509C4×C22⋊D53C2313yes—
510C4×C22⋊D53C2313yes—
511#13133177C2316yes—
512#13133177C2316yes—
513#13133177C2316yes—
514#13133177C2316yes—
515#13133177C2311yescharacteristic
516#13133177C2313yes—
517#13133177C2313yes—
518#13133177C2313yes—
519#13133176C2313yes—
520#13133176C2313yes—
521#13133176C2313yes—
522#13133176C2313yes—
523#13133175C2316yes—
524#13133175C2316yes—
525#13133175C2316yes—
526#13133175C2313yes—
527#13133175C2313yes—
528#13133175C2313yes—
529#13133175C2313yes—
530#13133175C2313yes—
531#13133175C2313yes—
532#13133175C2313yes—
533#13133175C2313yes—
534#13133175C2316yes—
535#13133175C2316yes—
536#13133174C2316yes—
537#13133174C2316yes—
538#13133174C2316yes—
539#13133174C2316yes—
540#13133174C2316yes—
541#13133174C2316yes—
542#13133174C2313yes—
543#13133174C2313yes—
544#13133174C2313yes—
545#13133174C2313yes—
546#13133174C2313yes—
547#13133174C2313yes—
548#13133173C2316yes—
549#13133173C2316yes—
550#13133173C2313yes—
551#13133173C2313yes—
552C2×C4⋊Dic53C2313yes—
553C4⋊C4×D53C2316yes—
554C4⋊C4×D53C2316yes—
555C4⋊C4×D53C2313yes—
556C4⋊C4×D53C2313yes—
557C4⋊C4×D53C2313yes—
558C4⋊C4×D53C2313yes—
559C4⋊C4×D53C2313yes—
560C4⋊C4×D53C2313yes—
561C22⋊C4×D53C2311yescharacteristic
562C22⋊C4×D53C2313yes—
563C2×C4×Dic53C2313yes—
564C42×D53C2313yes—
565C42×D53C2316yes—
566C42×D53C2313yes—
567C42×D53C2313yes—
568C42×D53C2316yes—
569C42×D53C2313yes—
570C42×D53C2316yes—
571C22×Q8×C53C2311yescharacteristic
572C22×Q8×C53C2311yescharacteristic
573C22×Q8×C53C2311yescharacteristic
574C4⋊Q8×C53C2313yes—
575C4⋊Q8×C53C2313yes—
576C4⋊Q8×C53C2313yes—
577C4⋊Q8×C53C2313yes—
578#126×C53C2313yes—
579#126×C53C2313yes—
580#126×C53C2316yes—
581#126×C53C2316yes—
582#125×C53C2316yes—
583#125×C53C2313yes—
584#125×C53C2316yes—
585#125×C53C2313yes—
586#125×C53C2316yes—
587#125×C53C2313yes—
588#124×C53C2313yes—
589#123×C53C2313yes—
590#123×C53C2313yes—
591C22⋊Q8×C53C2313yes—
592C22⋊Q8×C53C2313yes—
593C22⋊Q8×C53C2313yes—
594C22⋊Q8×C53C2313yes—
595C22⋊Q8×C53C2313yes—
596C22⋊Q8×C53C2313yes—
597C22⋊Q8×C53C2313yes—
598#121×C53C2311yescharacteristic
599C4×Q8×C53C2311yescharacteristic
600C4×Q8×C53C2311yescharacteristic
601C4×Q8×C53C2311yescharacteristic
602C4×Q8×C53C2313yes—
603C4×Q8×C53C2313yes—
604C4×Q8×C53C2311yescharacteristic
605C4×Q8×C53C2313yes—
606C4×Q8×C53C2313yes—
607C4×Q8×C53C2313yes—
608C4×Q8×C53C2313yes—
609C4×Q8×C53C2313yes—
610C4×Q8×C53C2316yes—
611C4×D4×C53C2313yes—
612C4×D4×C53C2313yes—
613C4×D4×C53C2313yes—
614#117×C53C2313yes—
615#117×C53C2313yes—
616#117×C53C2313yes—
617#117×C53C2313yes—
618#117×C53C2316yes—
619C2×C4⋊C4×C53C2313yes—
620C2×C42×C53C2313yes—
621C23×D53C2411yescharacteristic
622C2×Q8×C53—24no—
623C2×Q8×C53—24no—
624C2×Q8×C53—24no—
625C2×Q8×C53C2413yes—
626C2×Q8×C53C2413yes—
627C2×Q8×C53C2413yes—
628C2×Q8×C53C2413yes—
629C2×Q8×C53C2411yescharacteristic
630C2×D4×C53C2411yescharacteristic
631C2×D4×C53C2411yescharacteristic
632C2×D4×C53C2411yescharacteristic
633C22×C4×C53C2413yes—
634C22×C4×C53C2413yes—
635C22×C4×C53C2413yes—
636C22×C4×C53C2411yescharacteristic
637C22×C4×C53C2413yes—
638C2×C22⋊D53C2411yescharacteristic
639C2×C22⋊D53C2413yes—
640C2×C22⋊D53C2411yescharacteristic
641C2×C22⋊D53C2413yes—
642C2×C22⋊D53C2413yes—
643C2×C22⋊D53C2413yes—
644C2×C22⋊D53C2413yes—
645C2×C22⋊D53C2411yescharacteristic
646C2×C22⋊D53C2411yescharacteristic
647C2×C22⋊D53C2413yes—
648C22×Dic53C2413yes—
649C22×Dic53C2411yescharacteristic
650C22×Dic53C2413yes—
651#11719949—24no—
652#11719949—24no—
653#11719949—212no—
654#11719949—212no—
655Q8×D53—24no—
656Q8×D53—212no—
657Q8×D53—212no—
658Q8×D53—212no—
659Q8×D53—212no—
660Q8×D53#4118yes—
661#11719945—212no—
662#11719945—212no—
663#11719945—212no—
664#11719945—212no—
665C2×D212C2413yes—
666C2×D212C2413yes—
667C2×D212C2413yes—
668C2×D212C2413yes—
669C2×D212C2413yes—
670C2×D212C2413yes—
671C2×D212C2416yes—
672C2×D212C2413yes—
673C2×C4×D53—212no—
674C2×C4×D53C2413yes—
675C2×C4×D53C2416yes—
676C2×C4×D53C2416yes—
677C2×C4×D53C2413yes—
678C2×C4×D53C2413yes—
679C2×C4×D53C2413yes—
680C2×C4×D53C2413yes—
681C2×C4×D53C2411yescharacteristic
682C2×C4×D53C2413yes—
683C2×C4×D53C2411yescharacteristic
684C2×C4×D53C2413yes—
685C2×C4×D53C2413yes—
686C2×C4×D53C2413yes—
687C2×C4×D53C2416yes—
688C2×C4×D53C2413yes—
689C2×C4×D53C2416yes—
690C2×C4×D53C2413yes—
691C2×C4×D53C2413yes—
692C2×Dic106—212no—
693C2×Dic106C2413yes—
694C2×Dic106C2413yes—
695C2×Dic106C2416yes—
696C2×Dic106C2413yes—
697C2×Dic106C2413yes—
698C2×Dic106C2413yes—
699C2×Dic106C2416yes—
700C2×Dic106C2411yescharacteristic
701C2×Dic106C2413yes—
702C4⋊C4×C53C2413yes—
703C4⋊C4×C53C2413yes—
704C4⋊C4×C53C2416yes—
705C4⋊C4×C53C2413yes—
706C4⋊C4×C53C2413yes—
707C4⋊C4×C53C2413yes—
708C4⋊C4×C53C2413yes—
709C4⋊C4×C53C2413yes—
710C4⋊C4×C53C2413yes—
711C4⋊C4×C53C2416yes—
712C4⋊C4×C53C2416yes—
713C4⋊C4×C53C2413yes—
714C4⋊C4×C53C2413yes—
715C4⋊C4×C53C2413yes—
716C4⋊C4×C53C2411yescharacteristic
717C4⋊C4×C53C2416yes—
718C4⋊C4×C53C2416yes—
719C4⋊C4×C53C2413yes—
720C4⋊C4×C53C2413yes—
721C22⋊C4×C53C2411yescharacteristic
722C22⋊C4×C53C2411yescharacteristic
723C22⋊C4×C53C2413yes—
724C22⋊C4×C53C2413yes—
725C22⋊C4×C53C2413yes—
726C22⋊C4×C53C2413yes—
727C22⋊C4×C53C2413yes—
728C22⋊C4×C53C2413yes—
729C22⋊C4×C53C2413yes—
730C22⋊C4×C53C2413yes—
731C42×C53C2413yes—
732C42×C53C2413yes—
733C42×C53C2413yes—
734C42×C53C2413yes—
735C42×C53C2416yes—
736C42×C53C2416yes—
737C42×C53C2413yes—
738C42×C53C2413yes—
739C22⋊Dic53C2413yes—
740C22⋊Dic53C2411yescharacteristic
741C22⋊Dic53C2413yes—
742C22⋊Dic53C2413yes—
743C22⋊Dic53C2411yescharacteristic
744C22⋊Dic53C2411yescharacteristic
745C22⋊Dic53C2411yescharacteristic
746C22⋊Dic53C2411yescharacteristic
747C22⋊Dic53C2411yescharacteristic
748C22⋊Dic53C2413yes—
749#11719921C2411yescharacteristic
750#11719921C2413yes—
751#11719921C2413yes—
752#11719921C2411yescharacteristic
753#11719921C2411yescharacteristic
754#11719921C2413yes—
755#11719921C2411yescharacteristic
756#11719921C2413yes—
757#11719921C2413yes—
758#11719921C2413yes—
759#11719921C2413yes—
760#11719921C2413yes—
761#11719921C2416yes—
762#11719921C2413yes—
763#11719921C2416yes—
764#11719921C2413yes—
765#11719921C2416yes—
766#11719921C2416yes—
767#11719921C2416yes—
768#11719921C2416yes—
769#11719921C2413yes—
770#11719921C2413yes—
771#11719921C2416yes—
772#11719921C2416yes—
773#11719921C2413yes—
774#11719921C2413yes—
775#11719921C2413yes—
776#11719921C2413yes—
777#11719921C2413yes—
778#11719921C2413yes—
779#11719921C2411yescharacteristic
780#11719921C2411yescharacteristic
781C4⋊Dic53C2413yes—
782C4⋊Dic53C2413yes—
783C4⋊Dic53C2413yes—
784C4⋊Dic53C2416yes—
785C4⋊Dic53C2413yes—
786C4⋊Dic53C2413yes—
787C4⋊Dic53C2413yes—
788C4⋊Dic53C2413yes—
789C4⋊Dic53C2413yes—
790C4⋊Dic53C2413yes—
791C4⋊Dic53C2413yes—
792C4⋊Dic53C2413yes—
793C4⋊Dic53C2411yescharacteristic
794C4⋊Dic53C2413yes—
795C4⋊Dic53C2413yes—
796#11719919C2416yes—
797#11719919C2413yes—
798#11719919C2413yes—
799#11719919C2413yes—
800#11719919C2413yes—
801#11719919C2416yes—
802#11719919C2413yes—
803#11719919C2413yes—
804#11719919C2413yes—
805#11719919C2413yes—
806#11719919C2416yes—
807#11719919C2416yes—
808#11719919C2413yes—
809#11719919C2411yescharacteristic
810#11719919C2413yes—
811#11719919C2411yescharacteristic
812#11719919C2413yes—
813#11719919C2413yes—
814#11719919C2413yes—
815#11719919C2413yes—
816#11719919C2416yes—
817#11719919C2416yes—
818#11719919C2413yes—
819#11719919C2413yes—
820#11719919C2413yes—
821#11719919C2413yes—
822#11719919C2413yes—
823#11719919C2413yes—
824#11719919C2411yescharacteristic
825#11719919C2411yescharacteristic
826C4×Dic53C2413yes—
827C4×Dic53C2413yes—
828C4×Dic53C2411yescharacteristic
829C4×Dic53C2411yescharacteristic
830C4×Dic53C2413yes—
831C4×Dic53C2413yes—
832C4×Dic53C2416yes—
833C4×Dic53C2416yes—
834C4×Dic53C2416yes—
835C4×Dic53C2413yes—
836C4×Dic53C2413yes—
837C4×Dic53C2413yes—
838C4×Dic53C2416yes—
839C4×Dic53C2413yes—
840C4×Dic53C2413yes—
841C4×Dic53C2413yes—
842C4×Dic53C2416yes—
843C4×Dic53C2416yes—
844C4×Dic53C2413yes—
845C4×Dic53C2413yes—
846C23×C53C2511yescharacteristic
847C23×C53C2511yescharacteristic
848C23×C53C2511yescharacteristic
849C22×D53—22no—
850C22×D53—41no—
851C22×D53—41no—
852C22×D53C2513yes—
853C22×D53C2513yes—
854C22×D53C2511yescharacteristic
855C22×D53C2511yescharacteristic
856Q8×C53—26no—
857Q8×C53—26no—
858Q8×C53—26no—
859Q8×C53—43no—
860Q8×C53C2×#4114yes—
861D4×C53—41no—
862D4×C53—41no—
863D4×C53—41no—
864C2×C4×C53—26no—
865C2×C4×C53—26no—
866C2×C4×C53—26no—
867C2×C4×C53—43no—
868C2×C4×C53—41no—
869C2×C4×C53C2513yes—
870C2×C4×C53C2513yes—
871C2×C4×C53C2511yescharacteristic
872C2×C4×C53C2513yes—
873C2×C4×C53C2513yes—
874C2×C4×C53C2513yes—
875C2×C4×C53C2513yes—
876C2×C4×C53C2511yescharacteristic
877C2×C4×C53C2513yes—
878C2×C4×C53C2511yescharacteristic
879C2×C4×C53C2511yescharacteristic
880C2×C4×C53C2513yes—
881C22⋊D53—22no—
882C22⋊D53—22no—
883C22⋊D53—26no—
884C22⋊D53—26no—
885C22⋊D53—43no—
886C22⋊D53—41no—
887C22⋊D53—43no—
888C22⋊D53—43no—
889C22⋊D53—41no—
890C22⋊D53—43no—
891C2×Dic53—26no—
892C2×Dic53—41no—
893C2×Dic53—43no—
894C2×Dic53C2513yes—
895C2×Dic53C2511yescharacteristic
896C2×Dic53C2511yescharacteristic
897C2×Dic53C2511yescharacteristic
898C2×Dic53C2513yes—
899C2×Dic53C2511yescharacteristic
900C2×Dic53C2513yes—
901C2×Dic53C2511yescharacteristic
902C2×Dic53C2513yes—
903C2×Dic53C2511yescharacteristic
904C2×Dic53C2513yes—
905C2×Dic53C2513yes—
906D212—26no—
907D212—26no—
908D212—26no—
909D212—26no—
910D212—43no—
911D212—43no—
912D212—46no—
913D212—43no—
914C4×D53—26no—
915C4×D53—26no—
916C4×D53—26no—
917C4×D53—26no—
918C4×D53—26no—
919C4×D53—212no—
920C4×D53—212no—
921C4×D53—41no—
922C4×D53—43no—
923C4×D53—43no—
924C4×D53—43no—
925C4×D53—46no—
926C4×D53—43no—
927C4×D53—43no—
928C4×D53—46no—
929C4×D53—41no—
930C4×D53—43no—
931C4×D53C2×#41112yes—
932Dic106—26no—
933Dic106—212no—
934Dic106—26no—
935Dic106—26no—
936Dic106—41no—
937Dic106—43no—
938Dic106—43no—
939Dic106—46no—
940Dic106C2×#41112yes—
941#62850—531nomaximal, Sylow
942C22×C53—21no—
943C22×C53—21no—
944C22×C53—21no—
945C22×C53—21no—
946C22×C53—21no—
947C22×C53—21no—
948C22×C53—21no—
949C22×C53—21no—
950C22×C53—21no—
951C22×C53C2611yescharacteristic
952C2×D53—21no—
953C2×D53—21no—
954C2×D53—21no—
955C2×D53—23no—
956C2×D53—23no—
957C2×D53—23no—
958C2×D53—23no—
959C2×D53—23no—
960C2×D53—23no—
961C2×D53—21no—
962C2×D53—21no—
963C2×D53—44no—
964C2×D53C22×#4112yes—
965C4×C53—23no—
966C4×C53—23no—
967C4×C53—23no—
968C4×C53—23no—
969C4×C53—21no—
970C4×C53—23no—
971C4×C53—23no—
972C4×C53—23no—
973C4×C53—21no—
974C4×C53—21no—
975C4×C53—21no—
976C4×C53C22×#4116yes—
977Dic53—23no—
978Dic53—21no—
979Dic53—21no—
980Dic53—21no—
981Dic53—23no—
982Dic53—21no—
983Dic53—23no—
984Dic53—21no—
985Dic53—23no—
986Dic53—23no—
987Dic53—21no—
988Dic53C22×#4116yes—
989#3524—531no—
990#3524—533no—
991#3524—533no—
992#3524—531no—
993#3523—533no—
994#3523—531no—
995#3523—533no—
996#3523D5311yescharacteristic, complemented
997#3518—533no—
998#3518—531no—
999#3518—533no—
1000#3518—531no—
1001#3516—533no—
1002#3516—531no—
1003#3516—533no—
1004#3516—531no—
1005#3507—533no—
1006#3507—533no—
1007#3502—531no—
1008#3497—531no—
1009#3493—533no—
1010#3493—533no—
1011#3486—531no—
1012#3486—531no—
1013#3461—533no—
1014#3461—533no—
1015#3455—533no—
1016#3455—533no—
1017C4×2−1+4—531no—
1018C4×2−1+4—531no—
1019C2×#519—531no—
1020C2×C53—41no—
1021C2×C53—41no—
1022C2×C53—41no—
1023C2×C53C23×#4111yescharacteristic
1024C2×C532−1+611yescharacteristic
1025C2×C532−1+611yescharacteristic
1026D53—22no—
1027D53—43no—
1028D53—43no—
1029D53—41no—
1030C2×2−1+4—531no—
1031C2×2−1+4—531no—
1032C23×Q8—531no—
1033#559—536no—
1034#559—533no—
1035#559—533no—
1036Q82—533no—
1037Q82—531no—
1038#557—533no—
1039#557—533no—
1040#557—533no—
1041#557—536no—
1042#557—531no—
1043#557—531no—
1044#557—533no—
1045#557C2×D5311yescharacteristic, complemented
1046#557C2×D5313yescomplemented
1047#556—533no—
1048#556—533no—
1049#556—536no—
1050#556—536no—
1051#556—533no—
1052#556—533no—
1053#556—533no—
1054#556—536no—
1055#556—533no—
1056#556—533no—
1057#556—536no—
1058#556—533no—
1059#556—536no—
1060#556—533no—
1061#556C2×D5313yes—
1062#555—533no—
1063#555—536no—
1064#555—533no—
1065#555—533no—
1066#555—533no—
1067#555—536no—
1068#554—536no—
1069#554—533no—
1070#554—533no—
1071#553—536no—
1072#553—533no—
1073#553—536no—
1074#553—533no—
1075#553—533no—
1076#553—533no—
1077#552—536no—
1078#552—536no—
1079#552—536no—
1080#552—536no—
1081#552—533no—
1082#552—533no—
1083#552—533no—
1084#552—533no—
1085#552—533no—
1086#552—533no—
1087#552C2×D5313yes—
1088#552C2×D5313yescomplemented
1089#550—531no—
1090#550—533no—
1091D4×Q8—531no—
1092D4×Q8—531no—
1093D4×Q8—533no—
1094D4×Q8—533no—
1095D4×Q8—533no—
1096D4×Q8—533no—
1097D4×Q8—533no—
1098D4×Q8C2×D5311yescharacteristic
1099D4×Q8C2×D5311yescharacteristic
1100D4×Q8C2×D5311yescharacteristic, complemented
1101#548—531no—
1102#548—531no—
1103#548—531no—
1104#548—531no—
1105#548—533no—
1106#548—533no—
1107#548—533no—
1108#548—533no—
1109#548—531no—
1110#548—531no—
1111#548—533no—
1112#548—533no—
1113#544—533no—
1114#544—533no—
1115#542—533no—
1116#542—533no—
1117#542—536no—
1118#542—533no—
1119#542—533no—
1120#542—533no—
1121#542—533no—
1122#542—533no—
1123#542—536no—
1124#542—533no—
1125#542—533no—
1126#542—533no—
1127#542—533no—
1128#542—533no—
1129#541—533no—
1130#541—533no—
1131#541—533no—
1132#541—533no—
1133#541—536no—
1134#541—536no—
1135#541—533no—
1136#541—533no—
1137#541C2×D5313yes—
1138#541C2×D5313yescomplemented
1139#540—533no—
1140#540—533no—
1141#540—533no—
1142#540—533no—
1143#539—533no—
1144#539—536no—
1145#539—536no—
1146#539—533no—
1147#539—533no—
1148#539—533no—
1149#538—533no—
1150#538—536no—
1151#538—533no—
1152#538—533no—
1153#538—531no—
1154#537—533no—
1155#537—533no—
1156#536—533no—
1157#536—533no—
1158#536—533no—
1159#536—533no—
1160#533—533no—
1161#533—533no—
1162#533—536no—
1163#533—533no—
1164#533—533no—
1165#533—536no—
1166#533—533no—
1167#533C2×D5313yescomplemented
1168#532—533no—
1169#532—533no—
1170#529—536no—
1171#529—536no—
1172#529—536no—
1173#529—536no—
1174#529—536no—
1175#529—536no—
1176#529—536no—
1177#529—533no—
1178#529—533no—
1179#529—533no—
1180#529—536no—
1181#529—533no—
1182#529—533no—
1183#529—533no—
1184#529—533no—
1185#529—533no—
1186#529—533no—
1187#529—536no—
1188#529—536no—
1189#529—533no—
1190#529—533no—
1191#529C2×D5313yes—
1192#525—533no—
1193#525—533no—
1194#525—533no—
1195#525—533no—
1196#520—533no—
1197#520—533no—
1198#520—531no—
1199#520—531no—
1200#520—533no—
1201#520—533no—
1202#520—533no—
1203#520—533no—
1204#519—531no—
1205#519—531no—
1206#519—533no—
1207#519—531no—
1208#519—533no—
1209#519—531no—
1210#519—531no—
1211#519—531no—
1212#519—533no—
1213#519—533no—
1214#519—533no—
1215#519—533no—
1216#519C2×D5311yescharacteristic
1217#519C2×D5311yescharacteristic, complemented
1218C4×#41—533no—
1219C4×#41—533no—
1220C4×#41—531no—
1221C4×#41—531no—
1222C4×#41—533no—
1223C4×#41—533no—
1224C4×#41—533no—
1225C4×#41—533no—
1226C2×C4×Q8—531no—
1227C2×C4×Q8—531no—
1228C2×C4×Q8—533no—
1229C2×C4×Q8—531no—
1230C2×C4×Q8—533no—
1231C2×C4×Q8—533no—
1232C2×C4×Q8—533no—
1233C2×C4×Q8C2×D5311yescharacteristic, complemented
1234C2×#117—533no—
1235C2×#117—533no—
1236C53#6285011yescharacteristic, complemented, Sylow
12372−1+4—1068no—
12382−1+4—1068no—
1239C2×#41—533no—
1240C2×#41—533no—
1241C2×#41—531no—
1242C2×#41—531no—
1243C2×#41—533no—
1244C2×#41—533no—
1245C2×#41—533no—
1246C2×#41—533no—
1247C22×Q8—531no—
1248C22×Q8—533no—
1249C22×Q8—533no—
1250C22×Q8—533no—
1251C22×Q8—533no—
1252C22×Q8—531no—
1253C22×Q8—533no—
1254C22×Q8—1068no—
1255C22×Q8C22×D5311yescharacteristic
1256C22×Q8C22×D5311yescharacteristic
1257C22×Q8C22×D5311yescharacteristic
1258C23×C4—533no—
1259C4⋊Q8—533no—
1260C4⋊Q8—533no—
1261C4⋊Q8—533no—
1262C4⋊Q8—536no—
1263C4⋊Q8—533no—
1264C4⋊Q8—536no—
1265C4⋊Q8—536no—
1266C4⋊Q8—533no—
1267C4⋊Q8—533no—
1268C4⋊Q8—533no—
1269C4⋊Q8—536no—
1270C4⋊Q8—533no—
1271C4⋊Q8—533no—
1272C4⋊Q8—533no—
1273C4⋊Q8C22×D5313yes—
1274C4⋊Q8C22×D5313yes—
1275C4⋊Q8C22×D5313yes—
1276C4⋊Q8C22×D5313yes—
1277#127—533no—
1278#127—533no—
1279#126—531no—
1280#126—533no—
1281#126—533no—
1282#126—536no—
1283#126—533no—
1284#126—536no—
1285#126—533no—
1286#126—536no—
1287#126—533no—
1288#126—536no—
1289#126—536no—
1290#126—536no—
1291#126—536no—
1292#126—536no—
1293#126—531no—
1294#126—533no—
1295#126—533no—
1296#126—533no—
1297#126—533no—
1298#126—533no—
1299#126—536no—
1300#126—536no—
1301#126—533no—
1302#126—536no—
1303#126—533no—
1304#126—536no—
1305#126C22×D5313yes—
1306#126C22×D5313yes—
1307#126C22×D5316yes—
1308#126C22×D5316yes—
1309#125—536no—
1310#125—533no—
1311#125—533no—
1312#125—533no—
1313#125—533no—
1314#125—536no—
1315#125—533no—
1316#125—533no—
1317#125—536no—
1318#125—536no—
1319#125—536no—
1320#125—536no—
1321#125—536no—
1322#125—533no—
1323#125—533no—
1324#125—533no—
1325#125—533no—
1326#125—533no—
1327#125—533no—
1328#125—533no—
1329#125C22×D5316yes—
1330#125C22×D5316yes—
1331#125C22×D5316yes—
1332#125C22×D5313yes—
1333#125C22×D5313yes—
1334#125C22×D5313yes—
1335#124—533no—
1336#124—533no—
1337#124—533no—
1338#124—536no—
1339#124—533no—
1340#124—533no—
1341#124—531no—
1342#124—533no—
1343#124—531no—
1344#124—536no—
1345#124—536no—
1346#124—536no—
1347#124—533no—
1348#124—533no—
1349#124—536no—
1350#124—536no—
1351#124—533no—
1352#124—533no—
1353#124—533no—
1354#124—533no—
1355#124—533no—
1356#124—536no—
1357#124—536no—
1358#124C22×D5313yes—
1359#123—531no—
1360#123—533no—
1361#123—531no—
1362#123—533no—
1363#123—536no—
1364#123—533no—
1365#123—533no—
1366#123—536no—
1367#123—533no—
1368#123—536no—
1369#123—536no—
1370#123—533no—
1371#123—536no—
1372#123—536no—
1373#123—533no—
1374#123—536no—
1375#123—533no—
1376#123—533no—
1377#123—533no—
1378#123—533no—
1379#123—533no—
1380#123—533no—
1381#123—533no—
1382#123—536no—
1383#123—533no—
1384#123—533no—
1385#123C22×D5313yes—
1386#123C22×D5313yes—
1387C22⋊Q8—533no—
1388C22⋊Q8—533no—
1389C22⋊Q8—533no—
1390C22⋊Q8—533no—
1391C22⋊Q8—533no—
1392C22⋊Q8—533no—
1393C22⋊Q8—533no—
1394C22⋊Q8—533no—
1395C22⋊Q8—533no—
1396C22⋊Q8—533no—
1397C22⋊Q8—533no—
1398C22⋊Q8—533no—
1399C22⋊Q8—533no—
1400C22⋊Q8—536no—
1401C22⋊Q8—533no—
1402C22⋊Q8—536no—
1403C22⋊Q8—533no—
1404C22⋊Q8—536no—
1405C22⋊Q8—536no—
1406C22⋊Q8—536no—
1407C22⋊Q8—533no—
1408C22⋊Q8—533no—
1409C22⋊Q8—536no—
1410C22⋊Q8—533no—
1411C22⋊Q8—536no—
1412C22⋊Q8—533no—
1413C22⋊Q8—531no—
1414C22⋊Q8—536no—
1415C22⋊Q8—536no—
1416C22⋊Q8—533no—
1417C22⋊Q8—536no—
1418C22⋊Q8—536no—
1419C22⋊Q8—533no—
1420C22⋊Q8—533no—
1421C22⋊Q8—533no—
1422C22⋊Q8—533no—
1423C22⋊Q8C22×D5313yes—
1424C22⋊Q8C22×D5313yes—
1425C22⋊Q8C22×D5313yes—
1426C22⋊Q8C22×D5313yes—
1427C22⋊Q8C22×D5313yes—
1428C22⋊Q8C22×D5313yes—
1429C22⋊Q8C22×D5313yes—
1430#121—533no—
1431#121—533no—
1432#121—531no—
1433#121—533no—
1434#121—533no—
1435#121—531no—
1436#121—533no—
1437#121—533no—
1438#121—533no—
1439#121—533no—
1440#121—533no—
1441#121—533no—
1442#121—533no—
1443#121—533no—
1444#121—536no—
1445#121—533no—
1446#121—533no—
1447#121—536no—
1448#121—533no—
1449#121—533no—
1450#121—533no—
1451#121—533no—
1452#121—533no—
1453#121—533no—
1454#121—536no—
1455#121—536no—
1456#121—533no—
1457#121—536no—
1458#121C22×D5311yescharacteristic
1459#120—531no—
1460#120—531no—
1461#120—533no—
1462#120—533no—
1463C4×Q8—531no—
1464C4×Q8—533no—
1465C4×Q8—533no—
1466C4×Q8—531no—
1467C4×Q8—533no—
1468C4×Q8—531no—
1469C4×Q8—533no—
1470C4×Q8—533no—
1471C4×Q8—533no—
1472C4×Q8—531no—
1473C4×Q8—533no—
1474C4×Q8—533no—
1475C4×Q8—536no—
1476C4×Q8—533no—
1477C4×Q8—533no—
1478C4×Q8—536no—
1479C4×Q8—533no—
1480C4×Q8—533no—
1481C4×Q8—536no—
1482C4×Q8—533no—
1483C4×Q8—533no—
1484C4×Q8—536no—
1485C4×Q8—536no—
1486C4×Q8—536no—
1487C4×Q8—536no—
1488C4×Q8—533no—
1489C4×Q8—533no—
1490C4×Q8—536no—
1491C4×Q8—533no—
1492C4×Q8—533no—
1493C4×Q8—533no—
1494C4×Q8—536no—
1495C4×Q8—533no—
1496C4×Q8—536no—
1497C4×Q8—533no—
1498C4×Q8—533no—
1499C4×Q8—533no—
1500C4×Q8—533no—
1501C4×Q8—533no—
1502C4×Q8—536no—
1503C4×Q8C22×D5311yescharacteristic
1504C4×Q8C22×D5313yes—
1505C4×Q8C22×D5313yes—
1506C4×Q8C22×D5311yescharacteristic
1507C4×Q8C22×D5313yes—
1508C4×Q8C22×D5313yes—
1509C4×Q8C22×D5311yescharacteristic
1510C4×Q8C22×D5313yes—
1511C4×Q8C22×D5313yes—
1512C4×Q8C22×D5311yescharacteristic
1513C4×Q8C22×D5313yes—
1514C4×Q8C22×D5316yes—
1515C4×D4—531no—
1516C4×D4—533no—
1517C4×D4—533no—
1518C4×D4—533no—
1519C4×D4—536no—
1520C4×D4—533no—
1521C4×D4—533no—
1522C4×D4—533no—
1523C4×D4—533no—
1524C4×D4—536no—
1525C4×D4—533no—
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—536no—
1535C4×D4—536no—
1536C4×D4—536no—
1537C4×D4—536no—
1538C4×D4—536no—
1539C4×D4—531no—
1540C4×D4—533no—
1541C4×D4—533no—
1542C4×D4—533no—
1543C4×D4—536no—
1544C4×D4—536no—
1545C4×D4—536no—
1546C4×D4—536no—
1547C4×D4—533no—
1548C4×D4—533no—
1549C4×D4—536no—
1550C4×D4—533no—
1551C4×D4—533no—
1552C4×D4—533no—
1553C4×D4—533no—
1554C4×D4—533no—
1555C4×D4—533no—
1556C4×D4—536no—
1557C4×D4—533no—
1558C4×D4C22×D5313yes—
1559C4×D4C22×D5313yes—
1560C4×D4C22×D5313yes—
1561#117—533no—
1562#117—533no—
1563#117—533no—
1564#117—533no—
1565#117—533no—
1566#117—533no—
1567#117—533no—
1568#117—533no—
1569#117—533no—
1570#117—533no—
1571#117—536no—
1572#117—536no—
1573#117—533no—
1574#117—533no—
1575#117—536no—
1576#117—536no—
1577#117—536no—
1578#117—533no—
1579#117—533no—
1580#117—536no—
1581#117—536no—
1582#117—533no—
1583#117—533no—
1584#117—536no—
1585#117—533no—
1586#117—533no—
1587#117—533no—
1588#117—533no—
1589#117—536no—
1590#117—536no—
1591#117—536no—
1592#117—536no—
1593#117—536no—
1594#117C22×D5313yes—
1595#117C22×D5313yes—
1596#117C22×D5313yes—
1597#117C22×D5313yes—
1598#117C22×D5316yes—
1599C2×C4⋊C4—533no—
1600C2×C4⋊C4—533no—
1601C2×C4⋊C4—533no—
1602C2×C4⋊C4—533no—
1603C2×C4⋊C4—533no—
1604C2×C4⋊C4—536no—
1605C2×C4⋊C4—536no—
1606C2×C4⋊C4—533no—
1607C2×C4⋊C4—533no—
1608C2×C4⋊C4C22×D5313yes—
1609C2×C22⋊C4—533no—
1610C2×C22⋊C4—531no—
1611C2×C42—533no—
1612C2×C42—533no—
1613C2×C42—536no—
1614C2×C42—533no—
1615C2×C42—533no—
1616C2×C42—536no—
1617C2×C42—536no—
1618C2×C42—533no—
1619C2×C42C22×D5313yes—
1620C24—531no—
1621#41—10612no—
1622#41—10612no—
1623#41—10612no—
1624#41—10612no—
1625#41—10612no—
1626#41—10612no—
1627#41—1064no—
1628#41—1064no—
1629C2×Q8—24no—
1630C2×Q8—24no—
1631C2×Q8—24no—
1632C2×Q8—538no—
1633C2×Q8—533no—
1634C2×Q8—536no—
1635C2×Q8—533no—
1636C2×Q8—533no—
1637C2×Q8—533no—
1638C2×Q8—533no—
1639C2×Q8—531no—
1640C2×Q8—533no—
1641C2×Q8—536no—
1642C2×Q8—10612no—
1643C2×Q8—10612no—
1644C2×Q8—10612no—
1645C2×Q8—10612no—
1646C2×Q8—10612no—
1647C2×Q8—1064no—
1648C2×Q8C23×D5313yes—
1649C2×Q8C23×D5313yes—
1650C2×Q8C23×D5313yes—
1651C2×Q8C23×D5313yes—
1652C2×Q8C23×D5311yescharacteristic
1653C2×D4—531no—
1654C2×D4—531no—
1655C2×D4—533no—
1656C2×D4—533no—
1657C2×D4—531no—
1658C2×D4—533no—
1659C2×D4—531no—
1660C2×D4—533no—
1661C2×D4—533no—
1662C2×D4—533no—
1663C2×D4—533no—
1664C2×D4—533no—
1665C2×D4—533no—
1666C2×D4—533no—
1667C2×D4—533no—
1668C2×D4—533no—
1669C2×D4—536no—
1670C2×D4—533no—
1671C2×D4C23×D5311yescharacteristic
1672C2×D4C23×D5311yescharacteristic
1673C2×D4C23×D5311yescharacteristic
1674C22×C4—533no—
1675C22×C4—533no—
1676C22×C4—531no—
1677C22×C4—533no—
1678C22×C4—533no—
1679C22×C4—536no—
1680C22×C4—536no—
1681C22×C4—533no—
1682C22×C4—533no—
1683C22×C4—533no—
1684C22×C4—533no—
1685C22×C4—531no—
1686C22×C4—533no—
1687C22×C4—531no—
1688C22×C4—533no—
1689C22×C4—533no—
1690C22×C4—533no—
1691C22×C4—536no—
1692C22×C4—533no—
1693C22×C4—536no—
1694C22×C4—533no—
1695C22×C4—10612no—
1696C22×C4C23×D5313yes—
1697C22×C4C23×D5313yes—
1698C22×C4C23×D5313yes—
1699C22×C4C23×D5311yescharacteristic
1700C22×C4C23×D5313yes—
1701C4⋊C4—536no—
1702C4⋊C4—533no—
1703C4⋊C4—533no—
1704C4⋊C4—533no—
1705C4⋊C4—533no—
1706C4⋊C4—533no—
1707C4⋊C4—533no—
1708C4⋊C4—536no—
1709C4⋊C4—533no—
1710C4⋊C4—536no—
1711C4⋊C4—533no—
1712C4⋊C4—533no—
1713C4⋊C4—533no—
1714C4⋊C4—533no—
1715C4⋊C4—533no—
1716C4⋊C4—533no—
1717C4⋊C4—533no—
1718C4⋊C4—533no—
1719C4⋊C4—533no—
1720C4⋊C4—533no—
1721C4⋊C4—531no—
1722C4⋊C4—531no—
1723C4⋊C4—533no—
1724C4⋊C4—536no—
1725C4⋊C4—533no—
1726C4⋊C4—533no—
1727C4⋊C4—533no—
1728C4⋊C4—536no—
1729C4⋊C4—533no—
1730C4⋊C4—533no—
1731C4⋊C4—533no—
1732C4⋊C4—533no—
1733C4⋊C4—531no—
1734C4⋊C4—536no—
1735C4⋊C4—533no—
1736C4⋊C4—533no—
1737C4⋊C4—533no—
1738C4⋊C4—533no—
1739C4⋊C4—536no—
1740C4⋊C4—533no—
1741C4⋊C4—533no—
1742C4⋊C4—533no—
1743C4⋊C4—531no—
1744C4⋊C4—533no—
1745C4⋊C4—531no—
1746C4⋊C4C23×D5313yes—
1747C4⋊C4C23×D5313yes—
1748C4⋊C4C23×D5313yes—
1749C4⋊C4C23×D5316yes—
1750C4⋊C4C23×D5313yes—
1751C4⋊C4C23×D5313yes—
1752C4⋊C4C23×D5313yes—
1753C4⋊C4C23×D5313yes—
1754C4⋊C4C23×D5313yes—
1755C4⋊C4C23×D5313yes—
1756C4⋊C4C23×D5316yes—
1757C4⋊C4C23×D5316yes—
1758C4⋊C4C23×D5313yes—
1759C4⋊C4C23×D5313yes—
1760C4⋊C4C23×D5316yes—
1761C4⋊C4C23×D5316yes—
1762C4⋊C4C23×D5313yes—
1763C4⋊C4C23×D5313yes—
1764C4⋊C4C23×D5311yescharacteristic
1765C22⋊C4—533no—
1766C22⋊C4—531no—
1767C22⋊C4—531no—
1768C22⋊C4—533no—
1769C22⋊C4—533no—
1770C22⋊C4—531no—
1771C22⋊C4—531no—
1772C22⋊C4—533no—
1773C22⋊C4—531no—
1774C22⋊C4—531no—
1775C22⋊C4—531no—
1776C22⋊C4—533no—
1777C22⋊C4—533no—
1778C22⋊C4—531no—
1779C22⋊C4—533no—
1780C22⋊C4—531no—
1781C22⋊C4—533no—
1782C22⋊C4—531no—
1783C22⋊C4—533no—
1784C22⋊C4—533no—
1785C22⋊C4—536no—
1786C22⋊C4—533no—
1787C22⋊C4—536no—
1788C22⋊C4—533no—
1789C22⋊C4—536no—
1790C22⋊C4—536no—
1791C22⋊C4—533no—
1792C22⋊C4—533no—
1793C22⋊C4—533no—
1794C22⋊C4—536no—
1795C22⋊C4—536no—
1796C22⋊C4—533no—
1797C22⋊C4—533no—
1798C22⋊C4—531no—
1799C22⋊C4—533no—
1800C22⋊C4—531no—
1801C22⋊C4—536no—
1802C22⋊C4—533no—
1803C22⋊C4—533no—
1804C22⋊C4—536no—
1805C22⋊C4—533no—
1806C22⋊C4—533no—
1807C22⋊C4C23×D5311yescharacteristic
1808C22⋊C4C23×D5313yes—
1809C22⋊C4C23×D5313yes—
1810C22⋊C4C23×D5313yes—
1811C22⋊C4C23×D5311yescharacteristic
1812C22⋊C4C23×D5313yes—
1813C22⋊C4C23×D5313yes—
1814C22⋊C4C23×D5313yes—
1815C22⋊C4C23×D5313yes—
1816C22⋊C4C23×D5313yes—
1817C42—533no—
1818C42—533no—
1819C42—533no—
1820C42—533no—
1821C42—531no—
1822C42—531no—
1823C42—533no—
1824C42—536no—
1825C42—536no—
1826C42—536no—
1827C42—533no—
1828C42—533no—
1829C42—536no—
1830C42—536no—
1831C42—536no—
1832C42—533no—
1833C42—533no—
1834C42—533no—
1835C42—533no—
1836C42—533no—
1837C42C23×D5313yes—
1838C42C23×D5313yes—
1839C42C23×D5316yes—
1840C42C23×D5316yes—
1841C42C23×D5313yes—
1842C42C23×D5313yes—
1843C42C23×D5313yes—
1844C42C23×D5313yes—
1845C23—531no—
1846C23—531no—
1847C23—533no—
1848C23—533no—
1849C23—1062no—
1850C23—2121no—
1851C23—2121no—
1852C23C24×D5311yescharacteristic
1853C23C24×D5311yescharacteristic
1854C23C24×D5311yescharacteristic
1855Q8—26no—
1856Q8—26no—
1857Q8—26no—
1858Q8—43no—
1859Q8—5312no—
1860Q8—10612no—
1861Q8—1066no—
1862Q8—1066no—
1863Q8—1066no—
1864Q8—2123no—
1865Q8—2121no—
1866Q8—2123no—
1867Q8—2126no—
1868Q8#41×D5314yes—
1869D4—41no—
1870D4—41no—
1871D4—41no—
1872D4—1066no—
1873D4—1066no—
1874D4—1066no—
1875D4—1066no—
1876D4—1062no—
1877D4—1062no—
1878D4—1066no—
1879D4—1066no—
1880D4—2123no—
1881D4—2123no—
1882D4—2126no—
1883D4—2123no—
1884D4—2121no—
1885D4—2123no—
1886D4—2123no—
1887D4—2123no—
1888D4—2121no—
1889D4—2123no—
1890C2×C4—26no—
1891C2×C4—26no—
1892C2×C4—26no—
1893C2×C4—43no—
1894C2×C4—41no—
1895C2×C4—533no—
1896C2×C4—5312no—
1897C2×C4—531no—
1898C2×C4—533no—
1899C2×C4—531no—
1900C2×C4—533no—
1901C2×C4—531no—
1902C2×C4—533no—
1903C2×C4—533no—
1904C2×C4—531no—
1905C2×C4—533no—
1906C2×C4—531no—
1907C2×C4—531no—
1908C2×C4—1066no—
1909C2×C4—10612no—
1910C2×C4—10612no—
1911C2×C4—1066no—
1912C2×C4—1066no—
1913C2×C4—1066no—
1914C2×C4—1066no—
1915C2×C4—1066no—
1916C2×C4—2121no—
1917C2×C4—2123no—
1918C2×C4—2123no—
1919C2×C4—2126no—
1920C2×C4—2123no—
1921C2×C4—2126no—
1922C2×C4—2123no—
1923C2×C4—2121no—
1924C2×C4—2123no—
1925C2×C4—2123no—
1926C2×C4—2123no—
1927C2×C4—2121no—
1928C2×C4C24×D5311yescharacteristic
1929C2×C4C24×D5313yes—
1930C2×C4C24×D5313yes—
1931C2×C4C24×D5313yes—
1932C2×C4C24×D5311yescharacteristic
1933C2×C4C24×D5313yes—
1934C2×C4C24×D5313yes—
1935C2×C4C24×D5313yes—
1936C2×C4C24×D5313yes—
1937C2×C4C24×D5311yescharacteristic
1938C2×C4C24×D5311yescharacteristic
1939C2×C4C24×D5313yes—
1940C22—21no—
1941C22—21no—
1942C22—21no—
1943C22—21no—
1944C22—21no—
1945C22—21no—
1946C22—21no—
1947C22—21no—
1948C22—21no—
1949C22—532no—
1950C22—1061no—
1951C22—1061no—
1952C22—1061no—
1953C22—1063no—
1954C22—1063no—
1955C22—1063no—
1956C22—1063no—
1957C22—1063no—
1958C22—1063no—
1959C22—1061no—
1960C22—1061no—
1961C22—2124no—
1962C22C25×D5311yescharacteristic
1963C4—23no—
1964C4—23no—
1965C4—23no—
1966C4—23no—
1967C4—21no—
1968C4—23no—
1969C4—21no—
1970C4—21no—
1971C4—21no—
1972C4—23no—
1973C4—23no—
1974C4—536no—
1975C4—1061no—
1976C4—1061no—
1977C4—1063no—
1978C4—1063no—
1979C4—1061no—
1980C4—1061no—
1981C4—1063no—
1982C4—1063no—
1983C4—1063no—
1984C4—1061no—
1985C4—1061no—
1986C4C2×#41×D5316yes—
1987C2—41no—
1988C2—41no—
1989C2—41no—
1990C2—1062no—
1991C2—2121no—
1992C2—2123no—
1993C2—2123no—
1994C2C22×#41×D5311yescharacteristic
1995C2#2028952711yescharacteristic
1996C2#2028952711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3523C2
hypercenter#3523D53
hypocenterC53#62850
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3523

Complements

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

NH ≅ G/Ntype
1. #20288827C2semidirect
2. #20288826C2semidirect
3. #20288821C2semidirect
4. #20288820C2semidirect
5. #20288808C2semidirect
6. #20288807C2semidirect
7. #20288802C2semidirect
8. #20288727C2semidirect
9. #20288726C2semidirect
10. #20288725C2semidirect
11. #20288724C2semidirect
12. #20288709C2semidirect
13. #20288708C2semidirect
14. #20288707C2semidirect
15. #20288706C2semidirect
16. #20288581C2semidirect
17. #20288574C2semidirect
18. #20288522C2semidirect
19. #20288485C2semidirect
20. #20288433C2semidirect
21. #20288429C2semidirect
22. #20288365C2semidirect
23. #20288365C2semidirect
24. #20288147C2semidirect
25. #20288146C2semidirect
26. #20288106C2semidirect
27. #20288098C2semidirect
28. C4×#13133265C2semidirect
29. #20287924C2semidirect
30. #519×D53C2semidirect
31. C53×#3523C2semidirect
35. #16811358C22semidirect
36. #16811358C22semidirect
37. #16811357C22semidirect
38. Q8×Dic106C22semidirect
39. #16811353C22semidirect
40. #16811351C22semidirect
41. #16811350C22semidirect
42. #16811350C22semidirect
43. #16811350C22semidirect
44. #16811349C22semidirect
45. #16811349C22semidirect
46. #16811348C22semidirect
47. #16811347C22semidirect
48. #16811347C22semidirect
51. #16811345C22semidirect
52. #16811345C22semidirect
53. #16811345C22semidirect
56. #16811344C22semidirect
57. #16811341C22semidirect
58. #16811341C22semidirect
60. #16811340C22semidirect
67. #16811331C22semidirect
68. #16811329C22semidirect
69. #16811328C22semidirect
78. #16811314C22semidirect
79. #16811313C22semidirect
80. #16811311C22semidirect
84. #16811305C22semidirect
85. #16811305C22semidirect
86. #16811295C22semidirect
87. #16811294C22semidirect
90. #16811288C22semidirect
99. #16811284C22semidirect
100. #16811284C22semidirect
103. #16811283C22semidirect
104. #16811283C22semidirect
109. #16811247C22semidirect
112. #16811246C22semidirect
115. #16811245C22semidirect
116. #16811244C22semidirect
118. #16811243C22semidirect
121. #16811239C22semidirect
124. #16811234C22semidirect
125. #16811233C22semidirect
127. #16811232C22semidirect
128. #16811232C22semidirect
129. #16811231C22semidirect
153. #16811179C22semidirect
154. #16811178C22semidirect
156. #16811177C22semidirect
157. #16811177C22semidirect
158. #16811175C22semidirect
163. #16811160C22semidirect
164. #16811159C22semidirect
168. #16811158C22semidirect
170. #16811157C22semidirect
174. #16811156C22semidirect
181. #16811151C22semidirect
188. #16811105C22semidirect
189. #16811105C22semidirect
191. #16811104C22semidirect
193. #16811103C22semidirect
195. #16811101C22semidirect
204. #16811099C22semidirect
205. #16811099C22semidirect
208. C4×#11719949C22semidirect
209. C4×#11719949C22semidirect
211. C4×#11719945C22semidirect
213. #16811091C22semidirect
214. C2×Q8×Dic53C22semidirect
219. C4×Q8×D53C22semidirect
220. C4×Q8×D53C22semidirect
223. C53×#557C22semidirect
224. C53×#557C22semidirect
227. C53×#552C22semidirect
230. D4×Q8×C53C22semidirect
232. C53×#541C22semidirect
233. C53×#533C22semidirect
236. C53×#519C22semidirect
237. C2×C4×Q8×C53C22semidirect
996. #3523D53semidirect
1045. #557C2×D53semidirect
1046. #557C2×D53semidirect
1088. #552C2×D53semidirect
1100. D4×Q8C2×D53semidirect
1138. #541C2×D53semidirect
1167. #533C2×D53semidirect
1217. #519C2×D53semidirect
1233. C2×C4×Q8C2×D53semidirect
1236. C53#62850semidirect

Maximal subgroups

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

subgroupindex
#202888272
#202888262
#202888212
#202888202
#202888082
#202888072
#202888022
#202887272
#202887262
#202887252
#202887242
#202887092
#202887082
#202887072
#202887062
#202885812
#202885742
#202885222
#202884852
#202884332
#202884292
#202883652
#202881472
#202881462
#202881062
#202880982
C4×#131332652
#202879242
#519×D532
C53×#35232
#6285053