Finite Group Databasebeta

← #7698323

Subgroups — #7698323

Order 512.

5167 conjugacy classes of subgroups.

The subgroup lattice has 1362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59953C213yesmaximal, complemented
2#59750C213yesmaximal, complemented
3#59640C213yesmaximal, complemented
4#52270C213yesmaximal, complemented
5#45382C213yesmaximal, complemented
6#45208C213yesmaximal, complemented
7#45122C213yesmaximal, complemented
8#45052C213yesmaximal, complemented
9#45020C213yesmaximal, complemented
10#44925C213yesmaximal, complemented
11#39507C213yesmaximal, complemented
12#39502C213yesmaximal, complemented
13#38290C213yesmaximal, complemented
14#38288C213yesmaximal, complemented
15#38286C213yesmaximal, complemented
16#38285C213yesmaximal, complemented
17#36583C211yesmaximal, characteristic, complemented
18#36467C211yesmaximal, characteristic, complemented
19#36466C211yesmaximal, characteristic, complemented
20#36049C211yesmaximal, characteristic, complemented
21#36029C211yesmaximal, characteristic, complemented
22#36018C211yesmaximal, characteristic, complemented
23#35854C211yesmaximal, characteristic, complemented
24#35831C211yesmaximal, characteristic, complemented
25#35831C211yesmaximal, characteristic, complemented
26#34313C211yesmaximal, characteristic, complemented
27#34312C211yesmaximal, characteristic, complemented
28#34263C211yesmaximal, characteristic, complemented
29#34263C211yesmaximal, characteristic, complemented
30#34263C211yesmaximal, characteristic, complemented
31#34262C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#550C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#520C2211yescharacteristic
41C2×#520C2211yescharacteristic
42C2×#520C2211yescharacteristic
43C2×#519C2211yescharacteristic
44#2861C2213yes—
45#2859C2213yes—
46#2858C2213yes—
47#2809C2213yes—
48#2808C2213yes—
49#2808C2213yes—
50#2803C2213yes—
51#2803C2213yes—
52#2803C2213yes—
53#2803C2213yes—
54#2803C2216yes—
55#2803C2216yes—
56#2803C2216yes—
57#2803C2216yes—
58#2795C2213yes—
59#2795C2213yes—
60#2784C2216yes—
61#2783C2211yescharacteristic
62#2783C2213yes—
63#2783C2213yes—
64#2783C2213yes—
65#2783C2216yes—
66#2781C2216yes—
67#2756C2216yes—
68#2744C2216yes—
69#2737C2216yes—
70#2733C2213yes—
71#2731C2213yes—
72#2731C2213yes—
73#2699C2216yes—
74#2686C2216yes—
75#2686C2216yes—
76#2641C2213yes—
77#2640C2213yes—
78#2620C2213yes—
79#2620C2213yes—
80#2619C2213yes—
81#2619C2213yes—
82#2610C2216yes—
83#2609C2216yes—
84#2592C2213yes—
85#2592C2213yes—
86#2584C2213yes—
87#2584C2213yes—
88#2574C2216yes—
89#2563C2213yes—
90#2562C2213yes—
91#2562C2213yes—
92#2555C2216yes—
93#2552C2213yes—
94#2551C2213yes—
95#2550C2213yes—
96#2550C2213yes—
97#2548C2213yes—
98#2548C2213yes—
99#2548C2213yes—
100#2547C2213yes—
101#2544C2213yes—
102#2544C2213yes—
103#2541C2213yes—
104#2537C2213yes—
105#2537C2213yes—
106#2536C2213yes—
107#2535C2213yes—
108#2531C2216yes—
109#2526C2216yes—
110#2526C2216yes—
111#2518C2216yes—
112#2518C2216yes—
113#2500C2216yes—
114#2492C2213yes—
115#2491C2213yes—
116#2491C2213yes—
117#2491C2216yes—
118#2491C2213yes—
119#2490C2213yes—
120#2490C2213yes—
121#2490C2213yes—
122#2490C2213yes—
123#2490C2213yes—
124#2490C2213yes—
125#2490C2213yes—
126#2490C2213yes—
127#2490C2213yes—
128#2489C2213yes—
129#2489C2213yes—
130#2489C2213yes—
131#2485C2216yes—
132#2485C2216yes—
133#2476C2216yes—
134#2476C2216yes—
135#2474C2216yes—
136#2459C2216yes—
137#2459C2216yes—
138#2428C2213yes—
139#2428C2213yes—
140#2428C2213yes—
141#2428C2213yes—
142#2427C2213yes—
143#2427C2213yes—
144#2426C2213yes—
145#2426C2213yes—
146#2420C2216yes—
147#2417C2213yes—
148#2417C2213yes—
149#2416C2213yes—
150#2416C2213yes—
151#2416C2213yes—
152#2416C2213yes—
153#2414C2216yes—
154#2414C2216yes—
155#2414C2213yes—
156#2414C2213yes—
157#2398C2213yes—
158#2398C2213yes—
159#2392C2213yes—
160#2392C2213yes—
161#2392C2213yes—
162#2392C2213yes—
163#2367C2213yes—
164#2366C2213yes—
165#2363C2213yes—
166#2363C2216yes—
167#2361C2213yes—
168#2361C2213yes—
169#2360C2213yes—
170#2357C2213yes—
171#2357C2213yes—
172#2357C2213yes—
173#2356C2213yes—
174#2355C2213yes—
175#2354C2213yes—
176#2354C2213yes—
177#2354C2213yes—
178#2352C2213yes—
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185D4×C4⋊C4C2213yes—
186#2347C2213yes—
187#2346C2213yes—
188#2345C2213yes—
189#2345C2213yes—
190#2345C2213yes—
191#2344C2213yes—
192#2344C2213yes—
193#2344C2213yes—
194#2341C2211yescharacteristic
195#2341C2211yescharacteristic
196#2341C2211yescharacteristic
197#2341C2211yescharacteristic
198#2341C2211yescharacteristic
199#2341C2211yescharacteristic
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204Q8×C22⋊C4C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206#2324C2213yes—
207#2324C2213yes—
208#2324C2213yes—
209#2323C2213yes—
210#2320C2213yes—
211#2319C2213yes—
212#2319C2213yes—
213#2319C2213yes—
214#2314C2213yes—
215#2314C2213yes—
216#2314C2213yes—
217#2314C2213yes—
218C4×C4⋊Q8C2213yes—
219C4×#127C2213yes—
220C4×#124C2213yes—
221C4×#124C2213yes—
222C4×#124C2213yes—
223#2298C2213yes—
224#2298C2213yes—
225#2298C2213yes—
226#2298C2213yes—
227#2295C2213yes—
228#2293C2213yes—
229#2293C2213yes—
230#2293C2213yes—
231#2293C2213yes—
232#2293C2213yes—
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C22×#41C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242#557—44no—
243#557—44no—
244#550—28no—
245#550—44no—
246#550—44no—
247#548—28no—
248#548—44no—
249#548—44no—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×#127C2313yes—
254C2×#127C2313yes—
255C2×#127C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#124C2313yes—
261C2×#124C2313yes—
262C2×#124C2313yes—
263C2×#124C2313yes—
264C2×#124C2313yes—
265C2×#124C2316yes—
266C2×#124C2316yes—
267C2×C22⋊Q8C2313yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×#121C2313yes—
271C2×#121C2313yes—
272C2×#121C2313yes—
273C2×#121C2316yes—
274C2×#121C2313yes—
275C2×#121C2313yes—
276C2×#121C2313yes—
277C2×#121C2313yes—
278C2×#121C2313yes—
279C2×#121C2313yes—
280C2×#121C2316yes—
281C2×#121C2316yes—
282C2×#121C2316yes—
283#520—28no—
284#520—28no—
285#520—28no—
286#519—28no—
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2313yes—
299C2×C4×Q8C2313yes—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2311yescharacteristic
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2313yes—
306C2×C4×D4C2313yes—
307C2×C4×D4C2313yes—
308C2×C4×D4C2313yes—
309C2×C4×D4C2313yes—
310C2×C4×D4C2313yes—
311C2×C4×D4C2313yes—
312C2×C4×D4C2313yes—
313C2×C4×D4C2313yes—
314C2×C4×D4C2316yes—
315C2×C4×D4C2316yes—
316C2×#117C2313yes—
317C2×#117C2313yes—
318C2×#117C2313yes—
319C2×#117C2313yes—
320C2×#117C2313yes—
321C2×#117C2316yes—
322C2×#117C2316yes—
323C2×#117C2316yes—
324C22×C4⋊C4C2313yes—
325C22×C4⋊C4C2313yes—
326C22×C4⋊C4C2313yes—
327#400C2313yes—
328#400C2316yes—
329#400C2311yescharacteristic
330#400C2313yes—
331#400C2313yes—
332#398C2313yes—
333#398C2316yes—
334#398C2316yes—
335#398C2311yescharacteristic
336#398C2313yes—
337#398C2313yes—
338#397C2313yes—
339#397C2316yes—
340#397C2316yes—
341#397C2316yes—
342#397C2311yescharacteristic
343#397C2313yes—
344#397C2313yes—
345#397C2313yes—
346#397C2311yescharacteristic
347#397C2313yes—
348#397C2313yes—
349#397C2316yes—
350#397C2316yes—
351#396C2313yes—
352#396C2313yes—
353#396C2316yes—
354#396C2313yes—
355#396C2313yes—
356#396C2316yes—
357#396C2311yescharacteristic
358#396C2311yescharacteristic
359#396C2313yes—
360#396C2313yes—
361#395C2316yes—
362#395C2316yes—
363#394C2316yes—
364#394C2316yes—
365#394C2316yes—
366#394C2316yes—
367#394C2313yes—
368#394C2316yes—
369#394C2316yes—
370#394C2316yes—
371#394C2316yes—
372#394C2316yes—
373#394C2316yes—
374#394C2313yes—
375#394C2316yes—
376#394C2313yes—
377#394C2313yes—
378#394C2313yes—
379#394C2313yes—
380#394C2313yes—
381#394C2313yes—
382#394C2313yes—
383#394C2313yes—
384#394C2313yes—
385#394C2313yes—
386#394C2313yes—
387#394C2313yes—
388#394C2313yes—
389#394C2313yes—
390#394C2316yes—
391#394C2316yes—
392#393C2313yes—
393#393C2316yes—
394#393C2316yes—
395#393C2313yes—
396#393C2313yes—
397#393C2313yes—
398#392C2316yes—
399#392C2313yes—
400#392C2316yes—
401#392C2316yes—
402#392C2313yes—
403#392C2313yes—
404#392C2313yes—
405#391C2313yes—
406#391C2313yes—
407#391C2313yes—
408#391C2313yes—
409#391C2313yes—
410#391C2313yes—
411#391C2313yes—
412#391C2313yes—
413#391C2313yes—
414#391C2313yes—
415#390C2313yes—
416#390C2316yes—
417#390C2313yes—
418#390C2313yes—
419#390C2316yes—
420#390C2313yes—
421#390C2313yes—
422#390C2313yes—
423#390C2313yes—
424#390C2313yes—
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2313yes—
432#390C2313yes—
433#390C2313yes—
434#390C2313yes—
435#390C2313yes—
436#390C2313yes—
437#390C2316yes—
438#390C2316yes—
439#390C2316yes—
440#390C2313yes—
441#390C2313yes—
442#390C2316yes—
443#390C2316yes—
444#390C2313yes—
445#390C2313yes—
446#389C2311yescharacteristic
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2316yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2316yes—
465#389C2316yes—
466#389C2313yes—
467#389C2313yes—
468#389C2311yescharacteristic
469#388C2313yes—
470#388C2316yes—
471#388C2316yes—
472#388C2316yes—
473#388C2313yes—
474#388C2316yes—
475#388C2316yes—
476#388C2316yes—
477#388C2316yes—
478#388C2316yes—
479#388C2316yes—
480#388C2316yes—
481#388C2316yes—
482#388C2313yes—
483#388C2313yes—
484#388C2313yes—
485#388C2316yes—
486#388C2316yes—
487#388C2313yes—
488#388C2313yes—
489#388C2313yes—
490#388C2316yes—
491#388C2316yes—
492#388C2313yes—
493#388C2313yes—
494#388C2313yes—
495#388C2316yes—
496#388C2316yes—
497#388C2313yes—
498#388C2313yes—
499#388C2313yes—
500#388C2313yes—
501#388C2313yes—
502#388C2313yes—
503#388C2313yes—
504#388C2313yes—
505#388C2313yes—
506#388C2313yes—
507#388C2313yes—
508#388C2316yes—
509#388C2313yes—
510#388C2311yescharacteristic
511#388C2313yes—
512#388C2313yes—
513#388C2313yes—
514#388C2313yes—
515#388C2313yes—
516#388C2311yescharacteristic
517#388C2313yes—
518#388C2311yescharacteristic
519#387C2313yes—
520#387C2313yes—
521#387C2313yes—
522#387C2316yes—
523#387C2316yes—
524#387C2316yes—
525#387C2316yes—
526#387C2316yes—
527#387C2316yes—
528#387C2313yes—
529#387C2313yes—
530#387C2313yes—
531#387C2313yes—
532#387C2313yes—
533#387C2313yes—
534#387C2313yes—
535#387C2313yes—
536#387C2313yes—
537#387C2313yes—
538#387C2311yescharacteristic
539#387C2311yescharacteristic
540#387C2311yescharacteristic
541#386C2316yes—
542#386C2316yes—
543#386C2316yes—
544#386C2316yes—
545#386C2316yes—
546#386C2316yes—
547#386C2316yes—
548#386C2316yes—
549#386C2316yes—
550#385C2316yes—
551#385C2316yes—
552#385C2316yes—
553#384C2313yes—
554#384C2313yes—
555#384C2313yes—
556#384C2313yes—
557#383C2316yes—
558#382C2316yes—
559#382C2313yes—
560#382C2313yes—
561#382C2313yes—
562#382C2316yes—
563#382C2313yes—
564#382C2311yescharacteristic
565#381C2316yes—
566#381C2316yes—
567#381C2316yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2316yes—
581#380C2316yes—
582#380C2316yes—
583#380C2316yes—
584#380C2316yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2316yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C22⋊C4C2316yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2316yes—
621C4×C22⋊C4C2316yes—
622C4×C22⋊C4C2316yes—
623C4×C22⋊C4C2316yes—
624#376C2313yes—
625#376C2313yes—
626#376C2316yes—
627C43C2313yes—
628C43C2313yes—
629C43C2313yes—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41—24no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41—24no—
639C22×Q8—24no—
640C22×Q8—24no—
641C22×Q8—24no—
642C22×Q8C2413yes—
643C22×Q8C2413yes—
644C22×Q8C2413yes—
645C22×Q8C2411yescharacteristic
646C22×D4C2413yes—
647C22×D4C2413yes—
648C22×D4C2413yes—
649C22×D4C2413yes—
650C22×D4C2413yes—
651C22×D4C2416yes—
652C22×D4C2413yes—
653C22×D4C2413yes—
654C22×D4C2413yes—
655C22×D4C2413yes—
656C22×D4C2416yes—
657C22×D4C2416yes—
658C23×C4C2413yes—
659C23×C4C2413yes—
660C23×C4C2413yes—
661C23×C4C2413yes—
662C23×C4C2416yes—
663C23×C4C2416yes—
664C23×C4C2416yes—
665C4⋊Q8—46no—
666C4⋊Q8—46no—
667C4⋊Q8—46no—
668#127—212no—
669#127—46no—
670#127—46no—
671#125—46no—
672#125—46no—
673#125—46no—
674#125—46no—
675#124—212no—
676#124—46no—
677#124—46no—
678#124—46no—
679#124—46no—
680#124—86no—
681#124—86no—
682C22⋊Q8—212no—
683C22⋊Q8—46no—
684C22⋊Q8—46no—
685#121—212no—
686#121—212no—
687#121—212no—
688#121—412no—
689#121—46no—
690#121—46no—
691#121—46no—
692#121—46no—
693#121—46no—
694#121—46no—
695#121—86no—
696#121—86no—
697#121—86no—
698C4×Q8—24no—
699C4×Q8—24no—
700C4×Q8—24no—
701C4×Q8—24no—
702C4×Q8—24no—
703C4×Q8—24no—
704C4×Q8—24no—
705C4×Q8—24no—
706C4×Q8—24no—
707C4×Q8—212no—
708C4×Q8—212no—
709C4×Q8—46no—
710C4×Q8—46no—
711C4×Q8#4118yes—
712C4×Q8#4118yes—
713C4×D4—212no—
714C4×D4—212no—
715C4×D4—212no—
716C4×D4—212no—
717C4×D4—212no—
718C4×D4—212no—
719C4×D4—212no—
720C4×D4—212no—
721C4×D4—46no—
722C4×D4—46no—
723C4×D4—46no—
724C4×D4—46no—
725C4×D4—86no—
726C4×D4—86no—
727#117—212no—
728#117—212no—
729#117—212no—
730#117—212no—
731#117—212no—
732#117—86no—
733#117—86no—
734#117—86no—
735C2×C4⋊C4—212no—
736C2×C4⋊C4—212no—
737C2×C4⋊C4—212no—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2416yes—
763C2×C4⋊C4C2416yes—
764C2×C4⋊C4C2416yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2416yes—
778C2×C4⋊C4C2416yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2411yescharacteristic
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2411yescharacteristic
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2416yes—
800C2×C22⋊C4C2411yescharacteristic
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2416yes—
805C2×C22⋊C4C2416yes—
806C2×C22⋊C4C2416yes—
807C2×C22⋊C4C2411yescharacteristic
808C2×C22⋊C4C2411yescharacteristic
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2416yes—
818C2×C22⋊C4C2416yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2416yes—
823C2×C22⋊C4C2416yes—
824C2×C22⋊C4C2416yes—
825C2×C22⋊C4C2416yes—
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2416yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2413yes—
835C2×C22⋊C4C2411yescharacteristic
836C2×C22⋊C4C2413yes—
837C2×C22⋊C4C2411yescharacteristic
838C2×C22⋊C4C2413yes—
839C2×C22⋊C4C2413yes—
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2416yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2416yes—
847C2×C42C2413yes—
848C2×C42C2413yes—
849C2×C42C2413yes—
850C2×C42C2413yes—
851C2×C42C2413yes—
852C2×C42C2411yescharacteristic
853C2×C42C2413yes—
854C2×C42C2413yes—
855C2×C42C2413yes—
856C2×C42C2416yes—
857C2×C42C2416yes—
858C2×C42C2413yes—
859C2×C42C2413yes—
860C2×C42C2413yes—
861C2×C42C2413yes—
862C2×C42C2413yes—
863C2×C42C2411yescharacteristic
864C2×C42C2411yescharacteristic
865C2×C42C2413yes—
866C2×C42C2413yes—
867C2×C42C2413yes—
868#95C2411yescharacteristic
869#95C2411yescharacteristic
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2416yes—
879#95C2416yes—
880#95C2416yes—
881#95C2411yescharacteristic
882#95C2411yescharacteristic
883#95C2411yescharacteristic
884#95C2411yescharacteristic
885#95C2411yescharacteristic
886#95C2413yes—
887#95C2411yescharacteristic
888#95C2411yescharacteristic
889#95C2411yescharacteristic
890#95C2411yescharacteristic
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2416yes—
906#95C2416yes—
907#95C2413yes—
908#95C2413yes—
909#95C2413yes—
910#95C2416yes—
911#95C2416yes—
912#95C2416yes—
913#95C2411yescharacteristic
914#95C2411yescharacteristic
915#95C2411yescharacteristic
916#95C2416yes—
917#95C2413yes—
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921C24C2511yescharacteristic
922C24C2513yes—
923C24C2513yes—
924C24C2513yes—
925#41—416no—
926#41—416no—
927#41—416no—
928C2×Q8—26no—
929C2×Q8—26no—
930C2×Q8—26no—
931C2×Q8—26no—
932C2×Q8—43no—
933C2×Q8—43no—
934C2×Q8—43no—
935C2×Q8—43no—
936C2×Q8—43no—
937C2×Q8—416no—
938C2×Q8C2×#4114yes—
939C2×Q8C2×#4114yes—
940C2×Q8H(5,𝔽2)14yes—
941C2×D4—26no—
942C2×D4—26no—
943C2×D4—26no—
944C2×D4—26no—
945C2×D4—26no—
946C2×D4—26no—
947C2×D4—26no—
948C2×D4—26no—
949C2×D4—212no—
950C2×D4—26no—
951C2×D4—26no—
952C2×D4—26no—
953C2×D4—26no—
954C2×D4—43no—
955C2×D4—43no—
956C2×D4—43no—
957C2×D4—43no—
958C2×D4—43no—
959C2×D4—43no—
960C2×D4—46no—
961C2×D4—46no—
962C2×D4—43no—
963C2×D4—43no—
964C2×D4—43no—
965C2×D4—43no—
966C2×D4—43no—
967C2×D4—43no—
968C2×D4—43no—
969C2×D4—43no—
970C2×D4—43no—
971C2×D4—46no—
972C2×D4—46no—
973C2×D4—46no—
974C2×D4—46no—
975C2×D4—46no—
976C2×D4—46no—
977C22×C4—26no—
978C22×C4—26no—
979C22×C4—26no—
980C22×C4—26no—
981C22×C4—26no—
982C22×C4—26no—
983C22×C4—26no—
984C22×C4—26no—
985C22×C4—26no—
986C22×C4—26no—
987C22×C4—26no—
988C22×C4—26no—
989C22×C4—212no—
990C22×C4—212no—
991C22×C4—212no—
992C22×C4—46no—
993C22×C4—46no—
994C22×C4—46no—
995C22×C4—46no—
996C22×C4—46no—
997C22×C4—46no—
998C22×C4C2511yescharacteristic
999C22×C4C2511yescharacteristic
1000C22×C4C2513yes—
1001C22×C4C2511yescharacteristic
1002C22×C4C2513yes—
1003C22×C4C2511yescharacteristic
1004C22×C4C2511yescharacteristic
1005C22×C4C2511yescharacteristic
1006C22×C4C2511yescharacteristic
1007C22×C4C2513yes—
1008C22×C4C2513yes—
1009C22×C4C2513yes—
1010C22×C4C2511yescharacteristic
1011C22×C4C2513yes—
1012C22×C4C2513yes—
1013C22×C4C2511yescharacteristic
1014C22×C4C2513yes—
1015C22×C4C2513yes—
1016C22×C4C2513yes—
1017C22×C4C2511yescharacteristic
1018C22×C4C2511yescharacteristic
1019C22×C4C2511yescharacteristic
1020C22×C4C2513yes—
1021C22×C4C2513yes—
1022C22×C4C2511yescharacteristic
1023C22×C4C2511yescharacteristic
1024C22×C4C2513yes—
1025C4⋊C4—26no—
1026C4⋊C4—26no—
1027C4⋊C4—26no—
1028C4⋊C4—26no—
1029C4⋊C4—26no—
1030C4⋊C4—26no—
1031C4⋊C4—22no—
1032C4⋊C4—22no—
1033C4⋊C4—22no—
1034C4⋊C4—26no—
1035C4⋊C4—26no—
1036C4⋊C4—26no—
1037C4⋊C4—22no—
1038C4⋊C4—26no—
1039C4⋊C4—26no—
1040C4⋊C4—26no—
1041C4⋊C4—26no—
1042C4⋊C4—26no—
1043C4⋊C4—26no—
1044C4⋊C4—26no—
1045C4⋊C4—22no—
1046C4⋊C4—41no—
1047C4⋊C4—43no—
1048C4⋊C4—41no—
1049C4⋊C4—43no—
1050C4⋊C4—43no—
1051C4⋊C4—43no—
1052C4⋊C4—46no—
1053C4⋊C4—46no—
1054C4⋊C4—46no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—43no—
1058C4⋊C4—43no—
1059C4⋊C4—43no—
1060C4⋊C4—41no—
1061C4⋊C4—41no—
1062C4⋊C4—43no—
1063C4⋊C4—43no—
1064C4⋊C4—43no—
1065C4⋊C4—43no—
1066C4⋊C4—43no—
1067C4⋊C4—46no—
1068C4⋊C4—46no—
1069C4⋊C4—43no—
1070C4⋊C4—43no—
1071C4⋊C4C2×#41112yes—
1072C4⋊C4C2×#41112yes—
1073C22⋊C4—26no—
1074C22⋊C4—22no—
1075C22⋊C4—26no—
1076C22⋊C4—26no—
1077C22⋊C4—26no—
1078C22⋊C4—26no—
1079C22⋊C4—26no—
1080C22⋊C4—26no—
1081C22⋊C4—22no—
1082C22⋊C4—26no—
1083C22⋊C4—26no—
1084C22⋊C4—26no—
1085C22⋊C4—212no—
1086C22⋊C4—26no—
1087C22⋊C4—22no—
1088C22⋊C4—41no—
1089C22⋊C4—41no—
1090C22⋊C4—43no—
1091C22⋊C4—43no—
1092C22⋊C4—43no—
1093C22⋊C4—46no—
1094C22⋊C4—43no—
1095C22⋊C4—43no—
1096C22⋊C4—43no—
1097C22⋊C4—43no—
1098C22⋊C4—46no—
1099C22⋊C4—46no—
1100C22⋊C4—46no—
1101C22⋊C4—41no—
1102C22⋊C4—41no—
1103C22⋊C4—43no—
1104C22⋊C4—43no—
1105C22⋊C4—43no—
1106C22⋊C4—43no—
1107C22⋊C4—43no—
1108C22⋊C4—43no—
1109C22⋊C4—43no—
1110C22⋊C4—43no—
1111C22⋊C4—46no—
1112C22⋊C4—46no—
1113C22⋊C4—46no—
1114C22⋊C4—46no—
1115C22⋊C4—46no—
1116C22⋊C4—43no—
1117C22⋊C4—43no—
1118C22⋊C4—43no—
1119C22⋊C4—46no—
1120C22⋊C4—43no—
1121C22⋊C4—43no—
1122C22⋊C4—43no—
1123C22⋊C4—43no—
1124C22⋊C4—43no—
1125C22⋊C4—43no—
1126C22⋊C4—46no—
1127C22⋊C4—43no—
1128C22⋊C4—43no—
1129C42—26no—
1130C42—26no—
1131C42—26no—
1132C42—26no—
1133C42—212no—
1134C42—26no—
1135C42—26no—
1136C42—26no—
1137C42—26no—
1138C42—26no—
1139C42—22no—
1140C42—41no—
1141C42—43no—
1142C42—41no—
1143C42—43no—
1144C42—43no—
1145C42—43no—
1146C42—46no—
1147C42—46no—
1148C42—43no—
1149C42—43no—
1150C42—43no—
1151C42—43no—
1152C42—43no—
1153C42C2×#41112yes—
1154C42C2×#41112yes—
1155C23—21no—
1156C23—23no—
1157C23—23no—
1158C23—23no—
1159C23—23no—
1160C23—21no—
1161C23—23no—
1162C23—23no—
1163C23—23no—
1164C23—23no—
1165C23—21no—
1166C23—23no—
1167C23—21no—
1168C23—23no—
1169C23—23no—
1170C23—23no—
1171C23—23no—
1172C23—23no—
1173C23—23no—
1174C23—23no—
1175C23—23no—
1176C23—21no—
1177C23—21no—
1178C23—23no—
1179C23—23no—
1180C23—21no—
1181C23—23no—
1182C23—23no—
1183C23C2611yescharacteristic
1184Q8—412no—
1185Q8—86no—
1186Q8—86no—
1187Q8#555116yes—
1188D4—412no—
1189D4—412no—
1190D4—412no—
1191D4—412no—
1192D4—812no—
1193D4—86no—
1194D4—86no—
1195D4—86no—
1196D4—86no—
1197D4—86no—
1198D4—166no—
1199D4—166no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—23no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—23no—
1206C2×C4—23no—
1207C2×C4—23no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—23no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—23no—
1231C2×C4—23no—
1232C2×C4—23no—
1233C2×C4—23no—
1234C2×C4—23no—
1235C2×C4—21no—
1236C2×C4—23no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—23no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—23no—
1253C2×C4—23no—
1254C2×C4—23no—
1255C2×C4—23no—
1256C2×C4—23no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—23no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—23no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—23no—
1271C2×C4—23no—
1272C2×C4—21no—
1273C2×C4—412no—
1274C2×C4—412no—
1275C2×C4—412no—
1276C2×C4—412no—
1277C2×C4—812no—
1278C2×C4—812no—
1279C2×C4—812no—
1280C2×C4C22×#4116yes—
1281C2×C4C22×#4112yes—
1282C2×C4C22×#4112yes—
1283C2×C4C22×#4116yes—
1284C2×C4C22×#4116yes—
1285C2×C4C22×#4116yes—
1286C2×C4C2×H(5,𝔽2)16yes—
1287C2×C4#58512yes—
1288C22—43no—
1289C22—43no—
1290C22—43no—
1291C22—41no—
1292C22—43no—
1293C22—43no—
1294C22—43no—
1295C22—41no—
1296C22—41no—
1297C22—43no—
1298C22—43no—
1299C22—43no—
1300C22—43no—
1301C22—43no—
1302C22—41no—
1303C22—43no—
1304C22—43no—
1305C22—43no—
1306C22—41no—
1307C22—43no—
1308C22—41no—
1309C22—43no—
1310C22—43no—
1311C22—43no—
1312C22—41no—
1313C22—43no—
1314C22—43no—
1315C22—43no—
1316C22C23×#4111yescharacteristic
1317C22C23×#4111yescharacteristic
1318C22C22×H(5,𝔽2)11yescharacteristic
1319C22C2×#58511yescharacteristic
1320C22H(7,𝔽2)11yescharacteristic
1321C22H(7,𝔽2)11yescharacteristic
1322C222−1+611yescharacteristic
1323C4—22no—
1324C4—26no—
1325C4—22no—
1326C4—26no—
1327C4—22no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—43no—
1332C4—41no—
1333C4—41no—
1334C4—43no—
1335C4—41no—
1336C4—43no—
1337C4—41no—
1338C4—43no—
1339C4—43no—
1340C4—43no—
1341C4—43no—
1342C4—43no—
1343C4—43no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—43no—
1349C4C2×#555112yes—
1350C2—83no—
1351C2—83no—
1352C2—83no—
1353C2—81no—
1354C2C22×#55511yescharacteristic
1355C2#6285111yescharacteristic
1356C2#6285811yescharacteristic
1357C2#6289911yescharacteristic
1358C2#6300711yescharacteristic
1359C2#6301011yescharacteristic
1360C2#6305211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59953C2semidirect
2. #59750C2semidirect
3. #59640C2semidirect
4. #52270C2semidirect
5. #45382C2semidirect
6. #45208C2semidirect
7. #45122C2semidirect
8. #45052C2semidirect
9. #45020C2semidirect
10. #44925C2semidirect
11. #39507C2semidirect
12. #39502C2semidirect
13. #38290C2semidirect
14. #38288C2semidirect
15. #38286C2semidirect
16. #38285C2semidirect
17. #36583C2semidirect
18. #36467C2semidirect
19. #36466C2semidirect
20. #36049C2semidirect
21. #36029C2semidirect
22. #36018C2semidirect
23. #35854C2semidirect
24. #35831C2semidirect
25. #35831C2semidirect
26. #34313C2semidirect
27. #34312C2semidirect
28. #34263C2semidirect
29. #34263C2semidirect
30. #34263C2semidirect
31. #34262C2semidirect

Maximal subgroups

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

subgroupindex
#599532
#597502
#596402
#522702
#453822
#452082
#451222
#450522
#450202
#449252
#395072
#395022
#382902
#382882
#382862
#382852
#365832
#364672
#364662
#360492
#360292
#360182
#358542
#358312
#343132
#343122
#342632
#342622