Finite Group Databasebeta

← #7658437

Subgroups — #7658437

Order 512.

5001 conjugacy classes of subgroups.

The subgroup lattice has 1388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42759C213yesmaximal, complemented
2#42752C213yesmaximal, complemented
3#42726C213yesmaximal, complemented
4#42719C213yesmaximal, complemented
5#42705C213yesmaximal, complemented
6#42688C213yesmaximal, complemented
7#42668C213yesmaximal, complemented
8#42658C213yesmaximal, complemented
9#42641C213yesmaximal, complemented
10#42633C213yesmaximal, complemented
11#42629C213yesmaximal, complemented
12#42620C213yesmaximal, complemented
13#37627C213yesmaximal, complemented
14#37594C213yesmaximal, complemented
15#37570C213yesmaximal, complemented
16#36692C213yesmaximal, complemented
17#36018C211yesmaximal, characteristic, complemented
18#35996C211yesmaximal, characteristic, complemented
19#35927C211yesmaximal, characteristic, complemented
20#35868C211yesmaximal, characteristic, complemented
21#35831C211yesmaximal, characteristic, complemented
22#35831C211yesmaximal, characteristic, complemented
23#35801C211yesmaximal, characteristic, complemented
24#35771C211yesmaximal, characteristic, complemented
25#35771C211yesmaximal, characteristic, complemented
26#35737C211yesmaximal, characteristic, complemented
27#35723C211yesmaximal, characteristic, complemented
28#35723C211yesmaximal, characteristic, complemented
29#34312C211yesmaximal, characteristic, complemented
30#34311C211yesmaximal, characteristic, complemented
31#34263C211yesmaximal, characteristic, complemented
32C2×#550C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#548C2211yescharacteristic
42C2×#520C2211yescharacteristic
43C2×#520C2211yescharacteristic
44C2×#519C2211yescharacteristic
45C2×#519C2211yescharacteristic
46C2×#519C2211yescharacteristic
47#2837C2213yes—
48#2837C2213yes—
49#2837C2213yes—
50#2837C2213yes—
51#2837C2216yes—
52#2836C2213yes—
53#2836C2213yes—
54#2836C2213yes—
55#2836C2213yes—
56#2829C2213yes—
57#2829C2211yescharacteristic
58#2829C2213yes—
59#2829C2213yes—
60#2828C2213yes—
61#2828C2213yes—
62#2828C2213yes—
63#2828C2213yes—
64#2803C2216yes—
65#2800C2216yes—
66#2797C2216yes—
67#2793C2216yes—
68#2791C2216yes—
69#2786C2216yes—
70#2748C2216yes—
71#2743C2216yes—
72#2741C2216yes—
73#2741C2216yes—
74#2740C2216yes—
75#2740C2216yes—
76#2711C2216yes—
77#2707C2216yes—
78#2703C2216yes—
79#2699C2216yes—
80#2667C2216yes—
81#2661C2216yes—
82#2658C2213yes—
83#2654C2216yes—
84#2651C2216yes—
85#2651C2216yes—
86#2651C2216yes—
87#2649C2216yes—
88#2649C2216yes—
89#2648C2216yes—
90#2648C2216yes—
91#2647C2213yes—
92#2629C2216yes—
93#2625C2213yes—
94#2625C2213yes—
95#2625C2213yes—
96#2624C2216yes—
97#2624C2213yes—
98#2621C2213yes—
99#2620C2213yes—
100#2620C2213yes—
101#2620C2213yes—
102#2620C2213yes—
103#2619C2213yes—
104#2570C2213yes—
105#2552C2213yes—
106#2548C2213yes—
107#2547C2213yes—
108#2545C2213yes—
109#2545C2213yes—
110#2544C2213yes—
111#2544C2213yes—
112#2542C2213yes—
113#2542C2213yes—
114#2542C2213yes—
115#2540C2213yes—
116#2540C2213yes—
117#2540C2213yes—
118#2538C2213yes—
119#2538C2213yes—
120#2537C2213yes—
121#2537C2213yes—
122#2536C2213yes—
123#2535C2213yes—
124#2522C2216yes—
125#2516C2216yes—
126#2509C2213yes—
127#2507C2213yes—
128#2506C2213yes—
129#2506C2213yes—
130#2502C2213yes—
131#2500C2213yes—
132#2499C2213yes—
133#2499C2213yes—
134#2497C2216yes—
135#2490C2216yes—
136#2486C2213yes—
137#2485C2213yes—
138#2485C2213yes—
139#2485C2213yes—
140#2476C2216yes—
141#2471C2216yes—
142#2448C2213yes—
143#2448C2213yes—
144#2447C2213yes—
145#2447C2213yes—
146#2446C2213yes—
147#2446C2213yes—
148#2446C2213yes—
149#2446C2213yes—
150#2429C2213yes—
151#2429C2213yes—
152#2428C2213yes—
153#2428C2213yes—
154#2427C2213yes—
155#2427C2213yes—
156#2427C2213yes—
157#2427C2213yes—
158#2426C2213yes—
159#2426C2213yes—
160#2426C2213yes—
161#2426C2213yes—
162#2423C2213yes—
163#2423C2213yes—
164#2423C2213yes—
165#2422C2213yes—
166#2422C2213yes—
167#2421C2213yes—
168#2421C2213yes—
169#2421C2213yes—
170#2417C2213yes—
171#2417C2213yes—
172#2417C2213yes—
173#2417C2213yes—
174#2416C2213yes—
175#2416C2213yes—
176#2415C2213yes—
177#2415C2213yes—
178#2414C2213yes—
179#2414C2213yes—
180#2414C2213yes—
181#2414C2213yes—
182#2402C2213yes—
183#2397C2213yes—
184#2395C2213yes—
185#2395C2213yes—
186#2395C2213yes—
187#2395C2213yes—
188#2392C2213yes—
189#2392C2213yes—
190#2392C2213yes—
191#2392C2213yes—
192#2392C2213yes—
193#2392C2213yes—
194#2367C2213yes—
195#2365C2213yes—
196#2363C2213yes—
197#2362C2213yes—
198#2362C2213yes—
199#2360C2213yes—
200#2357C2213yes—
201#2354C2213yes—
202#2354C2213yes—
203#2352C2213yes—
204#2351C2211yescharacteristic
205#2351C2211yescharacteristic
206#2351C2211yescharacteristic
207Q8×C4⋊C4C2211yescharacteristic
208Q8×C4⋊C4C2211yescharacteristic
209Q8×C4⋊C4C2211yescharacteristic
210Q8×C4⋊C4C2211yescharacteristic
211Q8×C4⋊C4C2211yescharacteristic
212#2345C2213yes—
213#2344C2213yes—
214#2341C2211yescharacteristic
215#2341C2211yescharacteristic
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218Q8×C22⋊C4C2211yescharacteristic
219Q8×C22⋊C4C2211yescharacteristic
220Q8×C22⋊C4C2211yescharacteristic
221Q8×C22⋊C4C2211yescharacteristic
222Q8×C22⋊C4C2211yescharacteristic
223Q8×C22⋊C4C2211yescharacteristic
224#2324C2213yes—
225#2323C2213yes—
226#2323C2213yes—
227#2323C2213yes—
228#2319C2213yes—
229#2314C2213yes—
230C4×C4⋊Q8C2213yes—
231C4×#124C2213yes—
232#2298C2213yes—
233#2293C2213yes—
234#2293C2213yes—
235#2293C2213yes—
236#2276C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242C23×Q8C2311yescharacteristic
243#550—44no—
244D4×Q8—28no—
245D4×Q8—44no—
246D4×Q8—44no—
247#548—28no—
248#548—44no—
249#548—44no—
250#548—44no—
251#548—44no—
252#548—44no—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×C4⋊Q8C2313yes—
256C2×#127C2313yes—
257C2×#125C2316yes—
258C2×#124C2313yes—
259C2×#124C2313yes—
260C2×#124C2313yes—
261C2×#124C2313yes—
262C2×#124C2313yes—
263C2×#124C2313yes—
264C2×#123C2316yes—
265C2×C22⋊Q8C2313yes—
266C2×C22⋊Q8C2313yes—
267C2×C22⋊Q8C2313yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×C22⋊Q8C2313yes—
271C2×C22⋊Q8C2313yes—
272C2×C22⋊Q8C2313yes—
273C2×C22⋊Q8C2313yes—
274C2×C22⋊Q8C2313yes—
275C2×C22⋊Q8C2313yes—
276C2×C22⋊Q8C2313yes—
277C2×#121C2313yes—
278C2×#121C2313yes—
279C2×#121C2313yes—
280C2×#121C2313yes—
281C2×#121C2313yes—
282C2×#121C2313yes—
283C2×#121C2313yes—
284C2×#121C2313yes—
285C2×#121C2316yes—
286C2×#121C2316yes—
287#520—28no—
288#520—44no—
289#519—44no—
290#519—44no—
291#519—44no—
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2313yes—
302C2×C4×Q8C2313yes—
303C2×C4×Q8C2313yes—
304C2×C4×Q8C2313yes—
305C2×C4×Q8C2313yes—
306C2×C4×Q8C2313yes—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×D4C2313yes—
309C2×C4×D4C2313yes—
310C2×C4×D4C2313yes—
311C2×C4×D4C2313yes—
312C2×C4×D4C2313yes—
313C2×C4×D4C2313yes—
314C2×C4×D4C2313yes—
315C2×C4×D4C2313yes—
316C2×C4×D4C2313yes—
317C2×C4×D4C2313yes—
318C2×C4×D4C2313yes—
319C2×C4×D4C2313yes—
320C2×C4×D4C2313yes—
321C2×C4×D4C2313yes—
322C2×#117C2313yes—
323C2×#117C2313yes—
324C2×#117C2313yes—
325C2×#117C2313yes—
326C2×#117C2313yes—
327C2×#117C2313yes—
328C2×#117C2313yes—
329C2×#117C2313yes—
330C2×#117C2316yes—
331C22×C4⋊C4C2313yes—
332C22×C4⋊C4C2313yes—
333#400C2313yes—
334#400C2313yes—
335#400C2313yes—
336#400C2313yes—
337#400C2313yes—
338#400C2313yes—
339#400C2313yes—
340#400C2313yes—
341#400C2316yes—
342#400C2316yes—
343#400C2316yes—
344#399C2311yescharacteristic
345#399C2313yes—
346#399C2313yes—
347#399C2313yes—
348#399C2313yes—
349#399C2313yes—
350#399C2313yes—
351#399C2313yes—
352#399C2316yes—
353#399C2316yes—
354#399C2316yes—
355#399C2316yes—
356#398C2316yes—
357#398C2311yescharacteristic
358#398C2313yes—
359#398C2313yes—
360#398C2313yes—
361#398C2313yes—
362#398C2313yes—
363#398C2313yes—
364#398C2313yes—
365#398C2313yes—
366#398C2313yes—
367#398C2313yes—
368#398C2313yes—
369#398C2313yes—
370#398C2313yes—
371#398C2316yes—
372#398C2316yes—
373#398C2316yes—
374#398C2316yes—
375#398C2316yes—
376#397C2313yes—
377#397C2313yes—
378#397C2313yes—
379#397C2313yes—
380#397C2313yes—
381#397C2313yes—
382#397C2313yes—
383#397C2313yes—
384#397C2311yescharacteristic
385#397C2313yes—
386#397C2313yes—
387#397C2313yes—
388#397C2311yescharacteristic
389#397C2313yes—
390#397C2313yes—
391#397C2313yes—
392#397C2313yes—
393#397C2313yes—
394#397C2316yes—
395#397C2316yes—
396#397C2316yes—
397#397C2316yes—
398#397C2316yes—
399#397C2316yes—
400#397C2316yes—
401#396C2311yescharacteristic
402#396C2311yescharacteristic
403#396C2313yes—
404#396C2313yes—
405#396C2313yes—
406#396C2313yes—
407#396C2313yes—
408#396C2313yes—
409#396C2313yes—
410#396C2313yes—
411#396C2313yes—
412#396C2313yes—
413#396C2316yes—
414#396C2316yes—
415#396C2316yes—
416#396C2316yes—
417#396C2316yes—
418#396C2316yes—
419#394C2311yescharacteristic
420#394C2311yescharacteristic
421#394C2313yes—
422#394C2313yes—
423#394C2313yes—
424#394C2313yes—
425#394C2313yes—
426#394C2313yes—
427#394C2313yes—
428#394C2313yes—
429#394C2313yes—
430#394C2313yes—
431#394C2313yes—
432#394C2313yes—
433#394C2313yes—
434#394C2313yes—
435#394C2313yes—
436#394C2313yes—
437#394C2313yes—
438#394C2313yes—
439#394C2311yescharacteristic
440#394C2311yescharacteristic
441#394C2311yescharacteristic
442#394C2313yes—
443#394C2313yes—
444#394C2313yes—
445#394C2316yes—
446#394C2316yes—
447#394C2316yes—
448#394C2316yes—
449#394C2316yes—
450#394C2316yes—
451#394C2316yes—
452#394C2316yes—
453#394C2316yes—
454#392C2311yescharacteristic
455#392C2313yes—
456#392C2313yes—
457#392C2313yes—
458#392C2313yes—
459#392C2313yes—
460#392C2313yes—
461#392C2313yes—
462#392C2313yes—
463#392C2313yes—
464#392C2316yes—
465#391C2313yes—
466#391C2313yes—
467#391C2313yes—
468#391C2313yes—
469#391C2313yes—
470#391C2313yes—
471#391C2313yes—
472#391C2313yes—
473#391C2313yes—
474#391C2313yes—
475#391C2313yes—
476#391C2313yes—
477#390C2311yescharacteristic
478#390C2313yes—
479#390C2313yes—
480#390C2313yes—
481#390C2313yes—
482#390C2313yes—
483#390C2313yes—
484#390C2313yes—
485#390C2313yes—
486#390C2313yes—
487#390C2313yes—
488#390C2313yes—
489#390C2316yes—
490#390C2316yes—
491#390C2316yes—
492#390C2316yes—
493#390C2316yes—
494#390C2316yes—
495#390C2316yes—
496#389C2313yes—
497#389C2316yes—
498#389C2313yes—
499#389C2313yes—
500#389C2313yes—
501#389C2313yes—
502#389C2313yes—
503#389C2313yes—
504#389C2313yes—
505#389C2313yes—
506#389C2313yes—
507#389C2313yes—
508#389C2313yes—
509#389C2313yes—
510#389C2313yes—
511#389C2313yes—
512#389C2313yes—
513#389C2313yes—
514#389C2313yes—
515#389C2313yes—
516#389C2313yes—
517#389C2316yes—
518#389C2316yes—
519#389C2316yes—
520#388C2316yes—
521#388C2316yes—
522#388C2313yes—
523#388C2313yes—
524#388C2313yes—
525#388C2313yes—
526#388C2313yes—
527#388C2313yes—
528#388C2313yes—
529#388C2313yes—
530#388C2313yes—
531#388C2311yescharacteristic
532#388C2313yes—
533#388C2313yes—
534#388C2316yes—
535#388C2316yes—
536#388C2316yes—
537#388C2316yes—
538#388C2316yes—
539#388C2316yes—
540#388C2316yes—
541#388C2316yes—
542#388C2316yes—
543#388C2316yes—
544#388C2316yes—
545#388C2316yes—
546#388C2316yes—
547#388C2316yes—
548#388C2316yes—
549#387C2313yes—
550#387C2316yes—
551#387C2316yes—
552#387C2316yes—
553#387C2311yescharacteristic
554#387C2313yes—
555#387C2313yes—
556#387C2316yes—
557#387C2316yes—
558#387C2316yes—
559#387C2316yes—
560#387C2316yes—
561#387C2316yes—
562#387C2316yes—
563#387C2316yes—
564#387C2316yes—
565#387C2316yes—
566#386C2316yes—
567#386C2316yes—
568#386C2316yes—
569#386C2316yes—
570#386C2316yes—
571#386C2316yes—
572#386C2316yes—
573#385C2316yes—
574#385C2316yes—
575#385C2316yes—
576#384C2313yes—
577#384C2313yes—
578#384C2313yes—
579#384C2313yes—
580#384C2313yes—
581#384C2316yes—
582#382C2313yes—
583#382C2313yes—
584#382C2313yes—
585#381C2316yes—
586#381C2316yes—
587#380C2313yes—
588#380C2313yes—
589#380C2316yes—
590#380C2313yes—
591#380C2313yes—
592#380C2313yes—
593#380C2313yes—
594#380C2313yes—
595#380C2313yes—
596#380C2313yes—
597#380C2313yes—
598#380C2316yes—
599#380C2316yes—
600#380C2316yes—
601#380C2316yes—
602C4×C4⋊C4C2316yes—
603C4×C4⋊C4C2316yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C4⋊C4C2313yes—
614C4×C4⋊C4C2313yes—
615C4×C4⋊C4C2313yes—
616C4×C4⋊C4C2313yes—
617C4×C4⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C4×C22⋊C4C2313yes—
626C4×C22⋊C4C2313yes—
627C4×C22⋊C4C2313yes—
628C4×C22⋊C4C2316yes—
629C4×C22⋊C4C2316yes—
630C4×C22⋊C4C2316yes—
631#376C2313yes—
632C43C2313yes—
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×Q8—24no—
643C22×Q8—24no—
644C22×Q8—24no—
645C22×Q8—24no—
646C22×Q8—24no—
647C22×Q8—24no—
648C22×Q8C2413yes—
649C22×Q8C2413yes—
650C22×Q8C2413yes—
651C22×Q8C2411yescharacteristic
652C22×D4C2413yes—
653C22×D4C2413yes—
654C22×D4C2411yescharacteristic
655C22×D4C2413yes—
656C22×D4C2411yescharacteristic
657C22×D4C2411yescharacteristic
658C22×D4C2413yes—
659C22×D4C2413yes—
660C22×D4C2413yes—
661C22×D4C2413yes—
662C22×D4C2413yes—
663C22×D4C2413yes—
664C22×D4C2416yes—
665C23×C4C2413yes—
666C23×C4C2413yes—
667C23×C4C2413yes—
668C23×C4C2413yes—
669C23×C4C2413yes—
670C23×C4C2416yes—
671C23×C4C2416yes—
672C4⋊Q8—212no—
673C4⋊Q8—46no—
674C4⋊Q8—46no—
675#127—46no—
676#125—86no—
677#124—212no—
678#124—46no—
679#124—46no—
680#124—46no—
681#124—46no—
682#124—46no—
683#123—86no—
684C22⋊Q8—212no—
685C22⋊Q8—212no—
686C22⋊Q8—212no—
687C22⋊Q8—46no—
688C22⋊Q8—46no—
689C22⋊Q8—46no—
690C22⋊Q8—46no—
691C22⋊Q8—46no—
692C22⋊Q8—46no—
693C22⋊Q8—46no—
694C22⋊Q8—46no—
695C22⋊Q8—46no—
696#121—212no—
697#121—46no—
698#121—46no—
699#121—46no—
700#121—46no—
701#121—46no—
702#121—46no—
703#121—46no—
704#121—86no—
705#121—86no—
706C4×Q8—24no—
707C4×Q8—24no—
708C4×Q8—24no—
709C4×Q8—24no—
710C4×Q8—24no—
711C4×Q8—24no—
712C4×Q8—24no—
713C4×Q8—24no—
714C4×Q8—24no—
715C4×Q8—46no—
716C4×Q8—46no—
717C4×Q8—46no—
718C4×Q8—46no—
719C4×Q8—46no—
720C4×Q8—46no—
721C4×Q8#4118yes—
722C4×D4—212no—
723C4×D4—212no—
724C4×D4—212no—
725C4×D4—212no—
726C4×D4—46no—
727C4×D4—46no—
728C4×D4—46no—
729C4×D4—46no—
730C4×D4—46no—
731C4×D4—46no—
732C4×D4—46no—
733C4×D4—46no—
734C4×D4—46no—
735C4×D4—46no—
736#117—212no—
737#117—46no—
738#117—46no—
739#117—46no—
740#117—46no—
741#117—46no—
742#117—46no—
743#117—46no—
744#117—86no—
745C2×C4⋊C4—212no—
746C2×C4⋊C4—46no—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2416yes—
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2416yes—
780C2×C4⋊C4C2416yes—
781C2×C4⋊C4C2416yes—
782C2×C4⋊C4C2416yes—
783C2×C4⋊C4C2416yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2413yes—
797C2×C4⋊C4C2413yes—
798C2×C4⋊C4C2413yes—
799C2×C4⋊C4C2416yes—
800C2×C4⋊C4C2413yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2411yescharacteristic
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2416yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2411yescharacteristic
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2411yescharacteristic
813C2×C22⋊C4C2411yescharacteristic
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2416yes—
818C2×C22⋊C4C2411yescharacteristic
819C2×C22⋊C4C2411yescharacteristic
820C2×C22⋊C4C2411yescharacteristic
821C2×C22⋊C4C2411yescharacteristic
822C2×C22⋊C4C2411yescharacteristic
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2413yes—
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2416yes—
837C2×C22⋊C4C2416yes—
838C2×C22⋊C4C2416yes—
839C2×C22⋊C4C2416yes—
840C2×C22⋊C4C2416yes—
841C2×C22⋊C4C2416yes—
842C2×C22⋊C4C2413yes—
843C2×C22⋊C4C2413yes—
844C2×C22⋊C4C2411yescharacteristic
845C2×C22⋊C4C2411yescharacteristic
846C2×C22⋊C4C2413yes—
847C2×C22⋊C4C2413yes—
848C2×C22⋊C4C2411yescharacteristic
849C2×C22⋊C4C2411yescharacteristic
850C2×C22⋊C4C2411yescharacteristic
851C2×C22⋊C4C2411yescharacteristic
852C2×C22⋊C4C2413yes—
853C2×C22⋊C4C2413yes—
854C2×C22⋊C4C2413yes—
855C2×C22⋊C4C2416yes—
856C2×C22⋊C4C2416yes—
857C2×C22⋊C4C2413yes—
858C2×C22⋊C4C2413yes—
859C2×C22⋊C4C2413yes—
860C2×C22⋊C4C2413yes—
861C2×C42C2413yes—
862C2×C42C2413yes—
863C2×C42C2413yes—
864C2×C42C2413yes—
865C2×C42C2413yes—
866C2×C42C2413yes—
867C2×C42C2413yes—
868C2×C42C2413yes—
869C2×C42C2413yes—
870C2×C42C2413yes—
871C2×C42C2416yes—
872C2×C42C2416yes—
873C2×C42C2416yes—
874C2×C42C2416yes—
875C2×C42C2411yescharacteristic
876C2×C42C2413yes—
877C2×C42C2413yes—
878C2×C42C2413yes—
879#95C2411yescharacteristic
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2411yescharacteristic
884#95C2411yescharacteristic
885#95C2411yescharacteristic
886#95C2413yes—
887#95C2411yescharacteristic
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2416yes—
899#95C2416yes—
900#95C2416yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2416yes—
909#95C2411yescharacteristic
910#95C2411yescharacteristic
911#95C2411yescharacteristic
912#95C2416yes—
913#95C2416yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2413yes—
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921#95C2413yes—
922#95C2413yes—
923#95C2413yes—
924#95C2413yes—
925#95C2416yes—
926#95C2416yes—
927#95C2416yes—
928#95C2416yes—
929C24C2511yescharacteristic
930C24C2511yescharacteristic
931C24C2513yes—
932C24C2513yes—
933C24C2511yescharacteristic
934#41—416no—
935#41—416no—
936C2×Q8—26no—
937C2×Q8—26no—
938C2×Q8—26no—
939C2×Q8—26no—
940C2×Q8—26no—
941C2×Q8—26no—
942C2×Q8—26no—
943C2×Q8—26no—
944C2×Q8—26no—
945C2×Q8—416no—
946C2×Q8—416no—
947C2×Q8—416no—
948C2×Q8C2×#4114yes—
949C2×Q8H(5,𝔽2)14yes—
950C2×Q8H(5,𝔽2)14yes—
951C2×D4—22no—
952C2×D4—26no—
953C2×D4—26no—
954C2×D4—26no—
955C2×D4—26no—
956C2×D4—26no—
957C2×D4—26no—
958C2×D4—26no—
959C2×D4—41no—
960C2×D4—41no—
961C2×D4—41no—
962C2×D4—41no—
963C2×D4—41no—
964C2×D4—41no—
965C2×D4—41no—
966C2×D4—41no—
967C2×D4—43no—
968C2×D4—43no—
969C2×D4—43no—
970C2×D4—43no—
971C2×D4—43no—
972C2×D4—43no—
973C2×D4—43no—
974C2×D4—43no—
975C2×D4—43no—
976C2×D4—43no—
977C2×D4—43no—
978C2×D4—43no—
979C2×D4—43no—
980C2×D4—43no—
981C2×D4—43no—
982C2×D4—43no—
983C2×D4—43no—
984C2×D4—43no—
985C2×D4—43no—
986C2×D4—43no—
987C2×D4—46no—
988C2×D4—46no—
989C2×D4—46no—
990C22×C4—26no—
991C22×C4—26no—
992C22×C4—26no—
993C22×C4—26no—
994C22×C4—26no—
995C22×C4—26no—
996C22×C4—26no—
997C22×C4—26no—
998C22×C4—26no—
999C22×C4—26no—
1000C22×C4—26no—
1001C22×C4—26no—
1002C22×C4—26no—
1003C22×C4—26no—
1004C22×C4—26no—
1005C22×C4—212no—
1006C22×C4—46no—
1007C22×C4—46no—
1008C22×C4—46no—
1009C22×C4—46no—
1010C22×C4—46no—
1011C22×C4C2511yescharacteristic
1012C22×C4C2511yescharacteristic
1013C22×C4C2513yes—
1014C22×C4C2511yescharacteristic
1015C22×C4C2511yescharacteristic
1016C22×C4C2513yes—
1017C22×C4C2513yes—
1018C22×C4C2511yescharacteristic
1019C22×C4C2513yes—
1020C22×C4C2513yes—
1021C22×C4C2511yescharacteristic
1022C22×C4C2511yescharacteristic
1023C22×C4C2513yes—
1024C22×C4C2513yes—
1025C22×C4C2513yes—
1026C22×C4C2513yes—
1027C22×C4C2513yes—
1028C22×C4C2513yes—
1029C22×C4C2513yes—
1030C22×C4C2511yescharacteristic
1031C22×C4C2511yescharacteristic
1032C22×C4C2511yescharacteristic
1033C22×C4C2511yescharacteristic
1034C22×C4C2511yescharacteristic
1035C22×C4C2513yes—
1036C22×C4C2513yes—
1037C4⋊C4—26no—
1038C4⋊C4—26no—
1039C4⋊C4—22no—
1040C4⋊C4—26no—
1041C4⋊C4—26no—
1042C4⋊C4—212no—
1043C4⋊C4—26no—
1044C4⋊C4—26no—
1045C4⋊C4—26no—
1046C4⋊C4—26no—
1047C4⋊C4—26no—
1048C4⋊C4—26no—
1049C4⋊C4—26no—
1050C4⋊C4—26no—
1051C4⋊C4—43no—
1052C4⋊C4—41no—
1053C4⋊C4—43no—
1054C4⋊C4—43no—
1055C4⋊C4—41no—
1056C4⋊C4—43no—
1057C4⋊C4—43no—
1058C4⋊C4—41no—
1059C4⋊C4—41no—
1060C4⋊C4—43no—
1061C4⋊C4—43no—
1062C4⋊C4—46no—
1063C4⋊C4—43no—
1064C4⋊C4—41no—
1065C4⋊C4—41no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4—43no—
1070C4⋊C4—43no—
1071C4⋊C4—43no—
1072C4⋊C4—43no—
1073C4⋊C4—46no—
1074C4⋊C4—41no—
1075C4⋊C4—43no—
1076C4⋊C4—43no—
1077C4⋊C4—43no—
1078C4⋊C4—43no—
1079C4⋊C4—43no—
1080C4⋊C4—43no—
1081C4⋊C4—43no—
1082C4⋊C4—46no—
1083C4⋊C4—46no—
1084C4⋊C4—46no—
1085C4⋊C4—46no—
1086C4⋊C4—46no—
1087C4⋊C4—43no—
1088C4⋊C4—43no—
1089C4⋊C4—43no—
1090C4⋊C4C2×#41112yes—
1091C22⋊C4—26no—
1092C22⋊C4—26no—
1093C22⋊C4—22no—
1094C22⋊C4—26no—
1095C22⋊C4—26no—
1096C22⋊C4—26no—
1097C22⋊C4—212no—
1098C22⋊C4—41no—
1099C22⋊C4—41no—
1100C22⋊C4—43no—
1101C22⋊C4—41no—
1102C22⋊C4—46no—
1103C22⋊C4—43no—
1104C22⋊C4—43no—
1105C22⋊C4—46no—
1106C22⋊C4—43no—
1107C22⋊C4—43no—
1108C22⋊C4—43no—
1109C22⋊C4—41no—
1110C22⋊C4—41no—
1111C22⋊C4—43no—
1112C22⋊C4—43no—
1113C22⋊C4—43no—
1114C22⋊C4—41no—
1115C22⋊C4—41no—
1116C22⋊C4—41no—
1117C22⋊C4—41no—
1118C22⋊C4—43no—
1119C22⋊C4—43no—
1120C22⋊C4—43no—
1121C22⋊C4—43no—
1122C22⋊C4—43no—
1123C22⋊C4—43no—
1124C22⋊C4—46no—
1125C22⋊C4—41no—
1126C22⋊C4—41no—
1127C22⋊C4—41no—
1128C22⋊C4—41no—
1129C22⋊C4—41no—
1130C22⋊C4—43no—
1131C22⋊C4—43no—
1132C22⋊C4—43no—
1133C22⋊C4—43no—
1134C22⋊C4—43no—
1135C22⋊C4—43no—
1136C22⋊C4—43no—
1137C22⋊C4—43no—
1138C22⋊C4—43no—
1139C22⋊C4—43no—
1140C22⋊C4—43no—
1141C22⋊C4—46no—
1142C22⋊C4—46no—
1143C22⋊C4—46no—
1144C22⋊C4—46no—
1145C22⋊C4—46no—
1146C22⋊C4—43no—
1147C22⋊C4—43no—
1148C22⋊C4—46no—
1149C22⋊C4—43no—
1150C22⋊C4—43no—
1151C42—26no—
1152C42—26no—
1153C42—26no—
1154C42—26no—
1155C42—26no—
1156C42—26no—
1157C42—26no—
1158C42—26no—
1159C42—26no—
1160C42—43no—
1161C42—41no—
1162C42—43no—
1163C42—46no—
1164C42—46no—
1165C42—46no—
1166C42—43no—
1167C42—46no—
1168C42C2×#41112yes—
1169C23—21no—
1170C23—21no—
1171C23—23no—
1172C23—23no—
1173C23—21no—
1174C23—21no—
1175C23—21no—
1176C23—23no—
1177C23—21no—
1178C23—23no—
1179C23—21no—
1180C23—21no—
1181C23—23no—
1182C23—23no—
1183C23—21no—
1184C23—21no—
1185C23—23no—
1186C23—21no—
1187C23—21no—
1188C23—23no—
1189C23—21no—
1190C23—21no—
1191C23—23no—
1192C23—23no—
1193C23—23no—
1194C23—23no—
1195C23—23no—
1196C23—21no—
1197C23—21no—
1198C23—21no—
1199C23—23no—
1200C23—21no—
1201C23—21no—
1202C23—21no—
1203C23—21no—
1204C23C2611yescharacteristic
1205Q8—412no—
1206Q8—412no—
1207Q8—412no—
1208Q8#540116yes—
1209D4—44no—
1210D4—44no—
1211D4—44no—
1212D4—412no—
1213D4—412no—
1214D4—86no—
1215D4—86no—
1216D4—86no—
1217D4—86no—
1218D4—86no—
1219D4—86no—
1220D4—86no—
1221D4—166no—
1222C2×C4—23no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—23no—
1226C2×C4—21no—
1227C2×C4—23no—
1228C2×C4—23no—
1229C2×C4—21no—
1230C2×C4—23no—
1231C2×C4—23no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—23no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—23no—
1247C2×C4—23no—
1248C2×C4—23no—
1249C2×C4—23no—
1250C2×C4—23no—
1251C2×C4—23no—
1252C2×C4—23no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—23no—
1256C2×C4—23no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—23no—
1261C2×C4—23no—
1262C2×C4—23no—
1263C2×C4—23no—
1264C2×C4—23no—
1265C2×C4—23no—
1266C2×C4—23no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—23no—
1270C2×C4—21no—
1271C2×C4—23no—
1272C2×C4—21no—
1273C2×C4—23no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—23no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—23no—
1283C2×C4—23no—
1284C2×C4—23no—
1285C2×C4—23no—
1286C2×C4—23no—
1287C2×C4—23no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—23no—
1295C2×C4—412no—
1296C2×C4—412no—
1297C2×C4—412no—
1298C2×C4—412no—
1299C2×C4—412no—
1300C2×C4—812no—
1301C2×C4—166no—
1302C2×C4C22×#4112yes—
1303C2×C4C22×#4116yes—
1304C2×C4C22×#4116yes—
1305C2×C4C2×H(5,𝔽2)16yes—
1306C2×C4C2×H(5,𝔽2)16yes—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—43no—
1313C22—43no—
1314C22—43no—
1315C22—41no—
1316C22—43no—
1317C22—43no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—43no—
1323C22—43no—
1324C22—43no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—43no—
1330C22—43no—
1331C22—41no—
1332C22—43no—
1333C22—41no—
1334C22—43no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—43no—
1341C22—43no—
1342C22C23×#4111yescharacteristic
1343C22C22×H(5,𝔽2)11yescharacteristic
1344C22C22×H(5,𝔽2)11yescharacteristic
1345C22H(7,𝔽2)11yescharacteristic
1346C222−1+611yescharacteristic
1347C222−1+611yescharacteristic
1348C222−1+611yescharacteristic
1349C4—22no—
1350C4—26no—
1351C4—41no—
1352C4—41no—
1353C4—41no—
1354C4—43no—
1355C4—41no—
1356C4—41no—
1357C4—43no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—43no—
1362C4—43no—
1363C4—43no—
1364C4—43no—
1365C4—43no—
1366C4—43no—
1367C4—41no—
1368C4—43no—
1369C4—41no—
1370C4—41no—
1371C4—43no—
1372C4—43no—
1373C4—43no—
1374C4C2×#540112yes—
1375C2—81no—
1376C2—81no—
1377C2—81no—
1378C2—83no—
1379C2—83no—
1380C2C22×#54011yescharacteristic
1381C2#6285011yescharacteristic
1382C2#6285711yescharacteristic
1383C2#6304411yescharacteristic
1384C2#6304411yescharacteristic
1385C2#6305211yescharacteristic
1386C2#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. #42759C2semidirect
2. #42752C2semidirect
3. #42726C2semidirect
4. #42719C2semidirect
5. #42705C2semidirect
6. #42688C2semidirect
7. #42668C2semidirect
8. #42658C2semidirect
9. #42641C2semidirect
10. #42633C2semidirect
11. #42629C2semidirect
12. #42620C2semidirect
13. #37627C2semidirect
14. #37594C2semidirect
15. #37570C2semidirect
16. #36692C2semidirect
17. #36018C2semidirect
18. #35996C2semidirect
19. #35927C2semidirect
20. #35868C2semidirect
21. #35831C2semidirect
22. #35831C2semidirect
23. #35801C2semidirect
24. #35771C2semidirect
25. #35771C2semidirect
26. #35737C2semidirect
27. #35723C2semidirect
28. #35723C2semidirect
29. #34312C2semidirect
30. #34311C2semidirect
31. #34263C2semidirect

Maximal subgroups

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

subgroupindex
#427592
#427522
#427262
#427192
#427052
#426882
#426682
#426582
#426412
#426332
#426292
#426202
#376272
#375942
#375702
#366922
#360182
#359962
#359272
#358682
#358312
#358012
#357712
#357372
#357232
#343122
#343112
#342632