Finite Group Databasebeta

← #8097095

Subgroups — #8097095

Order 512.

4607 conjugacy classes of subgroups.

The subgroup lattice has 1274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53132C213yesmaximal, complemented
2#53123C213yesmaximal, complemented
3#53119C213yesmaximal, complemented
4#53104C213yesmaximal, complemented
5#53067C213yesmaximal, complemented
6#52997C213yesmaximal, complemented
7#52300C213yesmaximal, complemented
8#46340C213yesmaximal, complemented
9#46329C213yesmaximal, complemented
10#46108C213yesmaximal, complemented
11#46078C213yesmaximal, complemented
12#46019C213yesmaximal, complemented
13#45993C213yesmaximal, complemented
14#45668C213yesmaximal, complemented
15#45640C213yesmaximal, complemented
16#45485C213yesmaximal, complemented
17#36593C211yesmaximal, characteristic, complemented
18#36466C211yesmaximal, characteristic, complemented
19#36458C211yesmaximal, characteristic, complemented
20#36458C211yesmaximal, characteristic, complemented
21#36458C211yesmaximal, characteristic, complemented
22#36458C211yesmaximal, characteristic, complemented
23#36445C211yesmaximal, characteristic, complemented
24#36433C211yesmaximal, characteristic
25#36431C211yesmaximal, characteristic, complemented
26#36049C211yesmaximal, characteristic
27#36005C211yesmaximal, characteristic
28#35868C211yesmaximal, characteristic, complemented
29#35868C211yesmaximal, characteristic, complemented
30#35816C211yesmaximal, characteristic, complemented
31#35816C211yesmaximal, characteristic, complemented
32C2×#563C2216yes—
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#550C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic
39#2868C2213yes—
40#2860C2213yes—
41#2860C2213yes—
42#2860C2213yes—
43#2860C2213yes—
44#2859C2213yes—
45#2857C2213yes—
46#2854C2213yes—
47#2851C2213yes—
48#2839C2216yes—
49#2837C2216yes—
50#2837C2216yes—
51#2836C2216yes—
52#2836C2216yes—
53#2827C2216yes—
54#2827C2216yes—
55#2823C2216yes—
56#2823C2216yes—
57#2821C2216yes—
58#2814C2216yes—
59#2793C2216yes—
60#2791C2213yes—
61#2791C2211yescharacteristic
62#2777C2213yes—
63#2777C2213yes—
64#2771C2213yes—
65#2770C2216yes—
66#2764C2213yes—
67#2758C2213yes—
68#2758C2213yes—
69#2738C2216yes—
70#2731C2216yes—
71#2729C2216yes—
72#2728C2216yes—
73#2727C2216yes—
74#2725C2216yes—
75#2722C2213yes—
76#2721C2216yes—
77#2720C2216yes—
78#2718C2213yes—
79#2718C2216yes—
80#2718C2213yes—
81#2718C2216yes—
82#2716C2213yes—
83#2716C2213yes—
84#2715C2216yes—
85#2707C2216yes—
86#2707C2216yes—
87#2702C2216yes—
88#2702C2213yes—
89#2702C2213yes—
90#2695C2216yes—
91#2695C2216yes—
92#2690C2216yes—
93#2680C2216yes—
94#2677C2213yes—
95#2674C2216yes—
96#2647C2213yes—
97#2647C2213yes—
98#2641C2213yes—
99#2629C2213yes—
100#2629C2213yes—
101#2624C2213yes—
102#2584C2213yes—
103#2584C2213yes—
104#2580C2213yes—
105#2570C2213yes—
106#2570C2213yes—
107#2566C2213yes—
108#2566C2213yes—
109#2566C2213yes—
110#2562C2213yes—
111#2552C2213yes—
112#2552C2213yes—
113#2552C2213yes—
114#2552C2213yes—
115#2552C2213yes—
116#2552C2213yes—
117#2552C2213yes—
118#2551C2213yes—
119#2550C2213yes—
120#2550C2213yes—
121#2548C2213yes—
122#2546C2213yes—
123#2546C2213yes—
124#2542C2213yes—
125#2538C2213yes—
126#2538C2213yes—
127#2538C2213yes—
128#2513C2213yes—
129#2513C2213yes—
130#2513C2213yes—
131#2513C2213yes—
132#2512C2213yes—
133#2512C2213yes—
134#2512C2213yes—
135#2512C2213yes—
136#2512C2213yes—
137#2512C2213yes—
138#2512C2213yes—
139#2512C2213yes—
140#2509C2213yes—
141#2509C2213yes—
142#2507C2213yes—
143#2507C2213yes—
144#2506C2213yes—
145#2506C2213yes—
146#2506C2213yes—
147#2506C2213yes—
148#2501C2213yes—
149#2500C2213yes—
150#2497C2213yes—
151#2497C2213yes—
152#2497C2213yes—
153#2497C2213yes—
154#2496C2213yes—
155#2496C2213yes—
156#2496C2213yes—
157#2496C2213yes—
158#2495C2213yes—
159#2495C2213yes—
160#2495C2213yes—
161#2495C2213yes—
162#2491C2213yes—
163#2491C2213yes—
164#2490C2213yes—
165#2490C2213yes—
166#2487C2213yes—
167#2485C2213yes—
168#2454C2213yes—
169#2454C2213yes—
170#2454C2213yes—
171#2454C2213yes—
172#2454C2213yes—
173#2452C2213yes—
174#2452C2213yes—
175#2452C2213yes—
176#2445C2213yes—
177#2445C2213yes—
178#2445C2213yes—
179#2445C2213yes—
180#2442C2213yes—
181#2442C2213yes—
182#2441C2213yes—
183#2441C2213yes—
184#2441C2213yes—
185#2440C2213yes—
186#2440C2213yes—
187#2439C2213yes—
188#2422C2213yes—
189#2422C2213yes—
190#2422C2213yes—
191#2420C2213yes—
192#2402C2213yes—
193#2402C2213yes—
194#2398C2213yes—
195#2396C2213yes—
196#2396C2213yes—
197#2395C2213yes—
198#2383C2216yes—
199#2376C2216yes—
200#2351C2211yescharacteristic
201#2351C2211yescharacteristic
202#2351C2211yescharacteristic
203#2351C2211yescharacteristic
204#2351C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206Q8×C4⋊C4C2211yescharacteristic
207Q8×C4⋊C4C2211yescharacteristic
208Q8×C4⋊C4C2211yescharacteristic
209Q8×C4⋊C4C2211yescharacteristic
210Q8×C4⋊C4C2211yescharacteristic
211Q8×C4⋊C4C2211yescharacteristic
212Q8×C4⋊C4C2211yescharacteristic
213Q8×C4⋊C4C2211yescharacteristic
214Q8×C4⋊C4C2211yescharacteristic
215Q8×C4⋊C4C2211yescharacteristic
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218#2341C2211yescharacteristic
219#2341C2211yescharacteristic
220#2341C2211yescharacteristic
221#2341C2211yescharacteristic
222#2341C2211yescharacteristic
223#2341C2211yescharacteristic
224#2341C2211yescharacteristic
225#2341C2211yescharacteristic
226C4×C4⋊Q8C2213yes—
227C4×C4⋊Q8C2213yes—
228C4×#126C2213yes—
229C4×#126C2213yes—
230C4×#126C2213yes—
231C4×#126C2213yes—
232C4×C22⋊Q8C2213yes—
233C4×C22⋊Q8C2213yes—
234C4×#123C2213yes—
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240#563—424no—
241#557—44no—
242#557—44no—
243#557—44no—
244#550—44no—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2316yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×#127C2313yes—
252C2×#126C2313yes—
253C2×#126C2313yes—
254C2×#126C2313yes—
255C2×#126C2313yes—
256C2×#126C2316yes—
257C2×#126C2316yes—
258C2×#126C2316yes—
259C2×#126C2316yes—
260C2×#125C2313yes—
261C2×#125C2313yes—
262C2×#125C2313yes—
263C2×#125C2313yes—
264C2×#125C2313yes—
265C2×#125C2313yes—
266C2×#125C2316yes—
267C2×#125C2316yes—
268C2×#124C2316yes—
269C2×#123C2316yes—
270C2×#123C2316yes—
271C2×#123C2316yes—
272C2×#123C2313yes—
273C2×C22⋊Q8C2313yes—
274C2×C22⋊Q8C2316yes—
275C2×C22⋊Q8C2316yes—
276C2×C22⋊Q8C2313yes—
277C2×C22⋊Q8C2316yes—
278C2×#121C2313yes—
279C2×#121C2313yes—
280#520—44no—
281C4×#41—44no—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2313yes—
296C2×C4×Q8C2313yes—
297C2×C4×Q8C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×#117C2313yes—
304C2×#117C2313yes—
305C22×C4⋊C4C2313yes—
306C22×C42C2313yes—
307#400C2313yes—
308#400C2316yes—
309#400C2316yes—
310#400C2313yes—
311#400C2313yes—
312#400C2313yes—
313#400C2313yes—
314#400C2316yes—
315#400C2313yes—
316#400C2313yes—
317#400C2316yes—
318#400C2313yes—
319#400C2316yes—
320#400C2316yes—
321#400C2313yes—
322#400C2311yescharacteristic
323#400C2313yes—
324#400C2313yes—
325#400C2313yes—
326#399C2316yes—
327#399C2316yes—
328#399C2313yes—
329#399C2316yes—
330#399C2316yes—
331#399C2313yes—
332#399C2313yes—
333#398C2316yes—
334#398C2316yes—
335#398C2313yes—
336#398C2313yes—
337#398C2316yes—
338#398C2316yes—
339#398C2316yes—
340#398C2316yes—
341#398C2316yes—
342#398C2316yes—
343#398C2313yes—
344#398C2313yes—
345#398C2316yes—
346#398C2316yes—
347#398C2316yes—
348#398C2316yes—
349#398C2313yes—
350#398C2311yescharacteristic
351#398C2311yescharacteristic
352#398C2311yescharacteristic
353#398C2311yescharacteristic
354#398C2311yescharacteristic
355#398C2313yes—
356#398C2313yes—
357#398C2313yes—
358#397C2316yes—
359#397C2316yes—
360#397C2316yes—
361#397C2316yes—
362#397C2316yes—
363#397C2313yes—
364#397C2313yes—
365#397C2316yes—
366#397C2316yes—
367#397C2316yes—
368#397C2313yes—
369#397C2313yes—
370#397C2313yes—
371#397C2316yes—
372#396C2313yes—
373#396C2313yes—
374#396C2316yes—
375#396C2316yes—
376#396C2316yes—
377#396C2316yes—
378#396C2316yes—
379#396C2316yes—
380#396C2316yes—
381#396C2316yes—
382#396C2316yes—
383#396C2316yes—
384#396C2316yes—
385#396C2316yes—
386#396C2313yes—
387#396C2313yes—
388#395C2313yes—
389#395C2316yes—
390#395C2316yes—
391#395C2313yes—
392#394C2316yes—
393#394C2313yes—
394#394C2316yes—
395#394C2316yes—
396#394C2316yes—
397#394C2316yes—
398#394C2313yes—
399#394C2316yes—
400#394C2313yes—
401#394C2316yes—
402#394C2316yes—
403#394C2313yes—
404#393C2313yes—
405#393C2316yes—
406#393C2313yes—
407#393C2313yes—
408#393C2313yes—
409#391C2313yes—
410#391C2313yes—
411#391C2313yes—
412#391C2313yes—
413#391C2313yes—
414#391C2313yes—
415#390C2313yes—
416#390C2313yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
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#390C2316yes—
436#389C2311yescharacteristic
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2316yes—
451#389C2316yes—
452#389C2316yes—
453#389C2316yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2316yes—
464#389C2313yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2316yes—
482#389C2313yes—
483#389C2311yescharacteristic
484#388C2313yes—
485#388C2313yes—
486#388C2313yes—
487#388C2313yes—
488#388C2313yes—
489#388C2313yes—
490#388C2313yes—
491#388C2313yes—
492#388C2313yes—
493#388C2313yes—
494#388C2313yes—
495#388C2313yes—
496#388C2316yes—
497#388C2316yes—
498#388C2316yes—
499#388C2316yes—
500#388C2316yes—
501#388C2316yes—
502#388C2313yes—
503#388C2316yes—
504#388C2316yes—
505#388C2316yes—
506#388C2316yes—
507#388C2316yes—
508#388C2313yes—
509#387C2311yescharacteristic
510#387C2311yescharacteristic
511#387C2311yescharacteristic
512#387C2311yescharacteristic
513#387C2313yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2313yes—
518#387C2313yes—
519#387C2313yes—
520#387C2313yes—
521#387C2316yes—
522#387C2316yes—
523#387C2316yes—
524#387C2316yes—
525#387C2313yes—
526#387C2316yes—
527#387C2313yes—
528#387C2313yes—
529#387C2313yes—
530#387C2311yescharacteristic
531#387C2311yescharacteristic
532#386C2316yes—
533#386C2316yes—
534#386C2313yes—
535#385C2313yes—
536#385C2316yes—
537#385C2316yes—
538#385C2316yes—
539#385C2316yes—
540#385C2316yes—
541#385C2313yes—
542#385C2313yes—
543#385C2316yes—
544#385C2313yes—
545#385C2316yes—
546#385C2313yes—
547#384C2311yescharacteristic
548#384C2313yes—
549#384C2313yes—
550#384C2313yes—
551#384C2313yes—
552#384C2316yes—
553#384C2313yes—
554#384C2313yes—
555#384C2313yes—
556#384C2313yes—
557#384C2313yes—
558#384C2313yes—
559#384C2313yes—
560#384C2313yes—
561#384C2316yes—
562#383C2313yes—
563#383C2313yes—
564#383C2313yes—
565#383C2313yes—
566#382C2313yes—
567#382C2313yes—
568#382C2313yes—
569#382C2313yes—
570#382C2313yes—
571#381C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2316yes—
583#380C2316yes—
584#380C2316yes—
585#380C2313yes—
586#380C2313yes—
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⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
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×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⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622#376C2313yes—
623C43C2313yes—
624C43C2313yes—
625C2×#41—24no—
626C2×#41—24no—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41—24no—
631C22×Q8C2413yes—
632C22×Q8C2413yes—
633C22×Q8C2413yes—
634C22×Q8C2411yescharacteristic
635C22×D4C2413yes—
636C22×D4C2413yes—
637C22×D4C2413yes—
638C22×D4C2416yes—
639C23×C4C2413yes—
640C23×C4C2413yes—
641C23×C4C2413yes—
642C23×C4C2416yes—
643C23×C4C2413yes—
644C4⋊Q8—212no—
645C4⋊Q8—46no—
646C4⋊Q8—46no—
647C4⋊Q8—46no—
648C4⋊Q8—46no—
649C4⋊Q8—412no—
650#127—46no—
651#126—212no—
652#126—46no—
653#126—412no—
654#126—412no—
655#126—412no—
656#126—412no—
657#126—46no—
658#126—46no—
659#125—46no—
660#125—46no—
661#125—46no—
662#125—46no—
663#125—46no—
664#125—46no—
665#125—412no—
666#125—412no—
667#124—412no—
668#123—412no—
669#123—46no—
670#123—412no—
671#123—412no—
672C22⋊Q8—212no—
673C22⋊Q8—46no—
674C22⋊Q8—412no—
675C22⋊Q8—412no—
676C22⋊Q8—412no—
677#121—46no—
678#121—46no—
679C4×Q8—24no—
680C4×Q8—24no—
681C4×Q8—24no—
682C4×Q8—24no—
683C4×Q8—24no—
684C4×Q8—24no—
685C4×Q8—24no—
686C4×Q8—24no—
687C4×Q8—24no—
688C4×Q8—24no—
689C4×Q8—24no—
690C4×Q8—24no—
691C4×Q8—24no—
692C4×Q8—46no—
693C4×Q8—46no—
694C4×Q8—46no—
695C4×D4—46no—
696C4×D4—46no—
697C4×D4—46no—
698C4×D4—46no—
699C4×D4—46no—
700#117—46no—
701#117—46no—
702C2×C4⋊C4—46no—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2416yes—
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C2416yes—
746C2×C4⋊C4C2416yes—
747C2×C4⋊C4C2416yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2416yes—
750C2×C4⋊C4C2416yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2416yes—
753C2×C4⋊C4C2416yes—
754C2×C4⋊C4C2416yes—
755C2×C4⋊C4C2416yes—
756C2×C4⋊C4C2416yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2416yes—
762C2×C4⋊C4C2416yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2411yescharacteristic
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2416yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2416yes—
789C2×C22⋊C4C2416yes—
790C2×C22⋊C4C2416yes—
791C2×C22⋊C4C2416yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2416yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2416yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2416yes—
803C2×C22⋊C4C2416yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2416yes—
808C2×C22⋊C4C2416yes—
809C2×C42—46no—
810C2×C42C2413yes—
811C2×C42C2413yes—
812C2×C42C2413yes—
813C2×C42C2413yes—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2411yescharacteristic
827C2×C42C2413yes—
828C2×C42C2416yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2411yescharacteristic
832C2×C42C2413yes—
833C2×C42C2411yescharacteristic
834#95C2411yescharacteristic
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2411yescharacteristic
839#95C2411yescharacteristic
840#95C2411yescharacteristic
841#95C2411yescharacteristic
842#95C2411yescharacteristic
843#95C2411yescharacteristic
844#95C2411yescharacteristic
845#95C2411yescharacteristic
846#95C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2411yescharacteristic
859#95C2411yescharacteristic
860#95C2411yescharacteristic
861#95C2411yescharacteristic
862#95C2411yescharacteristic
863#95C2416yes—
864#95C2416yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2416yes—
893#95C2416yes—
894#95C2416yes—
895#95C2416yes—
896#95C2416yes—
897C24C2513yes—
898C24C2513yes—
899#41—416no—
900#41—416no—
901C2×Q8—26no—
902C2×Q8—26no—
903C2×Q8—26no—
904C2×Q8—43no—
905C2×Q8—43no—
906C2×Q8—43no—
907C2×Q8—43no—
908C2×Q8—43no—
909C2×Q8—43no—
910C2×Q8H(5,𝔽2)14yes—
911C2×Q82−1+414yes—
912C2×Q82−1+414yes—
913C2×D4—26no—
914C2×D4—26no—
915C2×D4—26no—
916C2×D4—26no—
917C2×D4—26no—
918C2×D4—26no—
919C2×D4—43no—
920C2×D4—43no—
921C2×D4—43no—
922C2×D4—46no—
923C2×D4—46no—
924C2×D4—46no—
925C22×C4—26no—
926C22×C4—26no—
927C22×C4—26no—
928C22×C4—26no—
929C22×C4—26no—
930C22×C4—26no—
931C22×C4—26no—
932C22×C4—43no—
933C22×C4—43no—
934C22×C4—43no—
935C22×C4—43no—
936C22×C4—43no—
937C22×C4—46no—
938C22×C4—46no—
939C22×C4—46no—
940C22×C4C2511yescharacteristic
941C22×C4C2511yescharacteristic
942C22×C4C2511yescharacteristic
943C22×C4C2511yescharacteristic
944C22×C4C2511yescharacteristic
945C22×C4C2511yescharacteristic
946C22×C4C2513yes—
947C22×C4C2511yescharacteristic
948C22×C4C2513yes—
949C22×C4C2513yes—
950C22×C4C2513yes—
951C22×C4C2513yes—
952C22×C4C2513yes—
953C22×C4C2513yes—
954C22×C4C2511yescharacteristic
955C22×C4C2511yescharacteristic
956C22×C4C2511yescharacteristic
957C22×C4C2513yes—
958C22×C4C2513yes—
959C22×C4C2513yes—
960C22×C4C2513yes—
961C22×C4C2513yes—
962C22×C4C2513yes—
963C22×C4C2511yescharacteristic
964C22×C4C2511yescharacteristic
965C22×C4C2511yescharacteristic
966C22×C4C2511yescharacteristic
967C22×C4C2511yescharacteristic
968C22×C4C2513yes—
969C4⋊C4—26no—
970C4⋊C4—26no—
971C4⋊C4—26no—
972C4⋊C4—26no—
973C4⋊C4—26no—
974C4⋊C4—26no—
975C4⋊C4—26no—
976C4⋊C4—26no—
977C4⋊C4—26no—
978C4⋊C4—26no—
979C4⋊C4—26no—
980C4⋊C4—26no—
981C4⋊C4—26no—
982C4⋊C4—26no—
983C4⋊C4—26no—
984C4⋊C4—26no—
985C4⋊C4—26no—
986C4⋊C4—26no—
987C4⋊C4—26no—
988C4⋊C4—26no—
989C4⋊C4—22no—
990C4⋊C4—26no—
991C4⋊C4—22no—
992C4⋊C4—26no—
993C4⋊C4—22no—
994C4⋊C4—22no—
995C4⋊C4—26no—
996C4⋊C4—22no—
997C4⋊C4—43no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—43no—
1001C4⋊C4—41no—
1002C4⋊C4—41no—
1003C4⋊C4—43no—
1004C4⋊C4—43no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—43no—
1012C4⋊C4—43no—
1013C4⋊C4—43no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—46no—
1019C4⋊C4—46no—
1020C4⋊C4—46no—
1021C4⋊C4—46no—
1022C4⋊C4—46no—
1023C4⋊C4—46no—
1024C4⋊C4—43no—
1025C4⋊C4—46no—
1026C4⋊C4—46no—
1027C4⋊C4—46no—
1028C4⋊C4—46no—
1029C4⋊C4—46no—
1030C4⋊C4—46no—
1031C4⋊C4—43no—
1032C4⋊C4—43no—
1033C4⋊C4—46no—
1034C4⋊C4—46no—
1035C4⋊C4—43no—
1036C4⋊C4—43no—
1037C4⋊C4—43no—
1038C4⋊C4—43no—
1039C4⋊C4H(5,𝔽2)14yes—
1040C22⋊C4—26no—
1041C22⋊C4—26no—
1042C22⋊C4—26no—
1043C22⋊C4—26no—
1044C22⋊C4—26no—
1045C22⋊C4—26no—
1046C22⋊C4—26no—
1047C22⋊C4—26no—
1048C22⋊C4—26no—
1049C22⋊C4—43no—
1050C22⋊C4—43no—
1051C22⋊C4—43no—
1052C22⋊C4—46no—
1053C22⋊C4—46no—
1054C22⋊C4—43no—
1055C22⋊C4—43no—
1056C22⋊C4—46no—
1057C22⋊C4—43no—
1058C22⋊C4—43no—
1059C22⋊C4—43no—
1060C22⋊C4—46no—
1061C22⋊C4—46no—
1062C22⋊C4—46no—
1063C22⋊C4—46no—
1064C22⋊C4—46no—
1065C22⋊C4—43no—
1066C22⋊C4—46no—
1067C22⋊C4—46no—
1068C22⋊C4—46no—
1069C22⋊C4—43no—
1070C22⋊C4—43no—
1071C22⋊C4—43no—
1072C22⋊C4—43no—
1073C22⋊C4—43no—
1074C22⋊C4—43no—
1075C42—26no—
1076C42—26no—
1077C42—26no—
1078C42—26no—
1079C42—26no—
1080C42—26no—
1081C42—26no—
1082C42—26no—
1083C42—26no—
1084C42—26no—
1085C42—26no—
1086C42—26no—
1087C42—26no—
1088C42—26no—
1089C42—26no—
1090C42—26no—
1091C42—22no—
1092C42—41no—
1093C42—43no—
1094C42—43no—
1095C42—41no—
1096C42—46no—
1097C42—43no—
1098C42—43no—
1099C23—23no—
1100C23—23no—
1101C23—23no—
1102C23—23no—
1103C23—23no—
1104C23—23no—
1105C23—23no—
1106C23—23no—
1107C23—23no—
1108C23—23no—
1109C23—23no—
1110C23—23no—
1111C23—23no—
1112C23—23no—
1113C23C2611yescharacteristic
1114Q8—86no—
1115Q8—86no—
1116Q8—86no—
1117Q8#563116yescomplemented
1118D4—412no—
1119D4—412no—
1120D4—86no—
1121D4—166no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—23no—
1138C2×C4—23no—
1139C2×C4—23no—
1140C2×C4—23no—
1141C2×C4—23no—
1142C2×C4—23no—
1143C2×C4—23no—
1144C2×C4—23no—
1145C2×C4—23no—
1146C2×C4—23no—
1147C2×C4—23no—
1148C2×C4—21no—
1149C2×C4—23no—
1150C2×C4—23no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—21no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—23no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—23no—
1170C2×C4—23no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—23no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—23no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—23no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—23no—
1187C2×C4—23no—
1188C2×C4—21no—
1189C2×C4—23no—
1190C2×C4—21no—
1191C2×C4—23no—
1192C2×C4—23no—
1193C2×C4—21no—
1194C2×C4—23no—
1195C2×C4—21no—
1196C2×C4—23no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—412no—
1202C2×C4—412no—
1203C2×C4—86no—
1204C2×C4—86no—
1205C2×C4—166no—
1206C2×C4C2×H(5,𝔽2)12yes—
1207C2×C4C2×H(5,𝔽2)12yes—
1208C2×C4C2×H(5,𝔽2)12yes—
1209C2×C4C2×H(5,𝔽2)16yes—
1210C2×C4C2×2−1+416yes—
1211C2×C4C2×2−1+416yes—
1212C2×C4#58512yes—
1213C2×C4#58512yes—
1214C22—43no—
1215C22—43no—
1216C22—43no—
1217C22—43no—
1218C22—43no—
1219C22—43no—
1220C22—43no—
1221C22—43no—
1222C22—43no—
1223C22—43no—
1224C22—43no—
1225C22—43no—
1226C22—43no—
1227C22—43no—
1228C22C22×H(5,𝔽2)11yescharacteristic
1229C22C22×H(5,𝔽2)11yescharacteristic
1230C22C22×2−1+411yescharacteristic
1231C22C22×2−1+411yescharacteristic
1232C22C2×#58511yescharacteristic
1233C22C2×#58511yescharacteristic
1234C222−1+611yescharacteristic
1235C4—22no—
1236C4—22no—
1237C4—22no—
1238C4—22no—
1239C4—22no—
1240C4—43no—
1241C4—43no—
1242C4—43no—
1243C4—43no—
1244C4—43no—
1245C4—41no—
1246C4—43no—
1247C4—43no—
1248C4—43no—
1249C4—43no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—43no—
1254C4—43no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—43no—
1260C4—43no—
1261C4—41no—
1262C4—41no—
1263C4C2×#563112yes—
1264C2—83no—
1265C2—83no—
1266C2C22×#56311yescharacteristic
1267C2#6292211yescharacteristic
1268C2#6294611yescharacteristic
1269C2#6294911yescharacteristic
1270C2#6301411yescharacteristic
1271C2#6303311yescharacteristic
1272C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#550C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53132C2semidirect
2. #53123C2semidirect
3. #53119C2semidirect
4. #53104C2semidirect
5. #53067C2semidirect
6. #52997C2semidirect
7. #52300C2semidirect
8. #46340C2semidirect
9. #46329C2semidirect
10. #46108C2semidirect
11. #46078C2semidirect
12. #46019C2semidirect
13. #45993C2semidirect
14. #45668C2semidirect
15. #45640C2semidirect
16. #45485C2semidirect
17. #36593C2semidirect
18. #36466C2semidirect
19. #36458C2semidirect
20. #36458C2semidirect
21. #36458C2semidirect
22. #36458C2semidirect
23. #36445C2semidirect
25. #36431C2semidirect
28. #35868C2semidirect
29. #35868C2semidirect
30. #35816C2semidirect
31. #35816C2semidirect
1117. Q8#563semidirect

Maximal subgroups

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

subgroupindex
#531322
#531232
#531192
#531042
#530672
#529972
#523002
#463402
#463292
#461082
#460782
#460192
#459932
#456682
#456402
#454852
#365932
#364662
#364582
#364452
#364332
#364312
#360492
#360052
#358682
#358162