Finite Group Databasebeta

← #8096652

Subgroups — #8096652

Order 512.

5176 conjugacy classes of subgroups.

The subgroup lattice has 1392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53108C213yesmaximal, complemented
2#53101C213yesmaximal, complemented
3#53056C213yesmaximal, complemented
4#53016C213yesmaximal, complemented
5#52972C213yesmaximal, complemented
6#52964C213yesmaximal, complemented
7#52296C213yesmaximal, complemented
8#46104C213yesmaximal, complemented
9#46044C213yesmaximal, complemented
10#45995C213yesmaximal, complemented
11#45676C213yesmaximal, complemented
12#45653C213yesmaximal, complemented
13#45610C213yesmaximal, complemented
14#45498C213yesmaximal, complemented
15#45486C213yesmaximal, complemented
16#45486C213yesmaximal, complemented
17#36576C211yesmaximal, characteristic, complemented
18Q8×#125C211yesmaximal, characteristic, complemented
19Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
20#36483C211yesmaximal, characteristic, complemented
21#36467C211yesmaximal, characteristic, complemented
22#36457C211yesmaximal, characteristic, complemented
23#36455C211yesmaximal, characteristic, complemented
24#36445C211yesmaximal, characteristic, complemented
25#36432C211yesmaximal, characteristic, complemented
26#36005C211yesmaximal, characteristic, complemented
27#36005C211yesmaximal, characteristic, complemented
28#35831C211yesmaximal, characteristic, complemented
29#35831C211yesmaximal, characteristic, complemented
30#35816C211yesmaximal, characteristic, complemented
31#35748C211yesmaximal, characteristic, complemented
32C2×#562C2216yes—
33C2×Q82C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#550C2211yescharacteristic
37C2×#550C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#520C2211yescharacteristic
42C2×#520C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44C22×C4×Q8C2211yescharacteristic
45#2861C2213yes—
46#2859C2213yes—
47#2858C2213yes—
48#2857C2213yes—
49#2857C2213yes—
50#2856C2213yes—
51#2856C2213yes—
52#2855C2213yes—
53#2854C2213yes—
54#2841C2216yes—
55#2837C2216yes—
56#2837C2216yes—
57#2830C2216yes—
58#2829C2216yes—
59#2829C2216yes—
60#2827C2216yes—
61#2820C2216yes—
62#2816C2216yes—
63#2816C2216yes—
64#2814C2216yes—
65#2800C2213yes—
66#2788C2216yes—
67#2772C2213yes—
68#2768C2216yes—
69#2768C2213yes—
70#2761C2213yes—
71#2755C2213yes—
72#2754C2213yes—
73#2750C2213yes—
74#2741C2213yes—
75#2740C2213yes—
76#2732C2216yes—
77#2730C2216yes—
78#2711C2213yes—
79#2710C2216yes—
80#2710C2216yes—
81#2710C2213yes—
82#2706C2216yes—
83#2706C2213yes—
84#2704C2211yescharacteristic
85#2701C2216yes—
86#2700C2213yes—
87#2694C2216yes—
88#2694C2216yes—
89#2692C2216yes—
90#2692C2216yes—
91#2686C2216yes—
92#2682C2216yes—
93#2681C2216yes—
94#2681C2216yes—
95#2676C2213yes—
96#2672C2216yes—
97#2672C2213yes—
98#2672C2216yes—
99#2672C2216yes—
100#2671C2216yes—
101#2671C2216yes—
102#2629C2213yes—
103#2628C2213yes—
104#2624C2213yes—
105#2624C2213yes—
106#2620C2213yes—
107#2620C2213yes—
108#2592C2213yes—
109#2582C2213yes—
110#2580C2213yes—
111#2567C2213yes—
112#2566C2213yes—
113#2563C2213yes—
114#2562C2213yes—
115#2552C2213yes—
116#2552C2213yes—
117#2548C2213yes—
118#2548C2213yes—
119#2544C2213yes—
120#2544C2213yes—
121#2542C2213yes—
122#2542C2213yes—
123#2541C2213yes—
124#2538C2213yes—
125#2538C2213yes—
126#2538C2213yes—
127#2537C2213yes—
128#2537C2213yes—
129#2537C2213yes—
130#2507C2213yes—
131#2507C2213yes—
132#2507C2213yes—
133#2507C2213yes—
134#2501C2213yes—
135#2501C2213yes—
136#2501C2213yes—
137#2499C2213yes—
138#2492C2213yes—
139#2491C2213yes—
140#2491C2213yes—
141#2491C2213yes—
142#2491C2213yes—
143#2491C2213yes—
144#2490C2213yes—
145#2489C2213yes—
146#2487C2213yes—
147#2487C2213yes—
148#2486C2213yes—
149#2485C2213yes—
150#2454C2213yes—
151#2454C2213yes—
152#2454C2213yes—
153#2452C2213yes—
154#2452C2213yes—
155#2452C2213yes—
156#2451C2213yes—
157#2451C2213yes—
158#2448C2213yes—
159#2448C2213yes—
160#2447C2213yes—
161#2447C2213yes—
162#2445C2213yes—
163#2445C2213yes—
164#2445C2213yes—
165#2445C2213yes—
166#2442C2213yes—
167#2441C2213yes—
168#2441C2213yes—
169#2440C2213yes—
170#2440C2213yes—
171#2440C2213yes—
172#2440C2213yes—
173#2440C2213yes—
174#2428C2213yes—
175#2428C2213yes—
176#2428C2213yes—
177#2428C2213yes—
178#2427C2213yes—
179#2427C2213yes—
180#2426C2213yes—
181#2426C2213yes—
182#2423C2213yes—
183#2423C2213yes—
184#2422C2213yes—
185#2422C2213yes—
186#2422C2213yes—
187#2422C2213yes—
188#2422C2213yes—
189#2420C2213yes—
190#2417C2213yes—
191#2417C2213yes—
192#2416C2213yes—
193#2416C2213yes—
194#2416C2213yes—
195#2416C2213yes—
196#2414C2213yes—
197#2414C2213yes—
198#2396C2213yes—
199#2396C2213yes—
200#2395C2213yes—
201#2395C2213yes—
202#2392C2213yes—
203#2392C2213yes—
204#2377C2216yes—
205#2376C2216yes—
206#2351C2211yescharacteristic
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
225Q8×C22⋊C4C2211yescharacteristic
226Q8×C22⋊C4C2211yescharacteristic
227Q8×C22⋊C4C2211yescharacteristic
228C4×#125C2213yes—
229C4×#124C2213yes—
230C4×#124C2213yes—
231C4×C22⋊Q8C2213yes—
232C4×C22⋊Q8C2213yes—
233C4×#123C2213yes—
234C4×#123C2213yes—
235C4×#121C2213yes—
236C4×#121C2213yes—
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C22×#41C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242#562—424no—
243Q82—44no—
244#557—44no—
245#550—44no—
246#550—44no—
247#550—44no—
248#548—44no—
249#548—44no—
250#548—44no—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×#127C2313yes—
256C2×#127C2313yes—
257C2×#127C2313yes—
258C2×#125C2311yescharacteristic
259C2×#125C2313yes—
260C2×#125C2316yes—
261C2×#125C2313yes—
262C2×#124C2313yes—
263C2×#124C2316yes—
264C2×#124C2313yes—
265C2×#124C2313yes—
266C2×#124C2313yes—
267C2×#124C2313yes—
268C2×#124C2316yes—
269C2×#123C2313yes—
270C2×#123C2313yes—
271C2×#123C2316yes—
272C2×#123C2316yes—
273C2×#123C2316yes—
274C2×#123C2316yes—
275C2×#123C2316yes—
276C2×C22⋊Q8C2311yescharacteristic
277C2×C22⋊Q8C2316yes—
278C2×C22⋊Q8C2316yes—
279C2×C22⋊Q8C2313yes—
280C2×C22⋊Q8C2313yes—
281C2×C22⋊Q8C2313yes—
282C2×C22⋊Q8C2313yes—
283C2×C22⋊Q8C2316yes—
284C2×C22⋊Q8C2316yes—
285C2×C22⋊Q8C2316yes—
286C2×#121C2313yes—
287C2×#121C2316yes—
288C2×#121C2316yes—
289C2×#121C2313yes—
290C2×#121C2313yes—
291C2×#121C2313yes—
292C2×#121C2313yes—
293C2×#121C2313yes—
294C2×#121C2313yes—
295C2×#121C2313yes—
296C2×#121C2313yes—
297C2×#121C2313yes—
298C2×#121C2313yes—
299C2×#121C2316yes—
300C2×#121C2316yes—
301C2×#121C2316yes—
302#520—44no—
303#520—44no—
304C4×#41—44no—
305C2×C4×Q8—44no—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2313yes—
318C2×C4×Q8C2313yes—
319C2×C4×Q8C2313yes—
320C2×C4×Q8C2313yes—
321C2×C4×D4C2313yes—
322C2×C4×D4C2313yes—
323C2×C4×D4C2313yes—
324C2×C4×D4C2313yes—
325C2×C4×D4C2313yes—
326C2×C4×D4C2313yes—
327C2×C4×D4C2313yes—
328C2×C4×D4C2313yes—
329C2×C4×D4C2313yes—
330C2×C4×D4C2313yes—
331C2×C4×D4C2313yes—
332C2×C4×D4C2313yes—
333C2×#117C2313yes—
334C2×#117C2313yes—
335C2×#117C2313yes—
336C22×C4⋊C4C2313yes—
337C22×C4⋊C4C2313yes—
338C22×C4⋊C4C2313yes—
339C22×C42C2313yes—
340C22×C42C2313yes—
341#400C2316yes—
342#400C2313yes—
343#400C2313yes—
344#400C2313yes—
345#400C2313yes—
346#399C2313yes—
347#399C2316yes—
348#399C2316yes—
349#399C2316yes—
350#399C2313yes—
351#399C2316yes—
352#399C2316yes—
353#399C2316yes—
354#399C2316yes—
355#399C2313yes—
356#399C2313yes—
357#398C2316yes—
358#398C2316yes—
359#398C2316yes—
360#398C2316yes—
361#398C2316yes—
362#398C2316yes—
363#398C2313yes—
364#398C2316yes—
365#398C2313yes—
366#398C2316yes—
367#398C2313yes—
368#398C2313yes—
369#398C2311yescharacteristic
370#398C2311yescharacteristic
371#398C2311yescharacteristic
372#398C2313yes—
373#397C2313yes—
374#397C2316yes—
375#397C2313yes—
376#397C2316yes—
377#397C2316yes—
378#397C2316yes—
379#397C2316yes—
380#397C2313yes—
381#397C2313yes—
382#397C2313yes—
383#397C2313yes—
384#397C2313yes—
385#397C2313yes—
386#396C2316yes—
387#396C2316yes—
388#396C2316yes—
389#396C2316yes—
390#396C2313yes—
391#396C2313yes—
392#396C2313yes—
393#396C2316yes—
394#396C2316yes—
395#396C2316yes—
396#396C2316yes—
397#396C2313yes—
398#396C2311yescharacteristic
399#396C2311yescharacteristic
400#396C2313yes—
401#396C2313yes—
402#395C2316yes—
403#395C2316yes—
404#395C2316yes—
405#395C2311yescharacteristic
406#395C2313yes—
407#394C2313yes—
408#394C2313yes—
409#394C2316yes—
410#394C2316yes—
411#394C2316yes—
412#394C2316yes—
413#394C2316yes—
414#394C2316yes—
415#394C2316yes—
416#394C2316yes—
417#394C2316yes—
418#394C2316yes—
419#394C2316yes—
420#394C2316yes—
421#394C2313yes—
422#394C2313yes—
423#394C2316yes—
424#394C2316yes—
425#394C2316yes—
426#394C2316yes—
427#394C2313yes—
428#394C2313yes—
429#394C2313yes—
430#394C2313yes—
431#394C2313yes—
432#394C2313yes—
433#393C2313yes—
434#393C2316yes—
435#393C2316yes—
436#393C2316yes—
437#393C2316yes—
438#393C2313yes—
439#392C2316yes—
440#392C2316yes—
441#392C2313yes—
442#392C2313yes—
443#391C2313yes—
444#391C2313yes—
445#391C2313yes—
446#391C2313yes—
447#391C2313yes—
448#391C2313yes—
449#391C2313yes—
450#391C2313yes—
451#391C2316yes—
452#391C2313yes—
453#391C2311yescharacteristic
454#390C2316yes—
455#390C2313yes—
456#390C2313yes—
457#390C2316yes—
458#390C2316yes—
459#390C2313yes—
460#390C2313yes—
461#390C2313yes—
462#390C2313yes—
463#390C2313yes—
464#390C2313yes—
465#390C2313yes—
466#390C2313yes—
467#390C2313yes—
468#390C2313yes—
469#390C2313yes—
470#390C2313yes—
471#390C2313yes—
472#390C2313yes—
473#390C2313yes—
474#390C2313yes—
475#390C2313yes—
476#390C2316yes—
477#390C2313yes—
478#390C2313yes—
479#390C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2316yes—
484#389C2313yes—
485#389C2313yes—
486#389C2316yes—
487#389C2313yes—
488#389C2313yes—
489#389C2313yes—
490#389C2313yes—
491#389C2313yes—
492#389C2313yes—
493#389C2313yes—
494#389C2313yes—
495#389C2313yes—
496#389C2316yes—
497#389C2313yes—
498#389C2313yes—
499#389C2316yes—
500#389C2313yes—
501#389C2313yes—
502#389C2313yes—
503#389C2313yes—
504#389C2313yes—
505#389C2313yes—
506#389C2313yes—
507#389C2311yescharacteristic
508#389C2311yescharacteristic
509#389C2313yes—
510#388C2313yes—
511#388C2316yes—
512#388C2316yes—
513#388C2316yes—
514#388C2313yes—
515#388C2313yes—
516#388C2316yes—
517#388C2313yes—
518#388C2313yes—
519#388C2316yes—
520#388C2313yes—
521#388C2313yes—
522#388C2313yes—
523#388C2313yes—
524#388C2313yes—
525#388C2313yes—
526#388C2313yes—
527#388C2313yes—
528#388C2313yes—
529#388C2311yescharacteristic
530#388C2311yescharacteristic
531#387C2313yes—
532#387C2313yes—
533#387C2313yes—
534#387C2313yes—
535#387C2313yes—
536#387C2313yes—
537#387C2316yes—
538#387C2313yes—
539#387C2313yes—
540#387C2313yes—
541#387C2313yes—
542#387C2313yes—
543#387C2313yes—
544#386C2316yes—
545#386C2313yes—
546#386C2316yes—
547#386C2316yes—
548#386C2316yes—
549#386C2316yes—
550#386C2316yes—
551#386C2313yes—
552#386C2313yes—
553#386C2313yes—
554#386C2313yes—
555#386C2313yes—
556#385C2316yes—
557#385C2316yes—
558#385C2316yes—
559#385C2316yes—
560#385C2316yes—
561#385C2316yes—
562#385C2316yes—
563#385C2313yes—
564#385C2311yescharacteristic
565#385C2313yes—
566#385C2313yes—
567#385C2313yes—
568#385C2313yes—
569#384C2313yes—
570#384C2313yes—
571#384C2313yes—
572#384C2313yes—
573#384C2313yes—
574#384C2313yes—
575#384C2313yes—
576#384C2313yes—
577#384C2313yes—
578#382C2313yes—
579#382C2313yes—
580#382C2313yes—
581#382C2313yes—
582#381C2313yes—
583#381C2313yes—
584#381C2316yes—
585#380C2313yes—
586#380C2313yes—
587#380C2313yes—
588#380C2313yes—
589#380C2313yes—
590#380C2313yes—
591#380C2313yes—
592#380C2313yes—
593#380C2313yes—
594#380C2316yes—
595#380C2313yes—
596#380C2313yes—
597#380C2313yes—
598#380C2313yes—
599#380C2313yes—
600#380C2316yes—
601#380C2316yes—
602#380C2313yes—
603#380C2316yes—
604#380C2311yescharacteristic
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⋊C4C2313yes—
629C4×C22⋊C4C2313yes—
630C43C2313yes—
631C2×#41—24no—
632C2×#41—24no—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41—24no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41—24no—
639C2×#41—24no—
640C22×Q8—24no—
641C22×Q8—24no—
642C22×Q8—24no—
643C22×Q8C2413yes—
644C22×Q8C2411yescharacteristic
645C22×Q8C2413yes—
646C22×Q8C2416yes—
647C22×Q8C2411yescharacteristic
648C22×D4C2413yes—
649C22×D4C2413yes—
650C22×D4C2413yes—
651C22×D4C2413yes—
652C22×D4C2413yes—
653C22×D4C2413yes—
654C22×D4C2413yes—
655C22×D4C2413yes—
656C22×D4C2413yes—
657C22×D4C2416yes—
658C22×D4C2416yes—
659C22×D4C2416yes—
660C23×C4C2413yes—
661C23×C4C2413yes—
662C23×C4C2413yes—
663C23×C4C2413yes—
664C23×C4C2411yescharacteristic
665C23×C4C2413yes—
666C23×C4C2413yes—
667C23×C4C2413yes—
668C23×C4C2416yes—
669C23×C4C2416yes—
670C4⋊Q8—46no—
671C4⋊Q8—46no—
672C4⋊Q8—46no—
673C4⋊Q8—46no—
674#127—46no—
675#127—46no—
676#127—46no—
677#125—24no—
678#125—46no—
679#125—46no—
680#125—412no—
681#124—212no—
682#124—412no—
683#124—46no—
684#124—46no—
685#124—46no—
686#124—46no—
687#124—86no—
688#123—212no—
689#123—212no—
690#123—412no—
691#123—412no—
692#123—412no—
693#123—86no—
694#123—86no—
695C22⋊Q8—24no—
696C22⋊Q8—412no—
697C22⋊Q8—46no—
698C22⋊Q8—412no—
699C22⋊Q8—412no—
700C22⋊Q8—46no—
701C22⋊Q8—46no—
702C22⋊Q8—46no—
703C22⋊Q8—412no—
704C22⋊Q8—86no—
705#121—212no—
706#121—46no—
707#121—412no—
708#121—412no—
709#121—412no—
710#121—46no—
711#121—46no—
712#121—46no—
713#121—46no—
714#121—46no—
715#121—46no—
716#121—46no—
717#121—46no—
718#121—46no—
719#121—412no—
720#121—86no—
721C4×Q8—24no—
722C4×Q8—24no—
723C4×Q8—24no—
724C4×Q8—24no—
725C4×Q8—24no—
726C4×Q8—24no—
727C4×Q8—24no—
728C4×Q8—24no—
729C4×Q8—24no—
730C4×Q8—24no—
731C4×Q8—24no—
732C4×Q8—46no—
733C4×Q8—46no—
734C4×Q8—46no—
735C4×Q8—46no—
736C4×D4—46no—
737C4×D4—46no—
738C4×D4—46no—
739C4×D4—46no—
740C4×D4—46no—
741C4×D4—46no—
742C4×D4—46no—
743C4×D4—46no—
744C4×D4—46no—
745C4×D4—46no—
746C4×D4—46no—
747C4×D4—46no—
748#117—46no—
749#117—46no—
750#117—46no—
751C2×C4⋊C4—46no—
752C2×C4⋊C4—46no—
753C2×C4⋊C4—46no—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2416yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2413yes—
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2416yes—
797C2×C4⋊C4C2416yes—
798C2×C4⋊C4C2416yes—
799C2×C4⋊C4C2416yes—
800C2×C4⋊C4C2413yes—
801C2×C4⋊C4C2416yes—
802C2×C4⋊C4C2416yes—
803C2×C4⋊C4C2413yes—
804C2×C4⋊C4C2413yes—
805C2×C4⋊C4C2416yes—
806C2×C4⋊C4C2413yes—
807C2×C4⋊C4C2413yes—
808C2×C4⋊C4C2416yes—
809C2×C4⋊C4C2416yes—
810C2×C4⋊C4C2416yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2411yescharacteristic
821C2×C22⋊C4C2411yescharacteristic
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2416yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2411yescharacteristic
832C2×C22⋊C4C2411yescharacteristic
833C2×C22⋊C4C2411yescharacteristic
834C2×C22⋊C4C2413yes—
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2413yes—
837C2×C22⋊C4C2413yes—
838C2×C22⋊C4C2413yes—
839C2×C22⋊C4C2413yes—
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2413yes—
842C2×C22⋊C4C2413yes—
843C2×C22⋊C4C2416yes—
844C2×C22⋊C4C2416yes—
845C2×C22⋊C4C2416yes—
846C2×C22⋊C4C2416yes—
847C2×C22⋊C4C2416yes—
848C2×C22⋊C4C2416yes—
849C2×C22⋊C4C2416yes—
850C2×C22⋊C4C2416yes—
851C2×C22⋊C4C2416yes—
852C2×C22⋊C4C2413yes—
853C2×C22⋊C4C2413yes—
854C2×C22⋊C4C2413yes—
855C2×C22⋊C4C2413yes—
856C2×C22⋊C4C2413yes—
857C2×C22⋊C4C2416yes—
858C2×C22⋊C4C2416yes—
859C2×C22⋊C4C2416yes—
860C2×C22⋊C4C2413yes—
861C2×C22⋊C4C2413yes—
862C2×C22⋊C4C2413yes—
863C2×C22⋊C4C2413yes—
864C2×C22⋊C4C2411yescharacteristic
865C2×C42—46no—
866C2×C42—46no—
867C2×C42C2413yes—
868C2×C42C2413yes—
869C2×C42C2413yes—
870C2×C42C2413yes—
871C2×C42C2413yes—
872C2×C42C2413yes—
873C2×C42C2413yes—
874C2×C42C2413yes—
875C2×C42C2413yes—
876C2×C42C2413yes—
877C2×C42C2413yes—
878C2×C42C2413yes—
879C2×C42C2411yescharacteristic
880C2×C42C2413yes—
881C2×C42C2413yes—
882C2×C42C2413yes—
883C2×C42C2413yes—
884C2×C42C2413yes—
885C2×C42C2411yescharacteristic
886#95C2411yescharacteristic
887#95C2411yescharacteristic
888#95C2411yescharacteristic
889#95C2411yescharacteristic
890#95C2411yescharacteristic
891#95C2411yescharacteristic
892#95C2411yescharacteristic
893#95C2411yescharacteristic
894#95C2411yescharacteristic
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2413yes—
910#95C2411yescharacteristic
911#95C2416yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2413yes—
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921#95C2413yes—
922#95C2413yes—
923#95C2413yes—
924#95C2413yes—
925#95C2413yes—
926#95C2413yes—
927#95C2413yes—
928#95C2413yes—
929#95C2413yes—
930#95C2413yes—
931#95C2416yes—
932#95C2416yes—
933#95C2416yes—
934#95C2416yes—
935C24C2513yes—
936C24C2513yes—
937C24C2513yes—
938C24C2511yescharacteristic
939#41—416no—
940#41—416no—
941#41—416no—
942C2×Q8—26no—
943C2×Q8—26no—
944C2×Q8—26no—
945C2×Q8—22no—
946C2×Q8—26no—
947C2×Q8—22no—
948C2×Q8—41no—
949C2×Q8—43no—
950C2×Q8—43no—
951C2×Q8—46no—
952C2×Q8—46no—
953C2×Q8—46no—
954C2×Q8—416no—
955C2×Q8H(5,𝔽2)14yes—
956C2×Q8H(5,𝔽2)14yes—
957C2×Q82−1+414yes—
958C2×D4—26no—
959C2×D4—26no—
960C2×D4—26no—
961C2×D4—26no—
962C2×D4—26no—
963C2×D4—26no—
964C2×D4—26no—
965C2×D4—26no—
966C2×D4—26no—
967C2×D4—26no—
968C2×D4—26no—
969C2×D4—26no—
970C2×D4—26no—
971C2×D4—26no—
972C2×D4—26no—
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—46no—
986C2×D4—46no—
987C2×D4—46no—
988C2×D4—46no—
989C2×D4—46no—
990C2×D4—46no—
991C2×D4—46no—
992C2×D4—46no—
993C2×D4—46no—
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—22no—
1004C22×C4—26no—
1005C22×C4—26no—
1006C22×C4—26no—
1007C22×C4—26no—
1008C22×C4—22no—
1009C22×C4—26no—
1010C22×C4—26no—
1011C22×C4—41no—
1012C22×C4—43no—
1013C22×C4—43no—
1014C22×C4—43no—
1015C22×C4—43no—
1016C22×C4—43no—
1017C22×C4—43no—
1018C22×C4—46no—
1019C22×C4—46no—
1020C22×C4—46no—
1021C22×C4—46no—
1022C22×C4—46no—
1023C22×C4—46no—
1024C22×C4C2511yescharacteristic
1025C22×C4C2513yes—
1026C22×C4C2511yescharacteristic
1027C22×C4C2513yes—
1028C22×C4C2511yescharacteristic
1029C22×C4C2511yescharacteristic
1030C22×C4C2511yescharacteristic
1031C22×C4C2513yes—
1032C22×C4C2511yescharacteristic
1033C22×C4C2511yescharacteristic
1034C22×C4C2511yescharacteristic
1035C22×C4C2513yes—
1036C22×C4C2513yes—
1037C22×C4C2513yes—
1038C22×C4C2513yes—
1039C22×C4C2513yes—
1040C22×C4C2513yes—
1041C22×C4C2513yes—
1042C22×C4C2513yes—
1043C22×C4C2513yes—
1044C22×C4C2511yescharacteristic
1045C22×C4C2511yescharacteristic
1046C22×C4C2511yescharacteristic
1047C22×C4C2511yescharacteristic
1048C22×C4C2511yescharacteristic
1049C22×C4C2511yescharacteristic
1050C22×C4C2513yes—
1051C4⋊C4—26no—
1052C4⋊C4—26no—
1053C4⋊C4—26no—
1054C4⋊C4—26no—
1055C4⋊C4—26no—
1056C4⋊C4—26no—
1057C4⋊C4—26no—
1058C4⋊C4—26no—
1059C4⋊C4—26no—
1060C4⋊C4—26no—
1061C4⋊C4—26no—
1062C4⋊C4—26no—
1063C4⋊C4—26no—
1064C4⋊C4—26no—
1065C4⋊C4—26no—
1066C4⋊C4—22no—
1067C4⋊C4—22no—
1068C4⋊C4—22no—
1069C4⋊C4—22no—
1070C4⋊C4—22no—
1071C4⋊C4—22no—
1072C4⋊C4—22no—
1073C4⋊C4—22no—
1074C4⋊C4—26no—
1075C4⋊C4—43no—
1076C4⋊C4—43no—
1077C4⋊C4—46no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
1082C4⋊C4—41no—
1083C4⋊C4—43no—
1084C4⋊C4—43no—
1085C4⋊C4—43no—
1086C4⋊C4—41no—
1087C4⋊C4—43no—
1088C4⋊C4—43no—
1089C4⋊C4—43no—
1090C4⋊C4—43no—
1091C4⋊C4—43no—
1092C4⋊C4—43no—
1093C4⋊C4—46no—
1094C4⋊C4—46no—
1095C4⋊C4—46no—
1096C4⋊C4—46no—
1097C4⋊C4—43no—
1098C4⋊C4—43no—
1099C4⋊C4—46no—
1100C4⋊C4—46no—
1101C4⋊C4—43no—
1102C4⋊C4—43no—
1103C4⋊C4—46no—
1104C4⋊C4—46no—
1105C4⋊C4—46no—
1106C4⋊C4—43no—
1107C4⋊C4—46no—
1108C4⋊C42−1+414yes—
1109C22⋊C4—26no—
1110C22⋊C4—26no—
1111C22⋊C4—26no—
1112C22⋊C4—26no—
1113C22⋊C4—26no—
1114C22⋊C4—26no—
1115C22⋊C4—26no—
1116C22⋊C4—26no—
1117C22⋊C4—26no—
1118C22⋊C4—22no—
1119C22⋊C4—22no—
1120C22⋊C4—26no—
1121C22⋊C4—26no—
1122C22⋊C4—26no—
1123C22⋊C4—43no—
1124C22⋊C4—43no—
1125C22⋊C4—43no—
1126C22⋊C4—43no—
1127C22⋊C4—46no—
1128C22⋊C4—41no—
1129C22⋊C4—41no—
1130C22⋊C4—41no—
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—46no—
1141C22⋊C4—46no—
1142C22⋊C4—46no—
1143C22⋊C4—46no—
1144C22⋊C4—46no—
1145C22⋊C4—46no—
1146C22⋊C4—46no—
1147C22⋊C4—46no—
1148C22⋊C4—46no—
1149C22⋊C4—43no—
1150C22⋊C4—43no—
1151C22⋊C4—46no—
1152C22⋊C4—43no—
1153C22⋊C4—43no—
1154C22⋊C4—43no—
1155C22⋊C4—46no—
1156C22⋊C4—46no—
1157C22⋊C4—43no—
1158C22⋊C4—43no—
1159C22⋊C4—43no—
1160C22⋊C4—43no—
1161C22⋊C4H(5,𝔽2)14yes—
1162C42—26no—
1163C42—26no—
1164C42—26no—
1165C42—26no—
1166C42—26no—
1167C42—26no—
1168C42—26no—
1169C42—26no—
1170C42—26no—
1171C42—26no—
1172C42—26no—
1173C42—26no—
1174C42—22no—
1175C42—41no—
1176C42—43no—
1177C42—43no—
1178C42—43no—
1179C42—43no—
1180C42—43no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—23no—
1188C23—23no—
1189C23—23no—
1190C23—23no—
1191C23—23no—
1192C23—23no—
1193C23—23no—
1194C23—23no—
1195C23—23no—
1196C23—23no—
1197C23—23no—
1198C23—23no—
1199C23—23no—
1200C23—23no—
1201C23—23no—
1202C23—23no—
1203C23—23no—
1204C23—23no—
1205C23—23no—
1206C23—23no—
1207C23—23no—
1208C23C2×H(5,𝔽2)12yes—
1209C23C2611yescharacteristic
1210Q8—44no—
1211Q8—412no—
1212Q8—86no—
1213Q8—166no—
1214Q8#562116yescomplemented
1215D4—412no—
1216D4—412no—
1217D4—412no—
1218D4—86no—
1219D4—86no—
1220D4—86no—
1221D4—86no—
1222D4—86no—
1223D4—86no—
1224D4—166no—
1225D4—166no—
1226D4—166no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
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—21no—
1242C2×C4—21no—
1243C2×C4—21no—
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—23no—
1254C2×C4—23no—
1255C2×C4—23no—
1256C2×C4—21no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—23no—
1262C2×C4—23no—
1263C2×C4—21no—
1264C2×C4—23no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—23no—
1270C2×C4—23no—
1271C2×C4—21no—
1272C2×C4—23no—
1273C2×C4—23no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—23no—
1282C2×C4—23no—
1283C2×C4—23no—
1284C2×C4—23no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—23no—
1288C2×C4—23no—
1289C2×C4—21no—
1290C2×C4—23no—
1291C2×C4—23no—
1292C2×C4—21no—
1293C2×C4—23no—
1294C2×C4—23no—
1295C2×C4—21no—
1296C2×C4—23no—
1297C2×C4—23no—
1298C2×C4—23no—
1299C2×C4—44no—
1300C2×C4—412no—
1301C2×C4—412no—
1302C2×C4—412no—
1303C2×C4—412no—
1304C2×C4—86no—
1305C2×C4—86no—
1306C2×C4—86no—
1307C2×C4—166no—
1308C2×C4—166no—
1309C2×C4C2×H(5,𝔽2)12yes—
1310C2×C4C2×H(5,𝔽2)12yes—
1311C2×C4C2×H(5,𝔽2)16yes—
1312C2×C4C2×H(5,𝔽2)16yes—
1313C2×C4C2×2−1+412yes—
1314C2×C4C2×2−1+412yes—
1315C2×C4C2×2−1+412yes—
1316C2×C4C2×2−1+416yes—
1317C2×C4#58512yes—
1318C22—22no—
1319C22—22no—
1320C22—22no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—43no—
1326C22—43no—
1327C22—43no—
1328C22—43no—
1329C22—43no—
1330C22—43no—
1331C22—43no—
1332C22—43no—
1333C22—43no—
1334C22—43no—
1335C22—43no—
1336C22—43no—
1337C22—43no—
1338C22—43no—
1339C22—43no—
1340C22—43no—
1341C22—43no—
1342C22—43no—
1343C22—43no—
1344C22—43no—
1345C22—43no—
1346C22C22×H(5,𝔽2)11yescharacteristic
1347C22C22×H(5,𝔽2)11yescharacteristic
1348C22C22×H(5,𝔽2)11yescharacteristic
1349C22C22×2−1+411yescharacteristic
1350C22C22×2−1+411yescharacteristic
1351C22C2×#58511yescharacteristic
1352C22H(7,𝔽2)11yescharacteristic
1353C4—22no—
1354C4—22no—
1355C4—22no—
1356C4—22no—
1357C4—22no—
1358C4—22no—
1359C4—43no—
1360C4—43no—
1361C4—43no—
1362C4—43no—
1363C4—41no—
1364C4—41no—
1365C4—43no—
1366C4—43no—
1367C4—43no—
1368C4—43no—
1369C4—43no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—43no—
1374C4—41no—
1375C4—41no—
1376C4—41no—
1377C4—43no—
1378C4—43no—
1379C4C2×#562112yes—
1380C2—42no—
1381C2—83no—
1382C2—83no—
1383C2—83no—
1384C2C22×#56211yescharacteristic
1385C2#6291611yescharacteristic
1386C2#6291711yescharacteristic
1387C2#6295211yescharacteristic
1388C2#6301411yescharacteristic
1389C2#6301511yescharacteristic
1390C2#6303711yescharacteristic
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. #53108C2semidirect
2. #53101C2semidirect
3. #53056C2semidirect
4. #53016C2semidirect
5. #52972C2semidirect
6. #52964C2semidirect
7. #52296C2semidirect
8. #46104C2semidirect
9. #46044C2semidirect
10. #45995C2semidirect
11. #45676C2semidirect
12. #45653C2semidirect
13. #45610C2semidirect
14. #45498C2semidirect
15. #45486C2semidirect
16. #45486C2semidirect
17. #36576C2semidirect
18. Q8×#125C2semidirect
19. Q8×C22⋊Q8C2semidirect
20. #36483C2semidirect
21. #36467C2semidirect
22. #36457C2semidirect
23. #36455C2semidirect
24. #36445C2semidirect
25. #36432C2semidirect
26. #36005C2semidirect
27. #36005C2semidirect
28. #35831C2semidirect
29. #35831C2semidirect
30. #35816C2semidirect
31. #35748C2semidirect
1214. Q8#562semidirect

Maximal subgroups

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

subgroupindex
#531082
#531012
#530562
#530162
#529722
#529642
#522962
#461042
#460442
#459952
#456762
#456532
#456102
#454982
#454862
#365762
Q8×#1252
Q8×C22⋊Q82
#364832
#364672
#364572
#364552
#364452
#364322
#360052
#358312
#358162
#357482