Finite Group Databasebeta

← #7659174

Subgroups — #7659174

Order 512.

4810 conjugacy classes of subgroups.

The subgroup lattice has 1314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52276C213yesmaximal, complemented
2#42946C213yesmaximal, complemented
3#42925C213yesmaximal, complemented
4#42904C213yesmaximal, complemented
5#42896C213yesmaximal, complemented
6#42873C213yesmaximal, complemented
7#42841C213yesmaximal, complemented
8#40128C213yesmaximal, complemented
9#40123C213yesmaximal, complemented
10#40029C213yesmaximal, complemented
11#40004C213yesmaximal, complemented
12#39658C213yesmaximal, complemented
13#39245C213yesmaximal, complemented
14#37350C213yesmaximal, complemented
15#37339C213yesmaximal, complemented
16#37315C213yesmaximal, complemented
17#36576C211yesmaximal, characteristic
18Q8×#125C211yesmaximal, characteristic, complemented
19Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
20#36458C211yesmaximal, characteristic, complemented
21#36456C211yesmaximal, characteristic, complemented
22#36433C211yesmaximal, characteristic, complemented
23#36005C211yesmaximal, characteristic, complemented
24#35971C211yesmaximal, characteristic, complemented
25#35898C211yesmaximal, characteristic, complemented
26#35801C211yesmaximal, characteristic, complemented
27#35801C211yesmaximal, characteristic, complemented
28#35748C211yesmaximal, characteristic, complemented
29#34312C211yesmaximal, characteristic, complemented
30#34293C211yesmaximal, characteristic, complemented
31#34249C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#548C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C2×#519C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41#2860C2213yes—
42#2859C2213yes—
43#2857C2213yes—
44#2857C2213yes—
45#2856C2213yes—
46#2854C2213yes—
47#2838C2216yes—
48#2837C2216yes—
49#2808C2216yes—
50#2807C2213yes—
51#2802C2213yes—
52#2798C2213yes—
53#2796C2213yes—
54#2796C2213yes—
55#2790C2216yes—
56#2785C2216yes—
57#2783C2213yes—
58#2783C2216yes—
59#2782C2213yes—
60#2781C2216yes—
61#2776C2213yes—
62#2775C2216yes—
63#2757C2213yes—
64#2747C2213yes—
65#2746C2213yes—
66#2732C2216yes—
67#2728C2216yes—
68#2727C2216yes—
69#2724C2216yes—
70#2723C2216yes—
71#2720C2216yes—
72#2718C2216yes—
73#2711C2216yes—
74#2708C2216yes—
75#2694C2213yes—
76#2691C2213yes—
77#2691C2216yes—
78#2690C2211yescharacteristic
79#2689C2213yes—
80#2681C2213yes—
81#2681C2216yes—
82#2681C2216yes—
83#2680C2216yes—
84#2667C2216yes—
85#2663C2216yes—
86#2663C2216yes—
87#2654C2216yes—
88#2654C2216yes—
89#2651C2216yes—
90#2647C2213yes—
91#2644C2213yes—
92#2628C2213yes—
93#2624C2213yes—
94#2624C2213yes—
95#2624C2213yes—
96#2588C2216yes—
97#2582C2213yes—
98#2580C2213yes—
99#2571C2213yes—
100#2570C2213yes—
101#2567C2213yes—
102#2563C2213yes—
103#2560C2216yes—
104#2560C2216yes—
105#2558C2216yes—
106#2556C2216yes—
107#2553C2216yes—
108#2552C2213yes—
109#2552C2213yes—
110#2548C2213yes—
111#2542C2213yes—
112#2538C2213yes—
113#2538C2213yes—
114#2513C2213yes—
115#2513C2213yes—
116#2512C2213yes—
117#2512C2213yes—
118#2512C2213yes—
119#2512C2213yes—
120#2509C2213yes—
121#2508C2213yes—
122#2508C2213yes—
123#2507C2213yes—
124#2507C2213yes—
125#2507C2213yes—
126#2507C2213yes—
127#2507C2213yes—
128#2501C2213yes—
129#2500C2213yes—
130#2500C2213yes—
131#2500C2213yes—
132#2497C2213yes—
133#2497C2213yes—
134#2496C2213yes—
135#2496C2213yes—
136#2495C2213yes—
137#2494C2213yes—
138#2487C2213yes—
139#2485C2213yes—
140#2485C2213yes—
141#2485C2213yes—
142#2452C2213yes—
143#2452C2213yes—
144#2452C2213yes—
145#2452C2213yes—
146#2451C2213yes—
147#2451C2213yes—
148#2448C2213yes—
149#2448C2213yes—
150#2448C2213yes—
151#2448C2213yes—
152#2445C2213yes—
153#2445C2213yes—
154#2445C2213yes—
155#2445C2213yes—
156#2440C2213yes—
157#2440C2213yes—
158#2440C2213yes—
159#2440C2213yes—
160#2439C2213yes—
161#2439C2213yes—
162#2426C2213yes—
163#2426C2213yes—
164#2423C2213yes—
165#2423C2213yes—
166#2422C2213yes—
167#2422C2213yes—
168#2422C2213yes—
169#2421C2213yes—
170#2421C2213yes—
171#2420C2213yes—
172#2416C2213yes—
173#2416C2213yes—
174#2402C2213yes—
175#2401C2213yes—
176#2396C2213yes—
177#2395C2213yes—
178#2395C2213yes—
179#2395C2213yes—
180#2367C2213yes—
181#2367C2213yes—
182#2363C2213yes—
183#2363C2213yes—
184#2362C2213yes—
185#2360C2213yes—
186#2354C2213yes—
187#2352C2213yes—
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2213yes—
194#2351C2213yes—
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2213yes—
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2213yes—
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204Q8×C4⋊C4C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216#2335C2216yes—
217#2334C2216yes—
218#2326C2213yes—
219#2324C2213yes—
220#2324C2213yes—
221#2323C2213yes—
222#2317C2213yes—
223#2317C2213yes—
224C4×#125C2213yes—
225C4×#126C2213yes—
226C4×#124C2213yes—
227C4×C22⋊Q8C2213yes—
228C4×C22⋊Q8C2213yes—
229C4×C22⋊Q8C2213yes—
230C4×#123C2213yes—
231C4×#121C2213yes—
232#2296C2213yes—
233#2296C2213yes—
234#2293C2213yes—
235#2290C2213yes—
236#2276C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241Q82—44no—
242#550—44no—
243#548—28no—
244#548—28no—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×#127C2313yes—
249C2×#126C2313yes—
250C2×#126C2316yes—
251C2×#126C2316yes—
252C2×#125C2311yescharacteristic
253C2×#125C2316yes—
254C2×#124C2313yes—
255C2×#124C2313yes—
256C2×#123C2313yes—
257C2×#123C2316yes—
258C2×#123C2316yes—
259C2×#123C2316yes—
260C2×C22⋊Q8C2313yes—
261C2×C22⋊Q8C2313yes—
262C2×C22⋊Q8C2311yescharacteristic
263C2×C22⋊Q8C2313yes—
264C2×C22⋊Q8C2316yes—
265C2×C22⋊Q8C2316yes—
266C2×C22⋊Q8C2316yes—
267C2×C22⋊Q8C2316yes—
268C2×#121C2313yes—
269C2×#121C2313yes—
270C2×#121C2313yes—
271C2×#121C2313yes—
272C2×#121C2313yes—
273C2×#121C2316yes—
274#520—44no—
275#519—28no—
276#519—44no—
277C4×#41—44no—
278C2×C4×Q8—44no—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
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×Q8C2313yes—
292C2×C4×Q8C2313yes—
293C2×C4×Q8C2313yes—
294C2×C4×Q8C2313yes—
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×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×#117C2313yes—
306C2×#117C2313yes—
307C2×#117C2313yes—
308C2×#117C2313yes—
309C2×#117C2313yes—
310C2×#117C2313yes—
311C22×C4⋊C4C2313yes—
312C22×C4⋊C4C2313yes—
313C22×C42C2313yes—
314C22×C42C2313yes—
315#401C2313yes—
316#400C2316yes—
317#400C2313yes—
318#400C2313yes—
319#400C2313yes—
320#400C2313yes—
321#400C2316yes—
322#400C2313yes—
323#400C2316yes—
324#400C2313yes—
325#400C2313yes—
326#400C2311yescharacteristic
327#400C2313yes—
328#400C2311yescharacteristic
329#400C2313yes—
330#399C2316yes—
331#399C2313yes—
332#399C2316yes—
333#399C2313yes—
334#399C2316yes—
335#399C2316yes—
336#399C2313yes—
337#399C2313yes—
338#398C2313yes—
339#398C2316yes—
340#398C2313yes—
341#398C2316yes—
342#398C2316yes—
343#398C2316yes—
344#398C2316yes—
345#398C2316yes—
346#398C2313yes—
347#398C2316yes—
348#398C2311yescharacteristic
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#398C2313yes—
353#398C2313yes—
354#397C2316yes—
355#397C2316yes—
356#397C2313yes—
357#397C2316yes—
358#397C2316yes—
359#397C2316yes—
360#397C2313yes—
361#397C2316yes—
362#397C2313yes—
363#397C2316yes—
364#397C2311yescharacteristic
365#397C2311yescharacteristic
366#397C2313yes—
367#397C2313yes—
368#397C2313yes—
369#397C2313yes—
370#397C2313yes—
371#397C2313yes—
372#397C2313yes—
373#396C2316yes—
374#396C2316yes—
375#396C2316yes—
376#396C2316yes—
377#396C2313yes—
378#396C2313yes—
379#396C2316yes—
380#396C2316yes—
381#396C2313yes—
382#395C2316yes—
383#395C2316yes—
384#395C2316yes—
385#395C2311yescharacteristic
386#394C2316yes—
387#394C2316yes—
388#394C2316yes—
389#394C2316yes—
390#394C2313yes—
391#394C2313yes—
392#394C2316yes—
393#394C2316yes—
394#394C2316yes—
395#394C2313yes—
396#394C2313yes—
397#394C2313yes—
398#394C2313yes—
399#394C2316yes—
400#394C2316yes—
401#393C2313yes—
402#393C2316yes—
403#393C2316yes—
404#393C2316yes—
405#391C2313yes—
406#391C2316yes—
407#391C2313yes—
408#391C2313yes—
409#391C2313yes—
410#391C2313yes—
411#391C2316yes—
412#391C2311yescharacteristic
413#390C2313yes—
414#390C2316yes—
415#390C2313yes—
416#390C2313yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
420#390C2316yes—
421#390C2313yes—
422#390C2313yes—
423#390C2313yes—
424#390C2316yes—
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2313yes—
432#390C2313yes—
433#390C2313yes—
434#390C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2316yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2316yes—
444#389C2316yes—
445#389C2316yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2316yes—
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#388C2313yes—
481#388C2313yes—
482#388C2313yes—
483#388C2316yes—
484#388C2316yes—
485#388C2316yes—
486#388C2316yes—
487#388C2316yes—
488#388C2316yes—
489#388C2316yes—
490#388C2316yes—
491#388C2316yes—
492#388C2313yes—
493#388C2316yes—
494#388C2316yes—
495#388C2316yes—
496#388C2316yes—
497#388C2313yes—
498#388C2316yes—
499#388C2313yes—
500#388C2313yes—
501#388C2313yes—
502#388C2316yes—
503#388C2313yes—
504#388C2316yes—
505#388C2311yescharacteristic
506#388C2311yescharacteristic
507#388C2313yes—
508#388C2313yes—
509#387C2311yescharacteristic
510#387C2313yes—
511#387C2313yes—
512#387C2313yes—
513#387C2316yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2316yes—
518#387C2316yes—
519#387C2313yes—
520#387C2316yes—
521#387C2316yes—
522#387C2316yes—
523#387C2313yes—
524#387C2313yes—
525#387C2313yes—
526#387C2313yes—
527#387C2313yes—
528#387C2311yescharacteristic
529#387C2313yes—
530#386C2316yes—
531#386C2316yes—
532#386C2313yes—
533#386C2316yes—
534#386C2313yes—
535#386C2313yes—
536#386C2313yes—
537#386C2313yes—
538#385C2313yes—
539#385C2313yes—
540#385C2316yes—
541#385C2316yes—
542#385C2316yes—
543#385C2316yes—
544#385C2316yes—
545#385C2313yes—
546#385C2316yes—
547#385C2313yes—
548#385C2313yes—
549#385C2313yes—
550#385C2311yescharacteristic
551#385C2313yes—
552#385C2313yes—
553#385C2313yes—
554#385C2313yes—
555#384C2313yes—
556#384C2313yes—
557#384C2313yes—
558#384C2313yes—
559#384C2316yes—
560#384C2313yes—
561#384C2313yes—
562#384C2313yes—
563#384C2313yes—
564#384C2313yes—
565#383C2313yes—
566#382C2313yes—
567#382C2313yes—
568#382C2313yes—
569#382C2313yes—
570#382C2313yes—
571#382C2313yes—
572#382C2316yes—
573#382C2316yes—
574#381C2313yes—
575#380C2313yes—
576#380C2316yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2313yes—
585#380C2313yes—
586#380C2313yes—
587#380C2313yes—
588#380C2311yescharacteristic
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2316yes—
593C4×C4⋊C4C2316yes—
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⋊C4C2316yes—
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⋊C4C2316yes—
616C4×C22⋊C4C2316yes—
617C4×C22⋊C4C2316yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625#376C2313yes—
626C43C2313yes—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8#4118yes—
636C22×Q8C2411yescharacteristic
637C22×Q8C2413yes—
638C22×Q8C2416yes—
639C22×Q8C2411yescharacteristic
640C22×D4C2413yes—
641C22×D4C2413yes—
642C22×D4C2413yes—
643C22×D4C2413yes—
644C22×D4C2413yes—
645C22×D4C2416yes—
646C23×C4C2413yes—
647C23×C4C2413yes—
648C23×C4C2411yescharacteristic
649C23×C4C2413yes—
650C23×C4C2413yes—
651C23×C4C2413yes—
652C23×C4C2416yes—
653C23×C4C2413yes—
654C4⋊Q8—46no—
655C4⋊Q8—46no—
656C4⋊Q8—46no—
657#127—46no—
658#126—46no—
659#126—412no—
660#126—86no—
661#125—24no—
662#125—86no—
663#124—212no—
664#124—212no—
665#123—212no—
666#123—86no—
667#123—86no—
668#123—86no—
669C22⋊Q8—212no—
670C22⋊Q8—212no—
671C22⋊Q8—24no—
672C22⋊Q8—46no—
673C22⋊Q8—86no—
674C22⋊Q8—86no—
675C22⋊Q8—86no—
676C22⋊Q8—86no—
677#121—212no—
678#121—212no—
679#121—46no—
680#121—46no—
681#121—46no—
682#121—86no—
683C4×Q8—212no—
684C4×Q8—212no—
685C4×Q8—24no—
686C4×Q8—24no—
687C4×Q8—24no—
688C4×Q8—24no—
689C4×Q8—24no—
690C4×Q8—24no—
691C4×Q8—24no—
692C4×Q8—24no—
693C4×Q8—24no—
694C4×Q8—24no—
695C4×Q8—24no—
696C4×Q8—24no—
697C4×Q8—46no—
698C4×Q8—46no—
699C4×Q8—46no—
700C4×Q8—46no—
701C4×Q8—46no—
702C4×D4—212no—
703C4×D4—212no—
704C4×D4—46no—
705C4×D4—46no—
706C4×D4—46no—
707C4×D4—46no—
708C4×D4—46no—
709#117—212no—
710#117—212no—
711#117—46no—
712#117—46no—
713#117—46no—
714#117—46no—
715C2×C4⋊C4—46no—
716C2×C4⋊C4—46no—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2416yes—
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2411yescharacteristic
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2416yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2416yes—
762C2×C4⋊C4C2416yes—
763C2×C4⋊C4C2416yes—
764C2×C4⋊C4C2416yes—
765C2×C4⋊C4C2416yes—
766C2×C4⋊C4C2416yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2416yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C22⋊C4C2411yescharacteristic
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2411yescharacteristic
782C2×C22⋊C4C2411yescharacteristic
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2416yes—
786C2×C22⋊C4C2416yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2411yescharacteristic
790C2×C22⋊C4C2411yescharacteristic
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2411yescharacteristic
796C2×C22⋊C4C2416yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2416yes—
802C2×C22⋊C4C2416yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2416yes—
808C2×C22⋊C4C2416yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2416yes—
816C2×C22⋊C4C2416yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2416yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2416yes—
822C2×C42—46no—
823C2×C42—46no—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2416yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2411yescharacteristic
838C2×C42C2413yes—
839C2×C42C2416yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2416yes—
846C2×C42C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2411yescharacteristic
852#95C2411yescharacteristic
853#95C2411yescharacteristic
854#95C2411yescharacteristic
855#95C2411yescharacteristic
856#95C2413yes—
857#95C2411yescharacteristic
858#95C2411yescharacteristic
859#95C2413yes—
860#95C2411yescharacteristic
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2416yes—
872#95C2416yes—
873#95C2413yes—
874#95C2413yes—
875#95C2411yescharacteristic
876#95C2413yes—
877#95C2411yescharacteristic
878#95C2411yescharacteristic
879#95C2413yes—
880#95C2416yes—
881#95C2411yescharacteristic
882#95C2411yescharacteristic
883#95C2413yes—
884#95C2416yes—
885#95C2416yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2416yes—
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—
907C24C2513yes—
908C24C2513yes—
909C24C2511yescharacteristic
910#41—416no—
911#41—416no—
912C2×Q8—232no—
913C2×Q8—26no—
914C2×Q8—26no—
915C2×Q8—22no—
916C2×Q8—22no—
917C2×Q8—41no—
918C2×Q8—46no—
919C2×Q8—46no—
920C2×Q8—46no—
921C2×Q8C2×#41112yes—
922C2×Q8C2×#4114yes—
923C2×Q8H(5,𝔽2)14yes—
924C2×Q82−1+414yes—
925C2×D4—26no—
926C2×D4—26no—
927C2×D4—26no—
928C2×D4—26no—
929C2×D4—26no—
930C2×D4—26no—
931C2×D4—26no—
932C2×D4—26no—
933C2×D4—26no—
934C2×D4—43no—
935C2×D4—43no—
936C2×D4—43no—
937C2×D4—43no—
938C2×D4—43no—
939C2×D4—43no—
940C2×D4—46no—
941C2×D4—46no—
942C2×D4—46no—
943C22×C4—26no—
944C22×C4—26no—
945C22×C4—26no—
946C22×C4—26no—
947C22×C4—26no—
948C22×C4—26no—
949C22×C4—22no—
950C22×C4—26no—
951C22×C4—26no—
952C22×C4—22no—
953C22×C4—26no—
954C22×C4—41no—
955C22×C4—43no—
956C22×C4—43no—
957C22×C4—43no—
958C22×C4—43no—
959C22×C4—43no—
960C22×C4—43no—
961C22×C4—43no—
962C22×C4—43no—
963C22×C4—46no—
964C22×C4—46no—
965C22×C4—46no—
966C22×C4C2×#41112yes—
967C22×C4C2511yescharacteristic
968C22×C4C2511yescharacteristic
969C22×C4C2511yescharacteristic
970C22×C4C2511yescharacteristic
971C22×C4C2513yes—
972C22×C4C2511yescharacteristic
973C22×C4C2513yes—
974C22×C4C2511yescharacteristic
975C22×C4C2513yes—
976C22×C4C2513yes—
977C22×C4C2511yescharacteristic
978C22×C4C2511yescharacteristic
979C22×C4C2513yes—
980C22×C4C2513yes—
981C22×C4C2513yes—
982C22×C4C2511yescharacteristic
983C22×C4C2511yescharacteristic
984C22×C4C2513yes—
985C22×C4C2513yes—
986C22×C4C2513yes—
987C22×C4C2513yes—
988C22×C4C2513yes—
989C22×C4C2513yes—
990C22×C4C2511yescharacteristic
991C22×C4C2511yescharacteristic
992C22×C4C2511yescharacteristic
993C22×C4C2511yescharacteristic
994C22×C4C2513yes—
995C4⋊C4—26no—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—26no—
999C4⋊C4—26no—
1000C4⋊C4—26no—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—26no—
1006C4⋊C4—26no—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4—26no—
1010C4⋊C4—26no—
1011C4⋊C4—22no—
1012C4⋊C4—22no—
1013C4⋊C4—26no—
1014C4⋊C4—22no—
1015C4⋊C4—22no—
1016C4⋊C4—22no—
1017C4⋊C4—22no—
1018C4⋊C4—22no—
1019C4⋊C4—26no—
1020C4⋊C4—22no—
1021C4⋊C4—26no—
1022C4⋊C4—43no—
1023C4⋊C4—46no—
1024C4⋊C4—41no—
1025C4⋊C4—43no—
1026C4⋊C4—43no—
1027C4⋊C4—41no—
1028C4⋊C4—43no—
1029C4⋊C4—43no—
1030C4⋊C4—43no—
1031C4⋊C4—43no—
1032C4⋊C4—46no—
1033C4⋊C4—43no—
1034C4⋊C4—43no—
1035C4⋊C4—43no—
1036C4⋊C4—43no—
1037C4⋊C4—43no—
1038C4⋊C4—43no—
1039C4⋊C4—43no—
1040C4⋊C4—43no—
1041C4⋊C4—46no—
1042C4⋊C4—46no—
1043C4⋊C4—46no—
1044C4⋊C4—46no—
1045C4⋊C4—46no—
1046C4⋊C4—46no—
1047C4⋊C4—43no—
1048C4⋊C4—43no—
1049C4⋊C4—43no—
1050C4⋊C4—46no—
1051C4⋊C4—43no—
1052C4⋊C4—43no—
1053C4⋊C4—46no—
1054C4⋊C4—43no—
1055C4⋊C4—43no—
1056C4⋊C42−1+414yes—
1057C22⋊C4—22no—
1058C22⋊C4—26no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—26no—
1062C22⋊C4—26no—
1063C22⋊C4—212no—
1064C22⋊C4—212no—
1065C22⋊C4—22no—
1066C22⋊C4—22no—
1067C22⋊C4—26no—
1068C22⋊C4—26no—
1069C22⋊C4—26no—
1070C22⋊C4—26no—
1071C22⋊C4—26no—
1072C22⋊C4—41no—
1073C22⋊C4—43no—
1074C22⋊C4—43no—
1075C22⋊C4—43no—
1076C22⋊C4—46no—
1077C22⋊C4—43no—
1078C22⋊C4—43no—
1079C22⋊C4—46no—
1080C22⋊C4—46no—
1081C22⋊C4—43no—
1082C22⋊C4—43no—
1083C22⋊C4—43no—
1084C22⋊C4—43no—
1085C22⋊C4—43no—
1086C22⋊C4—46no—
1087C22⋊C4—46no—
1088C22⋊C4—43no—
1089C22⋊C4—43no—
1090C22⋊C4—43no—
1091C22⋊C4—43no—
1092C22⋊C4—43no—
1093C22⋊C4—46no—
1094C22⋊C4—46no—
1095C22⋊C4—43no—
1096C22⋊C4—46no—
1097C22⋊C4—46no—
1098C22⋊C4—43no—
1099C22⋊C4—43no—
1100C42—212no—
1101C42—26no—
1102C42—26no—
1103C42—26no—
1104C42—26no—
1105C42—26no—
1106C42—26no—
1107C42—26no—
1108C42—26no—
1109C42—26no—
1110C42—26no—
1111C42—26no—
1112C42—26no—
1113C42—22no—
1114C42—41no—
1115C42—43no—
1116C42—43no—
1117C42—43no—
1118C42—46no—
1119C42—43no—
1120C42—43no—
1121C42—46no—
1122C42—43no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—23no—
1130C23—23no—
1131C23—23no—
1132C23—23no—
1133C23—23no—
1134C23—23no—
1135C23—23no—
1136C23—23no—
1137C23—23no—
1138C23—23no—
1139C23—23no—
1140C23—23no—
1141C23—23no—
1142C23—23no—
1143C23C22×#4112yes—
1144C23C2611yescharacteristic
1145Q8—224no—
1146Q8—44no—
1147Q8—166no—
1148Q8#539116yes—
1149D4—412no—
1150D4—412no—
1151D4—86no—
1152D4—86no—
1153D4—86no—
1154D4—166no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—23no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—23no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—224no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—23no—
1169C2×C4—21no—
1170C2×C4—23no—
1171C2×C4—21no—
1172C2×C4—23no—
1173C2×C4—23no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—23no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—23no—
1191C2×C4—23no—
1192C2×C4—23no—
1193C2×C4—21no—
1194C2×C4—23no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—23no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—23no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—23no—
1222C2×C4—21no—
1223C2×C4—23no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—23no—
1228C2×C4—23no—
1229C2×C4—21no—
1230C2×C4—23no—
1231C2×C4—23no—
1232C2×C4—44no—
1233C2×C4—412no—
1234C2×C4—412no—
1235C2×C4—86no—
1236C2×C4—86no—
1237C2×C4—86no—
1238C2×C4—166no—
1239C2×C4C22×#4116yes—
1240C2×C4C22×#4116yes—
1241C2×C4C2×H(5,𝔽2)16yes—
1242C2×C4C2×2−1+412yes—
1243C2×C4C2×2−1+412yes—
1244C2×C4C2×2−1+412yes—
1245C2×C4C2×2−1+416yes—
1246C2×C4#58512yes—
1247C22—22no—
1248C22—22no—
1249C22—22no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—43no—
1255C22—43no—
1256C22—43no—
1257C22—43no—
1258C22—43no—
1259C22—43no—
1260C22—43no—
1261C22—43no—
1262C22—43no—
1263C22—43no—
1264C22—43no—
1265C22—43no—
1266C22—43no—
1267C22—43no—
1268C22C23×#4111yescharacteristic
1269C22C22×H(5,𝔽2)11yescharacteristic
1270C22C22×2−1+411yescharacteristic
1271C22C22×2−1+411yescharacteristic
1272C22C2×#58511yescharacteristic
1273C22H(7,𝔽2)11yescharacteristic
1274C22H(7,𝔽2)11yescharacteristic
1275C4—22no—
1276C4—22no—
1277C4—22no—
1278C4—26no—
1279C4—22no—
1280C4—41no—
1281C4—41no—
1282C4—43no—
1283C4—41no—
1284C4—43no—
1285C4—41no—
1286C4—43no—
1287C4—43no—
1288C4—41no—
1289C4—43no—
1290C4—41no—
1291C4—41no—
1292C4—43no—
1293C4—43no—
1294C4—43no—
1295C4—43no—
1296C4—43no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—43no—
1301C4—43no—
1302C4C2×#539112yes—
1303C2—42no—
1304C2—83no—
1305C2—83no—
1306C2C22×#53911yescharacteristic
1307C2#6294311yescharacteristic
1308C2#6295211yescharacteristic
1309C2#6299911yescharacteristic
1310C2#6300611yescharacteristic
1311C2#6301511yescharacteristic
1312C2#6306611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36576C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52276C2semidirect
2. #42946C2semidirect
3. #42925C2semidirect
4. #42904C2semidirect
5. #42896C2semidirect
6. #42873C2semidirect
7. #42841C2semidirect
8. #40128C2semidirect
9. #40123C2semidirect
10. #40029C2semidirect
11. #40004C2semidirect
12. #39658C2semidirect
13. #39245C2semidirect
14. #37350C2semidirect
15. #37339C2semidirect
16. #37315C2semidirect
18. Q8×#125C2semidirect
19. Q8×C22⋊Q8C2semidirect
20. #36458C2semidirect
21. #36456C2semidirect
22. #36433C2semidirect
23. #36005C2semidirect
24. #35971C2semidirect
25. #35898C2semidirect
26. #35801C2semidirect
27. #35801C2semidirect
28. #35748C2semidirect
29. #34312C2semidirect
30. #34293C2semidirect
31. #34249C2semidirect

Maximal subgroups

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

subgroupindex
#522762
#429462
#429252
#429042
#428962
#428732
#428412
#401282
#401232
#400292
#400042
#396582
#392452
#373502
#373392
#373152
#365762
Q8×#1252
Q8×C22⋊Q82
#364582
#364562
#364332
#360052
#359712
#358982
#358012
#357482
#343122
#342932
#342492