Finite Group Databasebeta

← #8107409

Subgroups — #8107409

Order 512.

4426 conjugacy classes of subgroups.

The subgroup lattice has 1313 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53153C212yesmaximal, complemented
2#53113C212yesmaximal, complemented
3#52651C214yesmaximal, complemented
4#52414C214yesmaximal, complemented
5#45266C211yesmaximal, characteristic, complemented
6#45164C211yesmaximal, characteristic, complemented
7#45152C211yesmaximal, characteristic, complemented
8#44948C211yesmaximal, characteristic, complemented
9#43445C214yesmaximal, complemented
10#43221C214yesmaximal, complemented
11#42821C212yesmaximal, complemented
12#42687C212yesmaximal, complemented
13#42676C212yesmaximal, complemented
14#42525C212yesmaximal, complemented
15#41225C214yesmaximal, complemented
16#41082C214yesmaximal, complemented
17#40865C214yesmaximal, complemented
18#40836C214yesmaximal, complemented
19#36587C212yesmaximal
20#36579C212yesmaximal, complemented
21#36571C212yesmaximal, complemented
22#36544C212yesmaximal, complemented
23#35315C211yesmaximal, characteristic, complemented
24#35271C211yesmaximal, characteristic
25#35083C212yesmaximal, complemented
26#35024C212yesmaximal, complemented
27C2×#2399C211yesmaximal, characteristic, complemented
28C2×#556C2212yes—
29C2×#554C2212yes—
30C22×C4×Q8C2212yes—
31#2857C2212yes—
32#2857C2211yescharacteristic
33#2856C2211yescharacteristic
34#2855C2212yes—
35#2854C2212yes—
36#2851C2211yescharacteristic
37#2851C2212yes—
38#2851C2211yescharacteristic
39#2850C2212yes—
40#2850C2212yes—
41#2844C2214yes—
42#2838C2214yes—
43#2838C2214yes—
44#2838C2214yes—
45#2838C2214yes—
46#2835C2214yes—
47#2831C2214yes—
48#2831C2214yes—
49#2831C2214yes—
50#2830C2214yes—
51#2817C2214yes—
52#2817C2214yes—
53#2805C2214yes—
54#2793C2214yes—
55#2792C2214yes—
56#2789C2214yes—
57#2774C2214yes—
58#2774C2214yes—
59#2774C2214yes—
60#2773C2214yes—
61#2770C2214yes—
62#2767C2214yes—
63#2765C2214yes—
64#2761C2214yes—
65#2757C2214yes—
66#2755C2214yes—
67#2747C2214yes—
68#2745C2214yes—
69#2744C2214yes—
70#2738C2214yes—
71#2737C2214yes—
72#2723C2214yes—
73#2723C2214yes—
74#2723C2214yes—
75#2720C2214yes—
76#2698C2214yes—
77#2698C2214yes—
78#2692C2214yes—
79#2690C2214yes—
80#2690C2214yes—
81#2689C2214yes—
82#2689C2214yes—
83#2689C2214yes—
84#2683C2214yes—
85#2666C2214yes—
86#2666C2214yes—
87#2654C2214yes—
88#2654C2214yes—
89#2651C2214yes—
90#2650C2214yes—
91#2650C2214yes—
92#2647C2211yescharacteristic
93#2647C2211yescharacteristic
94#2645C2212yes—
95#2644C2212yes—
96#2643C2214yes—
97#2642C2211yescharacteristic
98#2641C2211yescharacteristic
99#2638C2214yes—
100#2627C2214yes—
101#2625C2214yes—
102#2623C2214yes—
103#2597C2214yes—
104#2597C2214yes—
105#2596C2214yes—
106#2594C2214yes—
107#2592C2212yes—
108#2592C2212yes—
109#2590C2214yes—
110#2588C2214yes—
111#2588C2214yes—
112#2585C2214yes—
113#2584C2212yes—
114#2584C2212yes—
115#2583C2214yes—
116#2581C2212yes—
117#2581C2212yes—
118#2580C2212yes—
119#2580C2212yes—
120#2577C2214yes—
121#2575C2214yes—
122#2571C2212yes—
123#2570C2214yes—
124#2568C2212yes—
125#2567C2212yes—
126#2565C2212yes—
127#2550C2212yes—
128#2548C2212yes—
129#2538C2212yes—
130#2538C2212yes—
131#2533C2214yes—
132#2531C2214yes—
133#2528C2214yes—
134#2526C2214yes—
135#2524C2214yes—
136#2520C2214yes—
137#2519C2214yes—
138#2514C2212yes—
139#2513C2214yes—
140#2513C2212yes—
141#2513C2212yes—
142#2513C2212yes—
143#2512C2212yes—
144#2511C2212yes—
145#2509C2212yes—
146#2509C2212yes—
147#2509C2212yes—
148#2508C2212yes—
149#2508C2212yes—
150#2508C2214yes—
151#2506C2212yes—
152#2505C2214yes—
153#2505C2214yes—
154#2504C2214yes—
155#2493C2214yes—
156#2488C2214yes—
157#2484C2214yes—
158#2481C2214yes—
159#2481C2214yes—
160#2481C2214yes—
161#2479C2214yes—
162#2479C2214yes—
163#2473C2214yes—
164#2469C2214yes—
165#2469C2214yes—
166#2468C2214yes—
167#2465C2214yes—
168#2465C2214yes—
169#2454C2212yes—
170#2453C2212yes—
171#2453C2212yes—
172#2452C2212yes—
173#2451C2212yes—
174#2451C2212yes—
175#2449C2214yes—
176#2449C2214yes—
177#2449C2214yes—
178#2449C2214yes—
179#2448C2212yes—
180#2448C2212yes—
181#2447C2212yes—
182#2447C2212yes—
183#2447C2212yes—
184#2447C2212yes—
185#2444C2214yes—
186#2444C2214yes—
187#2444C2214yes—
188#2425C2214yes—
189#2423C2214yes—
190#2421C2214yes—
191#2419C2214yes—
192#2417C2214yes—
193#2409C2214yes—
194#2409C2214yes—
195#2399C2212yes—
196#2399C2212yes—
197#2399C2211yescharacteristic
198#2399C2211yescharacteristic
199#2399C2211yescharacteristic
200#2399C2212yes—
201#2399C2211yescharacteristic
202#2399C2212yes—
203#2399C2212yes—
204#2399C2212yes—
205C2×#398C2212yes—
206C2×#398C2212yes—
207C2×#395C2212yes—
208C2×#395C2212yes—
209#2370C2214yes—
210#2370C2212yes—
211#2368C2214yes—
212#2366C2212yes—
213#2362C2214yes—
214#2361C2214yes—
215#2360C2214yes—
216#2357C2214yes—
217#2355C2212yes—
218#2355C2212yes—
219#2355C2212yes—
220#2352C2214yes—
221#2351C2212yes—
222D4×C4⋊C4C2214yes—
223#2334C2214yes—
224#2332C2214yes—
225#2330C2211yescharacteristic
226#2330C2211yescharacteristic
227#2328C2211yescharacteristic
228#2327C2211yescharacteristic
229#2322C2214yes—
230#2320C2212yes—
231#2319C2212yes—
232#2318C2214yes—
233C4×C22⋊Q8C2212yes—
234C4×C22⋊Q8C2212yes—
235C4×C22⋊Q8C2212yes—
236C4×#121C2212yes—
237C4×#121C2212yes—
238C4×#121C2212yes—
239C2×C4×C4⋊C4C2211yescharacteristic
240C2×C4×C4⋊C4C2211yescharacteristic
241C2×C4×C4⋊C4C2212yes—
242C2×#376C2211yescharacteristic
243C23×Q8C2312yes—
244#556—48no—
245#554—48no—
246C2×C4⋊Q8C2311yescharacteristic
247C2×C4⋊Q8C2312yes—
248C2×#127C2311yescharacteristic
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#125C2311yescharacteristic
253C2×#125C2311yescharacteristic
254C2×#125C2312yes—
255C2×#125C2314yes—
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#123C2314yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×#121C2312yes—
269C2×#121C2314yes—
270C2×C4×Q8—48no—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2312yes—
289C2×#117C2314yes—
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2312yes—
293C22×C4⋊C4C2314yes—
294C22×C4⋊C4C2312yes—
295C22×C4⋊C4C2312yes—
296C22×C4⋊C4C2312yes—
297C22×C4⋊C4C2312yes—
298C22×C42C2311yescharacteristic
299C22×C42C2311yescharacteristic
300C22×C42C2311yescharacteristic
301C22×C42C2312yes—
302C22×C42C2312yes—
303#401C2314yes—
304#401C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#399C2314yes—
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#399C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2312yes—
340#398C2314yes—
341#398C2314yes—
342#398C2312yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2312yes—
351#398C2314yes—
352#398C2312yes—
353#398C2314yes—
354#398C2312yes—
355#398C2312yes—
356#398C2312yes—
357#398C2312yes—
358#398C2312yes—
359#398C2312yes—
360#398C2312yes—
361#398C2312yes—
362#398C2312yes—
363#398C2312yes—
364#398C2312yes—
365#398C2312yes—
366#398C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#395C2312yes—
398#395C2312yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2312yes—
406#395C2312yes—
407#395C2314yes—
408#395C2314yes—
409#395C2312yes—
410#395C2314yes—
411#395C2312yes—
412#395C2312yes—
413#395C2312yes—
414#395C2312yes—
415#395C2312yes—
416#395C2312yes—
417#395C2312yes—
418#395C2312yes—
419#395C2312yes—
420#395C2312yes—
421#395C2312yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#393C2314yes—
427#393C2314yes—
428#393C2314yes—
429#393C2314yes—
430#393C2314yes—
431#391C2312yes—
432#391C2312yes—
433#391C2314yes—
434#391C2312yes—
435#391C2312yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2312yes—
447#390C2314yes—
448#390C2312yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#390C2312yes—
455#390C2312yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2314yes—
464#389C2314yes—
465#389C2312yes—
466#389C2314yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2312yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#384C2312yes—
592#384C2314yes—
593#384C2311yescharacteristic
594#384C2311yescharacteristic
595#383C2314yes—
596#383C2314yes—
597#382C2312yes—
598#382C2314yes—
599#382C2314yes—
600#382C2314yes—
601#382C2312yes—
602#382C2312yes—
603#382C2314yes—
604#382C2311yescharacteristic
605#382C2311yescharacteristic
606#382C2314yes—
607#382C2314yes—
608#382C2314yes—
609#381C2314yes—
610#381C2314yes—
611#381C2314yes—
612#381C2314yes—
613#381C2314yes—
614#381C2314yes—
615#380C2314yes—
616#380C2314yes—
617#380C2312yes—
618#380C2312yes—
619#380C2314yes—
620#380C2314yes—
621#380C2314yes—
622#380C2314yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2311yescharacteristic
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2314yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2311yescharacteristic
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2311yescharacteristic
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2311yescharacteristic
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2311yescharacteristic
654C4×C4⋊C4C2311yescharacteristic
655C4×C4⋊C4C2311yescharacteristic
656C4×C4⋊C4C2311yescharacteristic
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663#376C2311yescharacteristic
664#376C2311yescharacteristic
665#376C2311yescharacteristic
666#376C2311yescharacteristic
667#376C2312yes—
668#376C2312yes—
669C2×#95C2311yescharacteristic
670C2×#95C2312yes—
671C2×#95C2311yescharacteristic
672C2×#95C2311yescharacteristic
673C2×#95C2312yes—
674C2×#95C2312yes—
675C2×#95C2312yes—
676C2×#95C2311yescharacteristic
677C22×Q8—44no—
678C22×Q8—44no—
679C22×Q8—44no—
680C22×Q8C2412yes—
681C22×Q8C2412yes—
682C22×Q8C2412yes—
683C22×Q8C2412yes—
684C22×Q8C2412yes—
685C22×Q8C2414yes—
686C22×D4C2414yes—
687C22×D4C2412yes—
688C22×D4C2414yes—
689C23×C4C2411yescharacteristic
690C23×C4C2412yes—
691C23×C4C2412yes—
692C23×C4C2412yes—
693C23×C4C2411yescharacteristic
694C23×C4C2412yes—
695C23×C4C2412yes—
696C23×C4C2412yes—
697C23×C4C2411yescharacteristic
698C23×C4C2414yes—
699C23×C4C2414yes—
700C23×C4C2414yes—
701C4⋊Q8—24no—
702C4⋊Q8—44no—
703#127—24no—
704#126—48no—
705#126—48no—
706#126—48no—
707#125—24no—
708#125—24no—
709#125—44no—
710#125—48no—
711#124—44no—
712#124—44no—
713#123—48no—
714C22⋊Q8—28no—
715C22⋊Q8—48no—
716C22⋊Q8—48no—
717C22⋊Q8—48no—
718C22⋊Q8—48no—
719C22⋊Q8—48no—
720C22⋊Q8—48no—
721C22⋊Q8—48no—
722C22⋊Q8—48no—
723#121—28no—
724#121—48no—
725C4×Q8—28no—
726C4×Q8—28no—
727C4×Q8—28no—
728C4×Q8—44no—
729C4×Q8—44no—
730C4×Q8—44no—
731C4×Q8—44no—
732C4×Q8—44no—
733C4×Q8—44no—
734C4×Q8—44no—
735C4×Q8—44no—
736C4×D4—28no—
737C4×D4—44no—
738C4×D4—44no—
739C4×D4—48no—
740C4×D4—48no—
741C4×D4—48no—
742C4×D4—48no—
743#117—48no—
744C2×C4⋊C4—44no—
745C2×C4⋊C4—44no—
746C2×C4⋊C4—44no—
747C2×C4⋊C4—44no—
748C2×C4⋊C4—44no—
749C2×C4⋊C4—48no—
750C2×C4⋊C4—44no—
751C2×C4⋊C4—44no—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C42—24no—
844C2×C42—24no—
845C2×C42—24no—
846C2×C42—44no—
847C2×C42—44no—
848C2×C42C2412yes—
849C2×C42C2412yes—
850C2×C42C2412yes—
851C2×C42C2411yescharacteristic
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2414yes—
855C2×C42C2412yes—
856C2×C42C2411yescharacteristic
857C2×C42C2411yescharacteristic
858C2×C42C2411yescharacteristic
859C2×C42C2411yescharacteristic
860C2×C42C2411yescharacteristic
861C2×C42C2414yes—
862C2×C42C2414yes—
863C2×C42C2414yes—
864C2×C42C2414yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2414yes—
872C2×C42C2414yes—
873C2×C42C2411yescharacteristic
874C2×C42C2411yescharacteristic
875#95C2412yes—
876#95C2412yes—
877#95C2412yes—
878#95C2412yes—
879#95C2412yes—
880#95C2412yes—
881#95C2412yes—
882#95C2412yes—
883#95C2412yes—
884#95C2411yescharacteristic
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
888#95C2412yes—
889#95C2411yescharacteristic
890#95C2412yes—
891#95C2411yescharacteristic
892#95C2412yes—
893#95C2412yes—
894#95C2411yescharacteristic
895#95C2412yes—
896#95C2412yes—
897#95C2411yescharacteristic
898#95C2411yescharacteristic
899#95C2412yes—
900#95C2411yescharacteristic
901#95C2411yescharacteristic
902#95C2412yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951C24C2514yes—
952C24C2511yescharacteristic
953C2×Q8—24no—
954C2×Q8—24no—
955C2×Q8—24no—
956C2×Q8—24no—
957C2×Q8—24no—
958C2×Q8—24no—
959C2×Q8—24no—
960C2×Q8—42no—
961C2×Q8—42no—
962C2×Q8—42no—
963C2×Q8—42no—
964C2×Q8—42no—
965C2×Q8—42no—
966C2×Q8—42no—
967C2×Q8—42no—
968C2×Q8—44no—
969C2×Q8—44no—
970C2×Q8—44no—
971C2×Q8—432no—
972C2×D4—28no—
973C2×D4—28no—
974C2×D4—28no—
975C2×D4—24no—
976C2×D4—24no—
977C2×D4—24no—
978C2×D4—28no—
979C2×D4—44no—
980C2×D4—44no—
981C22×C4—22no—
982C22×C4—22no—
983C22×C4—22no—
984C22×C4—22no—
985C22×C4—24no—
986C22×C4—24no—
987C22×C4—24no—
988C22×C4—24no—
989C22×C4—24no—
990C22×C4—24no—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—28no—
996C22×C4—28no—
997C22×C4—42no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—42no—
1001C22×C4—42no—
1002C22×C4—42no—
1003C22×C4—42no—
1004C22×C4—42no—
1005C22×C4—44no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C42−1+414yes—
1015C22×C4C2514yes—
1016C22×C4C2514yes—
1017C22×C4C2512yes—
1018C22×C4C2511yescharacteristic
1019C22×C4C2511yescharacteristic
1020C22×C4C2511yescharacteristic
1021C22×C4C2511yescharacteristic
1022C22×C4C2514yes—
1023C22×C4C2514yes—
1024C22×C4C2514yes—
1025C22×C4C2512yes—
1026C22×C4C2512yes—
1027C22×C4C2512yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2512yes—
1031C22×C4C2514yes—
1032C22×C4C2514yes—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C22×C4C2511yescharacteristic
1038C22×C4C2512yes—
1039C22×C4C2511yescharacteristic
1040C4⋊C4—24no—
1041C4⋊C4—24no—
1042C4⋊C4—24no—
1043C4⋊C4—24no—
1044C4⋊C4—24no—
1045C4⋊C4—24no—
1046C4⋊C4—28no—
1047C4⋊C4—28no—
1048C4⋊C4—24no—
1049C4⋊C4—24no—
1050C4⋊C4—24no—
1051C4⋊C4—28no—
1052C4⋊C4—24no—
1053C4⋊C4—24no—
1054C4⋊C4—28no—
1055C4⋊C4—28no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—24no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—28no—
1062C4⋊C4—28no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C22⋊C4—28no—
1105C22⋊C4—28no—
1106C22⋊C4—28no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—28no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C42—24no—
1132C42—22no—
1133C42—24no—
1134C42—24no—
1135C42—24no—
1136C42—24no—
1137C42—24no—
1138C42—22no—
1139C42—22no—
1140C42—22no—
1141C42—22no—
1142C42—22no—
1143C42—28no—
1144C42—42no—
1145C42—42no—
1146C42—42no—
1147C42—42no—
1148C42—44no—
1149C42—44no—
1150C42—44no—
1151C42—44no—
1152C42—44no—
1153C42—44no—
1154C42—44no—
1155C42—44no—
1156C42H(5,𝔽2)14yes—
1157C422−1+414yes—
1158C23—21no—
1159C23—21no—
1160C23—22no—
1161C23—24no—
1162C23—24no—
1163C23—24no—
1164C23—24no—
1165C23—24no—
1166C23—24no—
1167C23—24no—
1168C23C2×2−1+412yes—
1169C23#58514yes—
1170C23C2611yescharacteristic
1171Q8—48no—
1172Q8—48no—
1173Q8—48no—
1174Q8—48no—
1175Q8—48no—
1176Q8—164no—
1177D4—416no—
1178D4—48no—
1179D4—88no—
1180C2×C4—21no—
1181C2×C4—22no—
1182C2×C4—21no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—28no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—48no—
1246C2×C4—48no—
1247C2×C4—48no—
1248C2×C4—44no—
1249C2×C4—48no—
1250C2×C4—44no—
1251C2×C4—88no—
1252C2×C4—88no—
1253C2×C4—84no—
1254C2×C4—84no—
1255C2×C4—164no—
1256C2×C4C2×H(5,𝔽2)14yes—
1257C2×C4C2×H(5,𝔽2)12yes—
1258C2×C4C2×2−1+414yes—
1259C2×C4C2×2−1+412yes—
1260C2×C4C2×2−1+412yes—
1261C2×C4C2×2−1+412yes—
1262C2×C4#58514yes—
1263C22—22no—
1264C22—22no—
1265C22—24no—
1266C22—24no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—44no—
1274C22#355714yes—
1275C22C22×H(5,𝔽2)11yescharacteristic
1276C22C22×2−1+411yescharacteristic
1277C22C22×2−1+411yescharacteristic
1278C22C2×#58512yes—
1279C22C2×#58512yes—
1280C4—22no—
1281C4—24no—
1282C4—24no—
1283C4—24no—
1284C4—41no—
1285C4—41no—
1286C4—44no—
1287C4—44no—
1288C4—44no—
1289C4—41no—
1290C4—41no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—44no—
1299C4—44no—
1300C4—42no—
1301C4—44no—
1302C4—44no—
1303C4—42no—
1304C4#355214yes—
1305C2—24no—
1306C2—84no—
1307C2C2×#355711yescharacteristic
1308C2C2×#355211yescharacteristic
1309C2#6276111yescharacteristic
1310C2#6282112yes—
1311C2#6283112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2856C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53153C2semidirect
2. #53113C2semidirect
3. #52651C2semidirect
4. #52414C2semidirect
5. #45266C2semidirect
6. #45164C2semidirect
7. #45152C2semidirect
8. #44948C2semidirect
9. #43445C2semidirect
10. #43221C2semidirect
11. #42821C2semidirect
12. #42687C2semidirect
13. #42676C2semidirect
14. #42525C2semidirect
15. #41225C2semidirect
16. #41082C2semidirect
17. #40865C2semidirect
18. #40836C2semidirect
20. #36579C2semidirect
21. #36571C2semidirect
22. #36544C2semidirect
23. #35315C2semidirect
25. #35083C2semidirect
26. #35024C2semidirect
27. C2×#2399C2semidirect

Maximal subgroups

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

subgroupindex
#531532
#531132
#526512
#524142
#452662
#451642
#451522
#449482
#434452
#432212
#428212
#426872
#426762
#425252
#412252
#410822
#408652
#408362
#365872
#365792
#365712
#365442
#353152
#352712
#350832
#350242
C2×#23992