Finite Group Databasebeta

← #7661929

Subgroups — #7661929

Order 512.

4616 conjugacy classes of subgroups.

The subgroup lattice has 1289 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52281C213yesmaximal, complemented
2#42948C213yesmaximal, complemented
3#42947C213yesmaximal, complemented
4#42904C213yesmaximal, complemented
5#42870C213yesmaximal, complemented
6#42840C213yesmaximal, complemented
7#42827C213yesmaximal, complemented
8#40224C213yesmaximal, complemented
9#40105C213yesmaximal, complemented
10#40035C213yesmaximal, complemented
11#40004C213yesmaximal, complemented
12#39782C213yesmaximal, complemented
13#39249C213yesmaximal, complemented
14#37403C213yesmaximal, complemented
15#37355C213yesmaximal, complemented
16#37326C213yesmaximal, complemented
17#36577C211yesmaximal, characteristic, complemented
18#36475C211yesmaximal, characteristic, complemented
19#36475C211yesmaximal, characteristic, complemented
20#36458C211yesmaximal, characteristic, complemented
21#36448C211yesmaximal, characteristic, complemented
22#36434C211yesmaximal, characteristic
23#35983C211yesmaximal, characteristic, complemented
24#35816C211yesmaximal, characteristic, complemented
25#35801C211yesmaximal, characteristic, complemented
26#35801C211yesmaximal, characteristic, complemented
27#35786C211yesmaximal, characteristic, complemented
28#35723C211yesmaximal, characteristic, complemented
29#34312C211yesmaximal, characteristic, complemented
30#34311C211yesmaximal, characteristic, complemented
31#34249C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#548C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C2×#519C2211yescharacteristic
39C2×#519C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41#2864C2213yes—
42#2864C2213yes—
43#2863C2213yes—
44#2860C2213yes—
45#2857C2213yes—
46#2850C2213yes—
47#2839C2216yes—
48#2837C2216yes—
49#2808C2213yes—
50#2807C2216yes—
51#2805C2213yes—
52#2798C2216yes—
53#2795C2216yes—
54#2793C2216yes—
55#2791C2216yes—
56#2786C2216yes—
57#2786C2211yescharacteristic
58#2786C2213yes—
59#2783C2216yes—
60#2783C2216yes—
61#2781C2216yes—
62#2777C2213yes—
63#2777C2213yes—
64#2773C2213yes—
65#2773C2213yes—
66#2770C2213yes—
67#2770C2213yes—
68#2769C2216yes—
69#2765C2216yes—
70#2757C2216yes—
71#2750C2216yes—
72#2747C2216yes—
73#2746C2216yes—
74#2728C2216yes—
75#2727C2213yes—
76#2726C2213yes—
77#2723C2213yes—
78#2723C2213yes—
79#2721C2216yes—
80#2711C2213yes—
81#2711C2213yes—
82#2691C2216yes—
83#2689C2216yes—
84#2667C2216yes—
85#2664C2216yes—
86#2655C2216yes—
87#2654C2216yes—
88#2654C2216yes—
89#2649C2216yes—
90#2629C2213yes—
91#2629C2213yes—
92#2625C2213yes—
93#2625C2213yes—
94#2624C2213yes—
95#2624C2213yes—
96#2594C2216yes—
97#2588C2216yes—
98#2582C2213yes—
99#2582C2213yes—
100#2577C2216yes—
101#2573C2216yes—
102#2573C2216yes—
103#2570C2213yes—
104#2570C2213yes—
105#2570C2213yes—
106#2570C2213yes—
107#2568C2213yes—
108#2566C2213yes—
109#2565C2213yes—
110#2560C2216yes—
111#2545C2213yes—
112#2538C2213yes—
113#2536C2213yes—
114#2514C2213yes—
115#2514C2213yes—
116#2513C2213yes—
117#2512C2213yes—
118#2512C2213yes—
119#2511C2213yes—
120#2509C2213yes—
121#2509C2213yes—
122#2508C2213yes—
123#2508C2213yes—
124#2507C2213yes—
125#2507C2213yes—
126#2506C2213yes—
127#2506C2213yes—
128#2503C2213yes—
129#2500C2213yes—
130#2500C2213yes—
131#2499C2213yes—
132#2497C2213yes—
133#2496C2213yes—
134#2496C2213yes—
135#2495C2213yes—
136#2495C2213yes—
137#2494C2213yes—
138#2487C2213yes—
139#2485C2213yes—
140#2485C2213yes—
141#2485C2213yes—
142#2454C2213yes—
143#2453C2213yes—
144#2453C2213yes—
145#2453C2213yes—
146#2452C2213yes—
147#2451C2213yes—
148#2448C2213yes—
149#2448C2213yes—
150#2448C2213yes—
151#2448C2213yes—
152#2447C2213yes—
153#2447C2213yes—
154#2446C2213yes—
155#2446C2213yes—
156#2442C2213yes—
157#2442C2213yes—
158#2442C2213yes—
159#2441C2213yes—
160#2440C2213yes—
161#2439C2213yes—
162#2429C2213yes—
163#2426C2213yes—
164#2423C2213yes—
165#2423C2213yes—
166#2423C2213yes—
167#2421C2213yes—
168#2421C2213yes—
169#2421C2213yes—
170#2420C2213yes—
171#2420C2213yes—
172#2417C2213yes—
173#2416C2213yes—
174#2396C2213yes—
175#2396C2213yes—
176#2395C2213yes—
177#2395C2213yes—
178#2395C2213yes—
179#2395C2213yes—
180#2367C2213yes—
181#2365C2213yes—
182#2363C2213yes—
183#2362C2213yes—
184#2362C2213yes—
185#2360C2213yes—
186#2354C2213yes—
187#2352C2213yes—
188#2351C2211yescharacteristic
189#2351C2213yes—
190#2351C2213yes—
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196#2351C2211yescharacteristic
197#2351C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2213yes—
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2213yes—
203Q8×C4⋊C4C2211yescharacteristic
204Q8×C4⋊C4C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210Q8×C22⋊C4C2211yescharacteristic
211Q8×C22⋊C4C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216#2334C2216yes—
217#2332C2216yes—
218#2324C2213yes—
219#2323C2213yes—
220#2323C2213yes—
221#2323C2213yes—
222#2317C2213yes—
223#2317C2213yes—
224C4×C4⋊Q8C2213yes—
225C4×#125C2213yes—
226C4×#125C2213yes—
227C4×#126C2213yes—
228C4×#126C2213yes—
229C4×#124C2213yes—
230C4×C22⋊Q8C2213yes—
231C4×#121C2213yes—
232#2296C2213yes—
233#2296C2213yes—
234#2293C2213yes—
235#2293C2213yes—
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241#557—44no—
242D4×Q8—28no—
243#548—28no—
244#548—44no—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×#126C2313yes—
248C2×#126C2313yes—
249C2×#126C2316yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#124C2313yes—
255C2×#124C2313yes—
256C2×C22⋊Q8C2313yes—
257C2×C22⋊Q8C2313yes—
258C2×C22⋊Q8C2313yes—
259C2×C22⋊Q8C2316yes—
260C2×C22⋊Q8C2313yes—
261C2×C22⋊Q8C2313yes—
262C2×#121C2313yes—
263C2×#121C2313yes—
264C2×#121C2313yes—
265#520—44no—
266#519—28no—
267#519—44no—
268#519—44no—
269C2×C4×Q8—44no—
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2313yes—
283C2×C4×Q8C2313yes—
284C2×C4×Q8C2313yes—
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2313yes—
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×D4C2313yes—
292C2×C4×D4C2313yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2313yes—
295C2×C4×D4C2313yes—
296C2×#117C2313yes—
297C2×#117C2313yes—
298C2×#117C2313yes—
299C2×#117C2313yes—
300C2×#117C2313yes—
301C2×#117C2313yes—
302C2×#117C2313yes—
303C22×C4⋊C4C2313yes—
304C22×C4⋊C4C2313yes—
305C22×C42C2313yes—
306#401C2316yes—
307#400C2316yes—
308#400C2316yes—
309#400C2316yes—
310#400C2316yes—
311#400C2316yes—
312#400C2316yes—
313#400C2313yes—
314#400C2316yes—
315#400C2313yes—
316#400C2316yes—
317#400C2316yes—
318#400C2316yes—
319#400C2316yes—
320#400C2313yes—
321#400C2313yes—
322#400C2313yes—
323#400C2313yes—
324#399C2313yes—
325#399C2313yes—
326#399C2316yes—
327#399C2316yes—
328#399C2313yes—
329#399C2313yes—
330#399C2313yes—
331#399C2313yes—
332#398C2316yes—
333#398C2313yes—
334#398C2316yes—
335#398C2316yes—
336#398C2316yes—
337#398C2316yes—
338#398C2316yes—
339#398C2313yes—
340#398C2316yes—
341#398C2313yes—
342#398C2313yes—
343#398C2316yes—
344#398C2313yes—
345#398C2316yes—
346#398C2313yes—
347#398C2316yes—
348#398C2316yes—
349#398C2313yes—
350#398C2311yescharacteristic
351#397C2316yes—
352#397C2313yes—
353#397C2316yes—
354#397C2313yes—
355#397C2316yes—
356#397C2316yes—
357#397C2313yes—
358#397C2316yes—
359#397C2313yes—
360#397C2316yes—
361#397C2316yes—
362#397C2316yes—
363#397C2313yes—
364#397C2311yescharacteristic
365#397C2311yescharacteristic
366#397C2311yescharacteristic
367#397C2313yes—
368#397C2313yes—
369#397C2313yes—
370#397C2313yes—
371#396C2313yes—
372#396C2316yes—
373#396C2316yes—
374#396C2316yes—
375#396C2316yes—
376#396C2313yes—
377#396C2316yes—
378#396C2316yes—
379#396C2311yescharacteristic
380#396C2313yes—
381#395C2313yes—
382#395C2313yes—
383#394C2316yes—
384#394C2313yes—
385#394C2316yes—
386#394C2313yes—
387#394C2313yes—
388#394C2316yes—
389#394C2313yes—
390#394C2311yescharacteristic
391#394C2313yes—
392#394C2313yes—
393#394C2313yes—
394#393C2313yes—
395#393C2313yes—
396#391C2316yes—
397#391C2313yes—
398#391C2313yes—
399#391C2313yes—
400#391C2313yes—
401#391C2313yes—
402#391C2313yes—
403#391C2313yes—
404#391C2313yes—
405#391C2313yes—
406#391C2316yes—
407#391C2313yes—
408#391C2313yes—
409#391C2313yes—
410#391C2313yes—
411#390C2313yes—
412#390C2313yes—
413#390C2313yes—
414#390C2313yes—
415#390C2313yes—
416#390C2313yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
420#390C2313yes—
421#390C2313yes—
422#390C2313yes—
423#390C2311yescharacteristic
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2316yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2316yes—
439#389C2316yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2316yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2316yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#388C2311yescharacteristic
472#388C2313yes—
473#388C2313yes—
474#388C2313yes—
475#388C2313yes—
476#388C2313yes—
477#388C2316yes—
478#388C2316yes—
479#388C2316yes—
480#388C2316yes—
481#388C2316yes—
482#388C2316yes—
483#388C2316yes—
484#388C2316yes—
485#388C2313yes—
486#388C2313yes—
487#388C2316yes—
488#388C2316yes—
489#388C2316yes—
490#388C2316yes—
491#388C2316yes—
492#388C2313yes—
493#388C2316yes—
494#388C2316yes—
495#388C2313yes—
496#388C2313yes—
497#388C2313yes—
498#388C2313yes—
499#388C2313yes—
500#388C2311yescharacteristic
501#388C2313yes—
502#387C2311yescharacteristic
503#387C2313yes—
504#387C2313yes—
505#387C2313yes—
506#387C2313yes—
507#387C2313yes—
508#387C2316yes—
509#387C2311yescharacteristic
510#387C2311yescharacteristic
511#387C2313yes—
512#387C2313yes—
513#387C2313yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2316yes—
518#387C2316yes—
519#387C2316yes—
520#387C2316yes—
521#387C2316yes—
522#387C2313yes—
523#387C2316yes—
524#387C2316yes—
525#387C2316yes—
526#387C2316yes—
527#387C2316yes—
528#387C2316yes—
529#387C2316yes—
530#387C2316yes—
531#387C2313yes—
532#387C2316yes—
533#387C2316yes—
534#387C2316yes—
535#387C2316yes—
536#386C2316yes—
537#386C2316yes—
538#386C2313yes—
539#386C2316yes—
540#386C2311yescharacteristic
541#385C2316yes—
542#385C2316yes—
543#385C2316yes—
544#385C2313yes—
545#385C2313yes—
546#385C2316yes—
547#385C2316yes—
548#385C2313yes—
549#385C2313yes—
550#385C2311yescharacteristic
551#385C2313yes—
552#384C2313yes—
553#384C2313yes—
554#384C2313yes—
555#384C2313yes—
556#384C2313yes—
557#384C2316yes—
558#384C2313yes—
559#383C2313yes—
560#383C2313yes—
561#383C2316yes—
562#382C2313yes—
563#382C2313yes—
564#382C2313yes—
565#382C2313yes—
566#382C2313yes—
567#382C2313yes—
568#382C2313yes—
569#382C2313yes—
570#382C2313yes—
571#382C2313yes—
572#382C2316yes—
573#381C2316yes—
574#381C2316yes—
575#380C2316yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2313yes—
585#380C2313yes—
586#380C2316yes—
587#380C2313yes—
588#380C2311yescharacteristic
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2316yes—
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⋊C4C2316yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2316yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2316yes—
620C4×C22⋊C4C2316yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C43C2313yes—
626C43C2313yes—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C22×Q8—24no—
631C22×Q8—24no—
632C22×Q8—24no—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8#4118yes—
636C22×Q8C2413yes—
637C22×Q8C2413yes—
638C22×Q8C2413yes—
639C22×Q8C2411yescharacteristic
640C22×D4C2413yes—
641C22×D4C2411yescharacteristic
642C22×D4C2413yes—
643C22×D4C2413yes—
644C23×C4C2413yes—
645C23×C4C2413yes—
646C23×C4C2413yes—
647C23×C4C2411yescharacteristic
648C23×C4C2413yes—
649C23×C4C2416yes—
650C4⋊Q8—212no—
651C4⋊Q8—46no—
652#126—412no—
653#126—46no—
654#126—46no—
655#125—46no—
656#125—46no—
657#125—46no—
658#125—46no—
659#124—212no—
660#124—46no—
661C22⋊Q8—212no—
662C22⋊Q8—212no—
663C22⋊Q8—212no—
664C22⋊Q8—412no—
665C22⋊Q8—46no—
666C22⋊Q8—46no—
667#121—212no—
668#121—46no—
669#121—46no—
670C4×Q8—212no—
671C4×Q8—212no—
672C4×Q8—24no—
673C4×Q8—24no—
674C4×Q8—24no—
675C4×Q8—24no—
676C4×Q8—24no—
677C4×Q8—24no—
678C4×Q8—24no—
679C4×Q8—24no—
680C4×Q8—24no—
681C4×Q8—24no—
682C4×Q8—24no—
683C4×Q8—24no—
684C4×Q8—46no—
685C4×Q8—46no—
686C4×Q8—46no—
687C4×Q8—46no—
688C4×Q8—46no—
689C4×Q8—46no—
690C4×Q8—46no—
691C4×D4—212no—
692C4×D4—212no—
693C4×D4—46no—
694C4×D4—46no—
695C4×D4—46no—
696#117—212no—
697#117—212no—
698#117—46no—
699#117—46no—
700#117—46no—
701#117—46no—
702#117—46no—
703C2×C4⋊C4—46no—
704C2×C4⋊C4—46no—
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⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2416yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2416yes—
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2416yes—
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2416yes—
755C2×C4⋊C4C2416yes—
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2411yescharacteristic
760C2×C4⋊C4C2411yescharacteristic
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2416yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2416yes—
768C2×C22⋊C4C2411yescharacteristic
769C2×C22⋊C4C2413yes—
770C2×C22⋊C4C2411yescharacteristic
771C2×C22⋊C4C2413yes—
772C2×C22⋊C4C2413yes—
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2416yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2411yescharacteristic
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2411yescharacteristic
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2411yescharacteristic
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2411yescharacteristic
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2416yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2416yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2416yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2416yes—
797C2×C22⋊C4C2411yescharacteristic
798C2×C22⋊C4C2411yescharacteristic
799C2×C22⋊C4C2411yescharacteristic
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2411yescharacteristic
802C2×C22⋊C4C2411yescharacteristic
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2416yes—
808C2×C42—46no—
809C2×C42C2413yes—
810C2×C42C2413yes—
811C2×C42C2413yes—
812C2×C42C2413yes—
813C2×C42C2413yes—
814C2×C42C2413yes—
815C2×C42C2416yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2416yes—
824C2×C42C2416yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2411yescharacteristic
831C2×C42C2411yescharacteristic
832C2×C42C2413yes—
833C2×C42C2413yes—
834#95C2411yescharacteristic
835#95C2411yescharacteristic
836#95C2411yescharacteristic
837#95C2413yes—
838#95C2411yescharacteristic
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2416yes—
848#95C2413yes—
849#95C2416yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2411yescharacteristic
858#95C2411yescharacteristic
859#95C2411yescharacteristic
860#95C2411yescharacteristic
861#95C2413yes—
862#95C2411yescharacteristic
863#95C2416yes—
864#95C2411yescharacteristic
865#95C2413yes—
866#95C2411yescharacteristic
867#95C2416yes—
868#95C2411yescharacteristic
869#95C2413yes—
870#95C2416yes—
871#95C2416yes—
872#95C2416yes—
873#95C2413yes—
874#95C2413yes—
875#95C2416yes—
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#95C2416yes—
891#95C2416yes—
892#95C2416yes—
893#95C2416yes—
894#95C2416yes—
895#95C2416yes—
896#95C2416yes—
897#95C2416yes—
898C24C2511yescharacteristic
899C24C2513yes—
900C24C2511yescharacteristic
901#41—416no—
902C2×Q8—232no—
903C2×Q8—26no—
904C2×Q8—26no—
905C2×Q8—26no—
906C2×Q8—26no—
907C2×Q8—26no—
908C2×Q8—26no—
909C2×Q8—43no—
910C2×Q8—43no—
911C2×Q8—416no—
912C2×Q8C2×#41112yes—
913C2×Q8C2×#4114yes—
914C2×Q8H(5,𝔽2)14yes—
915C2×Q82−1+414yes—
916C2×D4—22no—
917C2×D4—26no—
918C2×D4—26no—
919C2×D4—26no—
920C2×D4—26no—
921C2×D4—22no—
922C2×D4—41no—
923C2×D4—43no—
924C2×D4—43no—
925C2×D4—43no—
926C2×D4—43no—
927C2×D4—43no—
928C22×C4—26no—
929C22×C4—26no—
930C22×C4—26no—
931C22×C4—26no—
932C22×C4—26no—
933C22×C4—26no—
934C22×C4—26no—
935C22×C4—26no—
936C22×C4—22no—
937C22×C4—41no—
938C22×C4—41no—
939C22×C4—43no—
940C22×C4—43no—
941C22×C4—43no—
942C22×C4—46no—
943C22×C4—46no—
944C22×C4—46no—
945C22×C4C2×#41112yes—
946C22×C4C2511yescharacteristic
947C22×C4C2511yescharacteristic
948C22×C4C2513yes—
949C22×C4C2511yescharacteristic
950C22×C4C2513yes—
951C22×C4C2513yes—
952C22×C4C2513yes—
953C22×C4C2513yes—
954C22×C4C2511yescharacteristic
955C22×C4C2513yes—
956C22×C4C2511yescharacteristic
957C22×C4C2513yes—
958C22×C4C2513yes—
959C22×C4C2511yescharacteristic
960C22×C4C2513yes—
961C22×C4C2513yes—
962C22×C4C2511yescharacteristic
963C22×C4C2513yes—
964C22×C4C2513yes—
965C22×C4C2511yescharacteristic
966C22×C4C2511yescharacteristic
967C22×C4C2513yes—
968C22×C4C2511yescharacteristic
969C22×C4C2511yescharacteristic
970C22×C4C2513yes—
971C22×C4C2511yescharacteristic
972C22×C4C2511yescharacteristic
973C22×C4C2513yes—
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—212no—
983C4⋊C4—26no—
984C4⋊C4—26no—
985C4⋊C4—26no—
986C4⋊C4—26no—
987C4⋊C4—26no—
988C4⋊C4—26no—
989C4⋊C4—26no—
990C4⋊C4—26no—
991C4⋊C4—26no—
992C4⋊C4—26no—
993C4⋊C4—26no—
994C4⋊C4—22no—
995C4⋊C4—22no—
996C4⋊C4—26no—
997C4⋊C4—22no—
998C4⋊C4—43no—
999C4⋊C4—46no—
1000C4⋊C4—43no—
1001C4⋊C4—41no—
1002C4⋊C4—43no—
1003C4⋊C4—43no—
1004C4⋊C4—43no—
1005C4⋊C4—43no—
1006C4⋊C4—46no—
1007C4⋊C4—43no—
1008C4⋊C4—41no—
1009C4⋊C4—41no—
1010C4⋊C4—46no—
1011C4⋊C4—43no—
1012C4⋊C4—41no—
1013C4⋊C4—43no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—41no—
1019C4⋊C4—43no—
1020C4⋊C4—43no—
1021C4⋊C4—46no—
1022C4⋊C4—46no—
1023C4⋊C4—43no—
1024C4⋊C4—43no—
1025C4⋊C4—43no—
1026C4⋊C4—43no—
1027C4⋊C4—43no—
1028C4⋊C4—43no—
1029C4⋊C4—43no—
1030C4⋊C4—43no—
1031C4⋊C4—43no—
1032C4⋊C4—46no—
1033C4⋊C4—46no—
1034C4⋊C4—46no—
1035C4⋊C4—43no—
1036C4⋊C4—43no—
1037C22⋊C4—22no—
1038C22⋊C4—26no—
1039C22⋊C4—22no—
1040C22⋊C4—26no—
1041C22⋊C4—26no—
1042C22⋊C4—26no—
1043C22⋊C4—212no—
1044C22⋊C4—26no—
1045C22⋊C4—26no—
1046C22⋊C4—22no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—43no—
1051C22⋊C4—41no—
1052C22⋊C4—43no—
1053C22⋊C4—46no—
1054C22⋊C4—43no—
1055C22⋊C4—43no—
1056C22⋊C4—41no—
1057C22⋊C4—43no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—43no—
1061C22⋊C4—43no—
1062C22⋊C4—43no—
1063C22⋊C4—43no—
1064C22⋊C4—41no—
1065C22⋊C4—43no—
1066C22⋊C4—43no—
1067C22⋊C4—46no—
1068C22⋊C4—43no—
1069C22⋊C4—43no—
1070C22⋊C4—46no—
1071C22⋊C4—46no—
1072C22⋊C4—46no—
1073C22⋊C4—43no—
1074C22⋊C4—43no—
1075C22⋊C4—43no—
1076C22⋊C4—43no—
1077C42—212no—
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—43no—
1092C42—43no—
1093C42—41no—
1094C42—43no—
1095C42—43no—
1096C42—41no—
1097C42—46no—
1098C42—46no—
1099C42—43no—
1100C42—43no—
1101C42—43no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—23no—
1110C23—21no—
1111C23—23no—
1112C23—21no—
1113C23—23no—
1114C23—21no—
1115C23—23no—
1116C23—23no—
1117C23—21no—
1118C23—21no—
1119C23—23no—
1120C23—23no—
1121C23—21no—
1122C23C22×#4112yes—
1123C23C2611yescharacteristic
1124Q8—224no—
1125Q8—412no—
1126Q8—86no—
1127Q8#539116yes—
1128D4—44no—
1129D4—412no—
1130D4—86no—
1131D4—86no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—23no—
1135C2×C4—23no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—224no—
1139C2×C4—21no—
1140C2×C4—23no—
1141C2×C4—21no—
1142C2×C4—23no—
1143C2×C4—21no—
1144C2×C4—23no—
1145C2×C4—23no—
1146C2×C4—21no—
1147C2×C4—23no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—23no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—21no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—23no—
1173C2×C4—23no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—21no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—23no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—23no—
1194C2×C4—21no—
1195C2×C4—23no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—23no—
1203C2×C4—21no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—21no—
1207C2×C4—23no—
1208C2×C4—23no—
1209C2×C4—21no—
1210C2×C4—23no—
1211C2×C4—44no—
1212C2×C4—412no—
1213C2×C4—412no—
1214C2×C4—86no—
1215C2×C4—166no—
1216C2×C4C22×#4116yes—
1217C2×C4C22×#4116yes—
1218C2×C4C2×H(5,𝔽2)16yes—
1219C2×C4C2×2−1+416yes—
1220C2×C4#58512yes—
1221C2×C4#58512yes—
1222C22—22no—
1223C22—22no—
1224C22—22no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—43no—
1231C22—41no—
1232C22—43no—
1233C22—41no—
1234C22—43no—
1235C22—41no—
1236C22—43no—
1237C22—43no—
1238C22—41no—
1239C22—41no—
1240C22—43no—
1241C22—41no—
1242C22—43no—
1243C22C23×#4111yescharacteristic
1244C22C22×H(5,𝔽2)11yescharacteristic
1245C22C22×2−1+411yescharacteristic
1246C22C2×#58511yescharacteristic
1247C22C2×#58511yescharacteristic
1248C222−1+611yescharacteristic
1249C222−1+611yescharacteristic
1250C4—22no—
1251C4—22no—
1252C4—26no—
1253C4—43no—
1254C4—41no—
1255C4—43no—
1256C4—41no—
1257C4—43no—
1258C4—41no—
1259C4—43no—
1260C4—43no—
1261C4—43no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—43no—
1267C4—43no—
1268C4—43no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—43no—
1273C4—43no—
1274C4—43no—
1275C4—41no—
1276C4—43no—
1277C4C2×#539112yes—
1278C2—42no—
1279C2—81no—
1280C2—83no—
1281C2C22×#53911yescharacteristic
1282C2#6291911yescharacteristic
1283C2#6292211yescharacteristic
1284C2#6300511yescharacteristic
1285C2#6300711yescharacteristic
1286C2#6303411yescharacteristic
1287C2#6305711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36434C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52281C2semidirect
2. #42948C2semidirect
3. #42947C2semidirect
4. #42904C2semidirect
5. #42870C2semidirect
6. #42840C2semidirect
7. #42827C2semidirect
8. #40224C2semidirect
9. #40105C2semidirect
10. #40035C2semidirect
11. #40004C2semidirect
12. #39782C2semidirect
13. #39249C2semidirect
14. #37403C2semidirect
15. #37355C2semidirect
16. #37326C2semidirect
17. #36577C2semidirect
18. #36475C2semidirect
19. #36475C2semidirect
20. #36458C2semidirect
21. #36448C2semidirect
23. #35983C2semidirect
24. #35816C2semidirect
25. #35801C2semidirect
26. #35801C2semidirect
27. #35786C2semidirect
28. #35723C2semidirect
29. #34312C2semidirect
30. #34311C2semidirect
31. #34249C2semidirect

Maximal subgroups

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

subgroupindex
#522812
#429482
#429472
#429042
#428702
#428402
#428272
#402242
#401052
#400352
#400042
#397822
#392492
#374032
#373552
#373262
#365772
#364752
#364582
#364482
#364342
#359832
#358162
#358012
#357862
#357232
#343122
#343112
#342492