Finite Group Databasebeta

← #7657286

Subgroups — #7657286

Order 512.

4916 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42960C213yesmaximal, complemented
2#42957C213yesmaximal, complemented
3#42949C213yesmaximal, complemented
4#42947C213yesmaximal, complemented
5#42630C213yesmaximal, complemented
6#42592C213yesmaximal, complemented
7#42590C213yesmaximal, complemented
8#42580C213yesmaximal, complemented
9#40152C213yesmaximal, complemented
10#40141C213yesmaximal, complemented
11#39005C213yesmaximal, complemented
12#38996C213yesmaximal, complemented
13#37523C213yesmaximal, complemented
14#37502C213yesmaximal, complemented
15#36475C211yesmaximal, characteristic, complemented
16#36458C211yesmaximal, characteristic, complemented
17#36433C211yesmaximal, characteristic, complemented
18#36431C211yesmaximal, characteristic, complemented
19#36076C211yesmaximal, characteristic, complemented
20#36076C211yesmaximal, characteristic, complemented
21#36059C211yesmaximal, characteristic, complemented
22#36040C211yesmaximal, characteristic, complemented
23#36029C211yesmaximal, characteristic
24#36005C211yesmaximal, characteristic, complemented
25#35971C211yesmaximal, characteristic, complemented
26#35816C211yesmaximal, characteristic, complemented
27#35029C213yesmaximal, complemented
28#34592C213yesmaximal, complemented
29#34295C211yesmaximal, characteristic, complemented
30#34250C211yesmaximal, characteristic, complemented
31C4×#550C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41#2864C2213yes—
42#2860C2213yes—
43#2854C2213yes—
44#2851C2213yes—
45#2837C2216yes—
46#2836C2216yes—
47#2826C2216yes—
48#2824C2216yes—
49#2786C2216yes—
50#2782C2216yes—
51#2757C2216yes—
52#2750C2216yes—
53#2738C2216yes—
54#2737C2216yes—
55#2711C2216yes—
56#2708C2216yes—
57#2706C2216yes—
58#2706C2216yes—
59#2705C2216yes—
60#2696C2216yes—
61#2693C2216yes—
62#2691C2216yes—
63#2691C2216yes—
64#2687C2216yes—
65#2667C2213yes—
66#2666C2213yes—
67#2664C2213yes—
68#2663C2213yes—
69#2663C2216yes—
70#2655C2211yescharacteristic
71#2654C2213yes—
72#2653C2213yes—
73#2652C2213yes—
74#2652C2213yes—
75#2652C2213yes—
76#2649C2213yes—
77#2649C2213yes—
78#2649C2216yes—
79#2649C2216yes—
80#2647C2213yes—
81#2644C2213yes—
82#2638C2213yes—
83#2636C2213yes—
84#2633C2213yes—
85#2630C2213yes—
86#2629C2213yes—
87#2628C2213yes—
88#2624C2213yes—
89#2624C2213yes—
90#2624C2213yes—
91#2623C2216yes—
92#2619C2213yes—
93#2618C2216yes—
94#2580C2213yes—
95#2580C2213yes—
96#2573C2216yes—
97#2571C2213yes—
98#2570C2213yes—
99#2570C2213yes—
100#2570C2213yes—
101#2566C2213yes—
102#2566C2213yes—
103#2563C2213yes—
104#2553C2216yes—
105#2541C2213yes—
106#2538C2213yes—
107#2535C2213yes—
108#2513C2213yes—
109#2513C2213yes—
110#2513C2213yes—
111#2513C2213yes—
112#2512C2213yes—
113#2512C2213yes—
114#2509C2213yes—
115#2509C2213yes—
116#2508C2213yes—
117#2508C2213yes—
118#2508C2213yes—
119#2507C2213yes—
120#2507C2213yes—
121#2506C2213yes—
122#2504C2213yes—
123#2504C2213yes—
124#2501C2213yes—
125#2500C2213yes—
126#2497C2213yes—
127#2496C2213yes—
128#2495C2213yes—
129#2495C2213yes—
130#2495C2213yes—
131#2495C2213yes—
132#2487C2213yes—
133#2486C2213yes—
134#2486C2213yes—
135#2485C2213yes—
136#2481C2216yes—
137#2463C2216yes—
138#2455C2216yes—
139#2454C2213yes—
140#2454C2213yes—
141#2454C2213yes—
142#2454C2213yes—
143#2452C2213yes—
144#2452C2213yes—
145#2445C2213yes—
146#2445C2213yes—
147#2445C2213yes—
148#2445C2213yes—
149#2445C2213yes—
150#2445C2213yes—
151#2445C2213yes—
152#2445C2213yes—
153#2443C2216yes—
154#2442C2213yes—
155#2442C2213yes—
156#2442C2213yes—
157#2441C2213yes—
158#2440C2213yes—
159#2439C2213yes—
160#2428C2213yes—
161#2428C2213yes—
162#2425C2216yes—
163#2422C2213yes—
164#2422C2213yes—
165#2422C2213yes—
166#2420C2213yes—
167#2420C2213yes—
168#2420C2213yes—
169#2420C2213yes—
170#2420C2213yes—
171#2419C2216yes—
172#2416C2213yes—
173#2416C2213yes—
174#2402C2213yes—
175#2401C2213yes—
176#2396C2213yes—
177#2396C2213yes—
178#2395C2213yes—
179#2395C2213yes—
180#2395C2213yes—
181#2392C2213yes—
182#2366C2213yes—
183#2366C2213yes—
184#2363C2213yes—
185#2363C2213yes—
186#2363C2213yes—
187#2361C2213yes—
188#2354C2213yes—
189#2352C2213yes—
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196#2351C2211yescharacteristic
197#2351C2211yescharacteristic
198#2351C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204#2349C2213yes—
205#2349C2213yes—
206D4×C4⋊C4C2213yes—
207D4×C4⋊C4C2213yes—
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214#2341C2211yescharacteristic
215#2341C2211yescharacteristic
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218#2328C2213yes—
219#2325C2216yes—
220#2324C2213yes—
221#2318C2216yes—
222#2317C2213yes—
223#2316C2213yes—
224C4×#127C2213yes—
225C4×#125C2213yes—
226C4×#126C2213yes—
227C4×C22⋊Q8C2213yes—
228C4×#123C2213yes—
229C4×#121C2213yes—
230C4×#121C2213yes—
231C4×#121C2213yes—
232#2296C2213yes—
233C2×#389C2213yes—
234#2290C2213yes—
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×D4C2213yes—
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C22×#41C2311yescharacteristic
241#557—44no—
242#550—28no—
243#550—28no—
244#550—44no—
245C2×C4⋊Q8C2313yes—
246C2×#127C2313yes—
247C2×#127C2313yes—
248C2×#127C2313yes—
249C2×#126C2313yes—
250C2×#126C2316yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#123C2313yes—
255C2×#123C2316yes—
256C2×#123C2316yes—
257C2×#123C2316yes—
258C2×#123C2316yes—
259C2×#123C2316yes—
260C2×C22⋊Q8C2313yes—
261C2×C22⋊Q8C2316yes—
262C2×#121C2313yes—
263C2×#121C2313yes—
264C2×#121C2313yes—
265C2×#121C2313yes—
266C2×#121C2316yes—
267C2×#121C2313yes—
268C2×#121C2313yes—
269C2×#121C2316yes—
270#520—28no—
271#520—44no—
272#520—44no—
273C4×#41—44no—
274C4×#41—44no—
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
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×Q8C2313yes—
288C2×C4×D4C2313yes—
289C2×C4×D4C2313yes—
290C2×C4×D4C2313yes—
291C2×C4×D4C2313yes—
292C2×C4×D4C2313yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2313yes—
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2316yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2316yes—
305C2×#117C2313yes—
306C2×#117C2313yes—
307C2×#117C2313yes—
308C2×#117C2313yes—
309C2×#117C2313yes—
310C22×C4⋊C4C2313yes—
311C22×C4⋊C4C2313yes—
312C22×C4⋊C4C2313yes—
313C22×C4⋊C4C2316yes—
314C22×C42C2313yes—
315C22×C42C2313yes—
316#401C2311yescharacteristic
317#400C2316yes—
318#400C2316yes—
319#400C2316yes—
320#400C2316yes—
321#400C2313yes—
322#400C2313yes—
323#400C2313yes—
324#400C2316yes—
325#400C2316yes—
326#400C2311yescharacteristic
327#400C2311yescharacteristic
328#400C2313yes—
329#400C2313yes—
330#400C2311yescharacteristic
331#400C2311yescharacteristic
332#400C2313yes—
333#400C2313yes—
334#400C2313yes—
335#399C2316yes—
336#399C2313yes—
337#399C2316yes—
338#399C2316yes—
339#399C2313yes—
340#399C2313yes—
341#399C2313yes—
342#399C2313yes—
343#398C2313yes—
344#398C2316yes—
345#398C2316yes—
346#398C2313yes—
347#398C2316yes—
348#398C2316yes—
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#398C2313yes—
353#398C2311yescharacteristic
354#398C2313yes—
355#398C2311yescharacteristic
356#398C2311yescharacteristic
357#398C2313yes—
358#398C2313yes—
359#397C2313yes—
360#397C2316yes—
361#397C2316yes—
362#397C2316yes—
363#397C2316yes—
364#397C2316yes—
365#397C2316yes—
366#397C2316yes—
367#397C2316yes—
368#397C2313yes—
369#397C2313yes—
370#397C2313yes—
371#397C2313yes—
372#397C2313yes—
373#397C2313yes—
374#397C2313yes—
375#397C2313yes—
376#397C2313yes—
377#397C2313yes—
378#397C2313yes—
379#397C2313yes—
380#396C2313yes—
381#396C2316yes—
382#396C2316yes—
383#396C2316yes—
384#396C2316yes—
385#396C2313yes—
386#396C2313yes—
387#396C2316yes—
388#396C2313yes—
389#396C2313yes—
390#396C2313yes—
391#396C2313yes—
392#395C2313yes—
393#395C2313yes—
394#394C2316yes—
395#394C2316yes—
396#394C2316yes—
397#394C2316yes—
398#394C2313yes—
399#394C2316yes—
400#394C2316yes—
401#394C2316yes—
402#394C2316yes—
403#394C2316yes—
404#394C2316yes—
405#394C2313yes—
406#394C2313yes—
407#394C2313yes—
408#394C2313yes—
409#394C2313yes—
410#394C2313yes—
411#394C2313yes—
412#394C2313yes—
413#393C2313yes—
414#393C2316yes—
415#393C2313yes—
416#393C2316yes—
417#392C2316yes—
418#392C2316yes—
419#392C2313yes—
420#391C2313yes—
421#390C2313yes—
422#390C2313yes—
423#390C2316yes—
424#390C2316yes—
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2316yes—
432#390C2313yes—
433#390C2313yes—
434#390C2313yes—
435#390C2313yes—
436#390C2313yes—
437#390C2313yes—
438#390C2313yes—
439#390C2313yes—
440#390C2313yes—
441#390C2313yes—
442#390C2313yes—
443#390C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2316yes—
455#389C2313yes—
456#389C2316yes—
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#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2311yescharacteristic
481#388C2313yes—
482#388C2313yes—
483#388C2313yes—
484#388C2316yes—
485#388C2316yes—
486#388C2313yes—
487#388C2316yes—
488#388C2316yes—
489#388C2316yes—
490#388C2316yes—
491#388C2313yes—
492#388C2316yes—
493#388C2313yes—
494#388C2316yes—
495#388C2313yes—
496#388C2316yes—
497#387C2311yescharacteristic
498#387C2313yes—
499#387C2313yes—
500#387C2311yescharacteristic
501#387C2313yes—
502#387C2313yes—
503#387C2313yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2313yes—
510#387C2316yes—
511#387C2313yes—
512#387C2311yescharacteristic
513#387C2311yescharacteristic
514#387C2313yes—
515#387C2311yescharacteristic
516#386C2316yes—
517#386C2316yes—
518#386C2316yes—
519#386C2316yes—
520#386C2316yes—
521#386C2316yes—
522#386C2316yes—
523#386C2316yes—
524#386C2313yes—
525#386C2316yes—
526#386C2316yes—
527#386C2316yes—
528#386C2313yes—
529#386C2316yes—
530#386C2313yes—
531#386C2316yes—
532#385C2313yes—
533#385C2316yes—
534#385C2316yes—
535#385C2316yes—
536#385C2313yes—
537#385C2313yes—
538#385C2316yes—
539#385C2316yes—
540#385C2316yes—
541#385C2316yes—
542#385C2313yes—
543#385C2313yes—
544#385C2316yes—
545#385C2316yes—
546#385C2313yes—
547#385C2313yes—
548#385C2313yes—
549#385C2313yes—
550#384C2313yes—
551#384C2313yes—
552#384C2313yes—
553#384C2313yes—
554#384C2313yes—
555#383C2313yes—
556#383C2316yes—
557#382C2313yes—
558#382C2313yes—
559#382C2313yes—
560#382C2313yes—
561#382C2313yes—
562#382C2313yes—
563#382C2313yes—
564#382C2313yes—
565#382C2316yes—
566#382C2313yes—
567#382C2313yes—
568#381C2316yes—
569#381C2316yes—
570#381C2313yes—
571#380C2316yes—
572#380C2316yes—
573#380C2316yes—
574#380C2316yes—
575#380C2316yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2313yes—
585#380C2313yes—
586#380C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2311yescharacteristic
608C4×C4⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624#376C2313yes—
625C2×#95C2316yes—
626C43C2313yes—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41#4118yes—
636C22×Q8C2413yes—
637C22×Q8C2411yescharacteristic
638C22×D4C2413yes—
639C22×D4C2413yes—
640C22×D4C2413yes—
641C22×D4C2413yes—
642C22×D4C2416yes—
643C22×D4C2416yes—
644C22×D4C2413yes—
645C22×D4C2413yes—
646C22×D4C2416yes—
647C23×C4C2413yes—
648C23×C4C2413yes—
649C23×C4C2413yes—
650C23×C4C2416yes—
651C23×C4C2413yes—
652C23×C4C2413yes—
653C23×C4C2413yes—
654C23×C4C2416yes—
655C23×C4C2416yes—
656C23×C4C2413yes—
657C4⋊Q8—46no—
658#127—212no—
659#127—212no—
660#127—46no—
661#126—46no—
662#126—86no—
663#125—46no—
664#125—46no—
665#125—46no—
666#123—46no—
667#123—86no—
668#123—86no—
669#123—86no—
670#123—86no—
671#123—86no—
672C22⋊Q8—46no—
673C22⋊Q8—86no—
674#121—212no—
675#121—212no—
676#121—212no—
677#121—212no—
678#121—412no—
679#121—46no—
680#121—46no—
681#121—86no—
682C4×Q8—24no—
683C4×Q8—24no—
684C4×Q8—24no—
685C4×Q8—24no—
686C4×Q8—24no—
687C4×Q8—24no—
688C4×Q8—24no—
689C4×Q8—24no—
690C4×Q8—24no—
691C4×Q8—24no—
692C4×Q8—24no—
693C4×Q8—24no—
694C4×Q8—46no—
695C4×D4—212no—
696C4×D4—212no—
697C4×D4—212no—
698C4×D4—212no—
699C4×D4—46no—
700C4×D4—46no—
701C4×D4—46no—
702C4×D4—46no—
703C4×D4—46no—
704C4×D4—46no—
705C4×D4—46no—
706C4×D4—46no—
707C4×D4—46no—
708C4×D4—46no—
709C4×D4—46no—
710C4×D4—412no—
711C4×D4—86no—
712#117—212no—
713#117—46no—
714#117—46no—
715#117—46no—
716#117—46no—
717C2×C4⋊C4—212no—
718C2×C4⋊C4—46no—
719C2×C4⋊C4—46no—
720C2×C4⋊C4—86no—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2416yes—
749C2×C4⋊C4C2416yes—
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2416yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2416yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2416yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2416yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2416yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2416yes—
796C2×C22⋊C4C2416yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2416yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2416yes—
804C2×C22⋊C4C2416yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2416yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2416yes—
815C2×C22⋊C4C2416yes—
816C2×C22⋊C4C2416yes—
817C2×C22⋊C4C2416yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2413yes—
823C2×C42—46no—
824C2×C42—46no—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2411yescharacteristic
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2416yes—
843C2×C42C2413yes—
844C2×C42C2411yescharacteristic
845C2×C42C2411yescharacteristic
846#95C2413yes—
847#95C2413yes—
848#95C2416yes—
849#95C2416yes—
850#95C2411yescharacteristic
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2411yescharacteristic
855#95C2411yescharacteristic
856#95C2413yes—
857#95C2411yescharacteristic
858#95C2411yescharacteristic
859#95C2411yescharacteristic
860#95C2411yescharacteristic
861#95C2411yescharacteristic
862#95C2411yescharacteristic
863#95C2411yescharacteristic
864#95C2411yescharacteristic
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2416yes—
877#95C2411yescharacteristic
878#95C2411yescharacteristic
879#95C2411yescharacteristic
880#95C2411yescharacteristic
881#95C2411yescharacteristic
882#95C2411yescharacteristic
883#95C2416yes—
884#95C2411yescharacteristic
885#95C2411yescharacteristic
886#95C2411yescharacteristic
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2416yes—
903#95C2416yes—
904#95C2416yes—
905#95C2416yes—
906#95C2416yes—
907#95C2416yes—
908C24C2513yes—
909C24C2513yes—
910C24C2513yes—
911#41—232no—
912#41—416no—
913#41—416no—
914C2×Q8—43no—
915C2×Q8—43no—
916C2×Q8—43no—
917C2×Q8C2×#4114yes—
918C2×Q8H(5,𝔽2)14yes—
919C2×Q82−1+414yes—
920C2×D4—26no—
921C2×D4—26no—
922C2×D4—212no—
923C2×D4—212no—
924C2×D4—26no—
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—43no—
934C2×D4—43no—
935C2×D4—46no—
936C2×D4—46no—
937C2×D4—46no—
938C2×D4—43no—
939C2×D4—46no—
940C2×D4—43no—
941C2×D4—43no—
942C2×D4—43no—
943C2×D4—46no—
944C2×D4—46no—
945C2×D4—46no—
946C2×D4C2×#41112yes—
947C22×C4—26no—
948C22×C4—26no—
949C22×C4—212no—
950C22×C4—26no—
951C22×C4—26no—
952C22×C4—26no—
953C22×C4—26no—
954C22×C4—26no—
955C22×C4—26no—
956C22×C4—26no—
957C22×C4—26no—
958C22×C4—43no—
959C22×C4—43no—
960C22×C4—43no—
961C22×C4—43no—
962C22×C4—43no—
963C22×C4—46no—
964C22×C4—43no—
965C22×C4—43no—
966C22×C4—43no—
967C22×C4—43no—
968C22×C4—43no—
969C22×C4—46no—
970C22×C4—46no—
971C22×C4—46no—
972C22×C4—46no—
973C22×C4—46no—
974C22×C4—46no—
975C22×C4—46no—
976C22×C4C2×#41112yes—
977C22×C4C2511yescharacteristic
978C22×C4C2511yescharacteristic
979C22×C4C2513yes—
980C22×C4C2511yescharacteristic
981C22×C4C2511yescharacteristic
982C22×C4C2513yes—
983C22×C4C2513yes—
984C22×C4C2511yescharacteristic
985C22×C4C2513yes—
986C22×C4C2511yescharacteristic
987C22×C4C2511yescharacteristic
988C22×C4C2513yes—
989C22×C4C2511yescharacteristic
990C22×C4C2511yescharacteristic
991C22×C4C2511yescharacteristic
992C22×C4C2513yes—
993C22×C4C2511yescharacteristic
994C22×C4C2513yes—
995C22×C4C2513yes—
996C22×C4C2513yes—
997C22×C4C2513yes—
998C22×C4C2513yes—
999C22×C4C2513yes—
1000C22×C4C2511yescharacteristic
1001C22×C4C2511yescharacteristic
1002C22×C4C2511yescharacteristic
1003C22×C4C2511yescharacteristic
1004C22×C4C2513yes—
1005C4⋊C4—26no—
1006C4⋊C4—26no—
1007C4⋊C4—26no—
1008C4⋊C4—22no—
1009C4⋊C4—22no—
1010C4⋊C4—22no—
1011C4⋊C4—26no—
1012C4⋊C4—26no—
1013C4⋊C4—26no—
1014C4⋊C4—26no—
1015C4⋊C4—26no—
1016C4⋊C4—26no—
1017C4⋊C4—26no—
1018C4⋊C4—26no—
1019C4⋊C4—26no—
1020C4⋊C4—26no—
1021C4⋊C4—22no—
1022C4⋊C4—26no—
1023C4⋊C4—26no—
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—22no—
1028C4⋊C4—43no—
1029C4⋊C4—43no—
1030C4⋊C4—43no—
1031C4⋊C4—43no—
1032C4⋊C4—46no—
1033C4⋊C4—46no—
1034C4⋊C4—41no—
1035C4⋊C4—41no—
1036C4⋊C4—43no—
1037C4⋊C4—41no—
1038C4⋊C4—46no—
1039C4⋊C4—41no—
1040C4⋊C4—43no—
1041C4⋊C4—43no—
1042C4⋊C4—43no—
1043C4⋊C4—43no—
1044C4⋊C4—43no—
1045C4⋊C4—46no—
1046C4⋊C4—43no—
1047C4⋊C4—43no—
1048C4⋊C4—43no—
1049C4⋊C4—43no—
1050C4⋊C4—43no—
1051C4⋊C4—43no—
1052C4⋊C4—43no—
1053C4⋊C4—43no—
1054C4⋊C4—46no—
1055C4⋊C4—43no—
1056C4⋊C4—43no—
1057C4⋊C4—43no—
1058C4⋊C4—43no—
1059C4⋊C4—46no—
1060C4⋊C4—43no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C22⋊C4—26no—
1064C22⋊C4—26no—
1065C22⋊C4—26no—
1066C22⋊C4—26no—
1067C22⋊C4—26no—
1068C22⋊C4—26no—
1069C22⋊C4—26no—
1070C22⋊C4—26no—
1071C22⋊C4—43no—
1072C22⋊C4—43no—
1073C22⋊C4—43no—
1074C22⋊C4—43no—
1075C22⋊C4—46no—
1076C22⋊C4—46no—
1077C22⋊C4—43no—
1078C22⋊C4—43no—
1079C22⋊C4—43no—
1080C22⋊C4—43no—
1081C22⋊C4—46no—
1082C22⋊C4—43no—
1083C22⋊C4—43no—
1084C22⋊C4—46no—
1085C22⋊C4—46no—
1086C22⋊C4—46no—
1087C22⋊C4—43no—
1088C22⋊C4—46no—
1089C22⋊C4—43no—
1090C22⋊C4—43no—
1091C22⋊C4—43no—
1092C22⋊C4—46no—
1093C22⋊C4—43no—
1094C22⋊C4—43no—
1095C22⋊C4—46no—
1096C22⋊C4—43no—
1097C22⋊C4—43no—
1098C22⋊C4—43no—
1099C22⋊C4—43no—
1100C22⋊C4—46no—
1101C22⋊C4—46no—
1102C22⋊C4—43no—
1103C22⋊C4—46no—
1104C22⋊C4—43no—
1105C22⋊C4—43no—
1106C22⋊C4—43no—
1107C42—26no—
1108C42—26no—
1109C42—26no—
1110C42—26no—
1111C42—26no—
1112C42—26no—
1113C42—26no—
1114C42—26no—
1115C42—26no—
1116C42—26no—
1117C42—26no—
1118C42—26no—
1119C42—22no—
1120C42—26no—
1121C42—41no—
1122C42—41no—
1123C42—43no—
1124C42—43no—
1125C42—46no—
1126C42—43no—
1127C42—43no—
1128C23—23no—
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—
1143C23—23no—
1144C23—23no—
1145C23—23no—
1146C23—23no—
1147C23—23no—
1148C23C22×#4116yes—
1149C23C2611yescharacteristic
1150Q8—86no—
1151Q8#539116yes—
1152D4—224no—
1153D4—412no—
1154D4—412no—
1155D4—412no—
1156D4—812no—
1157D4—812no—
1158D4—86no—
1159D4—86no—
1160D4—166no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—224no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—23no—
1172C2×C4—23no—
1173C2×C4—23no—
1174C2×C4—23no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—23no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—23no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—23no—
1193C2×C4—23no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—23no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—23no—
1210C2×C4—21no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—23no—
1217C2×C4—21no—
1218C2×C4—23no—
1219C2×C4—23no—
1220C2×C4—23no—
1221C2×C4—23no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—23no—
1228C2×C4—23no—
1229C2×C4—23no—
1230C2×C4—21no—
1231C2×C4—23no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—23no—
1235C2×C4—23no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—23no—
1240C2×C4—412no—
1241C2×C4—412no—
1242C2×C4—86no—
1243C2×C4—86no—
1244C2×C4—812no—
1245C2×C4—86no—
1246C2×C4—86no—
1247C2×C4—166no—
1248C2×C4—166no—
1249C2×C4C22×#4112yes—
1250C2×C4C22×#4116yes—
1251C2×C4C2×H(5,𝔽2)16yes—
1252C2×C4C2×2−1+416yes—
1253C2×C4#58512yes—
1254C2×C4#58512yes—
1255C22—26no—
1256C22—26no—
1257C22—26no—
1258C22—43no—
1259C22—43no—
1260C22—43no—
1261C22—43no—
1262C22—43no—
1263C22—43no—
1264C22—43no—
1265C22—43no—
1266C22—43no—
1267C22—43no—
1268C22—43no—
1269C22—43no—
1270C22—43no—
1271C22—43no—
1272C22—43no—
1273C22—43no—
1274C22—43no—
1275C22—43no—
1276C22C23×#4111yescharacteristic
1277C22C22×H(5,𝔽2)11yescharacteristic
1278C22C22×2−1+411yescharacteristic
1279C22C2×#58511yescharacteristic
1280C22C2×#58511yescharacteristic
1281C22H(7,𝔽2)11yescharacteristic
1282C22H(7,𝔽2)11yescharacteristic
1283C4—22no—
1284C4—22no—
1285C4—22no—
1286C4—41no—
1287C4—41no—
1288C4—43no—
1289C4—43no—
1290C4—43no—
1291C4—43no—
1292C4—41no—
1293C4—43no—
1294C4—43no—
1295C4—43no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—43no—
1300C4—41no—
1301C4—41no—
1302C4—43no—
1303C4—43no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—43no—
1309C4—43no—
1310C4C2×#539112yes—
1311C2—46no—
1312C2—83no—
1313C2—83no—
1314C2C22×#53911yescharacteristic
1315C2#6281011yescharacteristic
1316C2#6285811yescharacteristic
1317C2#6289911yescharacteristic
1318C2#6292311yescharacteristic
1319C2#6295211yescharacteristic
1320C2#6295211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36029C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42960C2semidirect
2. #42957C2semidirect
3. #42949C2semidirect
4. #42947C2semidirect
5. #42630C2semidirect
6. #42592C2semidirect
7. #42590C2semidirect
8. #42580C2semidirect
9. #40152C2semidirect
10. #40141C2semidirect
11. #39005C2semidirect
12. #38996C2semidirect
13. #37523C2semidirect
14. #37502C2semidirect
15. #36475C2semidirect
16. #36458C2semidirect
17. #36433C2semidirect
18. #36431C2semidirect
19. #36076C2semidirect
20. #36076C2semidirect
21. #36059C2semidirect
22. #36040C2semidirect
24. #36005C2semidirect
25. #35971C2semidirect
26. #35816C2semidirect
27. #35029C2semidirect
28. #34592C2semidirect
29. #34295C2semidirect
30. #34250C2semidirect
31. C4×#550C2semidirect

Maximal subgroups

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

subgroupindex
#429602
#429572
#429492
#429472
#426302
#425922
#425902
#425802
#401522
#401412
#390052
#389962
#375232
#375022
#364752
#364582
#364332
#364312
#360762
#360592
#360402
#360292
#360052
#359712
#358162
#350292
#345922
#342952
#342502
C4×#5502