Finite Group Databasebeta

← #7658622

Subgroups — #7658622

Order 512.

4785 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#42613C213yesmaximal, complemented
2#42611C213yesmaximal, complemented
3#42585C213yesmaximal, complemented
4#42579C213yesmaximal, complemented
5#42571C213yesmaximal, complemented
6#42564C213yesmaximal, complemented
7#42545C213yesmaximal, complemented
8#42537C213yesmaximal, complemented
9#42524C213yesmaximal, complemented
10#42514C213yesmaximal, complemented
11#42467C213yesmaximal, complemented
12#42456C213yesmaximal, complemented
13#37625C213yesmaximal, complemented
14#37591C213yesmaximal, complemented
15#37573C213yesmaximal, complemented
16#36693C213yesmaximal, complemented
17#36076C211yesmaximal, characteristic, complemented
18#36049C211yesmaximal, characteristic, complemented
19#36049C211yesmaximal, characteristic, complemented
20#36049C211yesmaximal, characteristic, complemented
21#36040C211yesmaximal, characteristic, complemented
22#36029C211yesmaximal, characteristic
23#36005C211yesmaximal, characteristic, complemented
24#35957C211yesmaximal, characteristic, complemented
25#35898C211yesmaximal, characteristic, complemented
26#35898C211yesmaximal, characteristic, complemented
27#35816C211yesmaximal, characteristic, complemented
28#35816C211yesmaximal, characteristic, complemented
29#34336C211yesmaximal, characteristic, complemented
30#34313C211yesmaximal, characteristic, complemented
31#34263C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#550C2211yescharacteristic
37C2×#550C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×#520C2211yescharacteristic
40C2×#520C2211yescharacteristic
41#2839C2211yescharacteristic
42#2839C2213yes—
43#2838C2213yes—
44#2838C2213yes—
45#2838C2213yes—
46#2838C2213yes—
47#2837C2213yes—
48#2837C2213yes—
49#2832C2213yes—
50#2832C2213yes—
51#2831C2213yes—
52#2831C2213yes—
53#2830C2213yes—
54#2830C2213yes—
55#2829C2213yes—
56#2829C2213yes—
57#2829C2216yes—
58#2790C2216yes—
59#2779C2216yes—
60#2751C2216yes—
61#2746C2216yes—
62#2739C2216yes—
63#2718C2216yes—
64#2717C2216yes—
65#2715C2216yes—
66#2712C2216yes—
67#2705C2216yes—
68#2701C2216yes—
69#2692C2216yes—
70#2691C2216yes—
71#2687C2216yes—
72#2686C2216yes—
73#2672C2216yes—
74#2662C2216yes—
75#2662C2216yes—
76#2660C2213yes—
77#2654C2216yes—
78#2653C2216yes—
79#2651C2216yes—
80#2649C2216yes—
81#2644C2213yes—
82#2644C2213yes—
83#2641C2213yes—
84#2641C2213yes—
85#2641C2213yes—
86#2638C2216yes—
87#2630C2216yes—
88#2630C2216yes—
89#2630C2216yes—
90#2629C2213yes—
91#2629C2213yes—
92#2628C2213yes—
93#2624C2216yes—
94#2624C2213yes—
95#2624C2213yes—
96#2620C2216yes—
97#2619C2213yes—
98#2584C2213yes—
99#2580C2213yes—
100#2567C2213yes—
101#2566C2213yes—
102#2566C2213yes—
103#2563C2213yes—
104#2562C2213yes—
105#2562C2213yes—
106#2562C2213yes—
107#2552C2213yes—
108#2552C2213yes—
109#2550C2213yes—
110#2550C2213yes—
111#2548C2213yes—
112#2548C2213yes—
113#2548C2213yes—
114#2541C2213yes—
115#2538C2213yes—
116#2538C2213yes—
117#2535C2213yes—
118#2513C2213yes—
119#2513C2213yes—
120#2512C2213yes—
121#2512C2213yes—
122#2512C2213yes—
123#2512C2213yes—
124#2504C2213yes—
125#2501C2213yes—
126#2497C2213yes—
127#2497C2213yes—
128#2496C2213yes—
129#2496C2213yes—
130#2494C2213yes—
131#2494C2213yes—
132#2491C2213yes—
133#2491C2213yes—
134#2491C2213yes—
135#2491C2213yes—
136#2491C2213yes—
137#2491C2213yes—
138#2490C2213yes—
139#2490C2213yes—
140#2490C2213yes—
141#2490C2213yes—
142#2490C2213yes—
143#2490C2213yes—
144#2487C2213yes—
145#2486C2213yes—
146#2479C2216yes—
147#2474C2216yes—
148#2468C2216yes—
149#2461C2216yes—
150#2454C2213yes—
151#2454C2213yes—
152#2454C2213yes—
153#2454C2213yes—
154#2452C2213yes—
155#2452C2213yes—
156#2445C2213yes—
157#2445C2213yes—
158#2445C2213yes—
159#2445C2213yes—
160#2442C2213yes—
161#2442C2213yes—
162#2442C2213yes—
163#2442C2213yes—
164#2440C2213yes—
165#2440C2213yes—
166#2428C2213yes—
167#2428C2213yes—
168#2427C2216yes—
169#2422C2216yes—
170#2422C2213yes—
171#2422C2213yes—
172#2420C2213yes—
173#2420C2213yes—
174#2416C2213yes—
175#2416C2213yes—
176#2401C2213yes—
177#2401C2213yes—
178#2399C2213yes—
179#2398C2213yes—
180#2398C2213yes—
181#2398C2213yes—
182#2396C2213yes—
183#2396C2213yes—
184#2396C2213yes—
185#2395C2213yes—
186#2395C2213yes—
187#2392C2213yes—
188#2370C2213yes—
189#2370C2213yes—
190#2369C2213yes—
191#2366C2213yes—
192#2361C2213yes—
193#2361C2213yes—
194#2357C2213yes—
195#2355C2213yes—
196#2354C2213yes—
197#2351C2211yescharacteristic
198#2351C2211yescharacteristic
199#2351C2211yescharacteristic
200#2351C2211yescharacteristic
201#2351C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204Q8×C4⋊C4C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206Q8×C4⋊C4C2211yescharacteristic
207D4×C4⋊C4C2213yes—
208#2345C2213yes—
209#2344C2213yes—
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214#2341C2211yescharacteristic
215#2341C2211yescharacteristic
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218#2341C2211yescharacteristic
219#2341C2211yescharacteristic
220#2341C2211yescharacteristic
221#2341C2211yescharacteristic
222#2331C2213yes—
223#2330C2213yes—
224#2324C2213yes—
225#2324C2213yes—
226#2319C2213yes—
227#2314C2213yes—
228C4×#127C2213yes—
229C4×#125C2213yes—
230#2298C2213yes—
231#2295C2213yes—
232#2293C2213yes—
233#2293C2213yes—
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236#2276C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C22×#41C2311yescharacteristic
241#557—28no—
242#557—44no—
243#557—44no—
244#550—28no—
245#550—44no—
246#550—44no—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×#127C2313yes—
251C2×#127C2313yes—
252C2×#127C2313yes—
253C2×#126C2316yes—
254C2×#126C2316yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#125C2313yes—
261C2×#124C2316yes—
262C2×#124C2316yes—
263C2×#124C2316yes—
264C2×#123C2316yes—
265C2×#123C2316yes—
266C2×#123C2316yes—
267C2×C22⋊Q8C2316yes—
268C2×C22⋊Q8C2316yes—
269C2×#121C2313yes—
270C2×#121C2313yes—
271C2×#121C2313yes—
272C2×#121C2313yes—
273C2×#121C2313yes—
274C2×#121C2313yes—
275C2×#121C2316yes—
276C2×#121C2316yes—
277#520—28no—
278#520—44no—
279#520—44no—
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×Q8C2311yescharacteristic
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2316yes—
305C2×C4×D4C2316yes—
306C2×#117C2313yes—
307C2×#117C2313yes—
308C2×#117C2313yes—
309C2×#117C2316yes—
310C22×C4⋊C4C2313yes—
311C22×C4⋊C4C2313yes—
312C22×C4⋊C4C2313yes—
313#401C2313yes—
314#401C2313yes—
315#400C2313yes—
316#400C2313yes—
317#400C2313yes—
318#400C2311yescharacteristic
319#400C2311yescharacteristic
320#400C2313yes—
321#400C2313yes—
322#400C2313yes—
323#400C2311yescharacteristic
324#400C2311yescharacteristic
325#400C2313yes—
326#400C2313yes—
327#400C2311yescharacteristic
328#400C2313yes—
329#400C2311yescharacteristic
330#400C2311yescharacteristic
331#400C2313yes—
332#400C2316yes—
333#399C2313yes—
334#399C2313yes—
335#399C2316yes—
336#399C2313yes—
337#399C2313yes—
338#399C2313yes—
339#399C2316yes—
340#398C2311yescharacteristic
341#398C2313yes—
342#398C2316yes—
343#398C2311yescharacteristic
344#398C2313yes—
345#398C2313yes—
346#398C2313yes—
347#398C2313yes—
348#398C2313yes—
349#398C2311yescharacteristic
350#398C2313yes—
351#398C2311yescharacteristic
352#398C2313yes—
353#398C2311yescharacteristic
354#398C2316yes—
355#398C2316yes—
356#398C2316yes—
357#397C2313yes—
358#397C2313yes—
359#397C2313yes—
360#397C2313yes—
361#397C2316yes—
362#397C2316yes—
363#397C2313yes—
364#397C2313yes—
365#397C2313yes—
366#397C2313yes—
367#397C2313yes—
368#397C2313yes—
369#397C2313yes—
370#397C2313yes—
371#397C2313yes—
372#397C2313yes—
373#397C2313yes—
374#397C2313yes—
375#397C2313yes—
376#397C2313yes—
377#397C2313yes—
378#397C2316yes—
379#397C2316yes—
380#397C2316yes—
381#396C2313yes—
382#396C2313yes—
383#396C2316yes—
384#396C2316yes—
385#396C2313yes—
386#396C2313yes—
387#396C2313yes—
388#396C2316yes—
389#396C2313yes—
390#396C2313yes—
391#396C2313yes—
392#396C2313yes—
393#396C2313yes—
394#396C2316yes—
395#396C2316yes—
396#396C2316yes—
397#395C2313yes—
398#395C2316yes—
399#395C2313yes—
400#395C2313yes—
401#395C2313yes—
402#395C2313yes—
403#395C2313yes—
404#395C2313yes—
405#394C2316yes—
406#394C2316yes—
407#394C2316yes—
408#394C2313yes—
409#394C2313yes—
410#394C2313yes—
411#394C2313yes—
412#394C2313yes—
413#394C2313yes—
414#394C2313yes—
415#394C2313yes—
416#394C2313yes—
417#394C2313yes—
418#394C2316yes—
419#394C2316yes—
420#394C2316yes—
421#394C2316yes—
422#394C2313yes—
423#394C2313yes—
424#394C2313yes—
425#394C2316yes—
426#394C2316yes—
427#394C2316yes—
428#394C2316yes—
429#394C2316yes—
430#394C2316yes—
431#394C2316yes—
432#393C2313yes—
433#393C2316yes—
434#393C2313yes—
435#393C2313yes—
436#393C2313yes—
437#393C2313yes—
438#393C2313yes—
439#393C2313yes—
440#393C2313yes—
441#393C2313yes—
442#392C2313yes—
443#392C2316yes—
444#392C2316yes—
445#391C2316yes—
446#391C2313yes—
447#391C2313yes—
448#391C2316yes—
449#390C2313yes—
450#390C2316yes—
451#390C2313yes—
452#390C2313yes—
453#390C2313yes—
454#390C2313yes—
455#390C2313yes—
456#390C2313yes—
457#390C2313yes—
458#390C2313yes—
459#390C2313yes—
460#390C2313yes—
461#390C2313yes—
462#390C2313yes—
463#390C2313yes—
464#390C2313yes—
465#390C2313yes—
466#390C2313yes—
467#390C2313yes—
468#390C2313yes—
469#390C2313yes—
470#390C2313yes—
471#390C2313yes—
472#390C2313yes—
473#390C2313yes—
474#390C2313yes—
475#390C2313yes—
476#390C2316yes—
477#390C2316yes—
478#390C2316yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2313yes—
484#389C2313yes—
485#389C2313yes—
486#389C2313yes—
487#389C2313yes—
488#389C2313yes—
489#389C2313yes—
490#389C2313yes—
491#389C2311yescharacteristic
492#389C2313yes—
493#389C2313yes—
494#389C2313yes—
495#389C2313yes—
496#389C2316yes—
497#389C2316yes—
498#389C2316yes—
499#389C2313yes—
500#389C2313yes—
501#389C2313yes—
502#389C2313yes—
503#389C2313yes—
504#389C2313yes—
505#389C2313yes—
506#388C2316yes—
507#388C2316yes—
508#388C2316yes—
509#388C2316yes—
510#388C2316yes—
511#388C2316yes—
512#388C2316yes—
513#388C2316yes—
514#388C2313yes—
515#388C2313yes—
516#388C2313yes—
517#388C2313yes—
518#388C2313yes—
519#388C2313yes—
520#388C2313yes—
521#388C2313yes—
522#388C2316yes—
523#388C2316yes—
524#388C2316yes—
525#388C2316yes—
526#387C2313yes—
527#387C2316yes—
528#387C2313yes—
529#387C2316yes—
530#387C2311yescharacteristic
531#387C2313yes—
532#387C2311yescharacteristic
533#387C2313yes—
534#387C2313yes—
535#387C2313yes—
536#387C2316yes—
537#387C2316yes—
538#387C2316yes—
539#387C2316yes—
540#386C2316yes—
541#386C2316yes—
542#386C2316yes—
543#386C2316yes—
544#386C2316yes—
545#386C2316yes—
546#386C2316yes—
547#385C2316yes—
548#385C2316yes—
549#385C2316yes—
550#385C2316yes—
551#385C2316yes—
552#385C2316yes—
553#385C2316yes—
554#385C2316yes—
555#385C2316yes—
556#384C2313yes—
557#384C2313yes—
558#384C2313yes—
559#384C2316yes—
560#384C2313yes—
561#384C2313yes—
562#382C2313yes—
563#382C2313yes—
564#382C2313yes—
565#382C2313yes—
566#382C2313yes—
567#381C2316yes—
568#381C2316yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576#380C2313yes—
577#380C2313yes—
578#380C2316yes—
579#380C2316yes—
580#380C2313yes—
581#380C2316yes—
582#380C2313yes—
583#380C2313yes—
584#380C2316yes—
585#380C2316yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2316yes—
589C4×C4⋊C4C2316yes—
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⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
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⋊C4C2316yes—
623#376C2313yes—
624#376C2313yes—
625#376C2313yes—
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—24no—
636C22×Q8C2413yes—
637C22×Q8C2413yes—
638C22×Q8C2413yes—
639C22×Q8C2411yescharacteristic
640C22×D4C2413yes—
641C22×D4C2413yes—
642C22×D4C2413yes—
643C22×D4C2413yes—
644C22×D4C2416yes—
645C22×D4C2413yes—
646C22×D4C2413yes—
647C22×D4C2416yes—
648C22×D4C2416yes—
649C23×C4C2413yes—
650C23×C4C2413yes—
651C23×C4C2413yes—
652C23×C4C2416yes—
653C23×C4C2416yes—
654C23×C4C2416yes—
655C4⋊Q8—212no—
656C4⋊Q8—46no—
657C4⋊Q8—46no—
658#127—212no—
659#127—46no—
660#127—46no—
661#126—86no—
662#126—86no—
663#125—212no—
664#125—212no—
665#125—46no—
666#125—46no—
667#125—46no—
668#125—46no—
669#124—86no—
670#124—86no—
671#124—86no—
672#123—86no—
673#123—86no—
674#123—86no—
675C22⋊Q8—86no—
676C22⋊Q8—86no—
677#121—212no—
678#121—212no—
679#121—46no—
680#121—46no—
681#121—46no—
682#121—46no—
683#121—86no—
684#121—86no—
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—212no—
697C4×Q8—46no—
698C4×Q8—46no—
699C4×Q8#4118yes—
700C4×D4—212no—
701C4×D4—212no—
702C4×D4—212no—
703C4×D4—46no—
704C4×D4—46no—
705C4×D4—46no—
706C4×D4—46no—
707C4×D4—46no—
708C4×D4—46no—
709C4×D4—86no—
710C4×D4—86no—
711#117—212no—
712#117—46no—
713#117—46no—
714#117—86no—
715C2×C4⋊C4—212no—
716C2×C4⋊C4—46no—
717C2×C4⋊C4—46no—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2411yescharacteristic
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⋊C4C2413yes—
735C2×C4⋊C4C2416yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2416yes—
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2416yes—
757C2×C4⋊C4C2416yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2416yes—
763C2×C4⋊C4C2416yes—
764C2×C4⋊C4C2416yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2416yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2416yes—
793C2×C22⋊C4C2416yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2416yes—
797C2×C22⋊C4C2416yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2416yes—
801C2×C22⋊C4C2416yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2416yes—
807C2×C22⋊C4C2416yes—
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⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2416yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2416yes—
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2416yes—
840C2×C42C2416yes—
841C2×C42C2411yescharacteristic
842C2×C42C2413yes—
843#95C2411yescharacteristic
844#95C2411yescharacteristic
845#95C2411yescharacteristic
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2411yescharacteristic
856#95C2411yescharacteristic
857#95C2411yescharacteristic
858#95C2411yescharacteristic
859#95C2411yescharacteristic
860#95C2411yescharacteristic
861#95C2411yescharacteristic
862#95C2411yescharacteristic
863#95C2411yescharacteristic
864#95C2411yescharacteristic
865#95C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2416yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2416yes—
882#95C2413yes—
883#95C2411yescharacteristic
884#95C2411yescharacteristic
885#95C2413yes—
886#95C2411yescharacteristic
887#95C2411yescharacteristic
888#95C2411yescharacteristic
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2416yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2416yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2416yes—
904#95C2416yes—
905C24C2513yes—
906C24C2513yes—
907C24C2513yes—
908#41—416no—
909#41—416no—
910#41—416no—
911C2×Q8—26no—
912C2×Q8—43no—
913C2×Q8—43no—
914C2×Q8—43no—
915C2×Q8—43no—
916C2×Q8—43no—
917C2×Q8—43no—
918C2×Q8—43no—
919C2×Q8—43no—
920C2×Q8C2×#4114yes—
921C2×Q8H(5,𝔽2)14yes—
922C2×Q82−1+414yes—
923C2×D4—26no—
924C2×D4—26no—
925C2×D4—26no—
926C2×D4—26no—
927C2×D4—212no—
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—46no—
939C2×D4—43no—
940C2×D4—43no—
941C2×D4—46no—
942C2×D4—43no—
943C2×D4—43no—
944C2×D4—46no—
945C2×D4—46no—
946C2×D4—46no—
947C2×D4—46no—
948C2×D4—46no—
949C2×D4—46no—
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—26no—
959C22×C4—212no—
960C22×C4—46no—
961C22×C4—46no—
962C22×C4—46no—
963C22×C4—46no—
964C22×C4—46no—
965C22×C4—46no—
966C22×C4—46no—
967C22×C4—46no—
968C22×C4C2511yescharacteristic
969C22×C4C2511yescharacteristic
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C22×C4C2511yescharacteristic
973C22×C4C2511yescharacteristic
974C22×C4C2511yescharacteristic
975C22×C4C2513yes—
976C22×C4C2511yescharacteristic
977C22×C4C2513yes—
978C22×C4C2511yescharacteristic
979C22×C4C2511yescharacteristic
980C22×C4C2513yes—
981C22×C4C2513yes—
982C22×C4C2513yes—
983C22×C4C2513yes—
984C22×C4C2513yes—
985C22×C4C2513yes—
986C22×C4C2511yescharacteristic
987C22×C4C2513yes—
988C22×C4C2511yescharacteristic
989C22×C4C2513yes—
990C22×C4C2511yescharacteristic
991C22×C4C2511yescharacteristic
992C22×C4C2513yes—
993C22×C4C2511yescharacteristic
994C22×C4C2513yes—
995C22×C4C2513yes—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—22no—
999C4⋊C4—22no—
1000C4⋊C4—22no—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—212no—
1006C4⋊C4—26no—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4—26no—
1010C4⋊C4—26no—
1011C4⋊C4—26no—
1012C4⋊C4—26no—
1013C4⋊C4—26no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—43no—
1019C4⋊C4—41no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—43no—
1025C4⋊C4—46no—
1026C4⋊C4—41no—
1027C4⋊C4—41no—
1028C4⋊C4—43no—
1029C4⋊C4—46no—
1030C4⋊C4—41no—
1031C4⋊C4—41no—
1032C4⋊C4—43no—
1033C4⋊C4—43no—
1034C4⋊C4—43no—
1035C4⋊C4—43no—
1036C4⋊C4—43no—
1037C4⋊C4—43no—
1038C4⋊C4—43no—
1039C4⋊C4—46no—
1040C4⋊C4—43no—
1041C4⋊C4—46no—
1042C4⋊C4—43no—
1043C4⋊C4—43no—
1044C4⋊C4—43no—
1045C4⋊C4—43no—
1046C4⋊C4—46no—
1047C4⋊C4—46no—
1048C4⋊C4—46no—
1049C4⋊C4—43no—
1050C4⋊C4—43no—
1051C4⋊C4—43no—
1052C4⋊C4—43no—
1053C4⋊C4C2×#41112yes—
1054C22⋊C4—26no—
1055C22⋊C4—26no—
1056C22⋊C4—26no—
1057C22⋊C4—26no—
1058C22⋊C4—43no—
1059C22⋊C4—46no—
1060C22⋊C4—43no—
1061C22⋊C4—43no—
1062C22⋊C4—43no—
1063C22⋊C4—43no—
1064C22⋊C4—43no—
1065C22⋊C4—43no—
1066C22⋊C4—43no—
1067C22⋊C4—43no—
1068C22⋊C4—43no—
1069C22⋊C4—46no—
1070C22⋊C4—43no—
1071C22⋊C4—43no—
1072C22⋊C4—43no—
1073C22⋊C4—43no—
1074C22⋊C4—43no—
1075C22⋊C4—43no—
1076C22⋊C4—46no—
1077C22⋊C4—46no—
1078C22⋊C4—43no—
1079C22⋊C4—43no—
1080C22⋊C4—46no—
1081C22⋊C4—46no—
1082C22⋊C4—43no—
1083C22⋊C4—43no—
1084C22⋊C4—46no—
1085C22⋊C4—46no—
1086C22⋊C4—43no—
1087C22⋊C4—43no—
1088C22⋊C4—43no—
1089C22⋊C4—43no—
1090C22⋊C4—46no—
1091C22⋊C4—46no—
1092C22⋊C4—43no—
1093C22⋊C4—43no—
1094C22⋊C4—43no—
1095C22⋊C4—46no—
1096C22⋊C4—43no—
1097C22⋊C4—43no—
1098C22⋊C4—43no—
1099C22⋊C4—46no—
1100C22⋊C4—43no—
1101C22⋊C4—43no—
1102C42—26no—
1103C42—26no—
1104C42—26no—
1105C42—26no—
1106C42—26no—
1107C42—26no—
1108C42—26no—
1109C42—26no—
1110C42—26no—
1111C42—26no—
1112C42—26no—
1113C42—41no—
1114C42—43no—
1115C42—46no—
1116C42—43no—
1117C42—43no—
1118C42—46no—
1119C42—46no—
1120C42C2×#41112yes—
1121C23—23no—
1122C23—23no—
1123C23—23no—
1124C23—23no—
1125C23—23no—
1126C23—23no—
1127C23—23no—
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—
1142C23C2611yescharacteristic
1143Q8—86no—
1144Q8—86no—
1145Q8—86no—
1146Q8#542116yes—
1147D4—412no—
1148D4—412no—
1149D4—412no—
1150D4—412no—
1151D4—812no—
1152D4—86no—
1153D4—86no—
1154D4—166no—
1155D4—166no—
1156C2×C4—21no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—23no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
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—23no—
1196C2×C4—23no—
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—23no—
1209C2×C4—23no—
1210C2×C4—23no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—23no—
1222C2×C4—23no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—23no—
1227C2×C4—23no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—23no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—412no—
1236C2×C4—412no—
1237C2×C4—412no—
1238C2×C4—812no—
1239C2×C4—166no—
1240C2×C4—166no—
1241C2×C4C22×#4112yes—
1242C2×C4C22×#4116yes—
1243C2×C4C22×#4116yes—
1244C2×C4C2×H(5,𝔽2)16yes—
1245C2×C4C2×2−1+416yes—
1246C22—43no—
1247C22—43no—
1248C22—43no—
1249C22—43no—
1250C22—43no—
1251C22—43no—
1252C22—43no—
1253C22—43no—
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—
1267C22C23×#4111yescharacteristic
1268C22C22×H(5,𝔽2)11yescharacteristic
1269C22C22×2−1+411yescharacteristic
1270C22H(7,𝔽2)11yescharacteristic
1271C22H(7,𝔽2)11yescharacteristic
1272C22H(7,𝔽2)11yescharacteristic
1273C222−1+611yescharacteristic
1274C4—22no—
1275C4—26no—
1276C4—41no—
1277C4—41no—
1278C4—41no—
1279C4—43no—
1280C4—43no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—43no—
1285C4—43no—
1286C4—43no—
1287C4—41no—
1288C4—43no—
1289C4—41no—
1290C4—43no—
1291C4—43no—
1292C4—41no—
1293C4—41no—
1294C4—43no—
1295C4—43no—
1296C4—43no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4C2×#542112yes—
1302C2—83no—
1303C2—83no—
1304C2—83no—
1305C2C22×#54211yescharacteristic
1306C2#6285111yescharacteristic
1307C2#6285811yescharacteristic
1308C2#6305211yescharacteristic
1309C2#6306111yescharacteristic
1310C2#6306611yescharacteristic
1311C2#6307011yescharacteristic
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. #42613C2semidirect
2. #42611C2semidirect
3. #42585C2semidirect
4. #42579C2semidirect
5. #42571C2semidirect
6. #42564C2semidirect
7. #42545C2semidirect
8. #42537C2semidirect
9. #42524C2semidirect
10. #42514C2semidirect
11. #42467C2semidirect
12. #42456C2semidirect
13. #37625C2semidirect
14. #37591C2semidirect
15. #37573C2semidirect
16. #36693C2semidirect
17. #36076C2semidirect
18. #36049C2semidirect
19. #36049C2semidirect
20. #36049C2semidirect
21. #36040C2semidirect
23. #36005C2semidirect
24. #35957C2semidirect
25. #35898C2semidirect
26. #35898C2semidirect
27. #35816C2semidirect
28. #35816C2semidirect
29. #34336C2semidirect
30. #34313C2semidirect
31. #34263C2semidirect

Maximal subgroups

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

subgroupindex
#426132
#426112
#425852
#425792
#425712
#425642
#425452
#425372
#425242
#425142
#424672
#424562
#376252
#375912
#375732
#366932
#360762
#360492
#360402
#360292
#360052
#359572
#358982
#358162
#343362
#343132
#342632