Finite Group Databasebeta

← #7646708

Subgroups — #7646708

Order 512.

4430 conjugacy classes of subgroups.

The subgroup lattice has 1431 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42662C212yesmaximal, complemented
2#42658C212yesmaximal, complemented
3#42459C212yesmaximal, complemented
4#42455C212yesmaximal, complemented
5#41441C212yesmaximal, complemented
6#41437C212yesmaximal, complemented
7#40655C212yesmaximal, complemented
8#40651C212yesmaximal, complemented
9#39937C212yesmaximal, complemented
10#39932C212yesmaximal, complemented
11#39913C212yesmaximal, complemented
12#39909C212yesmaximal, complemented
13#38479C214yesmaximal, complemented
14#38477C214yesmaximal, complemented
15#37569C214yesmaximal, complemented
16#36994C214yesmaximal, complemented
17#36990C214yesmaximal, complemented
18#35609C212yesmaximal, complemented
19#35551C212yesmaximal, complemented
20#35302C211yesmaximal, characteristic, complemented
21#35202C211yesmaximal, characteristic, complemented
22#35163C212yesmaximal, complemented
23#35161C212yesmaximal, complemented
24#35113C214yesmaximal, complemented
25#34911C211yesmaximal, characteristic, complemented
26#34875C211yesmaximal, characteristic, complemented
27#34237C211yesmaximal, characteristic, complemented
28#34129C211yesmaximal, characteristic, complemented
29#34048C211yesmaximal, characteristic, complemented
30C2×#529C2211yescharacteristic
31C2×C4×#41C2211yescharacteristic
32C22×#117C2211yescharacteristic
33#2866C2214yes—
34#2865C2214yescomplemented
35#2864C2214yescomplemented
36#2864C2212yescomplemented
37#2860C2214yes—
38#2859C2212yescomplemented
39#2855C2211yescharacteristic
40#2854C2211yescharacteristic
41#2848C2211yescharacteristic
42#2847C2211yescharacteristic
43#2839C2214yescomplemented
44#2837C2214yes—
45#2829C2214yes—
46#2829C2214yescomplemented
47#2803C2214yes—
48#2802C2214yescomplemented
49#2801C2214yes—
50#2800C2214yes—
51#2800C2214yescomplemented
52#2795C2214yes—
53#2793C2214yescomplemented
54#2790C2214yescomplemented
55#2777C2214yescomplemented
56#2772C2214yescomplemented
57#2771C2214yes—
58#2761C2214yes—
59#2752C2214yes—
60#2750C2214yes—
61#2746C2214yes—
62#2740C2214yes—
63#2739C2214yes—
64#2738C2214yes—
65#2735C2214yes—
66#2725C2214yes—
67#2725C2214yes—
68#2719C2214yescomplemented
69#2718C2214yes—
70#2711C2214yes—
71#2707C2214yes—
72#2707C2214yescomplemented
73#2706C2214yes—
74#2705C2214yes—
75#2694C2214yes—
76#2685C2214yes—
77#2685C2214yes—
78#2678C2214yes—
79#2667C2212yes—
80#2667C2212yes—
81#2664C2214yes—
82#2661C2214yes—
83#2655C2214yescomplemented
84#2654C2214yescomplemented
85#2652C2214yescomplemented
86#2652C2214yescomplemented
87#2651C2214yes—
88#2651C2214yescomplemented
89#2651C2214yescomplemented
90#2649C2214yes—
91#2649C2214yes—
92#2649C2214yescomplemented
93#2648C2214yes—
94#2648C2214yes—
95#2637C2214yes—
96#2637C2214yescomplemented
97#2629C2212yes—
98#2620C2212yes—
99#2609C2212yes—
100#2609C2212yes—
101#2609C2214yes—
102#2606C2214yescomplemented
103#2604C2212yescomplemented
104#2603C2212yescomplemented
105#2602C2214yes—
106#2601C2214yes—
107#2599C2212yes—
108#2598C2212yes—
109#2597C2214yes—
110#2596C2214yescomplemented
111#2595C2214yes—
112#2594C2214yes—
113#2594C2214yescomplemented
114#2592C2211yescharacteristic, complemented
115#2590C2214yescomplemented
116#2590C2214yescomplemented
117#2587C2214yes—
118#2584C2211yescharacteristic, complemented
119#2579C2212yes—
120#2579C2212yes—
121#2577C2214yescomplemented
122#2566C2212yescomplemented
123#2565C2212yescomplemented
124#2562C2212yes—
125#2562C2212yes—
126#2562C2211yescharacteristic, complemented
127#2559C2214yes—
128#2558C2214yes—
129#2558C2214yescomplemented
130#2552C2212yescomplemented
131#2552C2212yescomplemented
132#2552C2212yescomplemented
133#2552C2212yescomplemented
134#2540C2211yescharacteristic, complemented
135#2538C2212yes—
136#2537C2212yes—
137#2534C2212yes—
138#2534C2212yes—
139#2533C2214yescomplemented
140#2531C2214yes—
141#2530C2214yescomplemented
142#2529C2214yes—
143#2528C2214yescomplemented
144#2526C2214yes—
145#2525C2214yes—
146#2522C2214yescomplemented
147#2522C2214yescomplemented
148#2519C2214yes—
149#2518C2214yes—
150#2518C2214yes—
151#2517C2214yescomplemented
152#2512C2212yescomplemented
153#2511C2212yescomplemented
154#2509C2212yescomplemented
155#2508C2212yescomplemented
156#2505C2214yescomplemented
157#2500C2212yescomplemented
158#2499C2212yescomplemented
159#2497C2212yes—
160#2497C2212yes—
161#2496C2212yes—
162#2496C2212yes—
163#2495C2212yescomplemented
164#2494C2212yescomplemented
165#2490C2212yes—
166#2489C2212yes—
167#2485C2212yes—
168#2485C2212yes—
169#2484C2211yescharacteristic
170#2482C2211yescharacteristic
171#2479C2214yes—
172#2476C2214yes—
173#2475C2214yescomplemented
174#2470C2214yescomplemented
175#2467C2214yes—
176#2466C2214yescomplemented
177#2462C2214yescomplemented
178#2460C2214yescomplemented
179#2458C2214yes—
180#2441C2212yes—
181#2441C2214yes—
182#2441C2212yes—
183#2441C2212yescomplemented
184#2441C2212yescomplemented
185#2425C2214yes—
186#2423C2212yes—
187#2423C2212yescomplemented
188#2422C2212yes—
189#2422C2212yescomplemented
190#2415C2212yes—
191#2415C2212yes—
192#2414C2212yes—
193#2414C2212yes—
194#2413C2212yes—
195#2411C2212yes—
196#2406C2211yescharacteristic
197#2404C2211yescharacteristic
198#2396C2212yes—
199#2395C2212yes—
200#2392C2212yes—
201#2388C2212yes—
202#2370C2212yescomplemented
203#2367C2212yescomplemented
204#2363C2212yes—
205#2362C2212yes—
206#2357C2212yes—
207#2354C2212yes—
208#2354C2212yes—
209#2354C2212yescomplemented
210#2353C2212yes—
211Q8×C4⋊C4C2212yescomplemented
212#2346C2212yes—
213#2346C2214yescomplemented
214#2346C2212yescomplemented
215#2343C2212yescomplemented
216#2341C2212yes—
217#2336C2214yescomplemented
218#2335C2214yes—
219#2335C2214yes—
220#2334C2214yes—
221#2334C2214yescomplemented
222#2330C2212yescomplemented
223#2330C2212yescomplemented
224#2324C2212yes—
225#2323C2212yes—
226#2320C2211yescharacteristic, complemented
227#2319C2211yescharacteristic, complemented
228#2314C2212yes—
229#2314C2212yes—
230#2314C2212yes—
231#2314C2212yes—
232#2313C2212yes—
233#2313C2212yes—
234#2312C2212yes—
235#2312C2212yes—
236C4×#126C2214yescomplemented
237C4×C22⋊Q8C2212yescomplemented
238C4×#123C2212yes—
239C4×#121C2212yescomplemented
240C4×#120C2212yes—
241#2298C2214yes—
242#2298C2214yes—
243#2293C2214yes—
244#2293C2214yescomplemented
245#2293C2212yescomplemented
246#2290C2212yes—
247#2290C2212yes—
248#2285C2212yes—
249#2285C2211yescharacteristic
250#2285C2212yescomplemented
251#2283C2211yescharacteristic
252#2280C2212yes—
253#2276C2211yescharacteristic, complemented
254#2275C2211yescharacteristic, complemented
255C42×Q8C2212yescomplemented
256C4×#117C2211yescharacteristic
257C4×#117C2211yescharacteristic
258C4×#117C2212yescomplemented
259C22×#41C2311yescharacteristic
260C24×C4C2311yescharacteristic
261#529—28no—
262C2×#126C2312yes—
263C2×#126C2314yes—
264C2×#126C2314yes—
265C2×#126C2314yes—
266C2×#125C2311yescharacteristic
267C2×#125C2312yes—
268C2×#125C2312yes—
269C2×#125C2314yes—
270C2×#125C2314yes—
271C2×#125C2314yes—
272C2×#124C2311yescharacteristic
273C2×#123C2312yes—
274C2×#123C2314yes—
275C2×#123C2312yes—
276C2×#123C2312yes—
277C2×#123C2314yes—
278C2×C22⋊Q8C2311yescharacteristic
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×#121C2311yescharacteristic
282C2×#121C2312yes—
283C2×#121C2312yes—
284C2×#121C2314yes—
285C2×#120C2312yes—
286C2×#120C2312yes—
287C4×#41—28no—
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2314yes—
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2311yescharacteristic
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2311yescharacteristic
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2314yes—
303C2×#117—28no—
304C2×#117C2312yes—
305C2×#117C2312yes—
306C2×#117C2312yes—
307C2×#117C2312yes—
308C2×#117C2311yescharacteristic
309C2×#117C2312yes—
310C2×#117C2312yes—
311C2×#117C2312yes—
312C2×#117C2312yes—
313C2×#117C2312yes—
314C2×#117C2312yes—
315C2×#117C2312yes—
316C2×#117C2314yes—
317C22×C4⋊C4C2311yescharacteristic
318C22×C4⋊C4C2311yescharacteristic
319C22×C22⋊C4C2311yescharacteristic
320C22×C22⋊C4C2311yescharacteristic
321C22×C42C2311yescharacteristic
322C22×C42C2312yes—
323C22×C42C2311yescharacteristic
324#401C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2312yes—
328#400C2314yes—
329#400C2312yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2312yes—
343#399C2314yes—
344#399C2312yes—
345#399C2314yes—
346#399C2314yes—
347#399C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2312yes—
355#398C2312yes—
356#398C2314yes—
357#398C2312yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2312yes—
365#398C2314yes—
366#398C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2312yes—
374#397C2314yes—
375#397C2314yes—
376#397C2312yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2312yes—
391#396C2312yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2312yes—
398#396C2312yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#395C2312yes—
404#395C2312yes—
405#394C2314yes—
406#394C2314yes—
407#394C2312yes—
408#394C2314yes—
409#394C2314yes—
410#394C2312yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2312yes—
423#394C2312yes—
424#394C2314yes—
425#394C2314yes—
426#393C2312yes—
427#393C2312yes—
428#392C2312yes—
429#392C2312yes—
430#392C2314yes—
431#392C2314yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#390C2312yes—
436#390C2312yes—
437#390C2314yes—
438#390C2312yes—
439#390C2314yes—
440#390C2314yes—
441#390C2314yes—
442#390C2314yes—
443#390C2314yes—
444#390C2314yes—
445#390C2314yes—
446#390C2314yes—
447#390C2314yes—
448#389C2312yes—
449#389C2312yes—
450#389C2314yes—
451#389C2312yes—
452#389C2312yes—
453#389C2314yes—
454#389C2314yes—
455#389C2312yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
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#388C2312yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2312yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2312yes—
526#388C2312yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2312yes—
532#388C2312yes—
533#388C2314yes—
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#387C2312yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2312yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2312yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2312yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2312yes—
579#387C2312yes—
580#386C2312yes—
581#386C2312yes—
582#386C2312yes—
583#386C2312yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2312yes—
588#386C2312yes—
589#386C2312yes—
590#386C2312yes—
591#386C2314yes—
592#386C2312yes—
593#386C2312yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2312yes—
598#385C2312yes—
599#385C2312yes—
600#385C2312yes—
601#385C2312yes—
602#385C2312yes—
603#385C2312yes—
604#385C2314yes—
605#385C2312yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2312yes—
610#385C2312yes—
611#385C2314yes—
612#384C2312yes—
613#384C2312yes—
614#384C2312yes—
615#384C2312yes—
616#384C2312yes—
617#384C2312yes—
618#384C2314yes—
619#384C2312yes—
620#383C2312yes—
621#383C2312yes—
622#383C2314yes—
623#382C2312yes—
624#382C2312yes—
625#382C2312yes—
626#382C2314yes—
627#382C2314yes—
628#382C2311yescharacteristic
629#382C2314yes—
630#382C2312yes—
631#382C2311yescharacteristic
632#381C2314yes—
633#381C2312yes—
634#381C2312yes—
635#381C2311yescharacteristic
636#381C2311yescharacteristic
637#381C2312yes—
638#380C2312yes—
639#380C2312yes—
640#380C2312yes—
641#380C2312yes—
642#380C2312yes—
643#380C2312yes—
644#380C2312yes—
645#380C2314yes—
646#380C2314yes—
647#380C2312yes—
648#380C2312yes—
649#380C2312yes—
650#380C2312yes—
651#380C2314yes—
652#380C2312yes—
653#380C2312yes—
654#380C2311yescharacteristic
655#380C2311yescharacteristic
656#380C2314yes—
657#379C2314yes—
658#379C2312yes—
659#379C2312yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2311yescharacteristic
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2312yes—
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705#376C2311yescharacteristic
706#376C2311yescharacteristic
707#376C2312yes—
708#376C2314yes—
709#376C2312yes—
710#376C2312yes—
711C2×#95C2312yes—
712C43C2312yes—
713C43C2312yes—
714C43C2314yes—
715C25C2411yescharacteristic
716C2×#41—24no—
717C2×#41—44no—
718C22×Q8C2411yescharacteristic
719C22×Q8C2411yescharacteristic
720C22×D4C2411yescharacteristic
721C22×D4C2412yes—
722C22×D4C2411yescharacteristic
723C22×D4C2412yes—
724C22×D4C2412yes—
725C22×D4C2412yes—
726C22×D4C2414yes—
727C22×D4C2414yes—
728C23×C4—24no—
729C23×C4—44no—
730C23×C4C2412yes—
731C23×C4C2412yes—
732C23×C4C2412yes—
733C23×C4C2411yescharacteristic
734C23×C4C2411yescharacteristic
735C23×C4C2411yescharacteristic
736C23×C4C2411yescharacteristic
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2412yes—
740C23×C4C2414yes—
741C23×C4C2411yescharacteristic
742C23×C4C2411yescharacteristic
743#126—28no—
744#126—48no—
745#126—48no—
746#126—84no—
747#125—24no—
748#125—44no—
749#125—44no—
750#125—48no—
751#125—84no—
752#125—84no—
753#124—24no—
754#123—28no—
755#123—48no—
756#123—44no—
757#123—82no—
758#123—84no—
759C22⋊Q8—24no—
760C22⋊Q8—44no—
761C22⋊Q8—44no—
762#121—24no—
763#121—44no—
764#121—44no—
765#121—84no—
766#120—44no—
767#120—82no—
768C4×Q8—24no—
769C4×Q8—24no—
770C4×Q8—24no—
771C4×Q8—44no—
772C4×Q8—48no—
773C4×D4—28no—
774C4×D4—28no—
775C4×D4—28no—
776C4×D4—24no—
777C4×D4—24no—
778C4×D4—24no—
779C4×D4—44no—
780C4×D4—44no—
781C4×D4—44no—
782C4×D4—48no—
783#117—24no—
784#117—28no—
785#117—28no—
786#117—28no—
787#117—28no—
788#117—28no—
789#117—28no—
790#117—44no—
791#117—44no—
792#117—44no—
793#117—44no—
794#117—82no—
795#117—84no—
796C2×C4⋊C4—24no—
797C2×C4⋊C4—24no—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C22⋊C4—24no—
858C2×C22⋊C4—24no—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C42—24no—
913C2×C42—28no—
914C2×C42#4118yes—
915C2×C42C2412yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2414yes—
924C2×C42C2412yes—
925C2×C42C2414yes—
926C2×C42C2414yes—
927C2×C42C2414yes—
928C2×C42C2414yes—
929C2×C42C2414yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2412yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2411yescharacteristic
940C2×C42C2411yescharacteristic
941C2×C42C2411yescharacteristic
942C2×C42C2411yescharacteristic
943#95C2411yescharacteristic
944#95C2412yes—
945#95C2414yes—
946#95C2412yes—
947#95C2411yescharacteristic
948#95C2412yes—
949#95C2411yescharacteristic
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2411yescharacteristic
959#95C2414yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2412yes—
995#95C2414yes—
996#95C2414yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008C24—22no—
1009C24—42no—
1010C24—42no—
1011C24—41no—
1012C24—41no—
1013C24C2512yes—
1014C24C2512yes—
1015C24C2512yes—
1016C24C2511yescharacteristic
1017#41—416no—
1018C2×Q8—22no—
1019C2×Q8—22no—
1020C2×Q8—24no—
1021C2×Q8—24no—
1022C2×D4—24no—
1023C2×D4—24no—
1024C2×D4—22no—
1025C2×D4—22no—
1026C2×D4—24no—
1027C2×D4—24no—
1028C2×D4—42no—
1029C2×D4—42no—
1030C2×D4—42no—
1031C2×D4—42no—
1032C2×D4—44no—
1033C2×D4—42no—
1034C2×D4—42no—
1035C2×D4—42no—
1036C2×D4—44no—
1037C2×D4—42no—
1038C2×D4—44no—
1039C2×D4—42no—
1040C2×D4—42no—
1041C2×D4—44no—
1042C2×D4—44no—
1043C2×D4—44no—
1044C22×C4—24no—
1045C22×C4—22no—
1046C22×C4—22no—
1047C22×C4—22no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—24no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—41no—
1060C22×C4—42no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—41no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—42no—
1068C22×C4—44no—
1069C22×C4—42no—
1070C22×C4—41no—
1071C22×C4—41no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—416no—
1076C22×C4C2×#4114yes—
1077C22×C4C2×#4114yes—
1078C22×C4C2×#4114yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2514yes—
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2514yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2514yes—
1093C22×C4C2514yes—
1094C22×C4C2514yes—
1095C22×C4C2514yes—
1096C22×C4C2512yes—
1097C22×C4C2511yescharacteristic
1098C22×C4C2511yescharacteristic
1099C22×C4C2511yescharacteristic
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2512yes—
1103C22×C4C2511yescharacteristic
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—22no—
1111C4⋊C4—22no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—22no—
1115C4⋊C4—24no—
1116C4⋊C4—22no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—28no—
1125C4⋊C4—28no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C22⋊C4—24no—
1164C22⋊C4—24no—
1165C22⋊C4—24no—
1166C22⋊C4—24no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—24no—
1170C22⋊C4—24no—
1171C22⋊C4—24no—
1172C22⋊C4—24no—
1173C22⋊C4—24no—
1174C22⋊C4—24no—
1175C22⋊C4—28no—
1176C22⋊C4—24no—
1177C22⋊C4—24no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—42no—
1183C22⋊C4—42no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—42no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—42no—
1192C22⋊C4—44no—
1193C22⋊C4—42no—
1194C22⋊C4—42no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—42no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—44no—
1208C22⋊C4—42no—
1209C22⋊C4—44no—
1210C22⋊C4—42no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—42no—
1216C42—24no—
1217C42—24no—
1218C42—24no—
1219C42—24no—
1220C42—24no—
1221C42—24no—
1222C42—24no—
1223C42—24no—
1224C42—28no—
1225C42—42no—
1226C42—42no—
1227C42—44no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42—42no—
1232C42—44no—
1233C42—44no—
1234C42—44no—
1235C42—44no—
1236C42—44no—
1237C42—44no—
1238C42—42no—
1239C42—44no—
1240C42C2×#4114yes—
1241C42C2×#4114yes—
1242C42C2×#4114yes—
1243C42C2×#4114yes—
1244C23—22no—
1245C23—22no—
1246C23—21no—
1247C23—21no—
1248C23—22no—
1249C23—22no—
1250C23—22no—
1251C23—22no—
1252C23—24no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—24no—
1257C23—22no—
1258C23—22no—
1259C23—22no—
1260C23—22no—
1261C23—22no—
1262C23—22no—
1263C23—22no—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23—44no—
1268C23—82no—
1269C23—82no—
1270C23—84no—
1271C23—84no—
1272C23C22×#4112yes—
1273C23C2611yescharacteristic
1274Q8—28no—
1275Q8—44no—
1276D4—48no—
1277D4—44no—
1278D4—44no—
1279D4—84no—
1280D4—84no—
1281D4—88no—
1282D4—84no—
1283D4—164no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—28no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—44no—
1347C2×C4—44no—
1348C2×C4—48no—
1349C2×C4—48no—
1350C2×C4—48no—
1351C2×C4—44no—
1352C2×C4—48no—
1353C2×C4—48no—
1354C2×C4—84no—
1355C2×C4—82no—
1356C2×C4—82no—
1357C2×C4—164no—
1358C2×C4C22×#4112yes—
1359C2×C4C22×#4112yes—
1360C2×C4C22×#4112yes—
1361C2×C4C22×#4112yes—
1362C2×C4C22×#4112yes—
1363C2×C4C22×#4112yes—
1364C2×C4#58514yes—
1365C2×C4#58514yes—
1366C22—22no—
1367C22—22no—
1368C22—22no—
1369C22—42no—
1370C22—42no—
1371C22—42no—
1372C22—42no—
1373C22—42no—
1374C22—42no—
1375C22—42no—
1376C22—42no—
1377C22—44no—
1378C22—42no—
1379C22—42no—
1380C22—42no—
1381C22—42no—
1382C22—42no—
1383C22—42no—
1384C22—42no—
1385C22—42no—
1386C22—42no—
1387C22—44no—
1388C22—42no—
1389C22—42no—
1390C22—88no—
1391C22C23×#4111yescharacteristic
1392C22C2×#58512yes—
1393C22C2×#58512yes—
1394C22H(7,𝔽2)11yescharacteristic
1395C222−1+611yescharacteristic
1396C4—22no—
1397C4—22no—
1398C4—24no—
1399C4—22no—
1400C4—22no—
1401C4—22no—
1402C4—42no—
1403C4—42no—
1404C4—42no—
1405C4—42no—
1406C4—42no—
1407C4—44no—
1408C4—42no—
1409C4—44no—
1410C4—42no—
1411C4—44no—
1412C4—44no—
1413C4—42no—
1414C4—42no—
1415C4—42no—
1416C4—44no—
1417C4—42no—
1418C4—44no—
1419C4—42no—
1420C4#345514yes—
1421C2—42no—
1422C2—82no—
1423C2—82no—
1424C2—82no—
1425C2C2×#345511yescharacteristic
1426C2#6281411yescharacteristic
1427C2#6285611yescharacteristic
1428C2#6293712yes—
1429C2#6296712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42662C2semidirect
2. #42658C2semidirect
3. #42459C2semidirect
4. #42455C2semidirect
5. #41441C2semidirect
6. #41437C2semidirect
7. #40655C2semidirect
8. #40651C2semidirect
9. #39937C2semidirect
10. #39932C2semidirect
11. #39913C2semidirect
12. #39909C2semidirect
13. #38479C2semidirect
14. #38477C2semidirect
15. #37569C2semidirect
16. #36994C2semidirect
17. #36990C2semidirect
18. #35609C2semidirect
19. #35551C2semidirect
20. #35302C2semidirect
21. #35202C2semidirect
22. #35163C2semidirect
23. #35161C2semidirect
24. #35113C2semidirect
25. #34911C2semidirect
26. #34875C2semidirect
27. #34237C2semidirect
28. #34129C2semidirect
29. #34048C2semidirect
34. #2865C22semidirect
35. #2864C22semidirect
36. #2864C22semidirect
38. #2859C22semidirect
43. #2839C22semidirect
46. #2829C22semidirect
48. #2802C22semidirect
51. #2800C22semidirect
53. #2793C22semidirect
54. #2790C22semidirect
55. #2777C22semidirect
56. #2772C22semidirect
68. #2719C22semidirect
72. #2707C22semidirect
83. #2655C22semidirect
84. #2654C22semidirect
85. #2652C22semidirect
86. #2652C22semidirect
88. #2651C22semidirect
89. #2651C22semidirect
92. #2649C22semidirect
96. #2637C22semidirect
102. #2606C22semidirect
103. #2604C22semidirect
104. #2603C22semidirect
110. #2596C22semidirect
113. #2594C22semidirect
114. #2592C22semidirect
115. #2590C22semidirect
116. #2590C22semidirect
118. #2584C22semidirect
121. #2577C22semidirect
122. #2566C22semidirect
123. #2565C22semidirect
126. #2562C22semidirect
129. #2558C22semidirect
130. #2552C22semidirect
131. #2552C22semidirect
132. #2552C22semidirect
133. #2552C22semidirect
134. #2540C22semidirect
139. #2533C22semidirect
141. #2530C22semidirect
143. #2528C22semidirect
146. #2522C22semidirect
147. #2522C22semidirect
151. #2517C22semidirect
152. #2512C22semidirect
153. #2511C22semidirect
154. #2509C22semidirect
155. #2508C22semidirect
156. #2505C22semidirect
157. #2500C22semidirect
158. #2499C22semidirect
163. #2495C22semidirect
164. #2494C22semidirect
173. #2475C22semidirect
174. #2470C22semidirect
176. #2466C22semidirect
177. #2462C22semidirect
178. #2460C22semidirect
183. #2441C22semidirect
184. #2441C22semidirect
187. #2423C22semidirect
189. #2422C22semidirect
202. #2370C22semidirect
203. #2367C22semidirect
209. #2354C22semidirect
211. Q8×C4⋊C4C22semidirect
213. #2346C22semidirect
214. #2346C22semidirect
215. #2343C22semidirect
217. #2336C22semidirect
221. #2334C22semidirect
222. #2330C22semidirect
223. #2330C22semidirect
226. #2320C22semidirect
227. #2319C22semidirect
236. C4×#126C22semidirect
237. C4×C22⋊Q8C22semidirect
239. C4×#121C22semidirect
244. #2293C22semidirect
245. #2293C22semidirect
250. #2285C22semidirect
253. #2276C22semidirect
254. #2275C22semidirect
255. C42×Q8C22semidirect
258. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#426622
#426582
#424592
#424552
#414412
#414372
#406552
#406512
#399372
#399322
#399132
#399092
#384792
#384772
#375692
#369942
#369902
#356092
#355512
#353022
#352022
#351632
#351612
#351132
#349112
#348752
#342372
#341292
#340482