Finite Group Databasebeta

← #7901057

Subgroups — #7901057

Order 512.

4313 conjugacy classes of subgroups.

The subgroup lattice has 1395 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59821C211yesmaximal, characteristic, complemented
2#59749C212yesmaximal, complemented
3#52274C211yesmaximal, characteristic, complemented
4#50970C214yesmaximal, complemented
5#49136C214yesmaximal, complemented
6#48652C214yesmaximal, complemented
7#47428C214yesmaximal, complemented
8#46294C212yesmaximal, complemented
9#45407C212yesmaximal, complemented
10#45312C212yesmaximal
11#45266C212yesmaximal, complemented
12#44515C214yesmaximal, complemented
13#42873C212yesmaximal, complemented
14#42509C212yesmaximal, complemented
15#41579C214yesmaximal, complemented
16#40128C212yesmaximal, complemented
17#39837C212yesmaximal, complemented
18#39629C211yesmaximal, characteristic, complemented
19#39628C211yesmaximal, characteristic, complemented
20#38821C212yesmaximal, complemented
21#38231C212yesmaximal, complemented
22#38228C212yesmaximal, complemented
23#37167C212yesmaximal, complemented
24#36476C211yesmaximal, characteristic, complemented
25#35971C212yesmaximal, complemented
26#35605C212yesmaximal, complemented
27#35197C211yesmaximal, characteristic
28#34499C212yesmaximal, complemented
29#34324C211yesmaximal, characteristic, complemented
30C2×#556C2211yescharacteristic
31C2×#556C2212yes—
32#2862C2211yescharacteristic
33#2860C2212yes—
34#2855C2212yes—
35#2854C2212yes—
36#2850C2212yes—
37#2837C2214yes—
38#2836C2214yes—
39#2809C2211yescharacteristic
40#2808C2214yes—
41#2806C2211yescharacteristic
42#2806C2212yes—
43#2806C2212yes—
44#2805C2212yes—
45#2805C2211yescharacteristic
46#2805C2212yes—
47#2804C2212yes—
48#2804C2212yes—
49#2802C2212yes—
50#2799C2212yes—
51#2796C2214yes—
52#2793C2214yes—
53#2791C2212yes—
54#2785C2214yes—
55#2781C2214yes—
56#2775C2214yes—
57#2774C2212yes—
58#2772C2214yes—
59#2768C2214yes—
60#2755C2212yes—
61#2754C2214yes—
62#2754C2214yes—
63#2753C2214yes—
64#2753C2214yes—
65#2750C2214yes—
66#2741C2214yes—
67#2739C2214yes—
68#2738C2214yes—
69#2732C2212yes—
70#2732C2214yes—
71#2732C2212yes—
72#2727C2212yes—
73#2727C2212yes—
74#2726C2211yescharacteristic
75#2723C2214yes—
76#2723C2214yes—
77#2723C2214yes—
78#2723C2214yes—
79#2722C2214yes—
80#2721C2214yes—
81#2718C2214yes—
82#2713C2212yes—
83#2704C2214yes—
84#2702C2214yes—
85#2701C2214yes—
86#2701C2214yes—
87#2698C2214yes—
88#2698C2214yes—
89#2698C2214yes—
90#2695C2214yes—
91#2694C2214yes—
92#2680C2214yes—
93#2664C2214yes—
94#2663C2214yes—
95#2663C2214yes—
96#2651C2214yes—
97#2648C2214yes—
98#2647C2212yes—
99#2647C2212yes—
100#2647C2214yes—
101#2644C2212yes—
102#2637C2214yes—
103#2609C2214yes—
104#2607C2214yes—
105#2604C2214yes—
106#2597C2214yes—
107#2595C2214yes—
108#2589C2214yes—
109#2581C2212yes—
110#2580C2212yes—
111#2580C2212yes—
112#2575C2214yes—
113#2571C2214yes—
114#2571C2211yescharacteristic
115#2570C2214yes—
116#2570C2212yes—
117#2563C2211yescharacteristic
118#2560C2214yes—
119#2560C2214yes—
120#2559C2214yes—
121#2559C2214yes—
122#2556C2214yes—
123#2556C2214yes—
124#2554C2214yes—
125#2554C2214yes—
126#2553C2214yes—
127#2548C2212yes—
128#2548C2212yes—
129#2548C2212yes—
130#2548C2211yescharacteristic
131#2542C2211yescharacteristic
132#2542C2212yes—
133#2541C2211yescharacteristic
134#2538C2212yes—
135#2538C2211yescharacteristic
136#2531C2214yes—
137#2530C2214yes—
138#2529C2214yes—
139#2529C2214yes—
140#2526C2214yes—
141#2525C2214yes—
142#2525C2214yes—
143#2521C2214yes—
144#2520C2214yes—
145#2520C2214yes—
146#2519C2214yes—
147#2517C2214yes—
148#2516C2214yes—
149#2513C2212yes—
150#2513C2212yes—
151#2512C2212yes—
152#2512C2212yes—
153#2512C2214yes—
154#2512C2212yes—
155#2509C2214yes—
156#2509C2212yes—
157#2508C2212yes—
158#2508C2214yes—
159#2508C2214yes—
160#2508C2212yes—
161#2507C2212yes—
162#2507C2212yes—
163#2507C2214yes—
164#2506C2212yes—
165#2498C2214yes—
166#2492C2212yes—
167#2489C2214yes—
168#2488C2214yes—
169#2479C2214yes—
170#2479C2214yes—
171#2479C2214yes—
172#2479C2214yes—
173#2479C2214yes—
174#2478C2214yes—
175#2474C2214yes—
176#2470C2214yes—
177#2469C2214yes—
178#2457C2214yes—
179#2452C2212yes—
180#2452C2212yes—
181#2451C2212yes—
182#2451C2212yes—
183#2450C2214yes—
184#2450C2214yes—
185#2448C2212yes—
186#2448C2212yes—
187#2448C2212yes—
188#2448C2212yes—
189#2448C2212yes—
190#2448C2212yes—
191#2445C2212yes—
192#2445C2212yes—
193#2445C2212yes—
194#2427C2212yes—
195#2423C2212yes—
196#2420C2212yes—
197#2415C2214yes—
198#2402C2212yes—
199#2402C2212yes—
200#2402C2214yes—
201#2399C2212yes—
202#2383C2214yes—
203#2378C2214yes—
204#2373C2214yes—
205#2373C2214yes—
206#2369C2211yescharacteristic
207#2367C2212yes—
208#2367C2212yes—
209#2367C2212yes—
210#2365C2211yescharacteristic
211#2365C2211yescharacteristic
212#2362C2212yes—
213#2362C2214yes—
214#2357C2212yes—
215#2355C2212yes—
216#2355C2212yes—
217#2354C2211yescharacteristic
218#2354C2212yes—
219#2351C2212yes—
220#2351C2212yes—
221#2351C2212yes—
222#2351C2212yes—
223Q8×C4⋊C4C2211yescharacteristic
224Q8×C4⋊C4C2212yes—
225Q8×C4⋊C4C2212yes—
226#2349C2212yes—
227#2346C2212yes—
228#2343C2214yes—
229#2335C2214yes—
230#2334C2214yes—
231#2334C2214yes—
232#2334C2214yes—
233#2329C2214yes—
234#2328C2212yes—
235#2328C2212yes—
236#2327C2212yes—
237#2326C2212yes—
238#2326C2212yes—
239#2320C2212yes—
240#2319C2212yes—
241#2319C2212yes—
242#2314C2214yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×C4⋊Q8C2211yescharacteristic
245C4×#127C2211yescharacteristic
246C4×#125C2212yes—
247C4×#124C2212yes—
248C4×C22⋊Q8C2212yes—
249C4×C22⋊Q8C2212yes—
250#2296C2212yes—
251#2295C2211yescharacteristic
252#2295C2212yes—
253#2295C2212yes—
254#2295C2211yescharacteristic
255#2295C2212yes—
256#2293C2212yes—
257#2276C2212yes—
258C42×D4C2211yescharacteristic
259#556—28no—
260#556—216no—
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×#127C2311yescharacteristic
266C2×#127C2312yes—
267C2×#126C2314yes—
268C2×#126C2314yes—
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#125C2312yes—
275C2×#125C2314yes—
276C2×#124C2312yes—
277C2×#124C2312yes—
278C2×#124C2312yes—
279C2×#124C2312yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×#121C2312yes—
292C2×#121C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2311yescharacteristic
307C2×C4×D4C2311yescharacteristic
308C2×C4×D4C2312yes—
309C2×C4×D4C2311yescharacteristic
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×#117C2314yes—
314C2×#117C2312yes—
315C2×#117C2312yes—
316C2×#117C2314yes—
317C22×C42C2312yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2312yes—
322#400C2312yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2312yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2312yes—
333#400C2314yes—
334#400C2312yes—
335#400C2312yes—
336#400C2312yes—
337#400C2312yes—
338#399C2314yes—
339#399C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#398C2312yes—
348#398C2314yes—
349#398C2314yes—
350#398C2312yes—
351#398C2312yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2312yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2312yes—
364#398C2312yes—
365#398C2312yes—
366#398C2312yes—
367#398C2312yes—
368#398C2314yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#398C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2312yes—
401#395C2312yes—
402#395C2312yes—
403#395C2312yes—
404#395C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#392C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2314yes—
433#391C2312yes—
434#391C2314yes—
435#391C2311yescharacteristic
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2311yescharacteristic
441#391C2312yes—
442#391C2311yescharacteristic
443#391C2312yes—
444#391C2312yes—
445#391C2311yescharacteristic
446#390C2314yes—
447#390C2314yes—
448#390C2312yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#390C2312yes—
455#390C2312yes—
456#390C2312yes—
457#390C2312yes—
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2314yes—
462#390C2312yes—
463#390C2314yes—
464#390C2314yes—
465#390C2314yes—
466#390C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2311yescharacteristic
472#389C2312yes—
473#389C2311yescharacteristic
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2312yes—
479#389C2314yes—
480#389C2314yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2312yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2311yescharacteristic
497#389C2312yes—
498#389C2311yescharacteristic
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2312yes—
506#389C2312yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2312yes—
512#389C2311yescharacteristic
513#389C2312yes—
514#389C2311yescharacteristic
515#389C2312yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#387C2312yes—
560#387C2314yes—
561#387C2312yes—
562#387C2312yes—
563#387C2312yes—
564#387C2312yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2312yes—
587#387C2312yes—
588#387C2314yes—
589#387C2312yes—
590#387C2312yes—
591#387C2312yes—
592#387C2314yes—
593#387C2312yes—
594#387C2312yes—
595#387C2314yes—
596#387C2312yes—
597#387C2314yes—
598#387C2312yes—
599#387C2312yes—
600#387C2312yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#384C2311yescharacteristic
628#384C2311yescharacteristic
629#384C2311yescharacteristic
630#384C2314yes—
631#384C2312yes—
632#384C2314yes—
633#384C2312yes—
634#383C2314yes—
635#382C2312yes—
636#382C2312yes—
637#382C2314yes—
638#382C2312yes—
639#382C2314yes—
640#382C2314yes—
641#382C2314yes—
642#382C2312yes—
643#382C2312yes—
644#382C2314yes—
645#382C2314yes—
646#382C2314yes—
647#382C2312yes—
648#382C2314yes—
649#381C2314yes—
650#381C2314yes—
651#381C2314yes—
652#380C2312yes—
653#380C2312yes—
654#380C2314yes—
655#380C2314yes—
656#380C2314yes—
657#380C2312yes—
658#380C2312yes—
659#380C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2311yescharacteristic
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2311yescharacteristic
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706#376C2312yes—
707#376C2312yes—
708#376C2312yes—
709#376C2314yes—
710#376C2314yes—
711C2×#95C2314yes—
712C43C2312yes—
713C43C2311yescharacteristic
714C22×Q8C2412yes—
715C22×Q8C2411yescharacteristic
716C22×Q8C2412yes—
717C22×Q8C2412yes—
718C22×Q8C2411yescharacteristic
719C22×Q8C2412yes—
720C22×D4C2411yescharacteristic
721C22×D4C2412yes—
722C22×D4C2412yes—
723C22×D4C2412yes—
724C22×D4C2414yes—
725C22×D4C2414yes—
726C23×C4C2412yes—
727C23×C4C2414yes—
728C23×C4C2412yes—
729C23×C4C2412yes—
730C23×C4C2414yes—
731C23×C4C2414yes—
732C4⋊Q8—42no—
733C4⋊Q8—42no—
734C4⋊Q8—42no—
735C4⋊Q8#4118yes—
736#127—24no—
737#127—44no—
738#126—216no—
739#126—216no—
740#126—216no—
741#126—84no—
742#126—84no—
743#126—84no—
744#126—84no—
745#125—44no—
746#125—84no—
747#124—28no—
748#124—28no—
749#124—28no—
750#124—82no—
751#123—48no—
752#123—84no—
753#123—84no—
754C22⋊Q8—216no—
755C22⋊Q8—28no—
756C22⋊Q8—48no—
757C22⋊Q8—44no—
758C22⋊Q8—84no—
759C22⋊Q8—82no—
760C22⋊Q8—84no—
761C22⋊Q8—82no—
762#121—82no—
763#121—82no—
764C4×Q8—28no—
765C4×Q8—28no—
766C4×Q8—28no—
767C4×Q8—24no—
768C4×Q8—28no—
769C4×Q8—28no—
770C4×Q8—24no—
771C4×Q8—44no—
772C4×Q8—44no—
773C4×Q8—44no—
774C4×Q8—82no—
775C4×Q8—82no—
776C4×D4—24no—
777C4×D4—28no—
778C4×D4—24no—
779C4×D4—44no—
780C4×D4—44no—
781C4×D4—44no—
782C4×D4—42no—
783C4×D4—82no—
784#117—216no—
785#117—28no—
786#117—82no—
787#117—84no—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C42—82no—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2412yes—
902C2×C42C2411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2414yes—
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2411yescharacteristic
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2412yes—
921C2×C42C2414yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2411yescharacteristic
926C2×C42C2411yescharacteristic
927C2×C42C2411yescharacteristic
928C2×C42C2411yescharacteristic
929#95C2412yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2412yes—
934#95C2412yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2412yes—
939#95C2414yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2414yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2412yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000C24C2512yes—
1001C24C2514yes—
1002C2×Q8—22no—
1003C2×Q8—24no—
1004C2×Q8—24no—
1005C2×Q8—22no—
1006C2×Q8—24no—
1007C2×Q8—24no—
1008C2×Q8—41no—
1009C2×Q8—41no—
1010C2×Q8—42no—
1011C2×Q8—41no—
1012C2×Q8—42no—
1013C2×Q8—41no—
1014C2×Q8—42no—
1015C2×Q8—42no—
1016C2×Q8—42no—
1017C2×Q8—42no—
1018C2×Q8—42no—
1019C2×Q8C2×#4118yes—
1020C2×D4—22no—
1021C2×D4—24no—
1022C2×D4—22no—
1023C2×D4—24no—
1024C2×D4—24no—
1025C2×D4—24no—
1026C2×D4—24no—
1027C2×D4—22no—
1028C2×D4—42no—
1029C2×D4—42no—
1030C2×D4—42no—
1031C2×D4—42no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—44no—
1037C2×D4—44no—
1038C22×C4—24no—
1039C22×C4—28no—
1040C22×C4—24no—
1041C22×C4—24no—
1042C22×C4—42no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—42no—
1046C22×C4—44no—
1047C22×C4—42no—
1048C22×C4—44no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4—42no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2511yescharacteristic
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2514yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2514yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2514yes—
1075C22×C4C2512yes—
1076C22×C4C2511yescharacteristic
1077C22×C4C2514yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2511yescharacteristic
1080C22×C4C2511yescharacteristic
1081C22×C4C2511yescharacteristic
1082C22×C4C2511yescharacteristic
1083C4⋊C4—22no—
1084C4⋊C4—24no—
1085C4⋊C4—22no—
1086C4⋊C4—24no—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—24no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—22no—
1094C4⋊C4—28no—
1095C4⋊C4—22no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—22no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—22no—
1103C4⋊C4—24no—
1104C4⋊C4—22no—
1105C4⋊C4—42no—
1106C4⋊C4—41no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—44no—
1111C4⋊C4—42no—
1112C4⋊C4—41no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—42no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—41no—
1122C4⋊C4—44no—
1123C4⋊C4—41no—
1124C4⋊C4—41no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—41no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4C2×#4118yes—
1155C4⋊C4C2×#4118yes—
1156C22⋊C4—28no—
1157C22⋊C4—28no—
1158C22⋊C4—28no—
1159C22⋊C4—28no—
1160C22⋊C4—24no—
1161C22⋊C4—28no—
1162C22⋊C4—28no—
1163C22⋊C4—28no—
1164C22⋊C4—24no—
1165C22⋊C4—28no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—42no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C42—28no—
1193C42—28no—
1194C42—28no—
1195C42—24no—
1196C42—24no—
1197C42—24no—
1198C42—28no—
1199C42—24no—
1200C42—24no—
1201C42—22no—
1202C42—22no—
1203C42—24no—
1204C42—41no—
1205C42—42no—
1206C42—42no—
1207C42—42no—
1208C42—41no—
1209C42—42no—
1210C42—44no—
1211C42—42no—
1212C42—41no—
1213C42—44no—
1214C42—44no—
1215C42—44no—
1216C42—44no—
1217C42—44no—
1218C42—42no—
1219C42—44no—
1220C42—42no—
1221C42C2×#4114yes—
1222C422−1+414yes—
1223C23—24no—
1224C23—22no—
1225C23—22no—
1226C23—24no—
1227C23—24no—
1228C23—22no—
1229C23—24no—
1230C23—22no—
1231C23—22no—
1232C23—24no—
1233C23—24no—
1234C23—22no—
1235C23—24no—
1236C23—22no—
1237C23C2611yescharacteristic
1238Q8—216no—
1239Q8—44no—
1240Q8—84no—
1241Q8—82no—
1242Q8—84no—
1243Q8—162no—
1244D4—44no—
1245D4—48no—
1246D4—84no—
1247D4—84no—
1248D4—164no—
1249D4—164no—
1250C2×C4—24no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—24no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—21no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—21no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—21no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—48no—
1323C2×C4—88no—
1324C2×C4—84no—
1325C2×C4—84no—
1326C2×C4—88no—
1327C2×C4—164no—
1328C2×C4C22×#4118yes—
1329C2×C4C22×#4112yes—
1330C2×C4C22×#4112yes—
1331C2×C4C22×#4112yes—
1332C2×C4C2×2−1+412yes—
1333C2×C4C2×2−1+412yes—
1334C2×C4C2×2−1+412yes—
1335C2×C4#58512yes—
1336C2×C4#58512yes—
1337C22—44no—
1338C22—42no—
1339C22—42no—
1340C22—44no—
1341C22—44no—
1342C22—42no—
1343C22—42no—
1344C22—44no—
1345C22—42no—
1346C22—44no—
1347C22—44no—
1348C22—42no—
1349C22—42no—
1350C22—44no—
1351C22C23×#4111yescharacteristic
1352C22C22×2−1+411yescharacteristic
1353C22C2×#58511yescharacteristic
1354C22C2×#58511yescharacteristic
1355C22H(7,𝔽2)11yescharacteristic
1356C22H(7,𝔽2)11yescharacteristic
1357C222−1+611yescharacteristic
1358C4—22no—
1359C4—28no—
1360C4—22no—
1361C4—22no—
1362C4—22no—
1363C4—22no—
1364C4—42no—
1365C4—44no—
1366C4—42no—
1367C4—42no—
1368C4—42no—
1369C4—44no—
1370C4—42no—
1371C4—41no—
1372C4—42no—
1373C4—42no—
1374C4—42no—
1375C4—42no—
1376C4—44no—
1377C4—42no—
1378C4—42no—
1379C4—42no—
1380C4—42no—
1381C4—42no—
1382C4—44no—
1383C4—42no—
1384C4#351514yes—
1385C2—84no—
1386C2—82no—
1387C2C2×#351511yescharacteristic
1388C2#6285111yescharacteristic
1389C2#6288111yescharacteristic
1390C2#6293211yescharacteristic
1391C2#6296511yescharacteristic
1392C2#6300611yescharacteristic
1393C2#6306911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2541C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59821C2semidirect
2. #59749C2semidirect
3. #52274C2semidirect
4. #50970C2semidirect
5. #49136C2semidirect
6. #48652C2semidirect
7. #47428C2semidirect
8. #46294C2semidirect
9. #45407C2semidirect
11. #45266C2semidirect
12. #44515C2semidirect
13. #42873C2semidirect
14. #42509C2semidirect
15. #41579C2semidirect
16. #40128C2semidirect
17. #39837C2semidirect
18. #39629C2semidirect
19. #39628C2semidirect
20. #38821C2semidirect
21. #38231C2semidirect
22. #38228C2semidirect
23. #37167C2semidirect
24. #36476C2semidirect
25. #35971C2semidirect
26. #35605C2semidirect
28. #34499C2semidirect
29. #34324C2semidirect

Maximal subgroups

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

subgroupindex
#598212
#597492
#522742
#509702
#491362
#486522
#474282
#462942
#454072
#453122
#452662
#445152
#428732
#425092
#415792
#401282
#398372
#396292
#396282
#388212
#382312
#382282
#371672
#364762
#359712
#356052
#351972
#344992
#343242