Finite Group Databasebeta

← #7697445

Subgroups — #7697445

Order 512.

4499 conjugacy classes of subgroups.

The subgroup lattice has 1169 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60043C212yesmaximal, complemented
2#59926C211yesmaximal, characteristic, complemented
3#59901C214yesmaximal, complemented
4#59866C212yesmaximal, complemented
5#52306C211yesmaximal, characteristic, complemented
6#52290C212yesmaximal, complemented
7#44717C212yesmaximal
8#44708C214yesmaximal, complemented
9#44208C214yesmaximal, complemented
10#43858C214yesmaximal, complemented
11#43591C214yesmaximal, complemented
12#39837C212yesmaximal, complemented
13#39826C214yesmaximal, complemented
14#38809C212yesmaximal, complemented
15#38799C214yesmaximal, complemented
16#38436C214yesmaximal, complemented
17#38427C212yesmaximal, complemented
18#36574C212yesmaximal, complemented
19#36539C211yesmaximal, characteristic
20#35960C212yesmaximal, complemented
21#35935C214yesmaximal, complemented
22#34318C214yesmaximal, complemented
23#34314C212yesmaximal, complemented
24C2×#552C2212yes—
25C2×#552C2214yes—
26#2864C2211yescharacteristic
27#2859C2214yes—
28#2859C2212yes—
29#2854C2212yes—
30#2809C2211yescharacteristic
31#2806C2212yes—
32#2805C2212yes—
33#2805C2212yes—
34#2804C2211yescharacteristic
35#2794C2212yes—
36#2793C2214yes—
37#2791C2214yes—
38#2788C2214yes—
39#2775C2214yes—
40#2774C2214yes—
41#2772C2214yes—
42#2769C2214yes—
43#2769C2212yes—
44#2768C2214yes—
45#2766C2214yes—
46#2766C2214yes—
47#2762C2214yes—
48#2750C2214yes—
49#2739C2214yes—
50#2738C2214yes—
51#2734C2211yescharacteristic
52#2731C2212yes—
53#2729C2214yes—
54#2727C2212yes—
55#2726C2212yes—
56#2726C2212yes—
57#2725C2214yes—
58#2723C2214yes—
59#2722C2212yes—
60#2721C2214yes—
61#2720C2214yes—
62#2719C2214yes—
63#2718C2214yes—
64#2706C2214yes—
65#2704C2214yes—
66#2698C2214yes—
67#2693C2212yes—
68#2683C2211yescharacteristic
69#2680C2212yes—
70#2667C2212yes—
71#2666C2214yes—
72#2664C2214yes—
73#2664C2214yes—
74#2663C2214yes—
75#2612C2212yes—
76#2611C2214yes—
77#2611C2214yes—
78#2609C2214yes—
79#2608C2214yes—
80#2606C2214yes—
81#2606C2214yes—
82#2604C2214yes—
83#2602C2214yes—
84#2601C2214yes—
85#2601C2214yes—
86#2599C2214yes—
87#2594C2214yes—
88#2590C2214yes—
89#2587C2214yes—
90#2586C2212yes—
91#2585C2214yes—
92#2585C2214yes—
93#2585C2214yes—
94#2585C2214yes—
95#2584C2214yes—
96#2584C2214yes—
97#2583C2214yes—
98#2581C2212yes—
99#2581C2212yes—
100#2579C2212yes—
101#2576C2214yes—
102#2575C2214yes—
103#2574C2214yes—
104#2574C2214yes—
105#2573C2214yes—
106#2573C2214yes—
107#2573C2214yes—
108#2572C2212yes—
109#2572C2214yes—
110#2569C2214yes—
111#2559C2214yes—
112#2558C2214yes—
113#2553C2214yes—
114#2536C2211yescharacteristic
115#2535C2211yescharacteristic
116#2533C2214yes—
117#2530C2214yes—
118#2528C2214yes—
119#2525C2214yes—
120#2525C2214yes—
121#2524C2214yes—
122#2524C2214yes—
123#2524C2214yes—
124#2519C2214yes—
125#2517C2212yes—
126#2516C2214yes—
127#2515C2214yes—
128#2509C2214yes—
129#2509C2214yes—
130#2508C2214yes—
131#2508C2214yes—
132#2494C2212yes—
133#2484C2212yes—
134#2478C2214yes—
135#2473C2214yes—
136#2473C2214yes—
137#2470C2214yes—
138#2469C2214yes—
139#2469C2214yes—
140#2466C2214yes—
141#2465C2214yes—
142#2462C2214yes—
143#2462C2214yes—
144#2458C2214yes—
145#2455C2212yes—
146#2453C2214yes—
147#2453C2214yes—
148#2449C2214yes—
149#2438C2214yes—
150#2426C2212yes—
151#2425C2214yes—
152#2413C2214yes—
153#2413C2214yes—
154#2402C2214yes—
155#2399C2214yes—
156#2396C2214yes—
157#2396C2214yes—
158#2395C2212yes—
159#2374C2214yes—
160#2374C2214yes—
161#2373C2214yes—
162#2373C2214yes—
163#2373C2214yes—
164#2372C2212yes—
165#2370C2214yes—
166#2370C2212yes—
167#2370C2214yes—
168#2370C2214yes—
169#2370C2214yes—
170#2368C2214yes—
171#2362C2212yes—
172#2362C2214yes—
173#2360C2212yes—
174#2360C2214yes—
175#2359C2214yes—
176#2357C2211yescharacteristic
177#2356C2214yes—
178#2352C2212yes—
179#2352C2214yes—
180#2351C2212yes—
181#2351C2212yes—
182#2351C2211yescharacteristic
183#2347C2212yes—
184#2347C2214yes—
185#2347C2214yes—
186#2347C2212yes—
187#2345C2214yes—
188#2344C2212yes—
189#2343C2214yes—
190#2336C2214yes—
191#2336C2214yes—
192#2336C2214yes—
193#2335C2214yes—
194#2335C2214yes—
195#2334C2214yes—
196#2323C2214yes—
197#2323C2214yes—
198#2322C2214yes—
199C4×C4⋊Q8C2214yes—
200C4×C4⋊Q8C2212yes—
201C4×#125C2212yes—
202C4×#125C2214yes—
203C4×#126C2214yes—
204C4×#126C2214yes—
205C4×#124C2211yescharacteristic
206C4×C22⋊Q8C2212yes—
207C4×C22⋊Q8C2212yes—
208C4×C22⋊Q8C2212yes—
209#2298C2214yes—
210#2298C2214yes—
211#2296C2212yes—
212#2295C2212yes—
213#2293C2214yes—
214C2×#389C2212yes—
215#2274C2214yes—
216#2274C2212yes—
217C42×Q8C2212yes—
218C42×D4C2211yescharacteristic
219#552—232no—
220#552—216no—
221C2×C4⋊Q8C2312yes—
222C2×#126C2314yes—
223C2×#126C2314yes—
224C2×#126C2314yes—
225C2×#126C2314yes—
226C2×#125C2312yes—
227C2×#125C2314yes—
228C2×#125C2314yes—
229C2×#125C2314yes—
230C2×#125C2314yes—
231C2×#125C2314yes—
232C2×#124C2311yescharacteristic
233C2×#123C2314yes—
234C2×#123C2314yes—
235C2×#123C2314yes—
236C2×#123C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×#121C2312yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2312yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×#117C2314yes—
257C2×#117C2314yes—
258C2×#117C2314yes—
259C2×#117C2314yes—
260C2×#117C2312yes—
261C2×#117C2312yes—
262C2×#117C2312yes—
263C22×C4⋊C4C2314yes—
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C42C2312yes—
268#401C2314yes—
269#400C2312yes—
270#400C2314yes—
271#400C2312yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2312yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#399C2314yes—
289#399C2314yes—
290#399C2314yes—
291#399C2312yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2312yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2312yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#397C2314yes—
318#397C2314yes—
319#397C2314yes—
320#397C2314yes—
321#397C2312yes—
322#397C2314yes—
323#397C2312yes—
324#397C2314yes—
325#396C2314yes—
326#396C2314yes—
327#396C2314yes—
328#396C2314yes—
329#396C2314yes—
330#396C2314yes—
331#396C2314yes—
332#396C2314yes—
333#396C2314yes—
334#396C2314yes—
335#395C2314yes—
336#395C2314yes—
337#395C2312yes—
338#395C2312yes—
339#395C2314yes—
340#395C2314yes—
341#395C2314yes—
342#395C2314yes—
343#394C2314yes—
344#394C2312yes—
345#394C2314yes—
346#394C2314yes—
347#394C2314yes—
348#393C2314yes—
349#393C2314yes—
350#393C2314yes—
351#392C2312yes—
352#391C2314yes—
353#391C2312yes—
354#391C2314yes—
355#391C2312yes—
356#391C2312yes—
357#391C2314yes—
358#391C2314yes—
359#391C2311yescharacteristic
360#391C2312yes—
361#390C2314yes—
362#390C2311yescharacteristic
363#390C2312yes—
364#390C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2312yes—
368#389C2312yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2312yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2312yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2312yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2312yes—
405#389C2314yes—
406#389C2312yes—
407#389C2312yes—
408#389C2312yes—
409#389C2312yes—
410#389C2312yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2314yes—
417#388C2314yes—
418#388C2314yes—
419#388C2314yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#386C2312yes—
507#386C2312yes—
508#385C2314yes—
509#385C2314yes—
510#385C2312yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2314yes—
516#385C2314yes—
517#385C2314yes—
518#385C2312yes—
519#385C2314yes—
520#385C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2314yes—
524#384C2312yes—
525#384C2314yes—
526#383C2314yes—
527#383C2314yes—
528#383C2314yes—
529#383C2314yes—
530#383C2314yes—
531#383C2314yes—
532#382C2312yes—
533#382C2314yes—
534#382C2312yes—
535#382C2314yes—
536#382C2314yes—
537#382C2312yes—
538#382C2314yes—
539#382C2311yescharacteristic
540#382C2314yes—
541#382C2311yescharacteristic
542#382C2311yescharacteristic
543#381C2314yes—
544#381C2314yes—
545#381C2314yes—
546#381C2312yes—
547#380C2312yes—
548#380C2314yes—
549#380C2314yes—
550#380C2312yes—
551#380C2314yes—
552#380C2312yes—
553#380C2312yes—
554#380C2312yes—
555C4×C4⋊C4C2312yes—
556C4×C4⋊C4C2314yes—
557C4×C4⋊C4C2314yes—
558C4×C4⋊C4C2314yes—
559C4×C4⋊C4C2314yes—
560C4×C4⋊C4C2314yes—
561C4×C4⋊C4C2312yes—
562C4×C4⋊C4C2314yes—
563C4×C4⋊C4C2314yes—
564C4×C4⋊C4C2314yes—
565C4×C4⋊C4C2314yes—
566C4×C4⋊C4C2314yes—
567C4×C4⋊C4C2314yes—
568C4×C4⋊C4C2312yes—
569C4×C4⋊C4C2314yes—
570C4×C4⋊C4C2314yes—
571C4×C4⋊C4C2314yes—
572C4×C4⋊C4C2314yes—
573C4×C4⋊C4C2314yes—
574C4×C4⋊C4C2314yes—
575C4×C4⋊C4C2312yes—
576C4×C4⋊C4C2312yes—
577C4×C4⋊C4C2314yes—
578C4×C4⋊C4C2314yes—
579C4×C4⋊C4C2314yes—
580C4×C4⋊C4C2314yes—
581C4×C4⋊C4C2312yes—
582C4×C4⋊C4C2314yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2312yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2314yes—
588C4×C4⋊C4C2312yes—
589C4×C4⋊C4C2311yescharacteristic
590C4×C4⋊C4C2314yes—
591C4×C22⋊C4C2312yes—
592C4×C22⋊C4C2314yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2314yes—
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2314yes—
598C4×C22⋊C4C2314yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2312yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2312yes—
607C4×C22⋊C4C2312yes—
608C4×C22⋊C4C2312yes—
609#376C2314yes—
610#376C2314yes—
611#376C2314yes—
612C2×#95C2314yes—
613C43C2312yes—
614C43C2314yes—
615C43C2311yescharacteristic
616C22×Q8C2412yes—
617C22×Q8C2412yes—
618C22×Q8C2412yes—
619C22×Q8C2411yescharacteristic
620C22×D4C2411yescharacteristic
621C22×D4C2411yescharacteristic
622C22×D4C2414yes—
623C23×C4C2414yes—
624C23×C4C2412yes—
625C23×C4C2414yes—
626C23×C4C2412yes—
627C23×C4C2412yes—
628C23×C4C2412yes—
629C23×C4C2412yes—
630C23×C4C2412yes—
631C4⋊Q8—28no—
632#126—216no—
633#126—216no—
634#126—216no—
635#126—84no—
636#125—216no—
637#125—216no—
638#125—28no—
639#125—216no—
640#125—216no—
641#125—84no—
642#124—24no—
643#123—216no—
644#123—216no—
645#123—216no—
646#123—84no—
647C22⋊Q8—28no—
648C22⋊Q8—28no—
649C22⋊Q8—28no—
650C22⋊Q8—216no—
651C22⋊Q8—216no—
652#121—82no—
653C4×Q8—28no—
654C4×Q8—216no—
655C4×Q8—44no—
656C4×Q8—42no—
657C4×Q8—44no—
658C4×Q8—82no—
659C4×Q8—82no—
660C4×Q8—82no—
661C4×Q8—84no—
662C4×D4—28no—
663C4×D4—216no—
664C4×D4—42no—
665C4×D4—42no—
666#117—216no—
667#117—216no—
668#117—216no—
669#117—44no—
670#117—48no—
671#117—82no—
672#117#41116yes—
673C2×C4⋊C4—216no—
674C2×C4⋊C4—28no—
675C2×C4⋊C4—44no—
676C2×C4⋊C4—82no—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C22⋊C4C2412yes—
738C2×C22⋊C4C2412yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2412yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2412yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2412yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2412yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C42—82no—
764C2×C42C2414yes—
765C2×C42C2414yes—
766C2×C42C2414yes—
767C2×C42C2414yes—
768C2×C42C2411yescharacteristic
769C2×C42C2412yes—
770C2×C42C2414yes—
771C2×C42C2412yes—
772C2×C42C2411yescharacteristic
773C2×C42C2412yes—
774C2×C42C2414yes—
775C2×C42C2414yes—
776C2×C42C2414yes—
777C2×C42C2414yes—
778C2×C42C2414yes—
779C2×C42C2414yes—
780C2×C42C2412yes—
781C2×C42C2412yes—
782C2×C42C2412yes—
783C2×C42C2412yes—
784C2×C42C2412yes—
785C2×C42C2414yes—
786C2×C42C2414yes—
787C2×C42C2414yes—
788C2×C42C2411yescharacteristic
789C2×C42C2414yes—
790C2×C42C2414yes—
791C2×C42C2414yes—
792C2×C42C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2411yescharacteristic
808#95C2414yes—
809#95C2412yes—
810#95C2411yescharacteristic
811#95C2412yes—
812#95C2414yes—
813#95C2414yes—
814#95C2412yes—
815#95C2414yes—
816#95C2412yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2412yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2412yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2412yes—
850#95C2412yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2412yes—
855#95C2412yes—
856#95C2414yes—
857#95C2414yes—
858C24C2512yes—
859C24C2512yes—
860C2×Q8—28no—
861C2×Q8—24no—
862C2×Q8—24no—
863C2×Q8—41no—
864C2×Q8—42no—
865C2×Q8—42no—
866C2×Q8—41no—
867C2×Q8—42no—
868C2×Q8—42no—
869C2×Q8—42no—
870C2×Q82−1+414yes—
871C2×D4—24no—
872C2×D4—28no—
873C2×D4—22no—
874C2×D4—41no—
875C2×D4—41no—
876C2×D4—41no—
877C2×D4—44no—
878C2×D4—44no—
879C22×C4—28no—
880C22×C4—28no—
881C22×C4—28no—
882C22×C4—24no—
883C22×C4—28no—
884C22×C4—24no—
885C22×C4—24no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—44no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—44no—
894C22×C4—42no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—42no—
898C22×C4—44no—
899C22×C4C2×#4118yes—
900C22×C4C2512yes—
901C22×C4C2514yes—
902C22×C4C2514yes—
903C22×C4C2512yes—
904C22×C4C2512yes—
905C22×C4C2514yes—
906C22×C4C2514yes—
907C22×C4C2512yes—
908C22×C4C2514yes—
909C22×C4C2511yescharacteristic
910C22×C4C2514yes—
911C22×C4C2514yes—
912C22×C4C2512yes—
913C22×C4C2514yes—
914C22×C4C2514yes—
915C22×C4C2514yes—
916C22×C4C2512yes—
917C22×C4C2512yes—
918C22×C4C2511yescharacteristic
919C22×C4C2512yes—
920C22×C4C2511yescharacteristic
921C4⋊C4—28no—
922C4⋊C4—28no—
923C4⋊C4—24no—
924C4⋊C4—28no—
925C4⋊C4—28no—
926C4⋊C4—28no—
927C4⋊C4—28no—
928C4⋊C4—28no—
929C4⋊C4—28no—
930C4⋊C4—28no—
931C4⋊C4—28no—
932C4⋊C4—28no—
933C4⋊C4—24no—
934C4⋊C4—28no—
935C4⋊C4—28no—
936C4⋊C4—28no—
937C4⋊C4—28no—
938C4⋊C4—28no—
939C4⋊C4—28no—
940C4⋊C4—28no—
941C4⋊C4—28no—
942C4⋊C4—28no—
943C4⋊C4—24no—
944C4⋊C4—28no—
945C4⋊C4—28no—
946C4⋊C4—28no—
947C4⋊C4—28no—
948C4⋊C4—44no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—44no—
954C4⋊C4—42no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—44no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—41no—
964C4⋊C4—41no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—41no—
968C4⋊C4—44no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C4⋊C4—44no—
978C4⋊C4—44no—
979C4⋊C4C2×#4118yes—
980C4⋊C4C2×#4118yes—
981C22⋊C4—28no—
982C22⋊C4—24no—
983C22⋊C4—28no—
984C22⋊C4—24no—
985C22⋊C4—28no—
986C22⋊C4—28no—
987C22⋊C4—28no—
988C22⋊C4—28no—
989C22⋊C4—28no—
990C22⋊C4—28no—
991C22⋊C4—28no—
992C22⋊C4—28no—
993C22⋊C4—24no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—42no—
1002C22⋊C4—44no—
1003C22⋊C4—42no—
1004C22⋊C4—44no—
1005C22⋊C4—42no—
1006C22⋊C4C2×#41116yes—
1007C42—28no—
1008C42—28no—
1009C42—28no—
1010C42—28no—
1011C42—24no—
1012C42—22no—
1013C42—24no—
1014C42—28no—
1015C42—22no—
1016C42—24no—
1017C42—41no—
1018C42—42no—
1019C42—42no—
1020C42—42no—
1021C42—44no—
1022C42—44no—
1023C42—44no—
1024C42—44no—
1025C42—42no—
1026C42—44no—
1027C42—44no—
1028C42—44no—
1029C42—44no—
1030C42—44no—
1031C42—44no—
1032C42—44no—
1033C42—44no—
1034C42—42no—
1035C42C2×#41116yes—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—24no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—24no—
1047C23C22×#4114yes—
1048C23C2611yescharacteristic
1049Q8—44no—
1050Q8—48no—
1051Q8—48no—
1052Q8—48no—
1053D4—44no—
1054D4—82no—
1055D4—88no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—21no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—21no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—22no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—21no—
1086C2×C4—24no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—24no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—48no—
1109C2×C4—48no—
1110C2×C4—416no—
1111C2×C4—48no—
1112C2×C4—84no—
1113C2×C4—84no—
1114C2×C4—88no—
1115C2×C4—162no—
1116C2×C4C22×#4118yes—
1117C2×C4C22×#4118yes—
1118C2×C4C22×#4114yes—
1119C2×C4C22×#4114yes—
1120C2×C4C2×2−1+414yes—
1121C2×C4C2×2−1+412yes—
1122C2×C4#58512yes—
1123C22—24no—
1124C22—24no—
1125C22—24no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—44no—
1131C22—42no—
1132C22—44no—
1133C22—42no—
1134C22—42no—
1135C22C23×#4112yes—
1136C22C22×2−1+411yescharacteristic
1137C22C2×#58511yescharacteristic
1138C22H(7,𝔽2)11yescharacteristic
1139C222−1+612yes—
1140C4—28no—
1141C4—22no—
1142C4—24no—
1143C4—24no—
1144C4—22no—
1145C4—24no—
1146C4—28no—
1147C4—42no—
1148C4—44no—
1149C4—42no—
1150C4—44no—
1151C4—42no—
1152C4—44no—
1153C4—44no—
1154C4—44no—
1155C4—44no—
1156C4—42no—
1157C4—44no—
1158C4—44no—
1159C4—41no—
1160C4—42no—
1161C2—44no—
1162C2—82no—
1163C2#41211yescharacteristic
1164C2#6285612yes—
1165C2#6290211yescharacteristic
1166C2#6300112yes—
1167C2#6306411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2535C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60043C2semidirect
2. #59926C2semidirect
3. #59901C2semidirect
4. #59866C2semidirect
5. #52306C2semidirect
6. #52290C2semidirect
8. #44708C2semidirect
9. #44208C2semidirect
10. #43858C2semidirect
11. #43591C2semidirect
12. #39837C2semidirect
13. #39826C2semidirect
14. #38809C2semidirect
15. #38799C2semidirect
16. #38436C2semidirect
17. #38427C2semidirect
18. #36574C2semidirect
20. #35960C2semidirect
21. #35935C2semidirect
22. #34318C2semidirect
23. #34314C2semidirect

Maximal subgroups

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

subgroupindex
#600432
#599262
#599012
#598662
#523062
#522902
#447172
#447082
#442082
#438582
#435912
#398372
#398262
#388092
#387992
#384362
#384272
#365742
#365392
#359602
#359352
#343182
#343142