Finite Group Databasebeta

← #7658909

Subgroups — #7658909

Order 512.

4278 conjugacy classes of subgroups.

The subgroup lattice has 1171 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42225C214yesmaximal, complemented
2#42200C212yesmaximal, complemented
3#42055C214yesmaximal, complemented
4#42021C212yesmaximal, complemented
5#41664C214yesmaximal, complemented
6#41652C214yesmaximal, complemented
7#41000C214yesmaximal, complemented
8#40984C214yesmaximal, complemented
9#40668C214yesmaximal, complemented
10#40666C214yesmaximal, complemented
11#37612C212yesmaximal, complemented
12#37608C211yesmaximal, characteristic
13#37603C212yesmaximal, complemented
14#37599C212yesmaximal, complemented
15#37555C212yesmaximal, complemented
16#36698C212yesmaximal, complemented
17C2×#2844C211yesmaximal, characteristic, complemented
18#36034C212yesmaximal, complemented
19#35964C214yesmaximal, complemented
20#35931C214yesmaximal, complemented
21#35742C212yesmaximal, complemented
22#34229C212yesmaximal, complemented
23#34215C211yesmaximal, characteristic, complemented
24C2×#533C2211yescharacteristic
25C2×#529C2212yes—
26#2844C2214yes—
27#2844C2214yes—
28#2844C2212yes—
29#2844C2211yescharacteristic
30#2844C2212yes—
31#2844C2211yescharacteristic
32#2844C2212yes—
33#2838C2214yes—
34#2838C2214yes—
35#2836C2214yes—
36#2836C2214yes—
37#2833C2214yes—
38#2830C2214yes—
39#2822C2212yes—
40#2822C2212yes—
41#2822C2211yescharacteristic
42#2820C2212yes—
43#2820C2212yes—
44#2820C2212yes—
45#2819C2211yescharacteristic
46#2795C2212yes—
47#2794C2212yes—
48#2793C2214yes—
49#2792C2212yes—
50#2789C2212yes—
51#2785C2212yes—
52#2782C2212yes—
53#2776C2214yes—
54#2775C2214yes—
55#2775C2214yes—
56#2769C2212yes—
57#2766C2214yes—
58#2765C2214yes—
59#2763C2214yes—
60#2762C2214yes—
61#2759C2214yes—
62#2758C2214yes—
63#2747C2214yes—
64#2739C2214yes—
65#2737C2214yes—
66#2720C2214yes—
67#2717C2214yes—
68#2700C2214yes—
69#2698C2214yes—
70#2698C2214yes—
71#2692C2214yes—
72#2690C2214yes—
73#2680C2212yes—
74#2666C2214yes—
75#2666C2214yes—
76#2666C2214yes—
77#2665C2214yes—
78#2663C2214yes—
79#2662C2214yes—
80#2659C2214yes—
81#2655C2214yes—
82#2655C2214yes—
83#2655C2214yes—
84#2654C2214yes—
85#2654C2214yes—
86#2650C2214yes—
87#2650C2214yes—
88#2650C2214yes—
89#2649C2214yes—
90#2648C2214yes—
91#2639C2214yes—
92#2638C2214yes—
93#2637C2214yes—
94#2637C2214yes—
95#2637C2214yes—
96#2636C2214yes—
97#2634C2214yes—
98#2628C2214yes—
99#2621C2214yes—
100#2618C2212yes—
101#2618C2212yes—
102#2612C2214yes—
103#2609C2212yes—
104#2609C2212yes—
105#2605C2214yes—
106#2596C2214yes—
107#2595C2214yes—
108#2593C2214yes—
109#2588C2214yes—
110#2586C2214yes—
111#2586C2214yes—
112#2581C2214yes—
113#2579C2214yes—
114#2578C2214yes—
115#2574C2214yes—
116#2574C2214yes—
117#2573C2214yes—
118#2573C2214yes—
119#2573C2214yes—
120#2569C2214yes—
121#2569C2212yes—
122#2569C2212yes—
123#2564C2214yes—
124#2556C2214yes—
125#2556C2214yes—
126#2549C2214yes—
127#2543C2214yes—
128#2536C2214yes—
129#2532C2214yes—
130#2530C2214yes—
131#2528C2214yes—
132#2527C2214yes—
133#2525C2214yes—
134#2524C2214yes—
135#2524C2214yes—
136#2524C2214yes—
137#2521C2214yes—
138#2520C2214yes—
139#2520C2214yes—
140#2520C2214yes—
141#2516C2214yes—
142#2510C2214yes—
143#2510C2214yes—
144#2510C2214yes—
145#2510C2214yes—
146#2504C2212yes—
147#2498C2214yes—
148#2498C2214yes—
149#2488C2214yes—
150#2481C2214yes—
151#2477C2214yes—
152#2474C2214yes—
153#2469C2214yes—
154#2469C2214yes—
155#2465C2214yes—
156#2465C2214yes—
157#2462C2214yes—
158#2461C2214yes—
159#2457C2214yes—
160#2444C2214yes—
161#2443C2214yes—
162#2442C2214yes—
163#2438C2214yes—
164#2436C2212yes—
165#2417C2214yes—
166#2417C2214yes—
167#2409C2214yes—
168#2401C2214yes—
169#2401C2214yes—
170#2399C2214yes—
171#2396C2214yes—
172#2396C2214yes—
173#2395C2214yes—
174C2×#400C2214yes—
175C2×#400C2212yes—
176C2×#395C2212yes—
177C2×#395C2214yes—
178#2368C2214yes—
179#2368C2214yes—
180#2364C2212yes—
181#2364C2212yes—
182#2361C2212yes—
183#2361C2212yes—
184#2360C2212yes—
185#2360C2212yes—
186#2359C2214yes—
187#2359C2214yes—
188#2357C2212yes—
189#2356C2212yes—
190#2355C2214yes—
191#2355C2214yes—
192#2353C2214yes—
193#2352C2214yes—
194#2351C2212yes—
195#2349C2212yes—
196#2346C2214yes—
197#2345C2212yes—
198#2343C2214yes—
199Q8×C22⋊C4C2212yes—
200#2334C2214yes—
201#2334C2214yes—
202#2331C2212yes—
203#2331C2212yes—
204#2318C2214yes—
205#2317C2211yescharacteristic
206#2317C2211yescharacteristic
207C4×#125C2212yes—
208C4×#125C2212yes—
209C4×#125C2212yes—
210C4×#125C2212yes—
211C4×#124C2212yes—
212C4×#124C2212yes—
213C2×#382C2211yescharacteristic
214C2×#382C2212yes—
215#2275C2214yes—
216#2274C2211yescharacteristic
217#2274C2211yescharacteristic
218C4×#117C2211yescharacteristic
219C23×Q8C2312yes—
220#533—28no—
221C2×C4⋊Q8C2312yes—
222#529—216no—
223C2×#126C2314yes—
224C2×#126C2314yes—
225C2×#125C2312yes—
226C2×#125C2312yes—
227C2×#125C2314yes—
228C2×#124C2312yes—
229C2×#124C2314yes—
230C2×#123C2314yes—
231C2×#123C2314yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×#121C2312yes—
239C2×#121C2312yes—
240C2×#121C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2312yes—
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2314yes—
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2314yes—
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2312yes—
264C22×C42C2311yescharacteristic
265#401C2314yes—
266#401C2314yes—
267#401C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2312yes—
278#400C2312yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2312yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2312yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#399C2314yes—
300#399C2314yes—
301#399C2314yes—
302#399C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2312yes—
310#398C2312yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2312yes—
323#398C2314yes—
324#398C2312yes—
325#398C2314yes—
326#398C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2312yes—
359#395C2314yes—
360#395C2314yes—
361#395C2312yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#395C2312yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2312yes—
375#395C2314yes—
376#394C2312yes—
377#394C2312yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2312yes—
383#394C2312yes—
384#394C2314yes—
385#393C2314yes—
386#393C2314yes—
387#393C2314yes—
388#393C2314yes—
389#393C2314yes—
390#393C2314yes—
391#393C2314yes—
392#392C2314yes—
393#391C2314yes—
394#391C2314yes—
395#391C2312yes—
396#391C2314yes—
397#391C2314yes—
398#391C2312yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#390C2312yes—
408#390C2312yes—
409#390C2314yes—
410#389C2312yes—
411#389C2312yes—
412#389C2312yes—
413#389C2312yes—
414#389C2312yes—
415#389C2312yes—
416#389C2312yes—
417#389C2312yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
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#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
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#387C2314yes—
502#387C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#385C2314yes—
517#385C2314yes—
518#385C2314yes—
519#385C2314yes—
520#385C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#384C2312yes—
530#384C2312yes—
531#383C2314yes—
532#383C2314yes—
533#383C2314yes—
534#383C2314yes—
535#383C2314yes—
536#382C2311yescharacteristic
537#382C2311yescharacteristic
538#382C2312yes—
539#382C2312yes—
540#382C2312yes—
541#382C2312yes—
542#382C2314yes—
543#382C2314yes—
544#382C2314yes—
545#382C2314yes—
546#382C2311yescharacteristic
547#382C2311yescharacteristic
548#382C2314yes—
549#382C2312yes—
550#382C2312yes—
551#382C2314yes—
552#382C2314yes—
553#381C2314yes—
554#381C2314yes—
555#381C2314yes—
556#380C2312yes—
557#380C2312yes—
558#380C2314yes—
559#380C2314yes—
560#380C2314yes—
561#380C2314yes—
562#380C2314yes—
563#380C2314yes—
564#380C2314yes—
565#380C2314yes—
566C4×C4⋊C4C2314yes—
567C4×C4⋊C4C2314yes—
568C4×C4⋊C4C2314yes—
569C4×C4⋊C4C2314yes—
570C4×C4⋊C4C2312yes—
571C4×C4⋊C4C2312yes—
572C4×C4⋊C4C2312yes—
573C4×C4⋊C4C2312yes—
574C4×C4⋊C4C2314yes—
575C4×C4⋊C4C2314yes—
576C4×C4⋊C4C2314yes—
577C4×C4⋊C4C2314yes—
578C4×C4⋊C4C2312yes—
579C4×C4⋊C4C2312yes—
580C4×C4⋊C4C2312yes—
581C4×C4⋊C4C2312yes—
582C4×C4⋊C4C2314yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2314yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2312yes—
588C4×C4⋊C4C2312yes—
589C4×C22⋊C4C2314yes—
590C4×C22⋊C4C2312yes—
591C4×C22⋊C4C2312yes—
592C4×C22⋊C4C2314yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2314yes—
595C4×C22⋊C4C2312yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2314yes—
598C4×C22⋊C4C2314yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2312yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2312yes—
604C4×C22⋊C4C2312yes—
605#376C2312yes—
606#376C2314yes—
607#376C2314yes—
608C2×#95C2314yes—
609C2×#95C2314yes—
610C2×#95C2312yes—
611C2×#95C2312yes—
612C2×#95C2314yes—
613C2×#95C2314yes—
614C2×#95C2314yes—
615C43C2312yes—
616C22×Q8—44no—
617C22×Q8—84no—
618C22×Q8C2412yes—
619C22×Q8C2414yes—
620C22×Q8C2412yes—
621C22×Q8C2412yes—
622C22×Q8C2414yes—
623C22×D4C2414yes—
624C22×D4C2412yes—
625C22×D4C2412yes—
626C22×D4C2412yes—
627C23×C4C2411yescharacteristic
628C23×C4C2414yes—
629C23×C4C2412yes—
630C23×C4C2414yes—
631C23×C4C2412yes—
632C23×C4C2414yes—
633C23×C4C2414yes—
634C23×C4C2414yes—
635C23×C4C2412yes—
636C4⋊Q8—28no—
637#126—216no—
638#126—84no—
639#125—28no—
640#125—28no—
641#125—84no—
642#124—28no—
643#124—84no—
644#123—216no—
645#123—84no—
646C22⋊Q8—28no—
647C22⋊Q8—216no—
648C22⋊Q8—84no—
649C22⋊Q8—84no—
650C22⋊Q8—84no—
651C22⋊Q8—84no—
652#121—28no—
653#121—44no—
654#121—44no—
655C4×Q8—28no—
656C4×Q8—216no—
657C4×Q8—84no—
658C4×Q8—82no—
659C4×Q8—82no—
660C4×D4—216no—
661C4×D4—216no—
662C4×D4—28no—
663C4×D4—48no—
664C4×D4—82no—
665C4×D4—82no—
666#117—24no—
667#117—24no—
668#117—24no—
669#117—216no—
670#117—42no—
671#117—84no—
672C2×C4⋊C4—42no—
673C2×C4⋊C4—42no—
674C2×C4⋊C4—44no—
675C2×C4⋊C4—84no—
676C2×C4⋊C4—82no—
677C2×C4⋊C4—82no—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2412yes—
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C22⋊C4C2412yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2412yes—
736C2×C22⋊C4C2412yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2411yescharacteristic
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2411yescharacteristic
763C2×C42#4118yes—
764C2×C42C2414yes—
765C2×C42C2412yes—
766C2×C42C2412yes—
767C2×C42C2412yes—
768C2×C42C2414yes—
769C2×C42C2414yes—
770C2×C42C2414yes—
771C2×C42C2412yes—
772C2×C42C2412yes—
773C2×C42C2412yes—
774C2×C42C2414yes—
775C2×C42C2414yes—
776C2×C42C2414yes—
777C2×C42C2414yes—
778C2×C42C2412yes—
779C2×C42C2412yes—
780C2×C42C2414yes—
781C2×C42C2414yes—
782C2×C42C2414yes—
783C2×C42C2411yescharacteristic
784C2×C42C2412yes—
785C2×C42C2411yescharacteristic
786#95C2412yes—
787#95C2414yes—
788#95C2414yes—
789#95C2412yes—
790#95C2412yes—
791#95C2414yes—
792#95C2414yes—
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#95C2412yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2412yes—
811#95C2412yes—
812#95C2414yes—
813#95C2414yes—
814#95C2412yes—
815#95C2412yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2412yes—
845#95C2414yes—
846#95C2412yes—
847#95C2414yes—
848#95C2412yes—
849#95C2412yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856C24C2514yes—
857C24C2511yescharacteristic
858C2×Q8—24no—
859C2×Q8—28no—
860C2×Q8—42no—
861C2×Q8—44no—
862C2×Q8—42no—
863C2×Q8—42no—
864C2×Q8—44no—
865C2×Q8—44no—
866C2×Q8—44no—
867C2×Q8—44no—
868C2×Q8—42no—
869C2×Q8—44no—
870C2×Q8—44no—
871C2×Q8—816no—
872C2×D4—28no—
873C2×D4—28no—
874C2×D4—28no—
875C2×D4—24no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—44no—
881C2×D4—44no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—28no—
885C22×C4—24no—
886C22×C4—28no—
887C22×C4—24no—
888C22×C4—28no—
889C22×C4—28no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—44no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—44no—
905C22×C4C2×#4114yes—
906C22×C4C2×#4118yes—
907C22×C4C2512yes—
908C22×C4C2514yes—
909C22×C4C2514yes—
910C22×C4C2514yes—
911C22×C4C2512yes—
912C22×C4C2512yes—
913C22×C4C2512yes—
914C22×C4C2512yes—
915C22×C4C2514yes—
916C22×C4C2514yes—
917C22×C4C2514yes—
918C22×C4C2514yes—
919C22×C4C2514yes—
920C22×C4C2512yes—
921C22×C4C2514yes—
922C22×C4C2512yes—
923C22×C4C2512yes—
924C22×C4C2511yescharacteristic
925C22×C4C2511yescharacteristic
926C22×C4C2512yes—
927C22×C4C2512yes—
928C4⋊C4—28no—
929C4⋊C4—28no—
930C4⋊C4—24no—
931C4⋊C4—24no—
932C4⋊C4—24no—
933C4⋊C4—28no—
934C4⋊C4—24no—
935C4⋊C4—28no—
936C4⋊C4—28no—
937C4⋊C4—28no—
938C4⋊C4—28no—
939C4⋊C4—24no—
940C4⋊C4—28no—
941C4⋊C4—41no—
942C4⋊C4—41no—
943C4⋊C4—41no—
944C4⋊C4—41no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—44no—
949C4⋊C4—42no—
950C4⋊C4—44no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—44no—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—44no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—44no—
966C4⋊C4—41no—
967C4⋊C4—41no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—44no—
978C4⋊C4—44no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C22⋊C4—24no—
984C22⋊C4—24no—
985C22⋊C4—28no—
986C22⋊C4—22no—
987C22⋊C4—24no—
988C22⋊C4—28no—
989C22⋊C4—28no—
990C22⋊C4—28no—
991C22⋊C4—28no—
992C22⋊C4—28no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C42−1+414yes—
1013C42—28no—
1014C42—24no—
1015C42—24no—
1016C42—24no—
1017C42—28no—
1018C42—42no—
1019C42—44no—
1020C42—42no—
1021C42—44no—
1022C42—44no—
1023C42—42no—
1024C42—44no—
1025C42—44no—
1026C42—44no—
1027C42—42no—
1028C42—42no—
1029C42—44no—
1030C42—44no—
1031C42—44no—
1032C42C2×#4114yes—
1033C42C2×#4118yes—
1034C42C2×#4114yes—
1035C23—22no—
1036C23—22no—
1037C23—24no—
1038C23—24no—
1039C23—24no—
1040C23—24no—
1041C23—24no—
1042C23—24no—
1043C23—24no—
1044C23C22×#4112yes—
1045C23C2×2−1+412yes—
1046C23#58512yes—
1047C23C2611yescharacteristic
1048Q8—48no—
1049Q8—48no—
1050Q8—88no—
1051Q8—84no—
1052Q8—88no—
1053D4—48no—
1054D4—416no—
1055D4—162no—
1056D4—162no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—28no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—48no—
1113C2×C4—88no—
1114C2×C4—88no—
1115C2×C4—88no—
1116C2×C4—84no—
1117C2×C4—88no—
1118C2×C4—84no—
1119C2×C4—164no—
1120C2×C4C22×#4112yes—
1121C2×C4C22×#4114yes—
1122C2×C4C22×#4112yes—
1123C2×C4C22×#4114yes—
1124C2×C4C2×2−1+414yes—
1125C22—22no—
1126C22—24no—
1127C22—22no—
1128C22—24no—
1129C22—44no—
1130C22—44no—
1131C22—44no—
1132C22—44no—
1133C22—44no—
1134C22—44no—
1135C22—44no—
1136C22#346114yes—
1137C22C23×#4111yescharacteristic
1138C22C22×2−1+411yescharacteristic
1139C22C2×#58511yescharacteristic
1140C22H(7,𝔽2)12yes—
1141C222−1+612yes—
1142C4—24no—
1143C4—24no—
1144C4—24no—
1145C4—22no—
1146C4—22no—
1147C4—44no—
1148C4—42no—
1149C4—42no—
1150C4—44no—
1151C4—42no—
1152C4—42no—
1153C4—44no—
1154C4—44no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—44no—
1159C4—44no—
1160C4—44no—
1161C4—44no—
1162C4—44no—
1163C2—24no—
1164C2—84no—
1165C2C2×#346111yescharacteristic
1166C2#6285612yes—
1167C2#6304611yescharacteristic
1168C2#6305812yes—
1169C2#6306411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37608C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42225C2semidirect
2. #42200C2semidirect
3. #42055C2semidirect
4. #42021C2semidirect
5. #41664C2semidirect
6. #41652C2semidirect
7. #41000C2semidirect
8. #40984C2semidirect
9. #40668C2semidirect
10. #40666C2semidirect
11. #37612C2semidirect
13. #37603C2semidirect
14. #37599C2semidirect
15. #37555C2semidirect
16. #36698C2semidirect
17. C2×#2844C2semidirect
18. #36034C2semidirect
19. #35964C2semidirect
20. #35931C2semidirect
21. #35742C2semidirect
22. #34229C2semidirect
23. #34215C2semidirect

Maximal subgroups

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

subgroupindex
#422252
#422002
#420552
#420212
#416642
#416522
#410002
#409842
#406682
#406662
#376122
#376082
#376032
#375992
#375552
#366982
C2×#28442
#360342
#359642
#359312
#357422
#342292
#342152