Finite Group Databasebeta

← #7665652

Subgroups — #7665652

Order 512.

4414 conjugacy classes of subgroups.

The subgroup lattice has 1210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40178C213yesmaximal
2#40143C213yesmaximal, complemented
3#40082C213yesmaximal, complemented
4#40051C213yesmaximal
5#40024C213yesmaximal, complemented
6#39999C213yesmaximal, complemented
7#39928C213yesmaximal
8#39907C213yesmaximal
9#39526C213yesmaximal, complemented
10#39407C213yesmaximal
11#39032C213yesmaximal
12#39003C213yesmaximal, complemented
13#36584C211yesmaximal, characteristic, complemented
14Q8×#126C211yesmaximal, characteristic
15#36475C211yesmaximal, characteristic, complemented
16#36475C211yesmaximal, characteristic, complemented
17#36475C211yesmaximal, characteristic, complemented
18#36466C211yesmaximal, characteristic, complemented
19#36448C211yesmaximal, characteristic
20#36448C211yesmaximal, characteristic
21#36448C211yesmaximal, characteristic
22#36447C211yesmaximal, characteristic, complemented
23#36435C211yesmaximal, characteristic
24#36435C211yesmaximal, characteristic
25#35142C213yesmaximal
26#35115C213yesmaximal, complemented
27#35115C213yesmaximal, complemented
28C4×#557C211yesmaximal, characteristic, complemented
29C4×#557C211yesmaximal, characteristic, complemented
30#34128C211yesmaximal, characteristic
31C4×#541C213yesmaximal
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#541C2213yes—
35C22×C4×Q8C2211yescharacteristic
36#2864C2213yes—
37#2864C2213yes—
38#2864C2213yes—
39#2863C2213yes—
40#2863C2213yes—
41#2863C2213yes—
42#2863C2213yes—
43#2859C2213yes—
44#2859C2213yes—
45#2859C2213yes—
46#2851C2213yes—
47#2851C2213yes—
48#2802C2216yes—
49#2794C2216yes—
50#2789C2216yes—
51#2776C2216yes—
52#2776C2216yes—
53#2769C2216yes—
54#2766C2216yes—
55#2762C2216yes—
56#2758C2216yes—
57#2758C2216yes—
58#2744C2216yes—
59#2739C2216yes—
60#2719C2216yes—
61#2713C2216yes—
62#2698C2216yes—
63#2689C2216yes—
64#2655C2216yes—
65#2655C2216yes—
66#2655C2216yes—
67#2652C2216yes—
68#2634C2216yes—
69#2634C2216yes—
70#2584C2213yes—
71#2584C2213yes—
72#2581C2213yes—
73#2581C2213yes—
74#2571C2213yes—
75#2571C2213yes—
76#2571C2213yes—
77#2570C2213yes—
78#2570C2213yes—
79#2570C2213yes—
80#2570C2213yes—
81#2570C2213yes—
82#2570C2213yes—
83#2565C2213yes—
84#2565C2213yes—
85#2552C2213yes—
86#2552C2213yes—
87#2551C2213yes—
88#2550C2213yes—
89#2550C2213yes—
90#2533C2216yes—
91#2533C2216yes—
92#2533C2216yes—
93#2528C2216yes—
94#2528C2216yes—
95#2528C2216yes—
96#2524C2216yes—
97#2524C2216yes—
98#2514C2213yes—
99#2514C2213yes—
100#2514C2213yes—
101#2514C2213yes—
102#2514C2213yes—
103#2514C2213yes—
104#2511C2213yes—
105#2511C2213yes—
106#2511C2213yes—
107#2511C2213yes—
108#2511C2213yes—
109#2511C2213yes—
110#2509C2213yes—
111#2509C2213yes—
112#2509C2213yes—
113#2509C2213yes—
114#2509C2213yes—
115#2509C2213yes—
116#2509C2213yes—
117#2508C2213yes—
118#2508C2213yes—
119#2508C2213yes—
120#2508C2213yes—
121#2508C2213yes—
122#2507C2213yes—
123#2507C2213yes—
124#2507C2213yes—
125#2506C2213yes—
126#2506C2213yes—
127#2506C2213yes—
128#2506C2213yes—
129#2506C2213yes—
130#2497C2213yes—
131#2497C2213yes—
132#2497C2213yes—
133#2496C2213yes—
134#2496C2213yes—
135#2496C2213yes—
136#2495C2213yes—
137#2495C2213yes—
138#2495C2213yes—
139#2494C2213yes—
140#2494C2213yes—
141#2494C2213yes—
142#2478C2216yes—
143#2475C2216yes—
144#2462C2216yes—
145#2462C2216yes—
146#2453C2213yes—
147#2453C2213yes—
148#2451C2213yes—
149#2451C2213yes—
150#2442C2213yes—
151#2442C2213yes—
152#2440C2213yes—
153#2440C2213yes—
154#2370C2213yes—
155#2370C2213yes—
156#2370C2213yes—
157#2370C2213yes—
158#2365C2213yes—
159#2365C2213yes—
160#2356C2213yes—
161#2356C2213yes—
162#2355C2213yes—
163#2355C2213yes—
164#2351C2211yescharacteristic
165#2351C2211yescharacteristic
166#2351C2211yescharacteristic
167#2351C2211yescharacteristic
168#2351C2211yescharacteristic
169#2351C2211yescharacteristic
170#2351C2211yescharacteristic
171#2351C2211yescharacteristic
172#2351C2211yescharacteristic
173#2351C2211yescharacteristic
174#2351C2211yescharacteristic
175#2351C2211yescharacteristic
176Q8×C4⋊C4C2211yescharacteristic
177Q8×C4⋊C4C2211yescharacteristic
178Q8×C4⋊C4C2211yescharacteristic
179Q8×C4⋊C4C2211yescharacteristic
180Q8×C4⋊C4C2211yescharacteristic
181Q8×C4⋊C4C2211yescharacteristic
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184#2344C2213yes—
185#2344C2213yes—
186Q8×C22⋊C4C2211yescharacteristic
187Q8×C22⋊C4C2211yescharacteristic
188Q8×C22⋊C4C2211yescharacteristic
189Q8×C22⋊C4C2211yescharacteristic
190Q8×C22⋊C4C2211yescharacteristic
191Q8×C22⋊C4C2211yescharacteristic
192#2336C2213yes—
193#2336C2213yes—
194#2336C2216yes—
195#2336C2213yes—
196#2336C2213yes—
197#2334C2211yescharacteristic
198#2334C2213yes—
199#2334C2213yes—
200#2334C2213yes—
201#2330C2213yes—
202#2327C2213yes—
203#2323C2213yes—
204#2323C2213yes—
205#2320C2213yes—
206#2320C2213yes—
207#2314C2213yes—
208C4×C4⋊Q8C2213yes—
209C4×C4⋊Q8C2213yes—
210C4×C4⋊Q8C2213yes—
211C4×#125C2213yes—
212C4×#125C2213yes—
213C4×#125C2213yes—
214C4×#125C2213yes—
215C4×#125C2213yes—
216C4×#125C2213yes—
217C4×#125C2213yes—
218C4×#125C2213yes—
219C4×#125C2213yes—
220C4×#126C2213yes—
221C4×#126C2213yes—
222C4×#126C2213yes—
223C4×#126C2213yes—
224C4×C22⋊Q8C2213yes—
225C4×C22⋊Q8C2213yes—
226#2295C2213yes—
227#2295C2213yes—
228#2283C2213yes—
229C42×Q8C2213yes—
230C42×Q8C2213yes—
231C42×Q8C2211yescharacteristic
232C42×Q8C2211yescharacteristic
233C42×Q8C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C4×#117C2213yes—
238C23×Q8C2311yescharacteristic
239#557—28no—
240#557—28no—
241#541—224no—
242C2×C4⋊Q8C2313yes—
243C2×C4⋊Q8C2313yes—
244C2×C4⋊Q8C2313yes—
245C2×#126C2313yes—
246C2×#126C2313yes—
247C2×#126C2313yes—
248C2×#126C2311yescharacteristic
249C2×#125C2313yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2316yes—
259C2×C22⋊Q8C2313yes—
260C2×C22⋊Q8C2313yes—
261C2×C4×Q8—28no—
262C2×C4×Q8C2313yes—
263C2×C4×Q8C2313yes—
264C2×C4×Q8C2313yes—
265C2×C4×Q8C2313yes—
266C2×C4×Q8C2313yes—
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2313yes—
281C2×C4×Q8C2313yes—
282C2×C4×Q8C2313yes—
283C2×C4×Q8C2311yescharacteristic
284C2×#117C2313yes—
285C2×#117C2313yes—
286C22×C4⋊C4C2313yes—
287C22×C42C2313yes—
288#401C2316yes—
289#401C2316yes—
290#401C2316yes—
291#400C2316yes—
292#400C2316yes—
293#400C2316yes—
294#400C2316yes—
295#400C2316yes—
296#400C2316yes—
297#400C2316yes—
298#400C2316yes—
299#400C2316yes—
300#400C2316yes—
301#400C2316yes—
302#400C2316yes—
303#400C2316yes—
304#400C2316yes—
305#400C2316yes—
306#400C2316yes—
307#400C2316yes—
308#400C2316yes—
309#400C2316yes—
310#400C2316yes—
311#400C2316yes—
312#400C2316yes—
313#400C2316yes—
314#398C2316yes—
315#398C2316yes—
316#398C2316yes—
317#398C2316yes—
318#398C2316yes—
319#398C2316yes—
320#398C2316yes—
321#398C2316yes—
322#398C2316yes—
323#398C2316yes—
324#398C2316yes—
325#398C2316yes—
326#398C2316yes—
327#398C2316yes—
328#397C2316yes—
329#397C2316yes—
330#397C2316yes—
331#396C2316yes—
332#395C2316yes—
333#395C2316yes—
334#395C2316yes—
335#395C2316yes—
336#391C2313yes—
337#391C2313yes—
338#391C2316yes—
339#391C2316yes—
340#391C2313yes—
341#391C2313yes—
342#391C2313yes—
343#391C2313yes—
344#391C2313yes—
345#391C2313yes—
346#391C2313yes—
347#391C2313yes—
348#391C2313yes—
349#391C2313yes—
350#391C2313yes—
351#391C2313yes—
352#391C2313yes—
353#391C2313yes—
354#389C2311yescharacteristic
355#389C2313yes—
356#389C2313yes—
357#389C2313yes—
358#389C2313yes—
359#389C2313yes—
360#389C2313yes—
361#389C2313yes—
362#389C2313yes—
363#389C2313yes—
364#389C2313yes—
365#389C2313yes—
366#389C2313yes—
367#389C2313yes—
368#389C2313yes—
369#389C2313yes—
370#389C2313yes—
371#389C2313yes—
372#389C2311yescharacteristic
373#389C2313yes—
374#389C2313yes—
375#389C2313yes—
376#389C2313yes—
377#389C2313yes—
378#389C2313yes—
379#389C2313yes—
380#389C2316yes—
381#389C2316yes—
382#389C2313yes—
383#389C2313yes—
384#389C2313yes—
385#389C2313yes—
386#389C2313yes—
387#389C2313yes—
388#389C2313yes—
389#389C2313yes—
390#389C2313yes—
391#389C2313yes—
392#389C2313yes—
393#389C2313yes—
394#389C2313yes—
395#389C2313yes—
396#389C2316yes—
397#389C2313yes—
398#389C2313yes—
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2316yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2316yes—
409#389C2313yes—
410#389C2313yes—
411#389C2316yes—
412#389C2316yes—
413#389C2316yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#388C2311yescharacteristic
419#388C2311yescharacteristic
420#388C2311yescharacteristic
421#388C2313yes—
422#388C2313yes—
423#388C2313yes—
424#388C2313yes—
425#388C2313yes—
426#388C2313yes—
427#388C2313yes—
428#388C2313yes—
429#388C2313yes—
430#387C2313yes—
431#387C2313yes—
432#387C2313yes—
433#387C2313yes—
434#387C2313yes—
435#387C2313yes—
436#387C2313yes—
437#387C2313yes—
438#387C2313yes—
439#387C2313yes—
440#387C2313yes—
441#387C2313yes—
442#387C2311yescharacteristic
443#387C2311yescharacteristic
444#387C2311yescharacteristic
445#387C2313yes—
446#387C2313yes—
447#387C2313yes—
448#387C2313yes—
449#387C2313yes—
450#387C2313yes—
451#387C2313yes—
452#387C2313yes—
453#387C2313yes—
454#387C2313yes—
455#387C2313yes—
456#387C2313yes—
457#387C2313yes—
458#387C2313yes—
459#387C2313yes—
460#387C2313yes—
461#387C2313yes—
462#387C2316yes—
463#387C2316yes—
464#387C2316yes—
465#387C2316yes—
466#387C2316yes—
467#387C2316yes—
468#387C2316yes—
469#387C2316yes—
470#387C2313yes—
471#387C2313yes—
472#387C2316yes—
473#387C2316yes—
474#387C2316yes—
475#387C2316yes—
476#387C2316yes—
477#387C2313yes—
478#387C2313yes—
479#387C2316yes—
480#387C2316yes—
481#387C2316yes—
482#387C2316yes—
483#387C2316yes—
484#387C2316yes—
485#387C2316yes—
486#387C2316yes—
487#387C2316yes—
488#387C2316yes—
489#387C2316yes—
490#387C2316yes—
491#387C2316yes—
492#387C2316yes—
493#387C2316yes—
494#387C2316yes—
495#387C2316yes—
496#387C2316yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#385C2311yescharacteristic
501#385C2311yescharacteristic
502#385C2313yes—
503#385C2313yes—
504#385C2316yes—
505#385C2316yes—
506#384C2313yes—
507#384C2313yes—
508#384C2313yes—
509#384C2313yes—
510#384C2313yes—
511#384C2313yes—
512#384C2313yes—
513#384C2313yes—
514#384C2313yes—
515#383C2313yes—
516#383C2313yes—
517#383C2313yes—
518#383C2313yes—
519#383C2316yes—
520#383C2316yes—
521#383C2316yes—
522#383C2316yes—
523#382C2311yescharacteristic
524#382C2313yes—
525#382C2313yes—
526#382C2313yes—
527#382C2313yes—
528#382C2313yes—
529#382C2313yes—
530#382C2313yes—
531#382C2313yes—
532#382C2313yes—
533#382C2313yes—
534#382C2313yes—
535#382C2313yes—
536#382C2313yes—
537#382C2313yes—
538#382C2313yes—
539#382C2316yes—
540#382C2313yes—
541#382C2316yes—
542#381C2316yes—
543#380C2313yes—
544#380C2313yes—
545#380C2313yes—
546#380C2313yes—
547#380C2313yes—
548#380C2313yes—
549#380C2313yes—
550#380C2313yes—
551C4×C4⋊C4C2313yes—
552C4×C4⋊C4C2313yes—
553C4×C4⋊C4C2313yes—
554C4×C4⋊C4C2313yes—
555C4×C4⋊C4C2313yes—
556C4×C4⋊C4C2313yes—
557C4×C4⋊C4C2313yes—
558C4×C4⋊C4C2313yes—
559C4×C4⋊C4C2313yes—
560C4×C4⋊C4C2313yes—
561C4×C4⋊C4C2313yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2316yes—
564C4×C4⋊C4C2316yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2311yescharacteristic
591C4×C4⋊C4C2311yescharacteristic
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2311yescharacteristic
612C4×C22⋊C4C2313yes—
613#376C2313yes—
614#376C2313yes—
615#376C2316yes—
616C43C2313yes—
617C43C2313yes—
618C43C2313yes—
619C43C2313yes—
620C43C2313yes—
621C43C2313yes—
622C22×Q8—24no—
623C22×Q8—24no—
624C22×Q8—24no—
625C22×Q8C2413yes—
626C22×Q8C2413yes—
627C22×Q8C2413yes—
628C22×Q8C2411yescharacteristic
629C23×C4C2413yes—
630C23×C4C2413yes—
631C23×C4C2411yescharacteristic
632C4⋊Q8—212no—
633C4⋊Q8—212no—
634C4⋊Q8—212no—
635#126—212no—
636#126—212no—
637#126—212no—
638#126#4118yes—
639#125—212no—
640#125—212no—
641#125—212no—
642#125—212no—
643#125—212no—
644#125—212no—
645#125—212no—
646#125—212no—
647#125—212no—
648#125—412no—
649C22⋊Q8—212no—
650C22⋊Q8—212no—
651C4×Q8—24no—
652C4×Q8—24no—
653C4×Q8—24no—
654C4×Q8—24no—
655C4×Q8—24no—
656C4×Q8—24no—
657C4×Q8—24no—
658C4×Q8—24no—
659C4×Q8—24no—
660C4×Q8—24no—
661C4×Q8—24no—
662C4×Q8—24no—
663C4×Q8—24no—
664C4×Q8—212no—
665C4×Q8—212no—
666C4×Q8—212no—
667C4×Q8—212no—
668C4×Q8—212no—
669C4×Q8—212no—
670C4×Q8—46no—
671C4×Q8—46no—
672C4×Q8#4118yes—
673#117—212no—
674#117—46no—
675C2×C4⋊C4—212no—
676C2×C4⋊C4C2413yes—
677C2×C4⋊C4C2416yes—
678C2×C4⋊C4C2413yes—
679C2×C4⋊C4C2413yes—
680C2×C4⋊C4C2413yes—
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2413yes—
685C2×C4⋊C4C2413yes—
686C2×C4⋊C4C2413yes—
687C2×C4⋊C4C2413yes—
688C2×C4⋊C4C2413yes—
689C2×C4⋊C4C2413yes—
690C2×C4⋊C4C2413yes—
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2416yes—
714C2×C4⋊C4C2416yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2416yes—
724C2×C4⋊C4C2416yes—
725C2×C4⋊C4C2416yes—
726C2×C4⋊C4C2416yes—
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2416yes—
738C2×C4⋊C4C2416yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2411yescharacteristic
747C2×C22⋊C4C2411yescharacteristic
748C2×C22⋊C4C2413yes—
749C2×C22⋊C4C2413yes—
750C2×C22⋊C4C2413yes—
751C2×C22⋊C4C2413yes—
752C2×C22⋊C4C2411yescharacteristic
753C2×C22⋊C4C2411yescharacteristic
754C2×C22⋊C4C2413yes—
755C2×C22⋊C4C2413yes—
756C2×C22⋊C4C2411yescharacteristic
757C2×C22⋊C4C2411yescharacteristic
758C2×C22⋊C4C2411yescharacteristic
759C2×C42—212no—
760C2×C42C2413yes—
761C2×C42C2413yes—
762C2×C42C2413yes—
763C2×C42C2411yescharacteristic
764C2×C42C2413yes—
765C2×C42C2413yes—
766C2×C42C2413yes—
767C2×C42C2413yes—
768C2×C42C2413yes—
769C2×C42C2413yes—
770C2×C42C2413yes—
771C2×C42C2413yes—
772C2×C42C2413yes—
773C2×C42C2413yes—
774C2×C42C2413yes—
775C2×C42C2413yes—
776C2×C42C2413yes—
777C2×C42C2413yes—
778C2×C42C2413yes—
779C2×C42C2413yes—
780C2×C42C2413yes—
781C2×C42C2413yes—
782C2×C42C2413yes—
783C2×C42C2413yes—
784C2×C42C2413yes—
785C2×C42C2413yes—
786C2×C42C2411yescharacteristic
787C2×C42C2411yescharacteristic
788C2×C42C2411yescharacteristic
789C2×C42C2411yescharacteristic
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2411yescharacteristic
800#95C2411yescharacteristic
801#95C2411yescharacteristic
802#95C2413yes—
803#95C2413yes—
804#95C2413yes—
805#95C2413yes—
806#95C2413yes—
807#95C2413yes—
808#95C2416yes—
809#95C2416yes—
810#95C2416yes—
811#95C2416yes—
812#95C2413yes—
813#95C2413yes—
814#95C2413yes—
815#95C2413yes—
816#95C2413yes—
817#95C2413yes—
818#95C2413yes—
819#95C2413yes—
820#95C2411yescharacteristic
821#95C2411yescharacteristic
822#95C2411yescharacteristic
823#95C2411yescharacteristic
824#95C2416yes—
825#95C2416yes—
826#95C2413yes—
827#95C2411yescharacteristic
828#95C2411yescharacteristic
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2411yescharacteristic
835#95C2411yescharacteristic
836#95C2411yescharacteristic
837#95C2411yescharacteristic
838#95C2413yes—
839#95C2413yes—
840#95C2416yes—
841#95C2416yes—
842#95C2416yes—
843#95C2416yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2416yes—
852#95C2416yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2416yes—
858#95C2416yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2416yes—
867#95C2416yes—
868#95C2416yes—
869#95C2416yes—
870#95C2416yes—
871#95C2416yes—
872#95C2416yes—
873#95C2416yes—
874#95C2416yes—
875#95C2416yes—
876C24C2511yescharacteristic
877C2×Q8—26no—
878C2×Q8—26no—
879C2×Q8—26no—
880C2×Q8—26no—
881C2×Q8—26no—
882C2×Q8—26no—
883C2×Q8—26no—
884C2×Q8—43no—
885C2×Q8—43no—
886C2×Q8—416no—
887C2×Q8C2×#4114yes—
888C2×Q82−1+414yes—
889C2×Q82−1+414yes—
890C22×C4—26no—
891C22×C4—22no—
892C22×C4—26no—
893C22×C4—26no—
894C22×C4—26no—
895C22×C4—26no—
896C22×C4—43no—
897C22×C4—41no—
898C22×C4—41no—
899C22×C4C2513yes—
900C22×C4C2513yes—
901C22×C4C2511yescharacteristic
902C22×C4C2511yescharacteristic
903C22×C4C2511yescharacteristic
904C22×C4C2513yes—
905C22×C4C2511yescharacteristic
906C22×C4C2513yes—
907C22×C4C2513yes—
908C22×C4C2513yes—
909C22×C4C2513yes—
910C22×C4C2513yes—
911C22×C4C2513yes—
912C22×C4C2511yescharacteristic
913C22×C4C2511yescharacteristic
914C22×C4C2513yes—
915C22×C4C2513yes—
916C22×C4C2513yes—
917C22×C4C2513yes—
918C22×C4C2513yes—
919C22×C4C2511yescharacteristic
920C22×C4C2511yescharacteristic
921C22×C4C2511yescharacteristic
922C22×C4C2511yescharacteristic
923C22×C4C2511yescharacteristic
924C22×C4C2511yescharacteristic
925C22×C4C2511yescharacteristic
926C22×C4C2513yes—
927C22×C4C2511yescharacteristic
928C22×C4C2513yes—
929C4⋊C4—26no—
930C4⋊C4—212no—
931C4⋊C4—26no—
932C4⋊C4—26no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—26no—
936C4⋊C4—26no—
937C4⋊C4—26no—
938C4⋊C4—26no—
939C4⋊C4—26no—
940C4⋊C4—26no—
941C4⋊C4—26no—
942C4⋊C4—26no—
943C4⋊C4—26no—
944C4⋊C4—26no—
945C4⋊C4—26no—
946C4⋊C4—26no—
947C4⋊C4—26no—
948C4⋊C4—26no—
949C4⋊C4—26no—
950C4⋊C4—26no—
951C4⋊C4—26no—
952C4⋊C4—26no—
953C4⋊C4—26no—
954C4⋊C4—26no—
955C4⋊C4—212no—
956C4⋊C4—212no—
957C4⋊C4—26no—
958C4⋊C4—26no—
959C4⋊C4—26no—
960C4⋊C4—26no—
961C4⋊C4—26no—
962C4⋊C4—26no—
963C4⋊C4—26no—
964C4⋊C4—26no—
965C4⋊C4—26no—
966C4⋊C4—26no—
967C4⋊C4—26no—
968C4⋊C4—26no—
969C4⋊C4—22no—
970C4⋊C4—26no—
971C4⋊C4—41no—
972C4⋊C4—41no—
973C4⋊C4—41no—
974C4⋊C4—43no—
975C4⋊C4—43no—
976C4⋊C4—41no—
977C4⋊C4—46no—
978C4⋊C4—46no—
979C4⋊C4—43no—
980C4⋊C4—43no—
981C4⋊C4—43no—
982C4⋊C4—43no—
983C4⋊C4—46no—
984C4⋊C4—46no—
985C4⋊C4—43no—
986C4⋊C4—43no—
987C4⋊C4—43no—
988C4⋊C4—43no—
989C4⋊C4—43no—
990C4⋊C4—43no—
991C4⋊C4—43no—
992C4⋊C4—46no—
993C4⋊C4—46no—
994C4⋊C4—46no—
995C4⋊C4—46no—
996C4⋊C4C2×#41112yes—
997C4⋊C4C2×#4114yes—
998C4⋊C4C2×#4114yes—
999C4⋊C4C2×#4114yes—
1000C22⋊C4—26no—
1001C22⋊C4—26no—
1002C22⋊C4—26no—
1003C22⋊C4—22no—
1004C22⋊C4—41no—
1005C22⋊C4—41no—
1006C22⋊C4—43no—
1007C22⋊C4—43no—
1008C22⋊C4—43no—
1009C22⋊C4C2×#4114yes—
1010C22⋊C4C2×#4114yes—
1011C22⋊C4C2×#4114yes—
1012C42—26no—
1013C42—26no—
1014C42—26no—
1015C42—26no—
1016C42—26no—
1017C42—26no—
1018C42—26no—
1019C42—26no—
1020C42—26no—
1021C42—26no—
1022C42—26no—
1023C42—26no—
1024C42—26no—
1025C42—26no—
1026C42—26no—
1027C42—26no—
1028C42—26no—
1029C42—26no—
1030C42—26no—
1031C42—26no—
1032C42—26no—
1033C42—22no—
1034C42—26no—
1035C42—41no—
1036C42—41no—
1037C42—41no—
1038C42—43no—
1039C42—43no—
1040C42—41no—
1041C42—43no—
1042C42—43no—
1043C42—43no—
1044C42—43no—
1045C42—43no—
1046C42—43no—
1047C42—43no—
1048C42—43no—
1049C42—43no—
1050C42C2×#41112yes—
1051C42C2×#4114yes—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23C22×#4112yes—
1059C23C2611yescharacteristic
1060Q8—412no—
1061Q8—412no—
1062Q8—412no—
1063Q8#541116yescomplemented
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—23no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—23no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—23no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—23no—
1087C2×C4—23no—
1088C2×C4—23no—
1089C2×C4—23no—
1090C2×C4—23no—
1091C2×C4—23no—
1092C2×C4—23no—
1093C2×C4—23no—
1094C2×C4—23no—
1095C2×C4—23no—
1096C2×C4—23no—
1097C2×C4—23no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—23no—
1102C2×C4—23no—
1103C2×C4—23no—
1104C2×C4—23no—
1105C2×C4—23no—
1106C2×C4—23no—
1107C2×C4—23no—
1108C2×C4—23no—
1109C2×C4—23no—
1110C2×C4—23no—
1111C2×C4—23no—
1112C2×C4—21no—
1113C2×C4—23no—
1114C2×C4—23no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—23no—
1118C2×C4—23no—
1119C2×C4—23no—
1120C2×C4—23no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—23no—
1124C2×C4—21no—
1125C2×C4—23no—
1126C2×C4—21no—
1127C2×C4—23no—
1128C2×C4—23no—
1129C2×C4—21no—
1130C2×C4—23no—
1131C2×C4—23no—
1132C2×C4—23no—
1133C2×C4—23no—
1134C2×C4—23no—
1135C2×C4—21no—
1136C2×C4—23no—
1137C2×C4—23no—
1138C2×C4—23no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—412no—
1143C2×C4—44no—
1144C2×C4—412no—
1145C2×C4C22×#4112yes—
1146C2×C4C22×#4112yes—
1147C2×C4C22×#4112yes—
1148C2×C4C22×#4112yes—
1149C2×C4C22×#4112yes—
1150C2×C4C22×#4116yes—
1151C2×C4C22×#4112yes—
1152C2×C4C22×#4112yes—
1153C2×C4C22×#4116yes—
1154C2×C4C2×2−1+416yes—
1155C2×C4C2×2−1+416yes—
1156C2×C4#58512yes—
1157C22—22no—
1158C22—22no—
1159C22—22no—
1160C22—41no—
1161C22—41no—
1162C22—41no—
1163C22—41no—
1164C22C23×#4111yescharacteristic
1165C22C23×#4111yescharacteristic
1166C22C22×2−1+411yescharacteristic
1167C22C22×2−1+411yescharacteristic
1168C22C2×#58511yescharacteristic
1169C222−1+611yescharacteristic
1170C222−1+611yescharacteristic
1171C4—22no—
1172C4—22no—
1173C4—22no—
1174C4—22no—
1175C4—22no—
1176C4—22no—
1177C4—26no—
1178C4—22no—
1179C4—22no—
1180C4—43no—
1181C4—43no—
1182C4—43no—
1183C4—43no—
1184C4—41no—
1185C4—41no—
1186C4—43no—
1187C4—43no—
1188C4—41no—
1189C4—43no—
1190C4—41no—
1191C4—43no—
1192C4—43no—
1193C4—41no—
1194C4—41no—
1195C4—43no—
1196C4—43no—
1197C4—43no—
1198C4—43no—
1199C4—43no—
1200C4C2×#541112yes—
1201C2—42no—
1202C2C22×#54111yescharacteristic
1203C2#41211yescharacteristic
1204C2#6285011yescharacteristic
1205C2#6294911yescharacteristic
1206C2#6295311yescharacteristic
1207C2#6300111yescharacteristic
1208C2#6300111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #40143C2semidirect
3. #40082C2semidirect
5. #40024C2semidirect
6. #39999C2semidirect
9. #39526C2semidirect
12. #39003C2semidirect
13. #36584C2semidirect
15. #36475C2semidirect
16. #36475C2semidirect
17. #36475C2semidirect
18. #36466C2semidirect
22. #36447C2semidirect
26. #35115C2semidirect
27. #35115C2semidirect
28. C4×#557C2semidirect
29. C4×#557C2semidirect
1063. Q8#541semidirect

Maximal subgroups

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

subgroupindex
#401782
#401432
#400822
#400512
#400242
#399992
#399282
#399072
#395262
#394072
#390322
#390032
#365842
Q8×#1262
#364752
#364662
#364482
#364472
#364352
#351422
#351152
C4×#5572
#341282
C4×#5412