Finite Group Databasebeta

← #7697462

Subgroups — #7697462

Order 512.

4291 conjugacy classes of subgroups.

The subgroup lattice has 1179 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59872C213yesmaximal
2#59672C213yesmaximal
3#59671C213yesmaximal
4#52274C213yesmaximal
5#45426C213yesmaximal
6#45223C213yesmaximal
7#45223C213yesmaximal
8#45202C213yesmaximal
9#44953C213yesmaximal
10#44949C213yesmaximal
11#39753C213yesmaximal
12#39682C213yesmaximal
13#39680C213yesmaximal
14#39642C213yesmaximal
15#39183C213yesmaximal
16#39177C213yesmaximal
17#36593C211yesmaximal, characteristic
18#36475C211yesmaximal, characteristic
19#36447C211yesmaximal, characteristic
20#35971C211yesmaximal, characteristic
21#35957C211yesmaximal, characteristic
22#35957C211yesmaximal, characteristic
23#35868C211yesmaximal, characteristic
24#35868C211yesmaximal, characteristic
25#35868C211yesmaximal, characteristic
26#34337C211yesmaximal, characteristic
27#34336C211yesmaximal, characteristic
28#34336C211yesmaximal, characteristic
29#34336C211yesmaximal, characteristic
30#34336C211yesmaximal, characteristic
31#34336C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2211yescharacteristic
36#2868C2213yes—
37#2864C2213yes—
38#2859C2213yes—
39#2809C2216yes—
40#2809C2213yes—
41#2806C2213yes—
42#2805C2213yes—
43#2802C2216yes—
44#2802C2216yes—
45#2802C2213yes—
46#2802C2213yes—
47#2799C2213yes—
48#2799C2216yes—
49#2799C2213yes—
50#2791C2216yes—
51#2791C2216yes—
52#2791C2211yescharacteristic
53#2791C2213yes—
54#2791C2216yes—
55#2791C2216yes—
56#2774C2213yes—
57#2774C2213yes—
58#2755C2213yes—
59#2755C2213yes—
60#2755C2216yes—
61#2726C2216yes—
62#2726C2213yes—
63#2713C2216yes—
64#2713C2213yes—
65#2713C2213yes—
66#2713C2216yes—
67#2713C2216yes—
68#2660C2213yes—
69#2660C2213yes—
70#2647C2213yes—
71#2647C2213yes—
72#2647C2213yes—
73#2647C2213yes—
74#2590C2216yes—
75#2590C2216yes—
76#2588C2216yes—
77#2588C2216yes—
78#2585C2216yes—
79#2585C2216yes—
80#2584C2213yes—
81#2584C2213yes—
82#2571C2213yes—
83#2571C2213yes—
84#2570C2213yes—
85#2570C2213yes—
86#2570C2213yes—
87#2570C2213yes—
88#2570C2213yes—
89#2570C2213yes—
90#2567C2213yes—
91#2567C2213yes—
92#2565C2216yes—
93#2565C2216yes—
94#2552C2213yes—
95#2552C2213yes—
96#2552C2213yes—
97#2552C2213yes—
98#2552C2213yes—
99#2552C2216yes—
100#2552C2213yes—
101#2552C2213yes—
102#2552C2213yes—
103#2552C2216yes—
104#2552C2213yes—
105#2552C2213yes—
106#2552C2213yes—
107#2552C2213yes—
108#2550C2216yes—
109#2550C2213yes—
110#2550C2213yes—
111#2550C2213yes—
112#2550C2213yes—
113#2546C2213yes—
114#2546C2213yes—
115#2520C2216yes—
116#2520C2216yes—
117#2511C2216yes—
118#2511C2216yes—
119#2509C2213yes—
120#2509C2213yes—
121#2509C2216yes—
122#2509C2213yes—
123#2509C2213yes—
124#2509C2213yes—
125#2508C2216yes—
126#2508C2213yes—
127#2508C2213yes—
128#2508C2213yes—
129#2508C2213yes—
130#2508C2213yes—
131#2507C2213yes—
132#2507C2213yes—
133#2507C2213yes—
134#2507C2213yes—
135#2507C2213yes—
136#2506C2213yes—
137#2506C2213yes—
138#2506C2213yes—
139#2506C2216yes—
140#2506C2213yes—
141#2506C2216yes—
142#2506C2213yes—
143#2506C2213yes—
144#2506C2213yes—
145#2506C2213yes—
146#2506C2213yes—
147#2453C2216yes—
148#2451C2216yes—
149#2402C2213yes—
150#2402C2213yes—
151#2402C2213yes—
152#2402C2213yes—
153#2399C2213yes—
154#2399C2213yes—
155#2370C2213yes—
156#2370C2216yes—
157#2370C2213yes—
158#2370C2213yes—
159#2370C2213yes—
160#2370C2213yes—
161#2370C2213yes—
162#2370C2213yes—
163#2370C2213yes—
164#2370C2213yes—
165#2370C2213yes—
166#2370C2213yes—
167#2370C2213yes—
168#2369C2213yes—
169#2369C2213yes—
170#2369C2213yes—
171#2369C2213yes—
172#2369C2213yes—
173#2365C2213yes—
174#2355C2213yes—
175#2355C2213yes—
176#2355C2213yes—
177#2355C2213yes—
178#2355C2213yes—
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182#2351C2211yescharacteristic
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189Q8×C4⋊C4C2213yes—
190Q8×C4⋊C4C2211yescharacteristic
191Q8×C4⋊C4C2211yescharacteristic
192Q8×C4⋊C4C2211yescharacteristic
193Q8×C4⋊C4C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202#2331C2213yes—
203#2331C2213yes—
204#2331C2213yes—
205#2331C2213yes—
206#2331C2213yes—
207#2330C2213yes—
208#2330C2213yes—
209#2330C2213yes—
210#2330C2213yes—
211#2330C2213yes—
212#2330C2213yes—
213#2330C2213yes—
214C4×C4⋊Q8C2213yes—
215C4×C4⋊Q8C2213yes—
216C4×#125C2213yes—
217C4×#125C2213yes—
218C4×#125C2213yes—
219C4×#125C2213yes—
220C4×#125C2213yes—
221C4×#125C2213yes—
222C4×#125C2213yes—
223#2295C2213yes—
224#2295C2213yes—
225#2295C2213yes—
226#2295C2213yes—
227#2295C2213yes—
228#2295C2213yes—
229#2276C2211yescharacteristic
230#2276C2211yescharacteristic
231#2276C2211yescharacteristic
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238#557—28no—
239#557—28no—
240#557—28no—
241#557Q8116yescomplemented
242C2×C4⋊Q8C2313yes—
243C2×C4⋊Q8C2313yes—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2316yes—
247C2×C4⋊Q8C2313yes—
248C2×#125C2313yes—
249C2×#125C2313yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2316yes—
257C2×#125C2316yes—
258C2×#125C2316yes—
259C2×#125C2316yes—
260C2×#125C2313yes—
261C2×#125C2313yes—
262C2×C4×Q8C2313yes—
263C2×C4×Q8C2313yes—
264C2×C4×Q8C2313yes—
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
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×Q8C2316yes—
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2313yes—
281C2×C4×Q8C2311yescharacteristic
282#400C2313yes—
283#400C2313yes—
284#400C2313yes—
285#400C2316yes—
286#400C2316yes—
287#400C2316yes—
288#400C2313yes—
289#400C2316yes—
290#400C2316yes—
291#400C2313yes—
292#400C2316yes—
293#400C2313yes—
294#400C2313yes—
295#400C2313yes—
296#400C2313yes—
297#400C2316yes—
298#400C2316yes—
299#400C2316yes—
300#400C2311yescharacteristic
301#400C2313yes—
302#400C2313yes—
303#400C2313yes—
304#400C2313yes—
305#400C2313yes—
306#400C2313yes—
307#398C2313yes—
308#398C2313yes—
309#398C2316yes—
310#398C2316yes—
311#398C2316yes—
312#398C2316yes—
313#398C2316yes—
314#398C2316yes—
315#398C2313yes—
316#398C2316yes—
317#398C2316yes—
318#398C2316yes—
319#398C2316yes—
320#398C2313yes—
321#398C2313yes—
322#398C2313yes—
323#398C2313yes—
324#398C2316yes—
325#398C2316yes—
326#398C2316yes—
327#398C2316yes—
328#398C2316yes—
329#398C2316yes—
330#398C2316yes—
331#398C2313yes—
332#398C2311yescharacteristic
333#398C2311yescharacteristic
334#398C2313yes—
335#398C2313yes—
336#398C2313yes—
337#398C2311yescharacteristic
338#398C2311yescharacteristic
339#398C2311yescharacteristic
340#398C2313yes—
341#398C2313yes—
342#398C2313yes—
343#398C2313yes—
344#398C2313yes—
345#398C2313yes—
346#398C2313yes—
347#398C2313yes—
348#398C2316yes—
349#398C2316yes—
350#395C2313yes—
351#395C2313yes—
352#395C2316yes—
353#395C2316yes—
354#395C2313yes—
355#395C2313yes—
356#395C2313yes—
357#395C2313yes—
358#395C2313yes—
359#395C2313yes—
360#391C2313yes—
361#391C2313yes—
362#391C2313yes—
363#391C2313yes—
364#391C2313yes—
365#391C2316yes—
366#391C2316yes—
367#391C2316yes—
368#391C2316yes—
369#391C2313yes—
370#391C2313yes—
371#391C2313yes—
372#391C2313yes—
373#391C2313yes—
374#391C2316yes—
375#391C2316yes—
376#391C2316yes—
377#391C2313yes—
378#391C2313yes—
379#391C2313yes—
380#391C2313yes—
381#389C2311yescharacteristic
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#389C2313yes—
397#389C2313yes—
398#389C2316yes—
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2316yes—
421#389C2316yes—
422#389C2313yes—
423#389C2316yes—
424#389C2316yes—
425#389C2316yes—
426#389C2313yes—
427#389C2313yes—
428#389C2316yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2316yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2316yes—
439#389C2316yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2316yes—
444#389C2316yes—
445#389C2316yes—
446#389C2316yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2316yes—
452#389C2316yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2316yes—
461#389C2311yescharacteristic
462#387C2311yescharacteristic
463#387C2313yes—
464#387C2313yes—
465#387C2313yes—
466#387C2313yes—
467#387C2313yes—
468#387C2313yes—
469#387C2313yes—
470#387C2316yes—
471#387C2316yes—
472#387C2316yes—
473#387C2316yes—
474#387C2316yes—
475#387C2313yes—
476#387C2313yes—
477#387C2313yes—
478#387C2313yes—
479#387C2313yes—
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#387C2313yes—
493#387C2316yes—
494#387C2316yes—
495#387C2316yes—
496#387C2316yes—
497#387C2316yes—
498#387C2313yes—
499#387C2313yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2313yes—
506#387C2313yes—
507#387C2316yes—
508#387C2313yes—
509#387C2313yes—
510#387C2313yes—
511#387C2313yes—
512#387C2313yes—
513#387C2313yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2311yescharacteristic
518#387C2311yescharacteristic
519#387C2311yescharacteristic
520#387C2311yescharacteristic
521#387C2311yescharacteristic
522#384C2311yescharacteristic
523#384C2313yes—
524#384C2316yes—
525#384C2316yes—
526#384C2316yes—
527#384C2313yes—
528#384C2313yes—
529#384C2313yes—
530#384C2313yes—
531#384C2313yes—
532#384C2313yes—
533#384C2313yes—
534#384C2313yes—
535#384C2313yes—
536#384C2313yes—
537#384C2313yes—
538#384C2316yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2313yes—
544#382C2313yes—
545#382C2313yes—
546#382C2316yes—
547#382C2316yes—
548#382C2313yes—
549#382C2313yes—
550#382C2313yes—
551#382C2313yes—
552#382C2313yes—
553C4×C4⋊C4C2313yes—
554C4×C4⋊C4C2316yes—
555C4×C4⋊C4C2316yes—
556C4×C4⋊C4C2313yes—
557C4×C4⋊C4C2313yes—
558C4×C4⋊C4C2313yes—
559C4×C4⋊C4C2313yes—
560C4×C4⋊C4C2313yes—
561C4×C4⋊C4C2313yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2316yes—
567C4×C4⋊C4C2316yes—
568C4×C4⋊C4C2316yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2316yes—
574C4×C4⋊C4C2316yes—
575C4×C4⋊C4C2316yes—
576C4×C4⋊C4C2316yes—
577C4×C4⋊C4C2316yes—
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⋊C4C2316yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
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×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613#376C2313yes—
614#376C2313yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2313yes—
619C43C2313yes—
620C43C2313yes—
621C43C2313yes—
622C22×Q8C2413yes—
623C22×Q8C2413yes—
624C22×Q8C2413yes—
625C22×Q8C2413yes—
626C22×Q8C2411yescharacteristic
627C4⋊Q8—212no—
628C4⋊Q8—212no—
629C4⋊Q8—212no—
630C4⋊Q8—46no—
631C4⋊Q8—86no—
632C4⋊Q8C2×Q8124yes—
633#125—212no—
634#125—212no—
635#125—212no—
636#125—212no—
637#125—212no—
638#125—212no—
639#125—46no—
640#125—46no—
641#125—412no—
642#125—86no—
643#125—86no—
644#125—86no—
645#125C2×Q8124yes—
646#125C2×Q8124yes—
647C4×Q8—24no—
648C4×Q8—24no—
649C4×Q8—24no—
650C4×Q8—24no—
651C4×Q8—24no—
652C4×Q8—24no—
653C4×Q8—24no—
654C4×Q8—24no—
655C4×Q8—24no—
656C4×Q8—24no—
657C4×Q8—24no—
658C4×Q8—212no—
659C4×Q8—212no—
660C4×Q8—212no—
661C4×Q8—86no—
662C4×Q8C2×Q818yes—
663C4×Q8C2×Q818yes—
664C4×Q8C2×Q8124yes—
665C4×Q8C2×Q818yes—
666C4×Q8#4118yes—
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2413yes—
671C2×C4⋊C4C2413yes—
672C2×C4⋊C4C2413yes—
673C2×C4⋊C4C2413yes—
674C2×C4⋊C4C2413yes—
675C2×C4⋊C4C2413yes—
676C2×C4⋊C4C2413yes—
677C2×C4⋊C4C2413yes—
678C2×C4⋊C4C2413yes—
679C2×C4⋊C4C2413yes—
680C2×C4⋊C4C2413yes—
681C2×C4⋊C4C2413yes—
682C2×C4⋊C4C2413yes—
683C2×C4⋊C4C2413yes—
684C2×C4⋊C4C2413yes—
685C2×C4⋊C4C2413yes—
686C2×C4⋊C4C2413yes—
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2413yes—
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2413yes—
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2416yes—
694C2×C4⋊C4C2416yes—
695C2×C4⋊C4C2416yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2416yes—
698C2×C4⋊C4C2416yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2416yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2416yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2416yes—
710C2×C4⋊C4C2416yes—
711C2×C4⋊C4C2416yes—
712C2×C4⋊C4C2416yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2416yes—
718C2×C4⋊C4C2416yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2416yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2416yes—
753C2×C4⋊C4C2413yes—
754C2×C42C2413yes—
755C2×C42C2413yes—
756C2×C42C2413yes—
757C2×C42C2413yes—
758C2×C42C2413yes—
759C2×C42C2413yes—
760C2×C42C2413yes—
761C2×C42C2413yes—
762C2×C42C2413yes—
763C2×C42C2413yes—
764C2×C42C2413yes—
765C2×C42C2411yescharacteristic
766C2×C42C2413yes—
767C2×C42C2416yes—
768C2×C42C2416yes—
769C2×C42C2413yes—
770C2×C42C2413yes—
771C2×C42C2413yes—
772C2×C42C2416yes—
773C2×C42C2413yes—
774C2×C42C2411yescharacteristic
775C2×C42C2411yescharacteristic
776C2×C42C2413yes—
777C2×C42C2413yes—
778C2×C42C2413yes—
779C2×C42C2413yes—
780C2×C42C2416yes—
781C2×C42C2416yes—
782C2×C42C2416yes—
783C2×C42C2413yes—
784C2×C42C2413yes—
785C2×C42C2413yes—
786C2×C42C2413yes—
787#95C2411yescharacteristic
788#95C2411yescharacteristic
789#95C2411yescharacteristic
790#95C2411yescharacteristic
791#95C2411yescharacteristic
792#95C2411yescharacteristic
793#95C2413yes—
794#95C2413yes—
795#95C2413yes—
796#95C2413yes—
797#95C2413yes—
798#95C2413yes—
799#95C2413yes—
800#95C2413yes—
801#95C2413yes—
802#95C2413yes—
803#95C2413yes—
804#95C2413yes—
805#95C2413yes—
806#95C2413yes—
807#95C2413yes—
808#95C2413yes—
809#95C2413yes—
810#95C2413yes—
811#95C2413yes—
812#95C2411yescharacteristic
813#95C2413yes—
814#95C2413yes—
815#95C2413yes—
816#95C2413yes—
817#95C2416yes—
818#95C2411yescharacteristic
819#95C2411yescharacteristic
820#95C2413yes—
821#95C2411yescharacteristic
822#95C2411yescharacteristic
823#95C2416yes—
824#95C2413yes—
825#95C2416yes—
826#95C2416yes—
827#95C2411yescharacteristic
828#95C2411yescharacteristic
829#95C2411yescharacteristic
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2411yescharacteristic
834#95C2413yes—
835#95C2413yes—
836#95C2411yescharacteristic
837#95C2413yes—
838#95C2413yes—
839#95C2416yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2416yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2416yes—
848#95C2416yes—
849#95C2413yes—
850#95C2416yes—
851#95C2416yes—
852#95C2413yes—
853#95C2416yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2416yes—
867#95C2416yes—
868C2×Q8—26no—
869C2×Q8—26no—
870C2×Q8—26no—
871C2×Q8—43no—
872C2×Q8—43no—
873C2×Q8—43no—
874C2×Q8—43no—
875C2×Q8—43no—
876C2×Q8—43no—
877C2×Q8—43no—
878C2×Q8—43no—
879C2×Q8C22×Q8112yes—
880C2×Q8C22×Q814yes—
881C2×Q8C2×#4114yes—
882C2×Q82−1+414yes—
883C22×C4C2511yescharacteristic
884C22×C4C2511yescharacteristic
885C22×C4C2513yes—
886C22×C4C2511yescharacteristic
887C22×C4C2513yes—
888C22×C4C2513yes—
889C22×C4C2511yescharacteristic
890C22×C4C2511yescharacteristic
891C22×C4C2511yescharacteristic
892C22×C4C2513yes—
893C22×C4C2511yescharacteristic
894C22×C4C2511yescharacteristic
895C22×C4C2511yescharacteristic
896C22×C4C2513yes—
897C22×C4C2513yes—
898C22×C4C2513yes—
899C22×C4C2513yes—
900C22×C4C2513yes—
901C22×C4C2513yes—
902C22×C4C2511yescharacteristic
903C22×C4C2513yes—
904C22×C4C2511yescharacteristic
905C22×C4C2511yescharacteristic
906C22×C4C2513yes—
907C22×C4C2511yescharacteristic
908C22×C4C2513yes—
909C22×C4C2513yes—
910C22×C4C2511yescharacteristic
911C22×C4C2513yes—
912C22×C4C2511yescharacteristic
913C22×C4C2513yes—
914C4⋊C4—22no—
915C4⋊C4—22no—
916C4⋊C4—22no—
917C4⋊C4—26no—
918C4⋊C4—26no—
919C4⋊C4—26no—
920C4⋊C4—26no—
921C4⋊C4—26no—
922C4⋊C4—26no—
923C4⋊C4—26no—
924C4⋊C4—26no—
925C4⋊C4—26no—
926C4⋊C4—26no—
927C4⋊C4—26no—
928C4⋊C4—26no—
929C4⋊C4—212no—
930C4⋊C4—212no—
931C4⋊C4—212no—
932C4⋊C4—26no—
933C4⋊C4—26no—
934C4⋊C4—26no—
935C4⋊C4—26no—
936C4⋊C4—26no—
937C4⋊C4—22no—
938C4⋊C4—26no—
939C4⋊C4—22no—
940C4⋊C4—26no—
941C4⋊C4—26no—
942C4⋊C4—26no—
943C4⋊C4—41no—
944C4⋊C4—41no—
945C4⋊C4—41no—
946C4⋊C4—43no—
947C4⋊C4—43no—
948C4⋊C4—41no—
949C4⋊C4—43no—
950C4⋊C4—43no—
951C4⋊C4—43no—
952C4⋊C4—43no—
953C4⋊C4—41no—
954C4⋊C4—43no—
955C4⋊C4—41no—
956C4⋊C4—43no—
957C4⋊C4—41no—
958C4⋊C4—43no—
959C4⋊C4—43no—
960C4⋊C4—43no—
961C4⋊C4—46no—
962C4⋊C4—41no—
963C4⋊C4—41no—
964C4⋊C4—41no—
965C4⋊C4—43no—
966C4⋊C4—46no—
967C4⋊C4—46no—
968C4⋊C4—43no—
969C4⋊C4—43no—
970C4⋊C4—46no—
971C4⋊C4—43no—
972C4⋊C4—43no—
973C4⋊C4—46no—
974C4⋊C4—46no—
975C4⋊C4—43no—
976C4⋊C4—43no—
977C4⋊C4—46no—
978C4⋊C4—43no—
979C4⋊C4—43no—
980C4⋊C4—43no—
981C4⋊C4—43no—
982C4⋊C4—46no—
983C4⋊C4—43no—
984C4⋊C4—43no—
985C4⋊C4—46no—
986C4⋊C4—43no—
987C4⋊C4—43no—
988C4⋊C4—46no—
989C4⋊C4—46no—
990C4⋊C4—46no—
991C4⋊C4—43no—
992C4⋊C4—43no—
993C4⋊C4C22×Q814yes—
994C4⋊C4C22×Q8112yes—
995C4⋊C4C22×Q8112yes—
996C4⋊C4C22×Q8112yes—
997C4⋊C4C22×Q8112yes—
998C4⋊C4C22×Q8112yes—
999C4⋊C4C22×Q8124yes—
1000C4⋊C4C2×#41112yes—
1001C42—26no—
1002C42—26no—
1003C42—26no—
1004C42—26no—
1005C42—26no—
1006C42—26no—
1007C42—26no—
1008C42—26no—
1009C42—26no—
1010C42—26no—
1011C42—26no—
1012C42—22no—
1013C42—43no—
1014C42—46no—
1015C42—43no—
1016C42—43no—
1017C42—46no—
1018C42—43no—
1019C42—46no—
1020C42—41no—
1021C42—41no—
1022C42—43no—
1023C42—46no—
1024C42—46no—
1025C42—46no—
1026C42—43no—
1027C42—43no—
1028C42—43no—
1029C42—43no—
1030C42C22×Q8112yes—
1031C42C22×Q8112yes—
1032C42C22×Q8112yes—
1033C42C2×#41112yes—
1034C23C2611yescharacteristic
1035Q8—412no—
1036Q8—86no—
1037Q8—86no—
1038Q8—86no—
1039Q8#557116yes—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—23no—
1044C2×C4—21no—
1045C2×C4—23no—
1046C2×C4—23no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—23no—
1051C2×C4—21no—
1052C2×C4—23no—
1053C2×C4—23no—
1054C2×C4—23no—
1055C2×C4—23no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—23no—
1065C2×C4—23no—
1066C2×C4—23no—
1067C2×C4—23no—
1068C2×C4—23no—
1069C2×C4—23no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—23no—
1075C2×C4—23no—
1076C2×C4—23no—
1077C2×C4—23no—
1078C2×C4—23no—
1079C2×C4—21no—
1080C2×C4—23no—
1081C2×C4—23no—
1082C2×C4—23no—
1083C2×C4—23no—
1084C2×C4—21no—
1085C2×C4—23no—
1086C2×C4—21no—
1087C2×C4—23no—
1088C2×C4—23no—
1089C2×C4—23no—
1090C2×C4—21no—
1091C2×C4—23no—
1092C2×C4—23no—
1093C2×C4—23no—
1094C2×C4—23no—
1095C2×C4—23no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—23no—
1099C2×C4—23no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—23no—
1103C2×C4—23no—
1104C2×C4—23no—
1105C2×C4—23no—
1106C2×C4—21no—
1107C2×C4—23no—
1108C2×C4—23no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—23no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4C23×Q812yes—
1122C2×C4C23×Q812yes—
1123C2×C4C23×Q812yes—
1124C2×C4C23×Q816yes—
1125C2×C4C23×Q816yes—
1126C2×C4C23×Q816yes—
1127C2×C4C23×Q816yes—
1128C2×C4C22×#4112yes—
1129C2×C4C22×#4116yes—
1130C2×C4C22×#4116yes—
1131C2×C4C2×2−1+416yes—
1132C2×C4#58512yes—
1133C22C24×Q811yescharacteristic
1134C22C23×#4111yescharacteristic
1135C22C22×2−1+411yescharacteristic
1136C22C2×#58511yescharacteristic
1137C22H(7,𝔽2)11yescharacteristic
1138C222−1+611yescharacteristic
1139C222−1+611yescharacteristic
1140C4—22no—
1141C4—26no—
1142C4—22no—
1143C4—22no—
1144C4—26no—
1145C4—26no—
1146C4—22no—
1147C4—26no—
1148C4—22no—
1149C4—41no—
1150C4—43no—
1151C4—43no—
1152C4—43no—
1153C4—43no—
1154C4—43no—
1155C4—41no—
1156C4—41no—
1157C4—43no—
1158C4—43no—
1159C4—43no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—43no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—43no—
1169C4—43no—
1170C4C2×#557112yes—
1171C2C22×#55711yescharacteristic
1172C2#6285411yescharacteristic
1173C2#6286111yescharacteristic
1174C2#6294911yescharacteristic
1175C2#6300411yescharacteristic
1176C2#6300611yescharacteristic
1177C2#6306111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
241. #557Q8semidirect

Maximal subgroups

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

subgroupindex
#598722
#596722
#596712
#522742
#454262
#452232
#452022
#449532
#449492
#397532
#396822
#396802
#396422
#391832
#391772
#365932
#364752
#364472
#359712
#359572
#358682
#343372
#343362