Finite Group Databasebeta

← #7695732

Subgroups — #7695732

Order 512.

4307 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59681C213yesmaximal
2#59673C213yesmaximal
3#59670C213yesmaximal
4#52274C213yesmaximal
5#45363C213yesmaximal
6#45281C213yesmaximal
7#45202C213yesmaximal
8#45164C213yesmaximal
9#45073C213yesmaximal
10#45044C213yesmaximal
11#39754C213yesmaximal
12#39682C213yesmaximal
13#39680C213yesmaximal
14#39638C213yesmaximal
15#39181C213yesmaximal
16#39177C213yesmaximal
17#36584C211yesmaximal, characteristic
18#36475C211yesmaximal, characteristic
19#36466C211yesmaximal, characteristic
20#35971C211yesmaximal, characteristic
21#35971C211yesmaximal, characteristic
22#35971C211yesmaximal, characteristic
23#35937C211yesmaximal, characteristic
24#35937C211yesmaximal, characteristic
25#35868C211yesmaximal, characteristic
26#34337C211yesmaximal, characteristic
27#34337C211yesmaximal, characteristic
28#34336C211yesmaximal, characteristic
29#34336C211yesmaximal, characteristic
30#34336C211yesmaximal, characteristic
31#34335C211yesmaximal, characteristic
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2211yescharacteristic
36#2864C2213yes—
37#2859C2213yes—
38#2859C2213yes—
39#2809C2213yes—
40#2809C2216yes—
41#2806C2213yes—
42#2805C2213yes—
43#2805C2216yes—
44#2802C2216yes—
45#2802C2216yes—
46#2802C2213yes—
47#2802C2216yes—
48#2802C2213yes—
49#2799C2216yes—
50#2799C2213yes—
51#2799C2213yes—
52#2791C2213yes—
53#2791C2213yes—
54#2774C2216yes—
55#2774C2216yes—
56#2774C2211yescharacteristic
57#2774C2213yes—
58#2774C2216yes—
59#2774C2216yes—
60#2755C2216yes—
61#2755C2213yes—
62#2755C2213yes—
63#2726C2213yes—
64#2713C2216yes—
65#2713C2216yes—
66#2713C2213yes—
67#2713C2213yes—
68#2660C2213yes—
69#2660C2213yes—
70#2647C2213yes—
71#2647C2213yes—
72#2647C2213yes—
73#2647C2213yes—
74#2590C2216yes—
75#2590C2216yes—
76#2590C2216yes—
77#2588C2216yes—
78#2585C2216yes—
79#2585C2216yes—
80#2584C2213yes—
81#2584C2213yes—
82#2584C2216yes—
83#2584C2213yes—
84#2584C2213yes—
85#2581C2216yes—
86#2581C2216yes—
87#2571C2213yes—
88#2571C2213yes—
89#2571C2213yes—
90#2571C2213yes—
91#2571C2213yes—
92#2570C2213yes—
93#2570C2213yes—
94#2570C2213yes—
95#2570C2213yes—
96#2570C2213yes—
97#2570C2213yes—
98#2552C2213yes—
99#2552C2213yes—
100#2551C2213yes—
101#2551C2213yes—
102#2551C2213yes—
103#2551C2213yes—
104#2551C2213yes—
105#2550C2216yes—
106#2550C2213yes—
107#2550C2213yes—
108#2550C2213yes—
109#2550C2213yes—
110#2550C2213yes—
111#2550C2213yes—
112#2546C2213yes—
113#2546C2213yes—
114#2546C2216yes—
115#2520C2216yes—
116#2511C2216yes—
117#2509C2213yes—
118#2509C2213yes—
119#2509C2216yes—
120#2509C2216yes—
121#2509C2213yes—
122#2509C2213yes—
123#2509C2213yes—
124#2509C2213yes—
125#2509C2213yes—
126#2509C2213yes—
127#2509C2213yes—
128#2508C2213yes—
129#2508C2216yes—
130#2508C2213yes—
131#2508C2213yes—
132#2508C2216yes—
133#2508C2213yes—
134#2508C2213yes—
135#2508C2213yes—
136#2508C2213yes—
137#2507C2213yes—
138#2507C2213yes—
139#2507C2213yes—
140#2507C2213yes—
141#2507C2213yes—
142#2506C2213yes—
143#2506C2213yes—
144#2506C2213yes—
145#2462C2216yes—
146#2453C2216yes—
147#2451C2216yes—
148#2446C2216yes—
149#2402C2213yes—
150#2402C2213yes—
151#2402C2213yes—
152#2402C2213yes—
153#2399C2213yes—
154#2399C2213yes—
155#2370C2213yes—
156#2370C2213yes—
157#2370C2213yes—
158#2370C2213yes—
159#2370C2213yes—
160#2370C2213yes—
161#2370C2213yes—
162#2370C2213yes—
163#2370C2213yes—
164#2370C2213yes—
165#2369C2213yes—
166#2369C2213yes—
167#2369C2213yes—
168#2369C2213yes—
169#2365C2213yes—
170#2365C2216yes—
171#2365C2213yes—
172#2365C2213yes—
173#2365C2213yes—
174#2355C2213yes—
175#2355C2213yes—
176#2355C2213yes—
177#2355C2213yes—
178#2351C2211yescharacteristic
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182#2351C2211yescharacteristic
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190Q8×C4⋊C4C2213yes—
191Q8×C4⋊C4C2211yescharacteristic
192Q8×C4⋊C4C2211yescharacteristic
193Q8×C4⋊C4C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2213yes—
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×C4⋊Q8C2213yes—
217C4×C4⋊Q8C2213yes—
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
238Q82—28no—
239#557—28no—
240#557—28no—
241#557Q8116yescomplemented
242C2×C4⋊Q8C2313yes—
243C2×C4⋊Q8C2313yes—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2316yes—
249C2×C4⋊Q8C2316yes—
250C2×C4⋊Q8C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2316yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×C4×Q8C2313yes—
261C2×C4×Q8C2313yes—
262C2×C4×Q8C2313yes—
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
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×Q8C2316yes—
275C2×C4×Q8C2316yes—
276C2×C4×Q8C2316yes—
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2313yes—
281C2×C4×Q8C2311yescharacteristic
282#400C2313yes—
283#400C2316yes—
284#400C2316yes—
285#400C2316yes—
286#400C2316yes—
287#400C2316yes—
288#400C2313yes—
289#400C2313yes—
290#400C2313yes—
291#400C2316yes—
292#400C2316yes—
293#400C2316yes—
294#400C2316yes—
295#400C2316yes—
296#400C2313yes—
297#400C2313yes—
298#400C2316yes—
299#400C2316yes—
300#400C2313yes—
301#400C2316yes—
302#400C2311yescharacteristic
303#400C2311yescharacteristic
304#400C2311yescharacteristic
305#400C2313yes—
306#400C2313yes—
307#400C2313yes—
308#400C2313yes—
309#400C2313yes—
310#400C2313yes—
311#398C2313yes—
312#398C2313yes—
313#398C2313yes—
314#398C2316yes—
315#398C2316yes—
316#398C2316yes—
317#398C2316yes—
318#398C2316yes—
319#398C2316yes—
320#398C2316yes—
321#398C2313yes—
322#398C2316yes—
323#398C2316yes—
324#398C2316yes—
325#398C2313yes—
326#398C2313yes—
327#398C2313yes—
328#398C2316yes—
329#398C2313yes—
330#398C2313yes—
331#398C2313yes—
332#398C2313yes—
333#398C2313yes—
334#398C2313yes—
335#398C2313yes—
336#398C2311yescharacteristic
337#398C2313yes—
338#398C2313yes—
339#398C2313yes—
340#398C2313yes—
341#398C2313yes—
342#398C2313yes—
343#398C2313yes—
344#398C2313yes—
345#398C2313yes—
346#395C2313yes—
347#395C2316yes—
348#395C2316yes—
349#395C2316yes—
350#395C2313yes—
351#395C2313yes—
352#395C2316yes—
353#395C2316yes—
354#395C2316yes—
355#395C2311yescharacteristic
356#395C2311yescharacteristic
357#395C2313yes—
358#395C2313yes—
359#395C2313yes—
360#391C2313yes—
361#391C2313yes—
362#391C2316yes—
363#391C2313yes—
364#391C2313yes—
365#391C2313yes—
366#391C2313yes—
367#391C2316yes—
368#391C2316yes—
369#391C2313yes—
370#391C2313yes—
371#391C2313yes—
372#391C2316yes—
373#391C2316yes—
374#391C2316yes—
375#391C2316yes—
376#391C2313yes—
377#391C2313yes—
378#391C2313yes—
379#391C2313yes—
380#391C2316yes—
381#391C2311yescharacteristic
382#389C2313yes—
383#389C2313yes—
384#389C2313yes—
385#389C2313yes—
386#389C2313yes—
387#389C2313yes—
388#389C2313yes—
389#389C2313yes—
390#389C2313yes—
391#389C2313yes—
392#389C2311yescharacteristic
393#389C2313yes—
394#389C2313yes—
395#389C2313yes—
396#389C2313yes—
397#389C2313yes—
398#389C2316yes—
399#389C2313yes—
400#389C2316yes—
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#389C2316yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2316yes—
421#389C2313yes—
422#389C2313yes—
423#389C2316yes—
424#389C2316yes—
425#389C2316yes—
426#389C2316yes—
427#389C2316yes—
428#389C2316yes—
429#389C2313yes—
430#389C2316yes—
431#389C2316yes—
432#389C2313yes—
433#389C2313yes—
434#389C2316yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2316yes—
439#389C2313yes—
440#389C2316yes—
441#389C2316yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2316yes—
446#389C2313yes—
447#389C2316yes—
448#389C2313yes—
449#389C2316yes—
450#389C2313yes—
451#389C2313yes—
452#389C2316yes—
453#389C2316yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2316yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2313yes—
466#389C2311yescharacteristic
467#389C2311yescharacteristic
468#387C2311yescharacteristic
469#387C2313yes—
470#387C2313yes—
471#387C2313yes—
472#387C2313yes—
473#387C2313yes—
474#387C2316yes—
475#387C2313yes—
476#387C2316yes—
477#387C2316yes—
478#387C2313yes—
479#387C2313yes—
480#387C2313yes—
481#387C2313yes—
482#387C2316yes—
483#387C2316yes—
484#387C2316yes—
485#387C2316yes—
486#387C2316yes—
487#387C2316yes—
488#387C2316yes—
489#387C2316yes—
490#387C2316yes—
491#387C2316yes—
492#387C2316yes—
493#387C2313yes—
494#387C2313yes—
495#387C2313yes—
496#387C2316yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2313yes—
502#387C2313yes—
503#387C2313yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2313yes—
508#387C2316yes—
509#387C2316yes—
510#387C2316yes—
511#387C2313yes—
512#387C2316yes—
513#387C2313yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2313yes—
518#387C2313yes—
519#387C2313yes—
520#387C2313yes—
521#387C2313yes—
522#387C2313yes—
523#387C2311yescharacteristic
524#387C2311yescharacteristic
525#387C2311yescharacteristic
526#384C2313yes—
527#384C2313yes—
528#384C2313yes—
529#384C2313yes—
530#384C2313yes—
531#384C2313yes—
532#384C2313yes—
533#384C2313yes—
534#384C2313yes—
535#384C2313yes—
536#384C2313yes—
537#382C2311yescharacteristic
538#382C2313yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2313yes—
544#382C2313yes—
545#382C2313yes—
546#382C2313yes—
547#382C2313yes—
548#382C2313yes—
549#382C2316yes—
550#382C2313yes—
551#382C2313yes—
552#382C2316yes—
553#382C2316yes—
554#382C2316yes—
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⋊C4C2316yes—
566C4×C4⋊C4C2316yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2316yes—
571C4×C4⋊C4C2316yes—
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⋊C4C2316yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2316yes—
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×Q8C2411yescharacteristic
624C22×Q8C2413yes—
625C22×Q8C2416yes—
626C22×Q8C2413yes—
627C22×Q8C2411yescharacteristic
628C4⋊Q8—212no—
629C4⋊Q8—212no—
630C4⋊Q8—212no—
631C4⋊Q8—212no—
632C4⋊Q8—212no—
633C4⋊Q8—46no—
634C4⋊Q8—412no—
635C4⋊Q8—86no—
636C4⋊Q8C2×Q8124yes—
637#125—212no—
638#125—212no—
639#125—212no—
640#125—212no—
641#125—46no—
642#125—46no—
643#125—86no—
644#125C2×Q8124yes—
645#125C2×Q8124yes—
646C4×Q8—24no—
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—212no—
658C4×Q8—212no—
659C4×Q8—212no—
660C4×Q8—86no—
661C4×Q8—86no—
662C4×Q8—86no—
663C4×Q8C2×Q818yes—
664C4×Q8C2×Q818yes—
665C4×Q8C2×Q8124yes—
666C4×Q8C2×Q818yes—
667C4×Q8#4118yes—
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⋊C4C2413yes—
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2416yes—
690C2×C4⋊C4C2416yes—
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2416yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2416yes—
701C2×C4⋊C4C2416yes—
702C2×C4⋊C4C2416yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2416yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2416yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2416yes—
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2416yes—
734C2×C4⋊C4C2416yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2416yes—
751C2×C4⋊C4C2413yes—
752C2×C42C2413yes—
753C2×C42C2413yes—
754C2×C42C2413yes—
755C2×C42C2413yes—
756C2×C42C2413yes—
757C2×C42C2413yes—
758C2×C42C2413yes—
759C2×C42C2413yes—
760C2×C42C2413yes—
761C2×C42C2413yes—
762C2×C42C2413yes—
763C2×C42C2411yescharacteristic
764C2×C42C2413yes—
765C2×C42C2413yes—
766C2×C42C2413yes—
767C2×C42C2416yes—
768C2×C42C2416yes—
769C2×C42C2416yes—
770C2×C42C2416yes—
771C2×C42C2413yes—
772C2×C42C2413yes—
773C2×C42C2416yes—
774C2×C42C2411yescharacteristic
775C2×C42C2411yescharacteristic
776C2×C42C2413yes—
777C2×C42C2413yes—
778C2×C42C2413yes—
779C2×C42C2413yes—
780C2×C42C2416yes—
781C2×C42C2413yes—
782C2×C42C2413yes—
783C2×C42C2413yes—
784C2×C42C2413yes—
785#95C2411yescharacteristic
786#95C2411yescharacteristic
787#95C2411yescharacteristic
788#95C2411yescharacteristic
789#95C2411yescharacteristic
790#95C2411yescharacteristic
791#95C2413yes—
792#95C2413yes—
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#95C2411yescharacteristic
810#95C2413yes—
811#95C2413yes—
812#95C2413yes—
813#95C2411yescharacteristic
814#95C2411yescharacteristic
815#95C2411yescharacteristic
816#95C2411yescharacteristic
817#95C2413yes—
818#95C2413yes—
819#95C2413yes—
820#95C2411yescharacteristic
821#95C2411yescharacteristic
822#95C2416yes—
823#95C2416yes—
824#95C2416yes—
825#95C2411yescharacteristic
826#95C2411yescharacteristic
827#95C2413yes—
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2411yescharacteristic
832#95C2411yescharacteristic
833#95C2411yescharacteristic
834#95C2413yes—
835#95C2413yes—
836#95C2416yes—
837#95C2413yes—
838#95C2416yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2416yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2416yes—
850#95C2413yes—
851#95C2416yes—
852#95C2416yes—
853#95C2416yes—
854#95C2416yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2416yes—
865#95C2416yes—
866#95C2416yes—
867#95C2416yes—
868C2×Q8—22no—
869C2×Q8—26no—
870C2×Q8—26no—
871C2×Q8—212no—
872C2×Q8—26no—
873C2×Q8—43no—
874C2×Q8—43no—
875C2×Q8—41no—
876C2×Q8—43no—
877C2×Q8—41no—
878C2×Q8—46no—
879C2×Q8—43no—
880C2×Q8—46no—
881C2×Q8—43no—
882C2×Q8C22×Q8112yes—
883C2×Q8C22×Q814yes—
884C2×Q8C2×#4114yes—
885C2×Q82−1+414yes—
886C22×C4C2511yescharacteristic
887C22×C4C2511yescharacteristic
888C22×C4C2511yescharacteristic
889C22×C4C2513yes—
890C22×C4C2513yes—
891C22×C4C2511yescharacteristic
892C22×C4C2511yescharacteristic
893C22×C4C2511yescharacteristic
894C22×C4C2511yescharacteristic
895C22×C4C2513yes—
896C22×C4C2513yes—
897C22×C4C2511yescharacteristic
898C22×C4C2513yes—
899C22×C4C2513yes—
900C22×C4C2511yescharacteristic
901C22×C4C2513yes—
902C22×C4C2511yescharacteristic
903C22×C4C2513yes—
904C22×C4C2513yes—
905C22×C4C2513yes—
906C22×C4C2513yes—
907C22×C4C2511yescharacteristic
908C22×C4C2511yescharacteristic
909C22×C4C2513yes—
910C22×C4C2511yescharacteristic
911C22×C4C2513yes—
912C22×C4C2513yes—
913C22×C4C2511yescharacteristic
914C22×C4C2513yes—
915C22×C4C2511yescharacteristic
916C22×C4C2513yes—
917C4⋊C4—22no—
918C4⋊C4—22no—
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—26no—
930C4⋊C4—26no—
931C4⋊C4—26no—
932C4⋊C4—212no—
933C4⋊C4—212no—
934C4⋊C4—26no—
935C4⋊C4—26no—
936C4⋊C4—26no—
937C4⋊C4—26no—
938C4⋊C4—26no—
939C4⋊C4—22no—
940C4⋊C4—26no—
941C4⋊C4—26no—
942C4⋊C4—26no—
943C4⋊C4—22no—
944C4⋊C4—41no—
945C4⋊C4—41no—
946C4⋊C4—43no—
947C4⋊C4—43no—
948C4⋊C4—41no—
949C4⋊C4—41no—
950C4⋊C4—43no—
951C4⋊C4—43no—
952C4⋊C4—46no—
953C4⋊C4—46no—
954C4⋊C4—43no—
955C4⋊C4—43no—
956C4⋊C4—41no—
957C4⋊C4—41no—
958C4⋊C4—43no—
959C4⋊C4—43no—
960C4⋊C4—43no—
961C4⋊C4—43no—
962C4⋊C4—46no—
963C4⋊C4—43no—
964C4⋊C4—43no—
965C4⋊C4—41no—
966C4⋊C4—43no—
967C4⋊C4—41no—
968C4⋊C4—43no—
969C4⋊C4—43no—
970C4⋊C4—46no—
971C4⋊C4—43no—
972C4⋊C4—43no—
973C4⋊C4—46no—
974C4⋊C4—46no—
975C4⋊C4—46no—
976C4⋊C4—43no—
977C4⋊C4—43no—
978C4⋊C4—43no—
979C4⋊C4—43no—
980C4⋊C4—43no—
981C4⋊C4—43no—
982C4⋊C4—43no—
983C4⋊C4—43no—
984C4⋊C4—43no—
985C4⋊C4—43no—
986C4⋊C4—46no—
987C4⋊C4—43no—
988C4⋊C4—46no—
989C4⋊C4—46no—
990C4⋊C4—43no—
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—46no—
1014C42—43no—
1015C42—43no—
1016C42—43no—
1017C42—41no—
1018C42—43no—
1019C42—41no—
1020C42—43no—
1021C42—43no—
1022C42—46no—
1023C42—46no—
1024C42—43no—
1025C42—46no—
1026C42—46no—
1027C42—43no—
1028C42—46no—
1029C42—43no—
1030C42C22×Q8112yes—
1031C42C22×Q8112yes—
1032C42C22×Q8112yes—
1033C42C2×#41112yes—
1034C23C2611yescharacteristic
1035Q8—412no—
1036Q8—412no—
1037Q8—44no—
1038Q8—86no—
1039Q8—812no—
1040Q8#557116yes—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—23no—
1044C2×C4—21no—
1045C2×C4—23no—
1046C2×C4—23no—
1047C2×C4—23no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—23no—
1051C2×C4—21no—
1052C2×C4—23no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—23no—
1057C2×C4—23no—
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—21no—
1075C2×C4—23no—
1076C2×C4—23no—
1077C2×C4—23no—
1078C2×C4—23no—
1079C2×C4—23no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—23no—
1083C2×C4—23no—
1084C2×C4—23no—
1085C2×C4—21no—
1086C2×C4—23no—
1087C2×C4—23no—
1088C2×C4—21no—
1089C2×C4—23no—
1090C2×C4—23no—
1091C2×C4—21no—
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—23no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—23no—
1104C2×C4—21no—
1105C2×C4—23no—
1106C2×C4—23no—
1107C2×C4—21no—
1108C2×C4—23no—
1109C2×C4—21no—
1110C2×C4—23no—
1111C2×C4—21no—
1112C2×C4—23no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—23no—
1116C2×C4—21no—
1117C2×C4—23no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4C23×Q812yes—
1123C2×C4C23×Q812yes—
1124C2×C4C23×Q812yes—
1125C2×C4C23×Q816yes—
1126C2×C4C23×Q816yes—
1127C2×C4C23×Q816yes—
1128C2×C4C23×Q816yes—
1129C2×C4C22×#4112yes—
1130C2×C4C22×#4116yes—
1131C2×C4C22×#4116yes—
1132C2×C4C2×2−1+416yes—
1133C2×C4#58512yes—
1134C22C24×Q811yescharacteristic
1135C22C23×#4111yescharacteristic
1136C22C22×2−1+411yescharacteristic
1137C22C2×#58511yescharacteristic
1138C22H(7,𝔽2)11yescharacteristic
1139C222−1+611yescharacteristic
1140C222−1+611yescharacteristic
1141C4—22no—
1142C4—26no—
1143C4—22no—
1144C4—26no—
1145C4—22no—
1146C4—22no—
1147C4—26no—
1148C4—26no—
1149C4—22no—
1150C4—43no—
1151C4—43no—
1152C4—43no—
1153C4—43no—
1154C4—41no—
1155C4—41no—
1156C4—41no—
1157C4—43no—
1158C4—43no—
1159C4—43no—
1160C4—41no—
1161C4—41no—
1162C4—43no—
1163C4—43no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—41no—
1169C4—43no—
1170C4—43no—
1171C4C2×#557112yes—
1172C2C22×#55711yescharacteristic
1173C2#6285011yescharacteristic
1174C2#6285411yescharacteristic
1175C2#6295311yescharacteristic
1176C2#6300411yescharacteristic
1177C2#6300811yescharacteristic
1178C2#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
#596812
#596732
#596702
#522742
#453632
#452812
#452022
#451642
#450732
#450442
#397542
#396822
#396802
#396382
#391812
#391772
#365842
#364752
#364662
#359712
#359372
#358682
#343372
#343362
#343352