Finite Group Databasebeta

← #7687547

Subgroups — #7687547

Order 512.

4433 conjugacy classes of subgroups.

The subgroup lattice has 1195 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59681C213yesmaximal
2#59671C213yesmaximal
3#59670C213yesmaximal
4#59669C213yesmaximal
5#59668C213yesmaximal
6#45363C213yesmaximal
7#45044C213yesmaximal
8#44982C213yesmaximal
9#44953C213yesmaximal
10#39749C213yesmaximal
11#39682C213yesmaximal
12#39680C213yesmaximal
13#39176C213yesmaximal
14#36567C213yesmaximal
15Q8×#125C211yesmaximal, characteristic
16#36497C213yesmaximal
17#36475C211yesmaximal, characteristic
18#36475C211yesmaximal, characteristic
19#36475C211yesmaximal, characteristic
20#36466C211yesmaximal, characteristic
21#35937C211yesmaximal, characteristic
22#35937C211yesmaximal, characteristic
23#35868C211yesmaximal, characteristic
24#35868C211yesmaximal, characteristic
25#34920C213yesmaximal
26#34337C211yesmaximal, characteristic
27#34336C211yesmaximal, characteristic
28#34336C211yesmaximal, characteristic
29#34336C211yesmaximal, characteristic
30C4×Q82C211yesmaximal, characteristic
31C4×#557C211yesmaximal, characteristic
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2211yescharacteristic
36#2864C2213yes—
37#2864C2213yes—
38#2864C2213yes—
39#2859C2213yes—
40#2859C2213yes—
41#2809C2216yes—
42#2806C2216yes—
43#2806C2216yes—
44#2805C2216yes—
45#2802C2216yes—
46#2802C2216yes—
47#2802C2216yes—
48#2799C2216yes—
49#2774C2216yes—
50#2755C2216yes—
51#2726C2216yes—
52#2726C2216yes—
53#2713C2216yes—
54#2713C2216yes—
55#2660C2213yes—
56#2660C2213yes—
57#2647C2213yes—
58#2647C2213yes—
59#2590C2216yes—
60#2590C2216yes—
61#2590C2213yes—
62#2590C2216yes—
63#2590C2213yes—
64#2588C2216yes—
65#2588C2213yes—
66#2588C2213yes—
67#2585C2216yes—
68#2585C2216yes—
69#2584C2213yes—
70#2584C2213yes—
71#2584C2216yes—
72#2584C2213yes—
73#2584C2213yes—
74#2584C2213yes—
75#2581C2213yes—
76#2570C2213yes—
77#2570C2213yes—
78#2570C2213yes—
79#2570C2213yes—
80#2570C2213yes—
81#2570C2213yes—
82#2570C2213yes—
83#2570C2213yes—
84#2565C2213yes—
85#2552C2213yes—
86#2552C2213yes—
87#2552C2213yes—
88#2552C2213yes—
89#2552C2213yes—
90#2551C2213yes—
91#2551C2213yes—
92#2551C2213yes—
93#2551C2213yes—
94#2551C2213yes—
95#2550C2216yes—
96#2550C2213yes—
97#2550C2213yes—
98#2550C2213yes—
99#2550C2213yes—
100#2550C2213yes—
101#2550C2213yes—
102#2550C2213yes—
103#2546C2213yes—
104#2546C2213yes—
105#2546C2216yes—
106#2520C2216yes—
107#2520C2213yes—
108#2520C2213yes—
109#2511C2216yes—
110#2509C2213yes—
111#2509C2213yes—
112#2509C2213yes—
113#2509C2213yes—
114#2509C2213yes—
115#2508C2213yes—
116#2508C2213yes—
117#2508C2213yes—
118#2508C2213yes—
119#2507C2213yes—
120#2507C2213yes—
121#2507C2213yes—
122#2507C2213yes—
123#2507C2213yes—
124#2507C2213yes—
125#2507C2213yes—
126#2507C2213yes—
127#2507C2213yes—
128#2506C2213yes—
129#2506C2213yes—
130#2506C2213yes—
131#2506C2213yes—
132#2506C2213yes—
133#2506C2213yes—
134#2506C2213yes—
135#2506C2213yes—
136#2462C2216yes—
137#2462C2216yes—
138#2462C2216yes—
139#2462C2211yescharacteristic
140#2462C2213yes—
141#2462C2216yes—
142#2453C2213yes—
143#2453C2216yes—
144#2451C2216yes—
145#2451C2213yes—
146#2446C2216yes—
147#2402C2213yes—
148#2402C2213yes—
149#2399C2213yes—
150#2399C2213yes—
151#2370C2213yes—
152#2370C2213yes—
153#2370C2216yes—
154#2370C2213yes—
155#2370C2213yes—
156#2370C2213yes—
157#2370C2216yes—
158#2370C2213yes—
159#2370C2213yes—
160#2370C2213yes—
161#2370C2213yes—
162#2370C2213yes—
163#2369C2213yes—
164#2369C2213yes—
165#2369C2213yes—
166#2369C2213yes—
167#2369C2213yes—
168#2369C2213yes—
169#2365C2213yes—
170#2365C2216yes—
171#2365C2213yes—
172#2355C2213yes—
173#2355C2213yes—
174#2355C2213yes—
175#2355C2213yes—
176#2351C2211yescharacteristic
177#2351C2211yescharacteristic
178#2351C2211yescharacteristic
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182#2351C2211yescharacteristic
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186Q8×C4⋊C4C2211yescharacteristic
187Q8×C4⋊C4C2211yescharacteristic
188Q8×C4⋊C4C2211yescharacteristic
189Q8×C4⋊C4C2211yescharacteristic
190Q8×C4⋊C4C2211yescharacteristic
191Q8×C4⋊C4C2211yescharacteristic
192Q8×C4⋊C4C2211yescharacteristic
193Q8×C4⋊C4C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2213yes—
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2213yes—
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200#2331C2213yes—
201#2331C2213yes—
202#2331C2213yes—
203#2330C2213yes—
204#2330C2213yes—
205#2330C2213yes—
206#2330C2213yes—
207#2330C2213yes—
208C4×C4⋊Q8C2213yes—
209C4×C4⋊Q8C2213yes—
210C4×C4⋊Q8C2213yes—
211C4×C4⋊Q8C2213yes—
212C4×C4⋊Q8C2213yes—
213C4×C4⋊Q8C2213yes—
214C4×#125C2213yes—
215C4×#125C2213yes—
216C4×#125C2213yes—
217C4×#125C2213yes—
218C4×#125C2213yes—
219C4×#125C2213yes—
220C4×#125C2213yes—
221C4×#125C2213yes—
222C4×#125C2213yes—
223#2295C2213yes—
224#2295C2213yes—
225#2295C2213yes—
226#2295C2213yes—
227#2276C2211yescharacteristic
228#2276C2211yescharacteristic
229#2276C2211yescharacteristic
230#2276C2211yescharacteristic
231C42×Q8C2211yescharacteristic
232C42×Q8C2211yescharacteristic
233C42×Q8C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2213yes—
236C42×Q8C2213yes—
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×#125C2311yescharacteristic
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2316yes—
260C2×#125C2316yes—
261C2×#125C2316yes—
262C2×#125C2313yes—
263C2×#125C2313yes—
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×Q8C2313yes—
280C2×C4×Q8C2313yes—
281C2×C4×Q8C2313yes—
282C2×C4×Q8C2316yes—
283C2×C4×Q8C2316yes—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2311yescharacteristic
289#400C2313yes—
290#400C2313yes—
291#400C2316yes—
292#400C2316yes—
293#400C2316yes—
294#400C2316yes—
295#400C2316yes—
296#400C2316yes—
297#400C2313yes—
298#400C2316yes—
299#400C2313yes—
300#400C2313yes—
301#400C2316yes—
302#400C2313yes—
303#400C2313yes—
304#400C2313yes—
305#398C2311yescharacteristic
306#398C2313yes—
307#398C2313yes—
308#398C2313yes—
309#398C2316yes—
310#398C2316yes—
311#398C2316yes—
312#398C2316yes—
313#398C2316yes—
314#398C2316yes—
315#398C2316yes—
316#398C2316yes—
317#398C2316yes—
318#398C2316yes—
319#398C2316yes—
320#398C2316yes—
321#398C2316yes—
322#398C2313yes—
323#398C2313yes—
324#398C2313yes—
325#398C2316yes—
326#398C2316yes—
327#398C2313yes—
328#398C2313yes—
329#398C2313yes—
330#398C2313yes—
331#398C2313yes—
332#398C2313yes—
333#398C2313yes—
334#398C2313yes—
335#398C2316yes—
336#398C2311yescharacteristic
337#398C2316yes—
338#398C2316yes—
339#395C2311yescharacteristic
340#395C2313yes—
341#395C2311yescharacteristic
342#395C2313yes—
343#395C2313yes—
344#395C2316yes—
345#395C2316yes—
346#395C2313yes—
347#395C2316yes—
348#395C2313yes—
349#395C2313yes—
350#395C2316yes—
351#395C2316yes—
352#395C2316yes—
353#391C2313yes—
354#391C2313yes—
355#391C2316yes—
356#391C2313yes—
357#391C2316yes—
358#391C2316yes—
359#391C2316yes—
360#391C2313yes—
361#391C2313yes—
362#391C2313yes—
363#391C2313yes—
364#391C2313yes—
365#391C2316yes—
366#391C2316yes—
367#391C2316yes—
368#391C2313yes—
369#391C2316yes—
370#391C2316yes—
371#391C2313yes—
372#389C2313yes—
373#389C2313yes—
374#389C2313yes—
375#389C2313yes—
376#389C2313yes—
377#389C2313yes—
378#389C2313yes—
379#389C2313yes—
380#389C2313yes—
381#389C2313yes—
382#389C2313yes—
383#389C2313yes—
384#389C2313yes—
385#389C2313yes—
386#389C2313yes—
387#389C2313yes—
388#389C2313yes—
389#389C2313yes—
390#389C2311yescharacteristic
391#389C2313yes—
392#389C2313yes—
393#389C2313yes—
394#389C2313yes—
395#389C2316yes—
396#389C2313yes—
397#389C2316yes—
398#389C2316yes—
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2316yes—
405#389C2316yes—
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#389C2316yes—
420#389C2316yes—
421#389C2316yes—
422#389C2316yes—
423#389C2316yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2316yes—
428#389C2316yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2316yes—
436#389C2313yes—
437#389C2316yes—
438#389C2316yes—
439#389C2313yes—
440#389C2316yes—
441#389C2313yes—
442#389C2316yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2316yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2316yes—
453#389C2316yes—
454#389C2316yes—
455#389C2313yes—
456#389C2311yescharacteristic
457#387C2311yescharacteristic
458#387C2311yescharacteristic
459#387C2311yescharacteristic
460#387C2313yes—
461#387C2313yes—
462#387C2313yes—
463#387C2313yes—
464#387C2313yes—
465#387C2313yes—
466#387C2313yes—
467#387C2313yes—
468#387C2313yes—
469#387C2313yes—
470#387C2313yes—
471#387C2313yes—
472#387C2316yes—
473#387C2316yes—
474#387C2316yes—
475#387C2316yes—
476#387C2316yes—
477#387C2313yes—
478#387C2316yes—
479#387C2313yes—
480#387C2313yes—
481#387C2316yes—
482#387C2313yes—
483#387C2313yes—
484#387C2313yes—
485#387C2316yes—
486#387C2316yes—
487#387C2316yes—
488#387C2316yes—
489#387C2316yes—
490#387C2316yes—
491#387C2316yes—
492#387C2313yes—
493#387C2313yes—
494#387C2316yes—
495#387C2316yes—
496#387C2316yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2311yescharacteristic
505#387C2313yes—
506#387C2316yes—
507#387C2313yes—
508#387C2313yes—
509#387C2311yescharacteristic
510#387C2313yes—
511#387C2316yes—
512#387C2313yes—
513#387C2313yes—
514#387C2316yes—
515#387C2316yes—
516#387C2311yescharacteristic
517#384C2313yes—
518#384C2313yes—
519#384C2313yes—
520#384C2313yes—
521#384C2313yes—
522#384C2313yes—
523#384C2313yes—
524#384C2313yes—
525#384C2313yes—
526#384C2313yes—
527#384C2313yes—
528#384C2313yes—
529#384C2313yes—
530#382C2313yes—
531#382C2313yes—
532#382C2313yes—
533#382C2313yes—
534#382C2313yes—
535#382C2313yes—
536#382C2313yes—
537#382C2313yes—
538#382C2313yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2313yes—
544C4×C4⋊C4C2316yes—
545C4×C4⋊C4C2313yes—
546C4×C4⋊C4C2313yes—
547C4×C4⋊C4C2313yes—
548C4×C4⋊C4C2313yes—
549C4×C4⋊C4C2313yes—
550C4×C4⋊C4C2313yes—
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⋊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⋊C4C2316yes—
573C4×C4⋊C4C2316yes—
574C4×C4⋊C4C2316yes—
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⋊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⋊C4C2311yescharacteristic
613#376C2313yes—
614#376C2313yes—
615#376C2313yes—
616#376C2313yes—
617C43C2313yes—
618C43C2313yes—
619C43C2313yes—
620C43C2313yes—
621C43C2313yes—
622C22×Q8C2411yescharacteristic
623C22×Q8C2413yes—
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—24no—
640#125—212no—
641#125—212no—
642#125—212no—
643#125—46no—
644#125—412no—
645#125—46no—
646#125—86no—
647#125—86no—
648#125C2×Q8124yes—
649#125C2×Q8124yes—
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—24no—
659C4×Q8—24no—
660C4×Q8—24no—
661C4×Q8—24no—
662C4×Q8—212no—
663C4×Q8—212no—
664C4×Q8—212no—
665C4×Q8—46no—
666C4×Q8—46no—
667C4×Q8—46no—
668C4×Q8—86no—
669C4×Q8—86no—
670C4×Q8C2×Q818yes—
671C4×Q8C2×Q818yes—
672C4×Q8C2×Q8124yes—
673C4×Q8C2×Q818yes—
674C4×Q8#4118yes—
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
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⋊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⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2416yes—
706C2×C4⋊C4C2416yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2416yes—
721C2×C4⋊C4C2416yes—
722C2×C4⋊C4C2416yes—
723C2×C4⋊C4C2416yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2416yes—
734C2×C4⋊C4C2416yes—
735C2×C4⋊C4C2416yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2416yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2416yes—
751C2×C4⋊C4C2416yes—
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2416yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2411yescharacteristic
761C2×C42C2411yescharacteristic
762C2×C42C2413yes—
763C2×C42C2413yes—
764C2×C42C2413yes—
765C2×C42C2413yes—
766C2×C42C2413yes—
767C2×C42C2413yes—
768C2×C42C2413yes—
769C2×C42C2411yescharacteristic
770C2×C42C2413yes—
771C2×C42C2411yescharacteristic
772C2×C42C2411yescharacteristic
773C2×C42C2413yes—
774C2×C42C2413yes—
775C2×C42C2413yes—
776C2×C42C2413yes—
777C2×C42C2411yescharacteristic
778C2×C42C2413yes—
779C2×C42C2413yes—
780C2×C42C2413yes—
781C2×C42C2413yes—
782C2×C42C2413yes—
783C2×C42C2416yes—
784C2×C42C2416yes—
785C2×C42C2413yes—
786C2×C42C2413yes—
787C2×C42C2413yes—
788C2×C42C2413yes—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2416yes—
794C2×C42C2413yes—
795C2×C42C2416yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2413yes—
800#95C2411yescharacteristic
801#95C2411yescharacteristic
802#95C2411yescharacteristic
803#95C2411yescharacteristic
804#95C2413yes—
805#95C2413yes—
806#95C2413yes—
807#95C2413yes—
808#95C2413yes—
809#95C2413yes—
810#95C2413yes—
811#95C2413yes—
812#95C2413yes—
813#95C2413yes—
814#95C2413yes—
815#95C2413yes—
816#95C2411yescharacteristic
817#95C2413yes—
818#95C2411yescharacteristic
819#95C2411yescharacteristic
820#95C2411yescharacteristic
821#95C2411yescharacteristic
822#95C2413yes—
823#95C2413yes—
824#95C2413yes—
825#95C2413yes—
826#95C2413yes—
827#95C2413yes—
828#95C2413yes—
829#95C2411yescharacteristic
830#95C2411yescharacteristic
831#95C2413yes—
832#95C2416yes—
833#95C2413yes—
834#95C2411yescharacteristic
835#95C2411yescharacteristic
836#95C2413yes—
837#95C2416yes—
838#95C2413yes—
839#95C2413yes—
840#95C2411yescharacteristic
841#95C2413yes—
842#95C2413yes—
843#95C2416yes—
844#95C2416yes—
845#95C2416yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2416yes—
854#95C2413yes—
855#95C2416yes—
856#95C2416yes—
857#95C2413yes—
858#95C2416yes—
859#95C2413yes—
860#95C2416yes—
861#95C2416yes—
862#95C2416yes—
863#95C2416yes—
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2416yes—
874#95C2416yes—
875C2×Q8—22no—
876C2×Q8—26no—
877C2×Q8—26no—
878C2×Q8—212no—
879C2×Q8—22no—
880C2×Q8—22no—
881C2×Q8—26no—
882C2×Q8—43no—
883C2×Q8—43no—
884C2×Q8—43no—
885C2×Q8—46no—
886C2×Q8—43no—
887C2×Q8—46no—
888C2×Q8—43no—
889C2×Q8C22×Q8112yes—
890C2×Q8C22×Q814yes—
891C2×Q8C2×#4114yes—
892C2×Q82−1+414yes—
893C22×C4C2511yescharacteristic
894C22×C4C2511yescharacteristic
895C22×C4C2513yes—
896C22×C4C2511yescharacteristic
897C22×C4C2511yescharacteristic
898C22×C4C2513yes—
899C22×C4C2513yes—
900C22×C4C2511yescharacteristic
901C22×C4C2513yes—
902C22×C4C2513yes—
903C22×C4C2511yescharacteristic
904C22×C4C2513yes—
905C22×C4C2513yes—
906C22×C4C2513yes—
907C22×C4C2513yes—
908C22×C4C2513yes—
909C22×C4C2513yes—
910C22×C4C2511yescharacteristic
911C22×C4C2511yescharacteristic
912C22×C4C2513yes—
913C22×C4C2511yescharacteristic
914C22×C4C2513yes—
915C22×C4C2513yes—
916C22×C4C2511yescharacteristic
917C22×C4C2513yes—
918C22×C4C2511yescharacteristic
919C22×C4C2511yescharacteristic
920C22×C4C2511yescharacteristic
921C22×C4C2511yescharacteristic
922C22×C4C2511yescharacteristic
923C22×C4C2513yes—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—26no—
927C4⋊C4—26no—
928C4⋊C4—26no—
929C4⋊C4—26no—
930C4⋊C4—26no—
931C4⋊C4—26no—
932C4⋊C4—26no—
933C4⋊C4—26no—
934C4⋊C4—26no—
935C4⋊C4—26no—
936C4⋊C4—26no—
937C4⋊C4—26no—
938C4⋊C4—26no—
939C4⋊C4—212no—
940C4⋊C4—212no—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—26no—
944C4⋊C4—26no—
945C4⋊C4—26no—
946C4⋊C4—26no—
947C4⋊C4—26no—
948C4⋊C4—22no—
949C4⋊C4—26no—
950C4⋊C4—22no—
951C4⋊C4—26no—
952C4⋊C4—22no—
953C4⋊C4—26no—
954C4⋊C4—22no—
955C4⋊C4—26no—
956C4⋊C4—22no—
957C4⋊C4—26no—
958C4⋊C4—22no—
959C4⋊C4—26no—
960C4⋊C4—26no—
961C4⋊C4—26no—
962C4⋊C4—26no—
963C4⋊C4—22no—
964C4⋊C4—26no—
965C4⋊C4—22no—
966C4⋊C4—26no—
967C4⋊C4—22no—
968C4⋊C4—43no—
969C4⋊C4—43no—
970C4⋊C4—43no—
971C4⋊C4—43no—
972C4⋊C4—43no—
973C4⋊C4—46no—
974C4⋊C4—46no—
975C4⋊C4—46no—
976C4⋊C4—46no—
977C4⋊C4—43no—
978C4⋊C4—43no—
979C4⋊C4—43no—
980C4⋊C4—46no—
981C4⋊C4—43no—
982C4⋊C4—43no—
983C4⋊C4—43no—
984C4⋊C4—46no—
985C4⋊C4—46no—
986C4⋊C4—43no—
987C4⋊C4—43no—
988C4⋊C4—43no—
989C4⋊C4—43no—
990C4⋊C4—43no—
991C4⋊C4—46no—
992C4⋊C4—43no—
993C4⋊C4—46no—
994C4⋊C4—46no—
995C4⋊C4—43no—
996C4⋊C4—46no—
997C4⋊C4—43no—
998C4⋊C4—46no—
999C4⋊C4—43no—
1000C4⋊C4—43no—
1001C4⋊C4C22×Q814yes—
1002C4⋊C4C22×Q8112yes—
1003C4⋊C4C22×Q8112yes—
1004C4⋊C4C22×Q8112yes—
1005C4⋊C4C22×Q8112yes—
1006C4⋊C4C22×Q8112yes—
1007C4⋊C4C22×Q8124yes—
1008C4⋊C4C2×#41112yes—
1009C4⋊C42−1+414yes—
1010C42—26no—
1011C42—26no—
1012C42—26no—
1013C42—26no—
1014C42—26no—
1015C42—26no—
1016C42—22no—
1017C42—22no—
1018C42—22no—
1019C42—26no—
1020C42—26no—
1021C42—26no—
1022C42—26no—
1023C42—26no—
1024C42—22no—
1025C42—26no—
1026C42—22no—
1027C42—26no—
1028C42—43no—
1029C42—43no—
1030C42—43no—
1031C42—43no—
1032C42—43no—
1033C42—43no—
1034C42—43no—
1035C42—43no—
1036C42—43no—
1037C42—43no—
1038C42—46no—
1039C42—46no—
1040C42—46no—
1041C42—43no—
1042C42—43no—
1043C42—43no—
1044C42—46no—
1045C42C22×Q8112yes—
1046C42C22×Q8112yes—
1047C42C22×Q8112yes—
1048C42C2×#41112yes—
1049C23C2611yescharacteristic
1050Q8—28no—
1051Q8—412no—
1052Q8—412no—
1053Q8—86no—
1054Q8—812no—
1055Q8#557116yes—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—23no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—23no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—23no—
1071C2×C4—23no—
1072C2×C4—23no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—23no—
1077C2×C4—21no—
1078C2×C4—23no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—23no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—23no—
1086C2×C4—23no—
1087C2×C4—23no—
1088C2×C4—23no—
1089C2×C4—23no—
1090C2×C4—23no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—23no—
1096C2×C4—21no—
1097C2×C4—23no—
1098C2×C4—23no—
1099C2×C4—23no—
1100C2×C4—23no—
1101C2×C4—23no—
1102C2×C4—21no—
1103C2×C4—23no—
1104C2×C4—21no—
1105C2×C4—23no—
1106C2×C4—23no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—23no—
1110C2×C4—23no—
1111C2×C4—23no—
1112C2×C4—23no—
1113C2×C4—23no—
1114C2×C4—23no—
1115C2×C4—23no—
1116C2×C4—23no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—23no—
1121C2×C4—21no—
1122C2×C4—23no—
1123C2×C4—23no—
1124C2×C4—23no—
1125C2×C4—23no—
1126C2×C4—23no—
1127C2×C4—23no—
1128C2×C4—23no—
1129C2×C4—23no—
1130C2×C4—23no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4C23×Q812yes—
1134C2×C4C23×Q812yes—
1135C2×C4C23×Q812yes—
1136C2×C4C23×Q816yes—
1137C2×C4C23×Q816yes—
1138C2×C4C23×Q816yes—
1139C2×C4C23×Q816yes—
1140C2×C4C22×#4112yes—
1141C2×C4C22×#4116yes—
1142C2×C4C22×#4116yes—
1143C2×C4C2×2−1+412yes—
1144C2×C4C2×2−1+412yes—
1145C2×C4C2×2−1+412yes—
1146C2×C4C2×2−1+416yes—
1147C2×C4#58512yes—
1148C2×C4#58512yes—
1149C22C24×Q811yescharacteristic
1150C22C23×#4111yescharacteristic
1151C22C22×2−1+411yescharacteristic
1152C22C22×2−1+411yescharacteristic
1153C22C2×#58511yescharacteristic
1154C22C2×#58511yescharacteristic
1155C22H(7,𝔽2)11yescharacteristic
1156C4—22no—
1157C4—26no—
1158C4—22no—
1159C4—26no—
1160C4—22no—
1161C4—22no—
1162C4—22no—
1163C4—22no—
1164C4—22no—
1165C4—22no—
1166C4—26no—
1167C4—26no—
1168C4—22no—
1169C4—43no—
1170C4—43no—
1171C4—43no—
1172C4—43no—
1173C4—41no—
1174C4—41no—
1175C4—41no—
1176C4—43no—
1177C4—41no—
1178C4—41no—
1179C4—43no—
1180C4—43no—
1181C4—41no—
1182C4—43no—
1183C4—43no—
1184C4—43no—
1185C4—43no—
1186C4C2×#557112yes—
1187C2C22×#55711yescharacteristic
1188C2#6278811yescharacteristic
1189C2#6281311yescharacteristic
1190C2#6295211yescharacteristic
1191C2Q8×2−1+411yescharacteristic
1192C2#6300811yescharacteristic
1193C2#6303211yescharacteristic
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
#596712
#596702
#596692
#596682
#453632
#450442
#449822
#449532
#397492
#396822
#396802
#391762
#365672
Q8×#1252
#364972
#364752
#364662
#359372
#358682
#349202
#343372
#343362
C4×Q822
C4×#5572