Finite Group Databasebeta

← #7692777

Subgroups — #7692777

Order 512.

4959 conjugacy classes of subgroups.

The subgroup lattice has 1298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59756C213yesmaximal, complemented
2#59664C213yesmaximal, complemented
3#59663C213yesmaximal, complemented
4#59459C213yesmaximal, complemented
5#59322C213yesmaximal, complemented
6#45395C213yesmaximal, complemented
7#45278C213yesmaximal, complemented
8#44997C213yesmaximal, complemented
9#44923C213yesmaximal, complemented
10#39689C213yesmaximal, complemented
11#39673C213yesmaximal, complemented
12#38098C213yesmaximal
13#37874C213yesmaximal
14#36571C213yesmaximal, complemented
15Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
16Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
17#36475C211yesmaximal, characteristic, complemented
18#36435C211yesmaximal, characteristic, complemented
19#36435C211yesmaximal, characteristic, complemented
20#36363C213yesmaximal
21#35937C211yesmaximal, characteristic, complemented
22#35868C211yesmaximal, characteristic, complemented
23#35845C211yesmaximal, characteristic, complemented
24#35786C211yesmaximal, characteristic, complemented
25#34840C213yesmaximal
26#34337C211yesmaximal, characteristic, complemented
27#34291C211yesmaximal, characteristic
28#34291C211yesmaximal, characteristic
29#34249C211yesmaximal, characteristic, complemented
30C4×D4×Q8C211yesmaximal, characteristic
31C2×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39C22×C4×Q8C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42#2864C2213yes—
43#2857C2213yes—
44#2857C2213yes—
45#2851C2213yes—
46#2851C2213yes—
47#2807C2216yes—
48#2805C2216yes—
49#2802C2216yes—
50#2792C2216yes—
51#2792C2216yes—
52#2792C2216yes—
53#2792C2216yes—
54#2791C2216yes—
55#2791C2216yes—
56#2790C2216yes—
57#2774C2216yes—
58#2755C2216yes—
59#2729C2216yes—
60#2720C2216yes—
61#2660C2213yes—
62#2647C2213yes—
63#2629C2213yes—
64#2628C2213yes—
65#2590C2216yes—
66#2590C2213yes—
67#2589C2213yes—
68#2588C2216yes—
69#2588C2216yes—
70#2588C2213yes—
71#2587C2213yes—
72#2586C2216yes—
73#2586C2213yes—
74#2585C2216yes—
75#2585C2213yes—
76#2585C2216yes—
77#2584C2216yes—
78#2584C2213yes—
79#2583C2213yes—
80#2583C2216yes—
81#2582C2213yes—
82#2582C2213yes—
83#2582C2213yes—
84#2581C2213yes—
85#2581C2213yes—
86#2581C2213yes—
87#2579C2213yes—
88#2574C2213yes—
89#2570C2213yes—
90#2570C2213yes—
91#2570C2213yes—
92#2567C2213yes—
93#2567C2213yes—
94#2567C2216yes—
95#2567C2213yes—
96#2565C2213yes—
97#2565C2213yes—
98#2565C2213yes—
99#2564C2213yes—
100#2556C2213yes—
101#2552C2213yes—
102#2551C2213yes—
103#2551C2213yes—
104#2550C2216yes—
105#2550C2213yes—
106#2550C2213yes—
107#2549C2213yes—
108#2546C2213yes—
109#2522C2216yes—
110#2520C2216yes—
111#2509C2213yes—
112#2509C2213yes—
113#2508C2213yes—
114#2507C2213yes—
115#2507C2216yes—
116#2507C2213yes—
117#2506C2213yes—
118#2506C2213yes—
119#2506C2213yes—
120#2505C2216yes—
121#2505C2213yes—
122#2473C2216yes—
123#2473C2213yes—
124#2465C2216yes—
125#2453C2213yes—
126#2453C2213yes—
127#2453C2213yes—
128#2453C2213yes—
129#2453C2213yes—
130#2451C2213yes—
131#2451C2213yes—
132#2451C2213yes—
133#2451C2213yes—
134#2451C2213yes—
135#2451C2213yes—
136#2451C2213yes—
137#2450C2213yes—
138#2449C2216yes—
139#2449C2211yescharacteristic
140#2442C2213yes—
141#2442C2213yes—
142#2441C2213yes—
143#2441C2213yes—
144#2441C2213yes—
145#2440C2213yes—
146#2440C2213yes—
147#2440C2216yes—
148#2440C2213yes—
149#2440C2213yes—
150#2440C2213yes—
151#2440C2213yes—
152#2439C2213yes—
153#2402C2213yes—
154#2399C2213yes—
155#2396C2213yes—
156#2396C2213yes—
157#2370C2213yes—
158#2370C2213yes—
159#2370C2216yes—
160#2368C2216yes—
161#2365C2213yes—
162#2365C2213yes—
163#2365C2213yes—
164#2365C2213yes—
165#2362C2213yes—
166#2362C2213yes—
167#2360C2216yes—
168#2360C2213yes—
169#2360C2213yes—
170#2360C2213yes—
171#2360C2213yes—
172#2352C2213yes—
173#2352C2213yes—
174#2351C2211yescharacteristic
175#2351C2213yes—
176#2351C2211yescharacteristic
177#2351C2211yescharacteristic
178#2351C2211yescharacteristic
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2213yes—
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2213yes—
185Q8×C4⋊C4C2213yes—
186Q8×C4⋊C4C2211yescharacteristic
187Q8×C4⋊C4C2211yescharacteristic
188Q8×C4⋊C4C2211yescharacteristic
189Q8×C4⋊C4C2211yescharacteristic
190Q8×C4⋊C4C2211yescharacteristic
191Q8×C4⋊C4C2213yes—
192Q8×C4⋊C4C2213yes—
193Q8×C4⋊C4C2213yes—
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2213yes—
197Q8×C4⋊C4C2213yes—
198Q8×C4⋊C4C2211yescharacteristic
199D4×C4⋊C4C2213yes—
200Q8×C22⋊C4C2211yescharacteristic
201Q8×C22⋊C4C2211yescharacteristic
202Q8×C22⋊C4C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204Q8×C22⋊C4C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206#2330C2213yes—
207#2330C2213yes—
208#2327C2213yes—
209#2327C2213yes—
210#2323C2213yes—
211#2323C2213yes—
212#2317C2213yes—
213#2317C2213yes—
214C4×C4⋊Q8C2213yes—
215C4×C4⋊Q8C2213yes—
216C4×#125C2213yes—
217C4×C22⋊Q8C2213yes—
218C4×C22⋊Q8C2213yes—
219C4×C22⋊Q8C2213yes—
220C4×C22⋊Q8C2213yes—
221C4×C22⋊Q8C2213yes—
222C4×C22⋊Q8C2213yes—
223C4×C22⋊Q8C2213yes—
224C4×C22⋊Q8C2213yes—
225#2296C2213yes—
226#2296C2213yes—
227#2295C2213yes—
228C2×#389C2213yes—
229C2×#389C2213yes—
230#2290C2213yes—
231#2290C2213yes—
232C2×#384C2213yes—
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×D4C2213yes—
237C2×C4×C4⋊C4C2213yes—
238C23×Q8C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240Q82—44no—
241#557—28no—
242#557—44no—
243D4×Q8Q8116yescomplemented
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2316yes—
250C2×C4⋊Q8C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2316yes—
257C2×C22⋊Q8C2313yes—
258C2×C22⋊Q8C2311yescharacteristic
259C2×C22⋊Q8C2311yescharacteristic
260C2×C22⋊Q8C2313yes—
261C2×C22⋊Q8C2316yes—
262C2×C22⋊Q8C2316yes—
263C2×C22⋊Q8C2313yes—
264C2×C22⋊Q8C2313yes—
265#519—28no—
266#519—44no—
267C2×C4×Q8—28no—
268C2×C4×Q8—44no—
269C2×C4×Q8—44no—
270C2×C4×Q8—44no—
271C2×C4×Q8C2313yes—
272C2×C4×Q8C2313yes—
273C2×C4×Q8C2313yes—
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2313yes—
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2313yes—
292C2×C4×Q8C2313yes—
293C2×C4×Q8C2313yes—
294C2×C4×Q8C2313yes—
295C2×C4×Q8C2313yes—
296C2×C4×Q8C2313yes—
297C2×C4×Q8C2316yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×D4C2311yescharacteristic
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×#117C2313yes—
304C2×#117C2313yes—
305C2×#117C2313yes—
306C2×#117C2313yes—
307C22×C4⋊C4C2313yes—
308C22×C4⋊C4C2311yescharacteristic
309C22×C4⋊C4C2313yes—
310C22×C4⋊C4C2313yes—
311C22×C4⋊C4C2313yes—
312C22×C4⋊C4C2313yes—
313C22×C4⋊C4C2316yes—
314C22×C42C2313yes—
315C22×C42C2313yes—
316C22×C42C2313yes—
317C22×C42C2313yes—
318#400C2313yes—
319#400C2313yes—
320#400C2316yes—
321#400C2316yes—
322#400C2313yes—
323#400C2316yes—
324#400C2316yes—
325#400C2313yes—
326#400C2316yes—
327#400C2316yes—
328#400C2313yes—
329#400C2313yes—
330#399C2313yes—
331#399C2311yescharacteristic
332#399C2316yes—
333#398C2313yes—
334#398C2316yes—
335#398C2316yes—
336#398C2316yes—
337#398C2316yes—
338#398C2316yes—
339#398C2316yes—
340#398C2316yes—
341#398C2316yes—
342#398C2313yes—
343#398C2313yes—
344#398C2313yes—
345#398C2313yes—
346#398C2316yes—
347#398C2316yes—
348#398C2316yes—
349#398C2316yes—
350#398C2313yes—
351#398C2316yes—
352#398C2313yes—
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#398C2311yescharacteristic
357#398C2316yes—
358#398C2313yes—
359#398C2316yes—
360#396C2313yes—
361#396C2313yes—
362#396C2311yescharacteristic
363#396C2313yes—
364#396C2316yes—
365#395C2313yes—
366#395C2313yes—
367#395C2316yes—
368#395C2316yes—
369#395C2316yes—
370#395C2316yes—
371#395C2316yes—
372#395C2316yes—
373#395C2313yes—
374#395C2316yes—
375#395C2316yes—
376#395C2313yes—
377#395C2313yes—
378#395C2316yes—
379#395C2311yescharacteristic
380#393C2313yes—
381#393C2313yes—
382#391C2313yes—
383#391C2313yes—
384#391C2313yes—
385#391C2313yes—
386#391C2313yes—
387#391C2313yes—
388#391C2313yes—
389#391C2313yes—
390#391C2313yes—
391#391C2313yes—
392#391C2313yes—
393#391C2313yes—
394#391C2316yes—
395#391C2313yes—
396#391C2313yes—
397#391C2313yes—
398#391C2313yes—
399#391C2313yes—
400#391C2316yes—
401#391C2316yes—
402#391C2313yes—
403#391C2316yes—
404#389C2313yes—
405#389C2313yes—
406#389C2316yes—
407#389C2316yes—
408#389C2313yes—
409#389C2316yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2316yes—
414#389C2316yes—
415#389C2316yes—
416#389C2316yes—
417#389C2316yes—
418#389C2316yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2316yes—
426#389C2316yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2316yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2316yes—
438#389C2313yes—
439#389C2313yes—
440#389C2316yes—
441#389C2313yes—
442#389C2313yes—
443#389C2316yes—
444#389C2316yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2316yes—
450#389C2311yescharacteristic
451#389C2313yes—
452#389C2313yes—
453#389C2316yes—
454#389C2313yes—
455#389C2316yes—
456#389C2316yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2316yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#388C2313yes—
470#388C2313yes—
471#388C2316yes—
472#388C2316yes—
473#388C2313yes—
474#388C2313yes—
475#387C2311yescharacteristic
476#387C2313yes—
477#387C2313yes—
478#387C2313yes—
479#387C2313yes—
480#387C2313yes—
481#387C2313yes—
482#387C2316yes—
483#387C2316yes—
484#387C2316yes—
485#387C2316yes—
486#387C2316yes—
487#387C2316yes—
488#387C2316yes—
489#387C2313yes—
490#387C2313yes—
491#387C2316yes—
492#387C2316yes—
493#387C2313yes—
494#387C2313yes—
495#387C2313yes—
496#387C2316yes—
497#387C2316yes—
498#387C2313yes—
499#387C2313yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2313yes—
505#387C2313yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2316yes—
510#387C2313yes—
511#387C2313yes—
512#387C2313yes—
513#387C2316yes—
514#387C2316yes—
515#387C2313yes—
516#387C2316yes—
517#387C2316yes—
518#386C2311yescharacteristic
519#386C2313yes—
520#386C2311yescharacteristic
521#386C2313yes—
522#385C2313yes—
523#385C2313yes—
524#385C2313yes—
525#385C2316yes—
526#385C2311yescharacteristic
527#385C2313yes—
528#385C2313yes—
529#385C2313yes—
530#385C2311yescharacteristic
531#385C2313yes—
532#385C2316yes—
533#385C2316yes—
534#385C2313yes—
535#385C2313yes—
536#385C2313yes—
537#385C2316yes—
538#385C2316yes—
539#385C2313yes—
540#385C2311yescharacteristic
541#385C2313yes—
542#385C2313yes—
543#384C2313yes—
544#384C2313yes—
545#384C2313yes—
546#384C2313yes—
547#384C2313yes—
548#384C2313yes—
549#384C2313yes—
550#384C2316yes—
551#384C2313yes—
552#384C2316yes—
553#384C2313yes—
554#384C2313yes—
555#384C2316yes—
556#382C2313yes—
557#382C2313yes—
558#382C2313yes—
559#382C2313yes—
560#382C2313yes—
561#382C2313yes—
562#382C2313yes—
563#382C2316yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2313yes—
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⋊C4C2316yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2316yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2316yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2316yes—
600C4×C4⋊C4C2316yes—
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×C22⋊C4C2313yes—
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2316yes—
622C4×C22⋊C4C2313yes—
623#376C2313yes—
624#376C2313yes—
625C2×#95C2313yes—
626C2×#95C2313yes—
627C43C2313yes—
628C22×Q8—24no—
629C22×Q8—24no—
630C22×Q8—24no—
631C22×Q8—24no—
632C22×Q8C2×Q818yes—
633C22×Q8C2×Q818yes—
634C22×Q8C2411yescharacteristic
635C22×Q8C2413yes—
636C22×Q8C2413yes—
637C22×Q8C2413yes—
638C22×Q8C2413yes—
639C22×Q8C2416yes—
640C22×Q8C2411yescharacteristic
641C22×D4C2411yescharacteristic
642C23×C4C2411yescharacteristic
643C23×C4C2413yes—
644C23×C4C2411yescharacteristic
645C23×C4C2411yescharacteristic
646C23×C4C2411yescharacteristic
647C23×C4C2413yes—
648C23×C4C2413yes—
649C23×C4C2413yes—
650C23×C4C2413yes—
651C23×C4C2413yes—
652C4⋊Q8—212no—
653C4⋊Q8—46no—
654C4⋊Q8—46no—
655C4⋊Q8—46no—
656C4⋊Q8—46no—
657C4⋊Q8—86no—
658C4⋊Q8C2×Q8124yes—
659#125—212no—
660#125—212no—
661#125—212no—
662#125—46no—
663#125—46no—
664#125—86no—
665C22⋊Q8—24no—
666C22⋊Q8—212no—
667C22⋊Q8—24no—
668C22⋊Q8—412no—
669C22⋊Q8—46no—
670C22⋊Q8—86no—
671C22⋊Q8C2×Q8124yes—
672C22⋊Q8C2×Q8124yes—
673C4×Q8—24no—
674C4×Q8—24no—
675C4×Q8—24no—
676C4×Q8—24no—
677C4×Q8—24no—
678C4×Q8—24no—
679C4×Q8—24no—
680C4×Q8—24no—
681C4×Q8—24no—
682C4×Q8—24no—
683C4×Q8—24no—
684C4×Q8—212no—
685C4×Q8—212no—
686C4×Q8—212no—
687C4×Q8—212no—
688C4×Q8—212no—
689C4×Q8—46no—
690C4×Q8—46no—
691C4×Q8—46no—
692C4×Q8—46no—
693C4×Q8—46no—
694C4×Q8—46no—
695C4×Q8—46no—
696C4×Q8—46no—
697C4×Q8—46no—
698C4×Q8—46no—
699C4×Q8—86no—
700C4×Q8C2×Q818yes—
701C4×Q8#4118yes—
702C4×D4—24no—
703C4×D4—46no—
704C4×D4C2×Q8124yes—
705#117—212no—
706#117—212no—
707#117—46no—
708#117—46no—
709C2×C4⋊C4—212no—
710C2×C4⋊C4—24no—
711C2×C4⋊C4—46no—
712C2×C4⋊C4—46no—
713C2×C4⋊C4—46no—
714C2×C4⋊C4—46no—
715C2×C4⋊C4—86no—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2416yes—
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2416yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2416yes—
752C2×C4⋊C4C2416yes—
753C2×C4⋊C4C2416yes—
754C2×C4⋊C4C2416yes—
755C2×C4⋊C4C2416yes—
756C2×C4⋊C4C2416yes—
757C2×C4⋊C4C2416yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2416yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2416yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2416yes—
777C2×C4⋊C4C2416yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2416yes—
780C2×C4⋊C4C2416yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2416yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2416yes—
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2411yescharacteristic
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2411yescharacteristic
796C2×C22⋊C4C2411yescharacteristic
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2411yescharacteristic
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2411yescharacteristic
801C2×C22⋊C4C2411yescharacteristic
802C2×C22⋊C4C2411yescharacteristic
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2411yescharacteristic
810C2×C42—212no—
811C2×C42—46no—
812C2×C42—46no—
813C2×C42—46no—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2416yes—
818C2×C42C2411yescharacteristic
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2416yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2416yes—
840C2×C42C2416yes—
841C2×C42C2413yes—
842C2×C42C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2411yescharacteristic
852#95C2411yescharacteristic
853#95C2413yes—
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#95C2413yes—
867#95C2416yes—
868#95C2416yes—
869#95C2416yes—
870#95C2416yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2411yescharacteristic
879#95C2416yes—
880#95C2411yescharacteristic
881#95C2413yes—
882#95C2411yescharacteristic
883#95C2411yescharacteristic
884#95C2411yescharacteristic
885#95C2411yescharacteristic
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2416yes—
891#95C2416yes—
892#95C2413yes—
893#95C2416yes—
894#95C2413yes—
895#95C2416yes—
896#95C2413yes—
897#95C2416yes—
898#95C2416yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2416yes—
907#95C2416yes—
908C24C2511yescharacteristic
909C24C2511yescharacteristic
910C2×Q8—232no—
911C2×Q8—232no—
912C2×Q8—26no—
913C2×Q8—26no—
914C2×Q8—26no—
915C2×Q8—26no—
916C2×Q8—26no—
917C2×Q8—26no—
918C2×Q8—22no—
919C2×Q8—22no—
920C2×Q8—41no—
921C2×Q8—43no—
922C2×Q8—43no—
923C2×Q8—43no—
924C2×Q8—43no—
925C2×Q8—46no—
926C2×Q8—46no—
927C2×Q8—46no—
928C2×Q8C22×Q8112yes—
929C2×Q8C22×Q8112yes—
930C2×Q8C22×Q814yes—
931C2×Q8C2×#4114yes—
932C2×Q8H(5,𝔽2)14yes—
933C2×D4—22no—
934C2×D4—22no—
935C2×D4C22×Q814yes—
936C22×C4—22no—
937C22×C4—22no—
938C22×C4—26no—
939C22×C4—26no—
940C22×C4—26no—
941C22×C4—26no—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—26no—
945C22×C4—22no—
946C22×C4—26no—
947C22×C4—26no—
948C22×C4—26no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—22no—
953C22×C4—41no—
954C22×C4—41no—
955C22×C4—41no—
956C22×C4—43no—
957C22×C4—43no—
958C22×C4—43no—
959C22×C4—43no—
960C22×C4—43no—
961C22×C4—43no—
962C22×C4—43no—
963C22×C4—43no—
964C22×C4C22×Q8112yes—
965C22×C4C22×Q8112yes—
966C22×C4C2511yescharacteristic
967C22×C4C2511yescharacteristic
968C22×C4C2511yescharacteristic
969C22×C4C2513yes—
970C22×C4C2511yescharacteristic
971C22×C4C2513yes—
972C22×C4C2513yes—
973C22×C4C2513yes—
974C22×C4C2513yes—
975C22×C4C2511yescharacteristic
976C22×C4C2511yescharacteristic
977C22×C4C2513yes—
978C22×C4C2513yes—
979C22×C4C2513yes—
980C22×C4C2513yes—
981C22×C4C2513yes—
982C22×C4C2513yes—
983C22×C4C2511yescharacteristic
984C22×C4C2513yes—
985C22×C4C2513yes—
986C22×C4C2513yes—
987C22×C4C2511yescharacteristic
988C22×C4C2513yes—
989C22×C4C2511yescharacteristic
990C22×C4C2511yescharacteristic
991C22×C4C2511yescharacteristic
992C22×C4C2511yescharacteristic
993C22×C4C2511yescharacteristic
994C22×C4C2513yes—
995C4⋊C4—212no—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—26no—
999C4⋊C4—26no—
1000C4⋊C4—22no—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—212no—
1006C4⋊C4—26no—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4—26no—
1010C4⋊C4—26no—
1011C4⋊C4—26no—
1012C4⋊C4—26no—
1013C4⋊C4—22no—
1014C4⋊C4—22no—
1015C4⋊C4—22no—
1016C4⋊C4—22no—
1017C4⋊C4—22no—
1018C4⋊C4—22no—
1019C4⋊C4—26no—
1020C4⋊C4—22no—
1021C4⋊C4—26no—
1022C4⋊C4—22no—
1023C4⋊C4—22no—
1024C4⋊C4—26no—
1025C4⋊C4—26no—
1026C4⋊C4—26no—
1027C4⋊C4—26no—
1028C4⋊C4—26no—
1029C4⋊C4—26no—
1030C4⋊C4—43no—
1031C4⋊C4—43no—
1032C4⋊C4—43no—
1033C4⋊C4—43no—
1034C4⋊C4—46no—
1035C4⋊C4—46no—
1036C4⋊C4—46no—
1037C4⋊C4—46no—
1038C4⋊C4—46no—
1039C4⋊C4—46no—
1040C4⋊C4—46no—
1041C4⋊C4—43no—
1042C4⋊C4—43no—
1043C4⋊C4—43no—
1044C4⋊C4—41no—
1045C4⋊C4—43no—
1046C4⋊C4—43no—
1047C4⋊C4—43no—
1048C4⋊C4—43no—
1049C4⋊C4—43no—
1050C4⋊C4—43no—
1051C4⋊C4—46no—
1052C4⋊C4—46no—
1053C4⋊C4—46no—
1054C4⋊C4—43no—
1055C4⋊C4—43no—
1056C4⋊C4—43no—
1057C4⋊C4—46no—
1058C4⋊C4—46no—
1059C4⋊C4—46no—
1060C4⋊C4—43no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—46no—
1064C4⋊C4—43no—
1065C4⋊C4—43no—
1066C4⋊C4C22×Q8112yes—
1067C4⋊C4C22×Q8112yes—
1068C4⋊C4C22×Q8124yes—
1069C4⋊C4C2×#41112yes—
1070C4⋊C42−1+414yes—
1071C22⋊C4—22no—
1072C22⋊C4—26no—
1073C22⋊C4—26no—
1074C22⋊C4—22no—
1075C22⋊C4—26no—
1076C22⋊C4—22no—
1077C22⋊C4—26no—
1078C22⋊C4—22no—
1079C22⋊C4—22no—
1080C22⋊C4—22no—
1081C22⋊C4—41no—
1082C22⋊C4—43no—
1083C22⋊C4—43no—
1084C22⋊C4—43no—
1085C22⋊C4—43no—
1086C22⋊C4C22×Q8112yes—
1087C22⋊C4C22×Q8112yes—
1088C22⋊C42−1+414yes—
1089C42—26no—
1090C42—26no—
1091C42—26no—
1092C42—212no—
1093C42—26no—
1094C42—26no—
1095C42—26no—
1096C42—26no—
1097C42—26no—
1098C42—26no—
1099C42—26no—
1100C42—26no—
1101C42—26no—
1102C42—26no—
1103C42—22no—
1104C42—26no—
1105C42—43no—
1106C42—43no—
1107C42—43no—
1108C42—43no—
1109C42—43no—
1110C42—43no—
1111C42—46no—
1112C42—43no—
1113C42—43no—
1114C42—46no—
1115C42—46no—
1116C42C22×Q8112yes—
1117C42C2×#41112yes—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23C23×Q812yes—
1129C23C23×Q812yes—
1130C23C2×2−1+412yes—
1131C23#58512yes—
1132C23C2611yescharacteristic
1133Q8—224no—
1134Q8—224no—
1135Q8—412no—
1136Q8—44no—
1137Q8—86no—
1138Q8—166no—
1139Q8#554116yes—
1140D4—28no—
1141C2×C4—28no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—23no—
1145C2×C4—23no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—23no—
1150C2×C4—23no—
1151C2×C4—23no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—23no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—23no—
1162C2×C4—21no—
1163C2×C4—23no—
1164C2×C4—224no—
1165C2×C4—224no—
1166C2×C4—21no—
1167C2×C4—23no—
1168C2×C4—21no—
1169C2×C4—23no—
1170C2×C4—23no—
1171C2×C4—23no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—21no—
1185C2×C4—23no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—23no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—23no—
1192C2×C4—23no—
1193C2×C4—23no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—21no—
1201C2×C4—23no—
1202C2×C4—21no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—23no—
1207C2×C4—23no—
1208C2×C4—23no—
1209C2×C4—23no—
1210C2×C4—23no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—21no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—21no—
1217C2×C4—44no—
1218C2×C4—412no—
1219C2×C4—44no—
1220C2×C4—44no—
1221C2×C4—86no—
1222C2×C4—86no—
1223C2×C4—86no—
1224C2×C4C23×Q812yes—
1225C2×C4C23×Q816yes—
1226C2×C4C23×Q816yes—
1227C2×C4C23×Q816yes—
1228C2×C4C23×Q816yes—
1229C2×C4C22×#4112yes—
1230C2×C4C22×#4116yes—
1231C2×C4C22×#4116yes—
1232C2×C4C2×H(5,𝔽2)16yes—
1233C2×C4C2×2−1+412yes—
1234C2×C4C2×2−1+412yes—
1235C2×C4C2×2−1+412yes—
1236C2×C4C2×2−1+412yes—
1237C2×C4C2×2−1+412yes—
1238C22—22no—
1239C22—22no—
1240C22—22no—
1241C22—22no—
1242C22—22no—
1243C22—22no—
1244C22—22no—
1245C22—22no—
1246C22—22no—
1247C22—41no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22#350214yes—
1252C22C24×Q811yescharacteristic
1253C22C23×#4111yescharacteristic
1254C22C22×H(5,𝔽2)11yescharacteristic
1255C22C22×2−1+411yescharacteristic
1256C22C22×2−1+411yescharacteristic
1257C22C2×#58511yescharacteristic
1258C22H(7,𝔽2)11yescharacteristic
1259C4—26no—
1260C4—26no—
1261C4—22no—
1262C4—22no—
1263C4—22no—
1264C4—22no—
1265C4—22no—
1266C4—22no—
1267C4—22no—
1268C4—26no—
1269C4—26no—
1270C4—41no—
1271C4—43no—
1272C4—43no—
1273C4—43no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—43no—
1278C4—41no—
1279C4—43no—
1280C4—43no—
1281C4—43no—
1282C4—43no—
1283C4—43no—
1284C4—43no—
1285C4—41no—
1286C4—43no—
1287C4C2×#554112yes—
1288C2—24no—
1289C2—42no—
1290C2C22×#55411yescharacteristic
1291C2C2×#350211yescharacteristic
1292C2#6278811yescharacteristic
1293C2#6289911yescharacteristic
1294C2Q8×2−1+411yescharacteristic
1295C2#6300011yescharacteristic
1296C2#6301611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59756C2semidirect
2. #59664C2semidirect
3. #59663C2semidirect
4. #59459C2semidirect
5. #59322C2semidirect
6. #45395C2semidirect
7. #45278C2semidirect
8. #44997C2semidirect
9. #44923C2semidirect
10. #39689C2semidirect
11. #39673C2semidirect
14. #36571C2semidirect
15. Q8×C22⋊Q8C2semidirect
16. Q8×C22⋊Q8C2semidirect
17. #36475C2semidirect
18. #36435C2semidirect
19. #36435C2semidirect
21. #35937C2semidirect
22. #35868C2semidirect
23. #35845C2semidirect
24. #35786C2semidirect
26. #34337C2semidirect
29. #34249C2semidirect
31. C2×Q8×C4⋊C4C2semidirect
243. D4×Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#597562
#596642
#596632
#594592
#593222
#453952
#452782
#449972
#449232
#396892
#396732
#380982
#378742
#365712
Q8×C22⋊Q82
#364752
#364352
#363632
#359372
#358682
#358452
#357862
#348402
#343372
#342912
#342492
C4×D4×Q82
C2×Q8×C4⋊C42