Finite Group Databasebeta

← #7693377

Subgroups — #7693377

Order 512.

5045 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59918C213yesmaximal, complemented
2#59463C213yesmaximal, complemented
3#59455C213yesmaximal, complemented
4#59454C213yesmaximal, complemented
5#59305C213yesmaximal, complemented
6#45405C213yesmaximal, complemented
7#45121C213yesmaximal, complemented
8#45059C213yesmaximal, complemented
9#44966C213yesmaximal, complemented
10#39693C213yesmaximal, complemented
11#39675C213yesmaximal, complemented
12#38099C213yesmaximal, complemented
13#37874C213yesmaximal, complemented
14#36577C211yesmaximal, characteristic, complemented
15#36570C213yesmaximal, complemented
16Q8×#125C211yesmaximal, characteristic, complemented
17#36435C211yesmaximal, characteristic, complemented
18#36435C211yesmaximal, characteristic, complemented
19#36431C211yesmaximal, characteristic, complemented
20#36290C213yesmaximal, complemented
21#35971C211yesmaximal, characteristic, complemented
22#35957C211yesmaximal, characteristic, complemented
23#35816C211yesmaximal, characteristic, complemented
24#35816C211yesmaximal, characteristic, complemented
25#34840C213yesmaximal, complemented
26#34336C211yesmaximal, characteristic, complemented
27#34294C211yesmaximal, characteristic
28#34294C211yesmaximal, characteristic
29#34250C211yesmaximal, characteristic, complemented
30C4×#548C211yesmaximal, characteristic
31C2×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic
39C22×C4×Q8C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42#2859C2213yes—
43#2857C2213yes—
44#2851C2213yes—
45#2851C2213yes—
46#2851C2213yes—
47#2806C2216yes—
48#2802C2216yes—
49#2792C2216yes—
50#2791C2216yes—
51#2790C2216yes—
52#2790C2216yes—
53#2790C2216yes—
54#2790C2216yes—
55#2788C2216yes—
56#2788C2216yes—
57#2768C2216yes—
58#2742C2216yes—
59#2720C2216yes—
60#2704C2216yes—
61#2660C2213yes—
62#2647C2213yes—
63#2629C2213yes—
64#2629C2213yes—
65#2590C2213yes—
66#2589C2213yes—
67#2589C2216yes—
68#2588C2213yes—
69#2587C2216yes—
70#2587C2216yes—
71#2587C2213yes—
72#2586C2213yes—
73#2585C2213yes—
74#2584C2213yes—
75#2583C2216yes—
76#2583C2213yes—
77#2582C2213yes—
78#2581C2213yes—
79#2581C2213yes—
80#2580C2213yes—
81#2579C2213yes—
82#2579C2216yes—
83#2574C2213yes—
84#2574C2216yes—
85#2571C2213yes—
86#2570C2213yes—
87#2568C2213yes—
88#2567C2213yes—
89#2566C2213yes—
90#2566C2213yes—
91#2566C2213yes—
92#2565C2213yes—
93#2565C2213yes—
94#2564C2213yes—
95#2556C2213yes—
96#2552C2213yes—
97#2552C2213yes—
98#2552C2213yes—
99#2552C2213yes—
100#2550C2213yes—
101#2550C2213yes—
102#2549C2216yes—
103#2549C2213yes—
104#2538C2213yes—
105#2538C2213yes—
106#2522C2216yes—
107#2509C2213yes—
108#2509C2216yes—
109#2508C2213yes—
110#2508C2213yes—
111#2507C2216yes—
112#2507C2213yes—
113#2507C2213yes—
114#2507C2213yes—
115#2507C2213yes—
116#2507C2213yes—
117#2505C2213yes—
118#2505C2216yes—
119#2502C2216yes—
120#2497C2216yes—
121#2473C2216yes—
122#2473C2211yescharacteristic
123#2473C2216yes—
124#2454C2213yes—
125#2454C2213yes—
126#2454C2213yes—
127#2453C2213yes—
128#2453C2213yes—
129#2453C2213yes—
130#2453C2213yes—
131#2452C2213yes—
132#2452C2213yes—
133#2452C2213yes—
134#2451C2213yes—
135#2451C2213yes—
136#2450C2213yes—
137#2450C2216yes—
138#2449C2213yes—
139#2449C2216yes—
140#2442C2213yes—
141#2442C2213yes—
142#2442C2213yes—
143#2442C2213yes—
144#2442C2213yes—
145#2442C2213yes—
146#2441C2213yes—
147#2440C2213yes—
148#2440C2213yes—
149#2440C2213yes—
150#2440C2213yes—
151#2439C2213yes—
152#2417C2216yes—
153#2402C2213yes—
154#2399C2213yes—
155#2396C2213yes—
156#2396C2213yes—
157#2370C2213yes—
158#2370C2213yes—
159#2369C2213yes—
160#2368C2216yes—
161#2367C2213yes—
162#2367C2213yes—
163#2367C2213yes—
164#2362C2213yes—
165#2361C2213yes—
166#2361C2213yes—
167#2361C2213yes—
168#2360C2213yes—
169#2360C2213yes—
170#2355C2213yes—
171#2352C2213yes—
172#2351C2211yescharacteristic
173#2351C2211yescharacteristic
174#2351C2211yescharacteristic
175#2351C2211yescharacteristic
176#2351C2211yescharacteristic
177#2351C2211yescharacteristic
178#2351C2211yescharacteristic
179Q8×C4⋊C4C2213yes—
180Q8×C4⋊C4C2213yes—
181Q8×C4⋊C4C2213yes—
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2213yes—
184Q8×C4⋊C4C2211yescharacteristic
185Q8×C4⋊C4C2211yescharacteristic
186Q8×C4⋊C4C2211yescharacteristic
187Q8×C4⋊C4C2211yescharacteristic
188Q8×C4⋊C4C2211yescharacteristic
189Q8×C4⋊C4C2211yescharacteristic
190Q8×C4⋊C4C2211yescharacteristic
191Q8×C4⋊C4C2211yescharacteristic
192#2349C2213yes—
193#2349C2216yes—
194#2349C2213yes—
195D4×C4⋊C4C2213yes—
196D4×C4⋊C4C2216yes—
197D4×C4⋊C4C2213yes—
198D4×C4⋊C4C2213yes—
199D4×C4⋊C4C2213yes—
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204Q8×C22⋊C4C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206#2331C2213yes—
207#2330C2213yes—
208#2326C2213yes—
209#2326C2213yes—
210#2323C2213yes—
211#2323C2213yes—
212#2317C2213yes—
213#2316C2213yes—
214C4×#125C2213yes—
215C4×#125C2213yes—
216C4×#124C2213yes—
217C4×C22⋊Q8C2213yes—
218C4×C22⋊Q8C2213yes—
219C4×C22⋊Q8C2213yes—
220C4×C22⋊Q8C2213yes—
221C4×C22⋊Q8C2213yes—
222C4×#121C2213yes—
223C4×#121C2213yes—
224C4×#121C2213yes—
225#2296C2213yes—
226#2295C2213yes—
227C2×#389C2213yes—
228C2×#389C2213yes—
229C2×#389C2213yes—
230#2290C2213yes—
231#2290C2213yes—
232C2×#384C2213yes—
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×D4C2213yes—
237C2×C4×C4⋊C4C2213yes—
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240#557—28no—
241#557—44no—
242#557—44no—
243#548Q8116yescomplemented
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×#125C2311yescharacteristic
248C2×#125C2313yes—
249C2×#125C2313yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2316yes—
255C2×#124C2313yes—
256C2×C22⋊Q8C2313yes—
257C2×C22⋊Q8C2313yes—
258C2×C22⋊Q8C2313yes—
259C2×C22⋊Q8C2313yes—
260C2×C22⋊Q8C2316yes—
261C2×C22⋊Q8C2316yes—
262C2×C22⋊Q8C2313yes—
263C2×#121C2313yes—
264#520—28no—
265#520—44no—
266C4×#41—44no—
267C2×C4×Q8—28no—
268C2×C4×Q8—44no—
269C2×C4×Q8—44no—
270C2×C4×Q8C2313yes—
271C2×C4×Q8C2313yes—
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2313yes—
284C2×C4×Q8C2313yes—
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2313yes—
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×D4C2313yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2313yes—
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2316yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2316yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×#117C2313yes—
304C2×#117C2313yes—
305C2×#117C2313yes—
306C22×C4⋊C4C2313yes—
307C22×C4⋊C4C2313yes—
308C22×C4⋊C4C2311yescharacteristic
309C22×C4⋊C4C2313yes—
310C22×C4⋊C4C2313yes—
311C22×C4⋊C4C2313yes—
312C22×C4⋊C4C2313yes—
313C22×C4⋊C4C2316yes—
314C22×C4⋊C4C2316yes—
315C22×C42C2313yes—
316C22×C42C2313yes—
317C22×C42C2313yes—
318C22×C42C2313yes—
319#400C2313yes—
320#400C2316yes—
321#400C2316yes—
322#400C2316yes—
323#400C2313yes—
324#400C2316yes—
325#400C2316yes—
326#400C2316yes—
327#400C2313yes—
328#400C2313yes—
329#400C2311yescharacteristic
330#400C2313yes—
331#399C2313yes—
332#399C2316yes—
333#399C2313yes—
334#398C2316yes—
335#398C2316yes—
336#398C2316yes—
337#398C2316yes—
338#398C2313yes—
339#398C2316yes—
340#398C2313yes—
341#398C2313yes—
342#398C2313yes—
343#398C2316yes—
344#398C2316yes—
345#398C2316yes—
346#398C2316yes—
347#398C2313yes—
348#398C2313yes—
349#398C2313yes—
350#398C2311yescharacteristic
351#398C2311yescharacteristic
352#398C2313yes—
353#398C2311yescharacteristic
354#398C2313yes—
355#398C2316yes—
356#398C2316yes—
357#398C2316yes—
358#398C2316yes—
359#398C2316yes—
360#398C2316yes—
361#396C2313yes—
362#396C2313yes—
363#396C2316yes—
364#396C2316yes—
365#396C2316yes—
366#396C2316yes—
367#396C2313yes—
368#396C2316yes—
369#396C2316yes—
370#396C2313yes—
371#395C2313yes—
372#395C2316yes—
373#395C2313yes—
374#395C2313yes—
375#395C2316yes—
376#395C2316yes—
377#395C2313yes—
378#395C2313yes—
379#395C2313yes—
380#393C2313yes—
381#393C2316yes—
382#393C2313yes—
383#391C2313yes—
384#391C2313yes—
385#391C2313yes—
386#391C2313yes—
387#391C2316yes—
388#391C2313yes—
389#391C2316yes—
390#391C2313yes—
391#391C2313yes—
392#391C2313yes—
393#391C2313yes—
394#391C2313yes—
395#391C2313yes—
396#391C2316yes—
397#391C2313yes—
398#390C2313yes—
399#390C2313yes—
400#390C2313yes—
401#390C2313yes—
402#390C2313yes—
403#390C2313yes—
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#389C2316yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2316yes—
426#389C2316yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2316yes—
436#389C2316yes—
437#389C2313yes—
438#389C2316yes—
439#389C2316yes—
440#389C2313yes—
441#389C2313yes—
442#389C2311yescharacteristic
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2316yes—
448#389C2316yes—
449#389C2316yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2316yes—
455#389C2313yes—
456#389C2313yes—
457#389C2316yes—
458#389C2316yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#388C2316yes—
463#388C2313yes—
464#388C2313yes—
465#388C2316yes—
466#388C2316yes—
467#388C2316yes—
468#388C2316yes—
469#388C2313yes—
470#388C2316yes—
471#388C2313yes—
472#388C2316yes—
473#387C2313yes—
474#387C2313yes—
475#387C2313yes—
476#387C2313yes—
477#387C2316yes—
478#387C2313yes—
479#387C2313yes—
480#387C2313yes—
481#387C2313yes—
482#387C2316yes—
483#387C2316yes—
484#387C2316yes—
485#387C2316yes—
486#387C2311yescharacteristic
487#387C2316yes—
488#387C2313yes—
489#387C2313yes—
490#387C2313yes—
491#387C2313yes—
492#387C2313yes—
493#387C2313yes—
494#387C2313yes—
495#387C2313yes—
496#387C2311yescharacteristic
497#387C2313yes—
498#387C2313yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#386C2313yes—
505#386C2313yes—
506#386C2313yes—
507#386C2316yes—
508#386C2313yes—
509#385C2313yes—
510#385C2313yes—
511#385C2313yes—
512#385C2316yes—
513#385C2316yes—
514#385C2316yes—
515#385C2316yes—
516#385C2316yes—
517#385C2316yes—
518#385C2316yes—
519#385C2313yes—
520#385C2311yescharacteristic
521#385C2313yes—
522#385C2313yes—
523#385C2316yes—
524#385C2313yes—
525#385C2316yes—
526#385C2316yes—
527#385C2316yes—
528#385C2316yes—
529#385C2311yescharacteristic
530#385C2313yes—
531#385C2316yes—
532#385C2313yes—
533#385C2316yes—
534#385C2313yes—
535#385C2313yes—
536#385C2316yes—
537#385C2313yes—
538#385C2311yescharacteristic
539#385C2311yescharacteristic
540#384C2313yes—
541#384C2313yes—
542#384C2313yes—
543#384C2313yes—
544#384C2313yes—
545#384C2316yes—
546#384C2313yes—
547#384C2313yes—
548#384C2313yes—
549#384C2313yes—
550#384C2316yes—
551#384C2316yes—
552#382C2313yes—
553#382C2313yes—
554#382C2313yes—
555#382C2313yes—
556#382C2313yes—
557#382C2313yes—
558#382C2313yes—
559#382C2316yes—
560#382C2313yes—
561#380C2311yescharacteristic
562#380C2313yes—
563#380C2316yes—
564#380C2316yes—
565#380C2316yes—
566#380C2313yes—
567#380C2313yes—
568#380C2313yes—
569#380C2316yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2316yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2316yes—
582C4×C4⋊C4C2316yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
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×C22⋊C4C2316yes—
610C4×C22⋊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⋊C4C2316yes—
621C4×C22⋊C4C2311yescharacteristic
622#376C2313yes—
623#376C2313yes—
624C2×#95C2313yes—
625C2×#95C2316yes—
626C2×#95C2313yes—
627C43C2313yes—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41C2×Q818yes—
631C22×Q8—24no—
632C22×Q8—24no—
633C22×Q8C2×Q818yes—
634C22×Q8C2413yes—
635C22×Q8C2413yes—
636C22×Q8C2413yes—
637C22×Q8C2413yes—
638C22×Q8C2411yescharacteristic
639C22×D4C2413yes—
640C22×D4C2413yes—
641C23×C4C2411yescharacteristic
642C23×C4C2413yes—
643C23×C4C2411yescharacteristic
644C23×C4C2411yescharacteristic
645C23×C4C2413yes—
646C23×C4C2413yes—
647C23×C4C2413yes—
648C23×C4C2413yes—
649C23×C4C2416yes—
650C23×C4C2413yes—
651C23×C4C2416yes—
652C23×C4C2413yes—
653C4⋊Q8—212no—
654C4⋊Q8—46no—
655C4⋊Q8—46no—
656#125—212no—
657#125—24no—
658#125—212no—
659#125—46no—
660#125—46no—
661#125—46no—
662#125—46no—
663#125—86no—
664#124C2×Q8124yes—
665C22⋊Q8—212no—
666C22⋊Q8—46no—
667C22⋊Q8—46no—
668C22⋊Q8—46no—
669C22⋊Q8—86no—
670C22⋊Q8—86no—
671C22⋊Q8C2×Q8124yes—
672#121C2×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—46no—
688C4×Q8—46no—
689C4×Q8—46no—
690C4×Q8—46no—
691C4×Q8—46no—
692C4×Q8—46no—
693C4×Q8C2×Q818yes—
694C4×Q8#4118yes—
695C4×D4—212no—
696C4×D4—212no—
697C4×D4—46no—
698C4×D4—46no—
699C4×D4—46no—
700C4×D4—46no—
701C4×D4—46no—
702C4×D4—412no—
703C4×D4—412no—
704C4×D4—46no—
705C4×D4C2×Q8124yes—
706#117—212no—
707#117—46no—
708#117—46no—
709C2×C4⋊C4—212no—
710C2×C4⋊C4—212no—
711C2×C4⋊C4—24no—
712C2×C4⋊C4—46no—
713C2×C4⋊C4—46no—
714C2×C4⋊C4—46no—
715C2×C4⋊C4—46no—
716C2×C4⋊C4—86no—
717C2×C4⋊C4—86no—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2416yes—
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2416yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2416yes—
751C2×C4⋊C4C2416yes—
752C2×C4⋊C4C2416yes—
753C2×C4⋊C4C2416yes—
754C2×C4⋊C4C2416yes—
755C2×C4⋊C4C2416yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2411yescharacteristic
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2416yes—
764C2×C4⋊C4C2416yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2416yes—
774C2×C4⋊C4C2416yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2416yes—
785C2×C4⋊C4C2416yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2411yescharacteristic
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2411yescharacteristic
799C2×C22⋊C4C2411yescharacteristic
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2416yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2416yes—
808C2×C22⋊C4C2416yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2416yes—
812C2×C22⋊C4C2411yescharacteristic
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2416yes—
815C2×C42—212no—
816C2×C42—46no—
817C2×C42—46no—
818C2×C42—46no—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2411yescharacteristic
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2416yes—
837C2×C42C2416yes—
838C2×C42C2413yes—
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2411yescharacteristic
844C2×C42C2413yes—
845C2×C42C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2416yes—
856#95C2416yes—
857#95C2411yescharacteristic
858#95C2411yescharacteristic
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2411yescharacteristic
868#95C2411yescharacteristic
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2416yes—
878#95C2416yes—
879#95C2416yes—
880#95C2416yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2411yescharacteristic
886#95C2411yescharacteristic
887#95C2411yescharacteristic
888#95C2413yes—
889#95C2411yescharacteristic
890#95C2411yescharacteristic
891#95C2416yes—
892#95C2411yescharacteristic
893#95C2413yes—
894#95C2413yes—
895#95C2416yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2416yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2416yes—
908#95C2416yes—
909C24C2513yes—
910C24C2511yescharacteristic
911#41—232no—
912C2×Q8—232no—
913C2×Q8—26no—
914C2×Q8—26no—
915C2×Q8—26no—
916C2×Q8—26no—
917C2×Q8—43no—
918C2×Q8—43no—
919C2×Q8—43no—
920C2×Q8—43no—
921C2×Q8—43no—
922C2×Q8—43no—
923C2×Q8—43no—
924C2×Q8C22×Q8112yes—
925C2×Q8C22×Q814yes—
926C2×Q8C2×#4114yes—
927C2×Q8H(5,𝔽2)14yes—
928C2×D4—26no—
929C2×D4—26no—
930C2×D4—26no—
931C2×D4—26no—
932C2×D4C22×Q8112yes—
933C2×D4C22×Q8112yes—
934C22×C4—22no—
935C22×C4—22no—
936C22×C4—26no—
937C22×C4—26no—
938C22×C4—26no—
939C22×C4—26no—
940C22×C4—22no—
941C22×C4—22no—
942C22×C4—26no—
943C22×C4—22no—
944C22×C4—26no—
945C22×C4—26no—
946C22×C4—26no—
947C22×C4—22no—
948C22×C4—22no—
949C22×C4—212no—
950C22×C4—26no—
951C22×C4—41no—
952C22×C4—41no—
953C22×C4—43no—
954C22×C4—43no—
955C22×C4—43no—
956C22×C4—43no—
957C22×C4—43no—
958C22×C4—43no—
959C22×C4—43no—
960C22×C4—43no—
961C22×C4—46no—
962C22×C4—43no—
963C22×C4—46no—
964C22×C4—43no—
965C22×C4—46no—
966C22×C4—46no—
967C22×C4—46no—
968C22×C4C22×Q8112yes—
969C22×C4C22×Q8112yes—
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C22×C4C2513yes—
973C22×C4C2511yescharacteristic
974C22×C4C2513yes—
975C22×C4C2511yescharacteristic
976C22×C4C2511yescharacteristic
977C22×C4C2513yes—
978C22×C4C2513yes—
979C22×C4C2511yescharacteristic
980C22×C4C2513yes—
981C22×C4C2511yescharacteristic
982C22×C4C2513yes—
983C22×C4C2511yescharacteristic
984C22×C4C2513yes—
985C22×C4C2513yes—
986C22×C4C2513yes—
987C22×C4C2513yes—
988C22×C4C2513yes—
989C22×C4C2511yescharacteristic
990C22×C4C2513yes—
991C22×C4C2513yes—
992C22×C4C2511yescharacteristic
993C22×C4C2511yescharacteristic
994C22×C4C2513yes—
995C22×C4C2511yescharacteristic
996C22×C4C2511yescharacteristic
997C22×C4C2511yescharacteristic
998C22×C4C2513yes—
999C4⋊C4—26no—
1000C4⋊C4—26no—
1001C4⋊C4—212no—
1002C4⋊C4—26no—
1003C4⋊C4—22no—
1004C4⋊C4—22no—
1005C4⋊C4—26no—
1006C4⋊C4—26no—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4—212no—
1010C4⋊C4—26no—
1011C4⋊C4—26no—
1012C4⋊C4—26no—
1013C4⋊C4—26no—
1014C4⋊C4—26no—
1015C4⋊C4—26no—
1016C4⋊C4—26no—
1017C4⋊C4—22no—
1018C4⋊C4—22no—
1019C4⋊C4—22no—
1020C4⋊C4—26no—
1021C4⋊C4—26no—
1022C4⋊C4—22no—
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—43no—
1028C4⋊C4—43no—
1029C4⋊C4—43no—
1030C4⋊C4—43no—
1031C4⋊C4—43no—
1032C4⋊C4—46no—
1033C4⋊C4—46no—
1034C4⋊C4—46no—
1035C4⋊C4—43no—
1036C4⋊C4—43no—
1037C4⋊C4—46no—
1038C4⋊C4—46no—
1039C4⋊C4—46no—
1040C4⋊C4—46no—
1041C4⋊C4—41no—
1042C4⋊C4—46no—
1043C4⋊C4—43no—
1044C4⋊C4—43no—
1045C4⋊C4—46no—
1046C4⋊C4—41no—
1047C4⋊C4—41no—
1048C4⋊C4—43no—
1049C4⋊C4—43no—
1050C4⋊C4—43no—
1051C4⋊C4—43no—
1052C4⋊C4—43no—
1053C4⋊C4—43no—
1054C4⋊C4—43no—
1055C4⋊C4—43no—
1056C4⋊C4—43no—
1057C4⋊C4—43no—
1058C4⋊C4—43no—
1059C4⋊C4—43no—
1060C4⋊C4—43no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—46no—
1064C4⋊C4—46no—
1065C4⋊C4—46no—
1066C4⋊C4—46no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4C22×Q8112yes—
1070C4⋊C4C22×Q8112yes—
1071C4⋊C4C2×#41112yes—
1072C4⋊C42−1+414yes—
1073C22⋊C4—22no—
1074C22⋊C4—26no—
1075C22⋊C4—26no—
1076C22⋊C4—26no—
1077C22⋊C4—22no—
1078C22⋊C4—22no—
1079C22⋊C4—26no—
1080C22⋊C4—26no—
1081C22⋊C4—26no—
1082C22⋊C4—26no—
1083C22⋊C4—43no—
1084C22⋊C4—43no—
1085C22⋊C4—46no—
1086C22⋊C4—43no—
1087C22⋊C4—46no—
1088C22⋊C4—46no—
1089C22⋊C4—43no—
1090C22⋊C4—46no—
1091C22⋊C4—43no—
1092C22⋊C4—43no—
1093C22⋊C4C22×Q814yes—
1094C22⋊C4C22×Q8112yes—
1095C22⋊C4C22×Q8124yes—
1096C42—26no—
1097C42—26no—
1098C42—26no—
1099C42—26no—
1100C42—26no—
1101C42—26no—
1102C42—26no—
1103C42—26no—
1104C42—26no—
1105C42—26no—
1106C42—26no—
1107C42—26no—
1108C42—26no—
1109C42—22no—
1110C42—41no—
1111C42—43no—
1112C42—43no—
1113C42—43no—
1114C42—43no—
1115C42—43no—
1116C42—43no—
1117C42—46no—
1118C42—43no—
1119C42—46no—
1120C42—43no—
1121C42C22×Q8112yes—
1122C42C2×#41112yes—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—23no—
1128C23—23no—
1129C23—23no—
1130C23—23no—
1131C23—23no—
1132C23—23no—
1133C23C23×Q816yes—
1134C23C23×Q812yes—
1135C23#58512yes—
1136C23#58512yes—
1137C23C2611yescharacteristic
1138Q8—224no—
1139Q8—86no—
1140Q8—86no—
1141Q8—86no—
1142Q8#554116yes—
1143D4—224no—
1144D4—224no—
1145C2×C4—28no—
1146C2×C4—21no—
1147C2×C4—23no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—23no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—21no—
1158C2×C4—23no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—23no—
1164C2×C4—224no—
1165C2×C4—224no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—23no—
1170C2×C4—23no—
1171C2×C4—23no—
1172C2×C4—23no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—23no—
1185C2×C4—21no—
1186C2×C4—23no—
1187C2×C4—23no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—23no—
1193C2×C4—21no—
1194C2×C4—23no—
1195C2×C4—23no—
1196C2×C4—23no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—21no—
1204C2×C4—23no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—23no—
1209C2×C4—23no—
1210C2×C4—23no—
1211C2×C4—21no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—23no—
1220C2×C4—21no—
1221C2×C4—23no—
1222C2×C4—23no—
1223C2×C4—412no—
1224C2×C4—44no—
1225C2×C4—44no—
1226C2×C4—812no—
1227C2×C4—86no—
1228C2×C4—86no—
1229C2×C4—86no—
1230C2×C4—86no—
1231C2×C4—166no—
1232C2×C4C23×Q812yes—
1233C2×C4C23×Q816yes—
1234C2×C4C23×Q816yes—
1235C2×C4C23×Q812yes—
1236C2×C4C23×Q816yes—
1237C2×C4C22×#4112yes—
1238C2×C4C22×#4116yes—
1239C2×C4C22×#4116yes—
1240C2×C4C2×H(5,𝔽2)16yes—
1241C2×C4C2×2−1+412yes—
1242C2×C4C2×2−1+412yes—
1243C2×C4C2×2−1+412yes—
1244C22—22no—
1245C22—22no—
1246C22—22no—
1247C22—22no—
1248C22—22no—
1249C22—22no—
1250C22—26no—
1251C22—26no—
1252C22—26no—
1253C22—43no—
1254C22—43no—
1255C22—43no—
1256C22—43no—
1257C22#350414yes—
1258C22C24×Q811yescharacteristic
1259C22C23×#4111yescharacteristic
1260C22C22×H(5,𝔽2)11yescharacteristic
1261C22C22×2−1+411yescharacteristic
1262C22C2×#58511yescharacteristic
1263C22C2×#58511yescharacteristic
1264C22H(7,𝔽2)11yescharacteristic
1265C4—22no—
1266C4—26no—
1267C4—22no—
1268C4—22no—
1269C4—22no—
1270C4—22no—
1271C4—26no—
1272C4—22no—
1273C4—26no—
1274C4—43no—
1275C4—43no—
1276C4—43no—
1277C4—41no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—43no—
1282C4—43no—
1283C4—41no—
1284C4—41no—
1285C4—43no—
1286C4—43no—
1287C4—43no—
1288C4—41no—
1289C4—43no—
1290C4—43no—
1291C4—43no—
1292C4—41no—
1293C4C2×#554112yes—
1294C2—24no—
1295C2—46no—
1296C2C22×#55411yescharacteristic
1297C2#6278811yescharacteristic
1298C2C2×#350411yescharacteristic
1299C2#6289911yescharacteristic
1300C2Q8×2−1+411yescharacteristic
1301C2#6300811yescharacteristic
1302C2#6301511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#548C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59918C2semidirect
2. #59463C2semidirect
3. #59455C2semidirect
4. #59454C2semidirect
5. #59305C2semidirect
6. #45405C2semidirect
7. #45121C2semidirect
8. #45059C2semidirect
9. #44966C2semidirect
10. #39693C2semidirect
11. #39675C2semidirect
12. #38099C2semidirect
13. #37874C2semidirect
14. #36577C2semidirect
15. #36570C2semidirect
16. Q8×#125C2semidirect
17. #36435C2semidirect
18. #36435C2semidirect
19. #36431C2semidirect
20. #36290C2semidirect
21. #35971C2semidirect
22. #35957C2semidirect
23. #35816C2semidirect
24. #35816C2semidirect
25. #34840C2semidirect
26. #34336C2semidirect
29. #34250C2semidirect
31. C2×Q8×C4⋊C4C2semidirect
243. #548Q8semidirect

Maximal subgroups

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

subgroupindex
#599182
#594632
#594552
#594542
#593052
#454052
#451212
#450592
#449662
#396932
#396752
#380992
#378742
#365772
#365702
Q8×#1252
#364352
#364312
#362902
#359712
#359572
#358162
#348402
#343362
#342942
#342502
C4×#5482
C2×Q8×C4⋊C42