Finite Group Databasebeta

← #7688265

Subgroups — #7688265

Order 512.

4979 conjugacy classes of subgroups.

The subgroup lattice has 1127 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59919C214yesmaximal, complemented
2#59871C212yesmaximal, complemented
3#59869C211yesmaximal, characteristic, complemented
4#59642C214yesmaximal, complemented
5#59305C212yesmaximal, complemented
6#59052C212yesmaximal, complemented
7#44908C214yesmaximal, complemented
8#44277C218yesmaximal, complemented
9#39986C214yesmaximal, complemented
10#39654C214yesmaximal, complemented
11#39596C212yesmaximal, complemented
12#39498C212yesmaximal, complemented
13#36563C211yesmaximal, characteristic, complemented
14#36544C212yesmaximal, complemented
15#36481C212yesmaximal, complemented
16#36480C212yesmaximal, complemented
17#36416C212yesmaximal, complemented
18#36180C211yesmaximal, characteristic, complemented
19#36134C211yesmaximal, characteristic, complemented
20#35815C214yesmaximal, complemented
21#34953C212yesmaximal, complemented
22#34929C211yesmaximal, characteristic, complemented
23#34321C212yesmaximal
24#34214C212yesmaximal, complemented
25C4×#555C211yesmaximal, characteristic
26C4×D4×Q8C211yesmaximal, characteristic, complemented
27C2×#555C2211yescharacteristic
28C2×#554C2212yes—
29C2×D4×Q8C2211yescharacteristic
30C2×#533C2212yes—
31C2×#533C2212yes—
32C22×C4×Q8C2212yes—
33#2868C2211yescharacteristic
34#2863C2214yes—
35#2859C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38#2851C2214yes—
39#2809C2214yes—
40#2807C2218yes—
41#2807C2218yes—
42#2806C2218yes—
43#2790C2218yes—
44#2788C2218yes—
45#2780C2218yes—
46#2768C2218yes—
47#2732C2218yes—
48#2720C2218yes—
49#2692C2218yes—
50#2666C2218yes—
51#2628C2214yes—
52#2606C2218yes—
53#2605C2218yes—
54#2589C2218yes—
55#2589C2218yes—
56#2587C2218yes—
57#2584C2214yes—
58#2584C2214yes—
59#2584C2214yes—
60#2583C2218yes—
61#2582C2212yes—
62#2582C2218yes—
63#2580C2214yes—
64#2580C2218yes—
65#2580C2214yes—
66#2579C2218yes—
67#2574C2218yes—
68#2571C2212yes—
69#2570C2218yes—
70#2568C2214yes—
71#2567C2212yes—
72#2567C2212yes—
73#2567C2214yes—
74#2566C2214yes—
75#2556C2214yes—
76#2552C2212yes—
77#2552C2212yes—
78#2552C2214yes—
79#2552C2212yes—
80#2552C2212yes—
81#2551C2211yescharacteristic
82#2550C2214yes—
83#2546C2211yescharacteristic
84#2546C2212yes—
85#2546C2212yes—
86#2542C2212yes—
87#2542C2211yescharacteristic
88#2542C2214yes—
89#2538C2212yes—
90#2538C2211yescharacteristic
91#2522C2218yes—
92#2509C2214yes—
93#2508C2214yes—
94#2508C2214yes—
95#2507C2214yes—
96#2507C2214yes—
97#2507C2214yes—
98#2506C2212yes—
99#2502C2214yes—
100#2502C2214yes—
101#2497C2214yes—
102#2492C2212yes—
103#2492C2214yes—
104#2465C2218yes—
105#2465C2218yes—
106#2454C2214yes—
107#2452C2212yes—
108#2451C2214yes—
109#2449C2218yes—
110#2442C2214yes—
111#2441C2214yes—
112#2441C2214yes—
113#2441C2214yes—
114#2440C2214yes—
115#2440C2214yes—
116#2439C2214yes—
117#2434C2214yes—
118#2429C2214yes—
119#2429C2212yes—
120#2429C2214yes—
121#2423C2214yes—
122#2423C2214yes—
123#2423C2218yes—
124#2417C2214yes—
125#2409C2214yes—
126#2399C2218yes—
127#2396C2214yes—
128#2372C2214yes—
129#2370C2214yes—
130#2369C2212yes—
131#2369C2211yescharacteristic
132#2369C2212yes—
133#2367C2218yes—
134#2365C2214yes—
135#2365C2212yes—
136#2365C2211yescharacteristic
137#2365C2212yes—
138#2363C2212yes—
139#2363C2214yes—
140#2363C2212yes—
141#2361C2214yes—
142#2360C2218yes—
143#2360C2214yes—
144#2360C2212yes—
145#2360C2214yes—
146#2360C2214yes—
147#2355C2214yes—
148#2355C2212yes—
149#2355C2212yes—
150#2355C2212yes—
151#2354C2212yes—
152#2354C2211yescharacteristic
153#2354C2211yescharacteristic
154Q8×C4⋊C4C2212yes—
155Q8×C4⋊C4C2214yes—
156Q8×C4⋊C4C2211yescharacteristic
157Q8×C4⋊C4C2212yes—
158D4×C4⋊C4C2212yes—
159D4×C4⋊C4C2212yes—
160D4×C4⋊C4C2212yes—
161D4×C4⋊C4C2211yescharacteristic
162D4×C4⋊C4C2214yes—
163#2347C2214yes—
164#2347C2214yes—
165#2346C2212yes—
166#2346C2212yes—
167Q8×C22⋊C4C2212yes—
168#2337C2218yes—
169#2330C2218yes—
170#2324C2214yes—
171#2317C2214yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2211yescharacteristic
177C4×C4⋊Q8C2211yescharacteristic
178C4×C4⋊Q8C2214yes—
179C4×C4⋊Q8C2214yes—
180C4×C4⋊Q8C2214yes—
181C4×#124C2214yes—
182C4×C22⋊Q8C2214yes—
183C4×C22⋊Q8C2212yes—
184C4×C22⋊Q8C2212yes—
185C4×#121C2214yes—
186C4×#121C2212yes—
187C4×#121C2212yes—
188#2296C2214yes—
189#2296C2214yes—
190#2293C2212yes—
191C2×#384C2212yes—
192#2274C2214yes—
193C42×Q8C2211yescharacteristic
194C42×D4C2212yes—
195C42×D4C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C4×#117C2212yes—
198C4×#117C2212yes—
199C23×Q8C2312yes—
200#555Q8116yescomplemented
201#554—48no—
202D4×Q8—28no—
203#533—216no—
204#533—48no—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2311yescharacteristic
216C2×#125C2314yes—
217C2×#125C2314yes—
218C2×#125C2314yes—
219C2×#125C2314yes—
220C2×#124C2314yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2318yes—
231C2×C22⋊Q8C2314yes—
232C2×#121C2312yes—
233C2×#121C2312yes—
234C2×C4×Q8—48no—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2318yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×D4C2312yes—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2312yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2314yes—
258C2×C4×D4C2318yes—
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×#117C2314yes—
262C2×#117C2312yes—
263C2×#117C2312yes—
264C2×#117C2314yes—
265C2×#117C2312yes—
266C2×#117C2312yes—
267C22×C4⋊C4C2314yes—
268C22×C4⋊C4C2314yes—
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2314yes—
271C22×C4⋊C4C2314yes—
272C22×C42C2312yes—
273C22×C42C2312yes—
274C22×C42C2314yes—
275#400C2318yes—
276#400C2318yes—
277#400C2314yes—
278#400C2318yes—
279#400C2318yes—
280#399C2318yes—
281#399C2318yes—
282#399C2318yes—
283#399C2318yes—
284#399C2314yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2314yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2314yes—
298#398C2318yes—
299#396C2318yes—
300#396C2318yes—
301#396C2314yes—
302#396C2318yes—
303#396C2314yes—
304#396C2318yes—
305#395C2318yes—
306#395C2318yes—
307#395C2318yes—
308#395C2318yes—
309#395C2318yes—
310#395C2314yes—
311#393C2318yes—
312#393C2314yes—
313#393C2318yes—
314#391C2312yes—
315#391C2314yes—
316#391C2314yes—
317#391C2312yes—
318#391C2312yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2318yes—
323#391C2314yes—
324#391C2312yes—
325#391C2318yes—
326#391C2318yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2312yes—
331#391C2314yes—
332#391C2318yes—
333#390C2312yes—
334#390C2314yes—
335#390C2318yes—
336#390C2312yes—
337#390C2314yes—
338#390C2312yes—
339#390C2312yes—
340#389C2312yes—
341#389C2314yes—
342#389C2318yes—
343#389C2318yes—
344#389C2318yes—
345#389C2314yes—
346#389C2318yes—
347#389C2318yes—
348#389C2312yes—
349#389C2312yes—
350#389C2314yes—
351#389C2314yes—
352#389C2312yes—
353#389C2312yes—
354#389C2314yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2318yes—
369#389C2318yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2318yes—
374#389C2314yes—
375#389C2314yes—
376#389C2312yes—
377#389C2312yes—
378#389C2318yes—
379#389C2314yes—
380#389C2314yes—
381#389C2318yes—
382#389C2318yes—
383#389C2314yes—
384#389C2314yes—
385#389C2312yes—
386#389C2314yes—
387#389C2312yes—
388#388C2314yes—
389#388C2318yes—
390#388C2318yes—
391#388C2314yes—
392#388C2318yes—
393#388C2318yes—
394#388C2314yes—
395#388C2318yes—
396#388C2314yes—
397#388C2314yes—
398#388C2314yes—
399#388C2314yes—
400#388C2314yes—
401#387C2314yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2314yes—
411#387C2318yes—
412#387C2314yes—
413#387C2314yes—
414#387C2318yes—
415#387C2318yes—
416#386C2314yes—
417#386C2318yes—
418#386C2318yes—
419#386C2314yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2314yes—
426#385C2314yes—
427#385C2318yes—
428#385C2318yes—
429#385C2314yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2314yes—
435#384C2314yes—
436#384C2314yes—
437#384C2311yescharacteristic
438#384C2312yes—
439#384C2311yescharacteristic
440#384C2312yes—
441#384C2311yescharacteristic
442#384C2312yes—
443#384C2314yes—
444#384C2318yes—
445#384C2314yes—
446#384C2312yes—
447#384C2314yes—
448#384C2312yes—
449#384C2312yes—
450#383C2318yes—
451#382C2314yes—
452#382C2318yes—
453#382C2314yes—
454#382C2314yes—
455#382C2314yes—
456#380C2318yes—
457#380C2314yes—
458#380C2312yes—
459#380C2314yes—
460#380C2312yes—
461#380C2314yes—
462#380C2314yes—
463#380C2314yes—
464#380C2312yes—
465#380C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2318yes—
475C4×C4⋊C4C2318yes—
476C4×C4⋊C4C2318yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C22⋊C4C2318yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2314yes—
520#376C2314yes—
521#376C2314yes—
522C43C2312yes—
523C43C2314yes—
524C43C2311yescharacteristic
525C22×Q8—28no—
526C22×Q8—44no—
527C22×Q8—44no—
528C22×Q8C2412yes—
529C22×Q8C2412yes—
530C22×Q8C2414yes—
531C22×Q8C2411yescharacteristic
532C22×Q8C2414yes—
533C22×Q8C2414yes—
534C22×Q8C2412yes—
535C22×D4C2411yescharacteristic
536C22×D4C2411yescharacteristic
537C22×D4C2414yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2414yes—
545C23×C4C2418yes—
546C23×C4C2414yes—
547C4⋊Q8—28no—
548C4⋊Q8—28no—
549C4⋊Q8—28no—
550C4⋊Q8—24no—
551C4⋊Q8—28no—
552C4⋊Q8—24no—
553C4⋊Q8—28no—
554C4⋊Q8—44no—
555C4⋊Q8—48no—
556C4⋊Q8—82no—
557C4⋊Q8C2×Q818yescomplemented
558#125—216no—
559#125—48no—
560#125—48no—
561#125—48no—
562#124C2×Q8132yescomplemented
563C22⋊Q8—28no—
564C22⋊Q8—28no—
565C22⋊Q8—216no—
566C22⋊Q8—216no—
567C22⋊Q8—28no—
568C22⋊Q8—416no—
569C22⋊Q8—44no—
570C22⋊Q8—48no—
571C22⋊Q8—48no—
572C22⋊Q8—48no—
573C22⋊Q8—84no—
574#121C2×Q8116yes—
575#121C2×Q8116yescomplemented
576C4×Q8—216no—
577C4×Q8—28no—
578C4×Q8—24no—
579C4×Q8—28no—
580C4×Q8—48no—
581C4×Q8—44no—
582C4×Q8—48no—
583C4×Q8—44no—
584C4×Q8—44no—
585C4×Q8—42no—
586C4×Q8—48no—
587C4×Q8—48no—
588C4×Q8—88no—
589C4×Q8—84no—
590C4×Q8#4118yes—
591C4×D4—24no—
592C4×D4—24no—
593C4×D4—28no—
594C4×D4—24no—
595C4×D4—44no—
596C4×D4—42no—
597C4×D4—48no—
598C4×D4—48no—
599C4×D4—88no—
600C4×D4C2×Q818yes—
601C4×D4C2×Q818yescomplemented
602#117—28no—
603#117—216no—
604#117—44no—
605#117—48no—
606#117C2×Q8116yescomplemented
607#117C2×Q8116yescomplemented
608C2×C4⋊C4—48no—
609C2×C4⋊C4—44no—
610C2×C4⋊C4—48no—
611C2×C4⋊C4—48no—
612C2×C4⋊C4—84no—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2412yes—
694C2×C22⋊C4C2412yes—
695C2×C42—28no—
696C2×C42—28no—
697C2×C42—48no—
698C2×C42C2414yes—
699C2×C42C2414yes—
700C2×C42C2414yes—
701C2×C42C2414yes—
702C2×C42C2412yes—
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2411yescharacteristic
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2418yes—
715C2×C42C2414yes—
716C2×C42C2418yes—
717C2×C42C2414yes—
718C2×C42C2412yes—
719C2×C42C2414yes—
720C2×C42C2414yes—
721C2×C42C2418yes—
722C2×C42C2412yes—
723C2×C42C2411yescharacteristic
724C2×C42C2414yes—
725C2×C42C2411yescharacteristic
726C2×C42C2412yes—
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729#95C2412yes—
730#95C2412yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2412yes—
739#95C2412yes—
740#95C2414yes—
741#95C2414yes—
742#95C2412yes—
743#95C2412yes—
744#95C2418yes—
745#95C2414yes—
746#95C2418yes—
747#95C2418yes—
748#95C2414yes—
749#95C2412yes—
750#95C2414yes—
751#95C2412yes—
752#95C2412yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756#95C2418yes—
757#95C2414yes—
758#95C2418yes—
759#95C2414yes—
760#95C2418yes—
761#95C2414yes—
762#95C2418yes—
763#95C2418yes—
764#95C2418yes—
765#95C2418yes—
766#95C2414yes—
767#95C2418yes—
768#95C2418yes—
769C24C2512yes—
770C24C2512yes—
771C2×Q8—28no—
772C2×Q8—24no—
773C2×Q8—28no—
774C2×Q8—24no—
775C2×Q8—22no—
776C2×Q8—24no—
777C2×Q8—24no—
778C2×Q8—28no—
779C2×Q8—28no—
780C2×Q8—22no—
781C2×Q8—24no—
782C2×Q8—24no—
783C2×Q8—44no—
784C2×Q8—42no—
785C2×Q8—42no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—44no—
790C2×Q8—432no—
791C2×Q8C22×Q818yes—
792C2×Q8C2×#4114yes—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—44no—
798C2×D4—44no—
799C2×D4C22×Q814yes—
800C2×D4C22×Q814yes—
801C2×D4C22×Q8116yes—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—28no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—44no—
817C22×C4—42no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—42no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—42no—
824C22×C4—48no—
825C22×C4—48no—
826C22×C4—48no—
827C22×C4C22×Q818yes—
828C22×C4C22×Q818yes—
829C22×C4C2511yescharacteristic
830C22×C4C2514yes—
831C22×C4C2512yes—
832C22×C4C2514yes—
833C22×C4C2512yes—
834C22×C4C2514yes—
835C22×C4C2514yes—
836C22×C4C2512yes—
837C22×C4C2514yes—
838C22×C4C2512yes—
839C22×C4C2518yes—
840C22×C4C2512yes—
841C22×C4C2512yes—
842C22×C4C2511yescharacteristic
843C22×C4C2514yes—
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2511yescharacteristic
847C22×C4C2512yes—
848C22×C4C2511yescharacteristic
849C22×C4C2512yes—
850C22×C4C2511yescharacteristic
851C22×C4C2511yescharacteristic
852C22×C4C2511yescharacteristic
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—24no—
856C4⋊C4—22no—
857C4⋊C4—28no—
858C4⋊C4—28no—
859C4⋊C4—28no—
860C4⋊C4—28no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—28no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—22no—
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—24no—
870C4⋊C4—28no—
871C4⋊C4—22no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—28no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—28no—
878C4⋊C4—22no—
879C4⋊C4—24no—
880C4⋊C4—22no—
881C4⋊C4—48no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—48no—
886C4⋊C4—42no—
887C4⋊C4—48no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—48no—
891C4⋊C4—42no—
892C4⋊C4—44no—
893C4⋊C4—42no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4—48no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—48no—
901C4⋊C4—42no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4—48no—
906C4⋊C4—44no—
907C4⋊C4C22×Q814yes—
908C4⋊C4C22×Q814yes—
909C4⋊C4C22×Q818yes—
910C4⋊C4C22×Q818yes—
911C4⋊C4C2×#4118yes—
912C4⋊C4C2×#4114yes—
913C4⋊C42−1+414yes—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—24no—
917C22⋊C4—28no—
918C22⋊C4—24no—
919C22⋊C4—28no—
920C22⋊C4—24no—
921C22⋊C4—44no—
922C22⋊C4—48no—
923C22⋊C4—42no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—48no—
928C22⋊C4—44no—
929C22⋊C4—48no—
930C22⋊C4—44no—
931C22⋊C4C22×Q8116yes—
932C22⋊C4C22×Q8116yes—
933C22⋊C4C22×Q818yes—
934C22⋊C4C22×Q818yes—
935C42—24no—
936C42—24no—
937C42—24no—
938C42—28no—
939C42—24no—
940C42—24no—
941C42—24no—
942C42—24no—
943C42—28no—
944C42—28no—
945C42—22no—
946C42—24no—
947C42—28no—
948C42—24no—
949C42—22no—
950C42—22no—
951C42—44no—
952C42—44no—
953C42—44no—
954C42—48no—
955C42—48no—
956C42—42no—
957C42—48no—
958C42—44no—
959C42—42no—
960C42—41no—
961C42C22×Q8116yes—
962C42C22×Q814yes—
963C42C2×#4114yes—
964C42C2×#4118yes—
965C42H(5,𝔽2)14yes—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23C23×Q814yes—
979C23C23×Q814yes—
980C23C2611yescharacteristic
981Q8—28no—
982Q8—48no—
983Q8—416no—
984Q8—416no—
985Q8—48no—
986Q8—48no—
987Q8—88no—
988D4—28no—
989D4—28no—
990D4—416no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—21no—
997C2×C4—22no—
998C2×C4—21no—
999C2×C4—24no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—21no—
1006C2×C4—22no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—216no—
1010C2×C4—216no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—28no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—28no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—28no—
1047C2×C4—48no—
1048C2×C4—416no—
1049C2×C4—48no—
1050C2×C4—48no—
1051C2×C4—84no—
1052C2×C4—88no—
1053C2×C4—168no—
1054C2×C4C23×Q814yes—
1055C2×C4C23×Q814yes—
1056C2×C4C23×Q812yes—
1057C2×C4C23×Q818yes—
1058C2×C4C23×Q812yes—
1059C2×C4C23×Q812yes—
1060C2×C4C22×#4112yes—
1061C2×C4C22×#4114yes—
1062C2×C4C22×#4114yes—
1063C2×C4C22×#4112yes—
1064C2×C4C22×#4112yes—
1065C2×C4C2×H(5,𝔽2)12yes—
1066C2×C4C2×H(5,𝔽2)12yes—
1067C2×C4C2×H(5,𝔽2)12yes—
1068C2×C4C2×2−1+414yes—
1069C2×C4C2×2−1+412yes—
1070C2×C4#58512yes—
1071C2×C4#58512yes—
1072C22—24no—
1073C22—24no—
1074C22—24no—
1075C22—24no—
1076C22—24no—
1077C22—24no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22C24×Q811yescharacteristic
1087C22C23×#4111yescharacteristic
1088C22C22×H(5,𝔽2)11yescharacteristic
1089C22C22×2−1+411yescharacteristic
1090C22C2×#58511yescharacteristic
1091C22C2×#58511yescharacteristic
1092C22H(7,𝔽2)11yescharacteristic
1093C4—28no—
1094C4—22no—
1095C4—22no—
1096C4—24no—
1097C4—24no—
1098C4—24no—
1099C4—24no—
1100C4—22no—
1101C4—24no—
1102C4—44no—
1103C4—42no—
1104C4—42no—
1105C4—44no—
1106C4—44no—
1107C4—41no—
1108C4—44no—
1109C4—42no—
1110C4—42no—
1111C4—42no—
1112C4—44no—
1113C4—48no—
1114C4Q8×#4114yes—
1115C4#350314yes—
1116C4#350614yes—
1117C2—44no—
1118C2—44no—
1119C2C2×Q8×#4111yescharacteristic
1120C2C2×#350611yescharacteristic
1121C2C2×#350311yescharacteristic
1122C2#6295511yescharacteristic
1123C2#6298911yescharacteristic
1124C2#6300011yescharacteristic
1125C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#555C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59919C2semidirect
2. #59871C2semidirect
3. #59869C2semidirect
4. #59642C2semidirect
5. #59305C2semidirect
6. #59052C2semidirect
7. #44908C2semidirect
8. #44277C2semidirect
9. #39986C2semidirect
10. #39654C2semidirect
11. #39596C2semidirect
12. #39498C2semidirect
13. #36563C2semidirect
14. #36544C2semidirect
15. #36481C2semidirect
16. #36480C2semidirect
17. #36416C2semidirect
18. #36180C2semidirect
19. #36134C2semidirect
20. #35815C2semidirect
21. #34953C2semidirect
22. #34929C2semidirect
24. #34214C2semidirect
26. C4×D4×Q8C2semidirect
200. #555Q8semidirect
557. C4⋊Q8C2×Q8semidirect
562. #124C2×Q8semidirect
575. #121C2×Q8semidirect
601. C4×D4C2×Q8semidirect
606. #117C2×Q8semidirect
607. #117C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#599192
#598712
#598692
#596422
#593052
#590522
#449082
#442772
#399862
#396542
#395962
#394982
#365632
#365442
#364812
#364802
#364162
#361802
#361342
#358152
#349532
#349292
#343212
#342142
C4×#5552
C4×D4×Q82