Finite Group Databasebeta

← #7688308

Subgroups — #7688308

Order 512.

5189 conjugacy classes of subgroups.

The subgroup lattice has 1105 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59869C211yesmaximal, characteristic, complemented
2#59681C212yesmaximal, complemented
3#59668C212yesmaximal, complemented
4#59664C214yesmaximal, complemented
5#59144C212yesmaximal, complemented
6#59144C214yesmaximal, complemented
7#45044C214yesmaximal, complemented
8#43556C218yesmaximal, complemented
9#39641C212yesmaximal, complemented
10#39640C214yesmaximal, complemented
11#39181C212yesmaximal, complemented
12#39178C214yesmaximal, complemented
13#36599C212yesmaximal, complemented
14#36593C211yesmaximal, characteristic, complemented
15#36560C211yesmaximal, characteristic, complemented
16#36545C212yesmaximal, complemented
17#36290C212yesmaximal
18D4×C4⋊Q8C212yesmaximal
19D4×C4⋊Q8C211yesmaximal, characteristic
20#35858C214yesmaximal
21#34951C211yesmaximal, characteristic, complemented
22C2×#2546C212yesmaximal, complemented
23#34334C212yesmaximal
24#34332C212yesmaximal
25C4×#554C211yesmaximal, characteristic
26C4×D4×Q8C211yesmaximal, characteristic
27C2×#557C2212yes—
28C2×#557C2212yes—
29C2×#554C2211yescharacteristic
30C2×D4×Q8C2212yes—
31C2×D4×Q8C2211yescharacteristic
32C22×C4⋊Q8C2214yes—
33C22×C4⋊Q8C2212yes—
34C22×C4×Q8C2212yes—
35#2868C2211yescharacteristic
36#2868C2212yes—
37#2859C2212yes—
38#2857C2212yes—
39#2857C2214yes—
40#2851C2214yes—
41#2809C2214yes—
42#2806C2218yes—
43#2805C2218yes—
44#2802C2218yes—
45#2791C2218yes—
46#2791C2218yes—
47#2774C2218yes—
48#2774C2218yes—
49#2713C2218yes—
50#2713C2218yes—
51#2713C2218yes—
52#2647C2214yes—
53#2646C2218yes—
54#2590C2218yes—
55#2585C2214yes—
56#2585C2218yes—
57#2584C2214yes—
58#2582C2211yescharacteristic
59#2581C2214yes—
60#2571C2212yes—
61#2570C2214yes—
62#2569C2218yes—
63#2568C2211yescharacteristic
64#2568C2214yes—
65#2568C2212yes—
66#2565C2214yes—
67#2552C2212yes—
68#2552C2214yes—
69#2552C2212yes—
70#2552C2214yes—
71#2552C2211yescharacteristic
72#2551C2212yes—
73#2551C2214yes—
74#2551C2214yes—
75#2551C2212yes—
76#2550C2214yes—
77#2550C2218yes—
78#2546C2214yes—
79#2546C2214yes—
80#2546C2212yes—
81#2546C2214yes—
82#2546C2214yes—
83#2546C2214yes—
84#2546C2212yes—
85#2546C2212yes—
86#2546C2212yes—
87#2546C2218yes—
88#2546C2211yescharacteristic
89#2546C2212yes—
90#2546C2214yes—
91#2546C2212yes—
92#2511C2214yes—
93#2511C2212yes—
94#2509C2212yes—
95#2509C2214yes—
96#2509C2214yes—
97#2508C2214yes—
98#2508C2214yes—
99#2507C2214yes—
100#2507C2214yes—
101#2507C2214yes—
102#2506C2214yes—
103#2506C2214yes—
104#2505C2218yes—
105#2505C2218yes—
106#2473C2218yes—
107#2473C2218yes—
108#2473C2218yes—
109#2473C2218yes—
110#2462C2218yes—
111#2453C2212yes—
112#2451C2214yes—
113#2451C2218yes—
114#2446C2212yes—
115#2446C2214yes—
116#2446C2214yes—
117#2446C2214yes—
118#2442C2218yes—
119#2442C2214yes—
120#2442C2214yes—
121#2440C2214yes—
122#2440C2218yes—
123#2440C2218yes—
124#2440C2214yes—
125#2434C2214yes—
126#2434C2214yes—
127#2434C2214yes—
128#2402C2214yes—
129C2×#398C2218yes—
130#2370C2214yes—
131#2370C2214yes—
132#2370C2212yes—
133#2369C2211yescharacteristic
134#2369C2212yes—
135#2369C2214yes—
136#2368C2218yes—
137#2368C2214yes—
138#2365C2214yes—
139#2365C2212yes—
140#2365C2212yes—
141#2365C2211yescharacteristic
142#2365C2212yes—
143#2360C2214yes—
144#2360C2218yes—
145#2360C2212yes—
146#2360C2214yes—
147#2360C2214yes—
148#2360C2212yes—
149#2355C2211yescharacteristic
150#2355C2212yes—
151#2355C2212yes—
152Q8×C4⋊C4C2212yes—
153Q8×C4⋊C4C2212yes—
154Q8×C4⋊C4C2211yescharacteristic
155#2349C2212yes—
156#2349C2214yes—
157D4×C4⋊C4C2212yes—
158D4×C4⋊C4C2212yes—
159D4×C4⋊C4C2214yes—
160D4×C4⋊C4C2214yes—
161D4×C4⋊C4C2212yes—
162D4×C4⋊C4C2211yescharacteristic
163D4×C4⋊C4C2211yescharacteristic
164#2345C2212yes—
165#2345C2214yes—
166Q8×C22⋊C4C2214yes—
167Q8×C22⋊C4C2212yes—
168#2331C2214yes—
169#2330C2214yes—
170#2329C2218yes—
171#2329C2218yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2211yescharacteristic
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2211yescharacteristic
178C4×C4⋊Q8C2211yescharacteristic
179C4×#125C2212yes—
180C4×#125C2212yes—
181C4×C22⋊Q8C2214yes—
182C4×C22⋊Q8C2212yes—
183C4×C22⋊Q8C2212yes—
184C4×C22⋊Q8C2214yes—
185C4×C22⋊Q8C2214yes—
186C4×C22⋊Q8C2214yes—
187#2295C2212yes—
188#2295C2212yes—
189C2×#391C2214yes—
190C2×#389C2214yes—
191C2×#389C2214yes—
192#2275C2214yes—
193C42×Q8C2211yescharacteristic
194C42×Q8C2211yescharacteristic
195C42×D4C2212yes—
196C42×D4C2211yescharacteristic
197C42×D4C2212yes—
198C2×C4×C4⋊C4C2212yes—
199C23×Q8C2312yes—
200C23×Q8C2314yes—
201#557—48no—
202#557—48no—
203#554Q8116yescomplemented
204D4×Q8—28no—
205D4×Q8—216no—
206C2×C4⋊Q8—48no—
207C2×C4⋊Q8—416no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2314yes—
219C2×C4⋊Q8C2314yes—
220C2×C4⋊Q8C2314yes—
221C2×C4⋊Q8C2314yes—
222C2×C4⋊Q8C2318yes—
223C2×C4⋊Q8C2314yes—
224C2×C4⋊Q8C2318yes—
225C2×C4⋊Q8C2311yescharacteristic
226C2×#125C2312yes—
227C2×#125C2314yes—
228C2×#125C2314yes—
229C2×#125C2318yes—
230C2×#125C2318yes—
231C2×#125C2312yes—
232C2×C22⋊Q8C2318yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2312yes—
238C2×C4×Q8—48no—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2311yescharacteristic
256C2×C4×D4C2312yes—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2314yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2312yes—
263C2×C4×D4C2311yescharacteristic
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2314yes—
267C22×C4⋊C4C2318yes—
268C22×C4⋊C4C2314yes—
269C22×C4⋊C4C2314yes—
270C22×C4⋊C4C2318yes—
271C22×C4⋊C4C2312yes—
272C22×C42C2312yes—
273C22×C42C2314yes—
274C22×C42C2314yes—
275#400C2318yes—
276#400C2314yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2314yes—
290#398C2318yes—
291#398C2318yes—
292#398C2314yes—
293#398C2318yes—
294#398C2314yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2314yes—
305#398C2318yes—
306#398C2318yes—
307#398C2318yes—
308#395C2318yes—
309#395C2318yes—
310#395C2318yes—
311#395C2318yes—
312#395C2318yes—
313#395C2318yes—
314#391C2312yes—
315#391C2314yes—
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2314yes—
321#391C2314yes—
322#391C2318yes—
323#391C2312yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2312yes—
328#391C2314yes—
329#391C2312yes—
330#391C2312yes—
331#391C2318yes—
332#391C2318yes—
333#391C2318yes—
334#391C2312yes—
335#391C2314yes—
336#391C2314yes—
337#391C2314yes—
338#391C2318yes—
339#391C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2314yes—
345#389C2314yes—
346#389C2312yes—
347#389C2314yes—
348#389C2314yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2314yes—
354#389C2314yes—
355#389C2312yes—
356#389C2314yes—
357#389C2312yes—
358#389C2312yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2312yes—
366#389C2312yes—
367#389C2318yes—
368#389C2318yes—
369#389C2318yes—
370#389C2318yes—
371#389C2314yes—
372#389C2318yes—
373#389C2318yes—
374#389C2314yes—
375#389C2314yes—
376#389C2318yes—
377#389C2314yes—
378#389C2314yes—
379#389C2318yes—
380#389C2312yes—
381#389C2314yes—
382#389C2314yes—
383#389C2312yes—
384#389C2314yes—
385#389C2318yes—
386#389C2314yes—
387#389C2318yes—
388#389C2314yes—
389#389C2318yes—
390#389C2312yes—
391#389C2318yes—
392#389C2312yes—
393#387C2314yes—
394#387C2314yes—
395#387C2314yes—
396#387C2314yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2314yes—
406#387C2314yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2314yes—
413#387C2318yes—
414#387C2314yes—
415#387C2314yes—
416#387C2318yes—
417#387C2318yes—
418#387C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2314yes—
422#387C2314yes—
423#385C2314yes—
424#385C2318yes—
425#385C2314yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2314yes—
431#385C2318yes—
432#385C2314yes—
433#385C2318yes—
434#385C2318yes—
435#385C2314yes—
436#385C2314yes—
437#384C2311yescharacteristic
438#384C2312yes—
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#384C2312yes—
442#384C2312yes—
443#384C2312yes—
444#384C2314yes—
445#384C2312yes—
446#384C2314yes—
447#384C2312yes—
448#384C2314yes—
449#384C2314yes—
450#382C2312yes—
451#382C2312yes—
452#382C2314yes—
453#382C2318yes—
454#382C2314yes—
455#382C2314yes—
456#380C2314yes—
457#380C2318yes—
458#380C2318yes—
459#380C2318yes—
460#380C2312yes—
461#380C2314yes—
462#380C2312yes—
463#380C2314yes—
464#380C2314yes—
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2318yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2318yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2311yescharacteristic
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2314yes—
520#376C2314yes—
521C2×#95C2314yes—
522C2×#95C2318yes—
523C2×#95C2318yes—
524C43C2312yes—
525C43C2312yes—
526C43C2311yescharacteristic
527C22×Q8—28no—
528C22×Q8—28no—
529C22×Q8—216no—
530C22×Q8—44no—
531C22×Q8—48no—
532C22×Q8—48no—
533C22×Q8C2412yes—
534C22×Q8C2414yes—
535C22×Q8C2412yes—
536C22×Q8C2414yes—
537C22×Q8C2411yescharacteristic
538C22×Q8C2411yescharacteristic
539C22×Q8C2418yes—
540C22×Q8C2412yes—
541C22×D4C2411yescharacteristic
542C23×C4C2414yes—
543C23×C4C2412yes—
544C23×C4C2414yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2418yes—
548C23×C4C2414yes—
549C23×C4C2414yes—
550C4⋊Q8—28no—
551C4⋊Q8—216no—
552C4⋊Q8—28no—
553C4⋊Q8—216no—
554C4⋊Q8—24no—
555C4⋊Q8—28no—
556C4⋊Q8—24no—
557C4⋊Q8—28no—
558C4⋊Q8—48no—
559C4⋊Q8—48no—
560C4⋊Q8—48no—
561C4⋊Q8—48no—
562C4⋊Q8—48no—
563C4⋊Q8—48no—
564C4⋊Q8—44no—
565C4⋊Q8—416no—
566C4⋊Q8—416no—
567C4⋊Q8C2×Q818yescomplemented
568#125—28no—
569#125—48no—
570#125—48no—
571#125—416no—
572#125—416no—
573#125C2×Q8116yescomplemented
574C22⋊Q8—28no—
575C22⋊Q8—216no—
576C22⋊Q8—216no—
577C22⋊Q8—232no—
578C22⋊Q8C2×Q8132yescomplemented
579C22⋊Q8C2×Q8116yescomplemented
580C4×Q8—24no—
581C4×Q8—24no—
582C4×Q8—24no—
583C4×Q8—28no—
584C4×Q8—24no—
585C4×Q8—28no—
586C4×Q8—24no—
587C4×Q8—48no—
588C4×Q8—44no—
589C4×Q8—48no—
590C4×Q8—48no—
591C4×Q8—44no—
592C4×Q8—44no—
593C4×Q8—48no—
594C4×Q8—48no—
595C4×Q8—48no—
596C4×Q8C2×Q818yescomplemented
597C4×D4—28no—
598C4×D4—216no—
599C4×D4—24no—
600C4×D4—28no—
601C4×D4—28no—
602C4×D4C2×Q8116yes—
603C4×D4C2×Q818yes—
604C4×D4#4118yes—
605C2×C4⋊C4—28no—
606C2×C4⋊C4—44no—
607C2×C4⋊C4—48no—
608C2×C4⋊C4—48no—
609C2×C4⋊C4—416no—
610C2×C4⋊C4—48no—
611C2×C4⋊C4—416no—
612C2×C4⋊C4C2×Q8116yescomplemented
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2412yes—
688C2×C42—28no—
689C2×C42—48no—
690C2×C42—48no—
691C2×C42C2412yes—
692C2×C42C2414yes—
693C2×C42C2412yes—
694C2×C42C2411yescharacteristic
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2414yes—
698C2×C42C2412yes—
699C2×C42C2411yescharacteristic
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2414yes—
704C2×C42C2412yes—
705C2×C42C2411yescharacteristic
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2418yes—
710C2×C42C2418yes—
711C2×C42C2414yes—
712C2×C42C2414yes—
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2411yescharacteristic
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2418yes—
719C2×C42C2412yes—
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723#95C2414yes—
724#95C2412yes—
725#95C2414yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2412yes—
739#95C2414yes—
740#95C2414yes—
741#95C2412yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2412yes—
746#95C2414yes—
747#95C2412yes—
748#95C2414yes—
749#95C2412yes—
750#95C2412yes—
751#95C2412yes—
752#95C2414yes—
753#95C2412yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2414yes—
761#95C2418yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771C24C2512yes—
772C2×Q8—22no—
773C2×Q8—24no—
774C2×Q8—28no—
775C2×Q8—24no—
776C2×Q8—28no—
777C2×Q8—216no—
778C2×Q8—22no—
779C2×Q8—22no—
780C2×Q8—24no—
781C2×Q8—28no—
782C2×Q8—28no—
783C2×Q8—24no—
784C2×Q8—24no—
785C2×Q8—28no—
786C2×Q8—24no—
787C2×Q8—22no—
788C2×Q8—42no—
789C2×Q8—44no—
790C2×Q8—42no—
791C2×Q8—48no—
792C2×Q8—48no—
793C2×Q8—432no—
794C2×Q8—832no—
795C2×Q8C22×Q814yes—
796C2×Q8C22×Q818yes—
797C2×Q8H(5,𝔽2)14yes—
798C2×D4C22×Q814yes—
799C2×D4C2×#4114yes—
800C2×D42−1+414yes—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—28no—
806C22×C4—24no—
807C22×C4—28no—
808C22×C4—216no—
809C22×C4—28no—
810C22×C4—24no—
811C22×C4—28no—
812C22×C4—28no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—42no—
818C22×C4—44no—
819C22×C4—48no—
820C22×C4—48no—
821C22×C4—44no—
822C22×C4C22×Q818yes—
823C22×C4C22×Q8116yes—
824C22×C4C2×#4118yes—
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2514yes—
828C22×C4C2514yes—
829C22×C4C2512yes—
830C22×C4C2514yes—
831C22×C4C2511yescharacteristic
832C22×C4C2512yes—
833C22×C4C2512yes—
834C22×C4C2514yes—
835C22×C4C2514yes—
836C22×C4C2518yes—
837C22×C4C2512yes—
838C22×C4C2511yescharacteristic
839C22×C4C2512yes—
840C22×C4C2514yes—
841C22×C4C2512yes—
842C22×C4C2511yescharacteristic
843C22×C4C2512yes—
844C22×C4C2511yescharacteristic
845C22×C4C2512yes—
846C22×C4C2512yes—
847C22×C4C2511yescharacteristic
848C22×C4C2511yescharacteristic
849C22×C4C2511yescharacteristic
850C4⋊C4—24no—
851C4⋊C4—28no—
852C4⋊C4—24no—
853C4⋊C4—22no—
854C4⋊C4—24no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—216no—
858C4⋊C4—24no—
859C4⋊C4—28no—
860C4⋊C4—24no—
861C4⋊C4—22no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—28no—
868C4⋊C4—216no—
869C4⋊C4—28no—
870C4⋊C4—216no—
871C4⋊C4—28no—
872C4⋊C4—22no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—22no—
876C4⋊C4—28no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—22no—
881C4⋊C4—24no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—24no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4—48no—
891C4⋊C4—48no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—42no—
895C4⋊C4—44no—
896C4⋊C4—42no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—42no—
901C4⋊C4—44no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—44no—
905C4⋊C4—48no—
906C4⋊C4—48no—
907C4⋊C4—44no—
908C4⋊C4C22×Q814yes—
909C4⋊C4C22×Q8116yes—
910C4⋊C4C22×Q818yes—
911C4⋊C4C22×Q814yes—
912C4⋊C4C22×Q818yes—
913C4⋊C4C22×Q818yes—
914C4⋊C4C22×Q8116yes—
915C4⋊C4C2×#4114yes—
916C4⋊C42−1+414yes—
917C22⋊C4—28no—
918C22⋊C4—216no—
919C22⋊C4—28no—
920C22⋊C4—24no—
921C22⋊C4—28no—
922C22⋊C4C22×Q8116yes—
923C22⋊C4C22×Q818yes—
924C22⋊C4C2×#4118yes—
925C42—24no—
926C42—28no—
927C42—24no—
928C42—24no—
929C42—24no—
930C42—24no—
931C42—24no—
932C42—28no—
933C42—28no—
934C42—24no—
935C42—22no—
936C42—24no—
937C42—24no—
938C42—22no—
939C42—24no—
940C42—24no—
941C42—22no—
942C42—24no—
943C42—44no—
944C42—44no—
945C42—44no—
946C42—44no—
947C42—41no—
948C42—42no—
949C42—42no—
950C42—48no—
951C42—48no—
952C42—48no—
953C42C22×Q818yes—
954C42C22×Q814yes—
955C42C2×#4114yes—
956C42H(5,𝔽2)14yes—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23C23×Q814yes—
962C23C22×#4114yes—
963C23C2×2−1+414yes—
964C23C2611yescharacteristic
965Q8—28no—
966Q8—28no—
967Q8—48no—
968Q8—416no—
969Q8—48no—
970Q8—416no—
971Q8—48no—
972Q8—816no—
973D4#557116yescomplemented
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—21no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—21no—
988C2×C4—22no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—24no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—216no—
995C2×C4—216no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—28no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—21no—
1008C2×C4—22no—
1009C2×C4—28no—
1010C2×C4—28no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—21no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—416no—
1033C2×C4—416no—
1034C2×C4—48no—
1035C2×C4—416no—
1036C2×C4—88no—
1037C2×C4—816no—
1038C2×C4C23×Q814yes—
1039C2×C4C23×Q812yes—
1040C2×C4C23×Q814yes—
1041C2×C4C23×Q814yes—
1042C2×C4C23×Q818yes—
1043C2×C4C23×Q812yes—
1044C2×C4C23×Q812yes—
1045C2×C4C22×#4112yes—
1046C2×C4C22×#4114yes—
1047C2×C4C22×#4112yes—
1048C2×C4C22×#4112yes—
1049C2×C4C2×H(5,𝔽2)12yes—
1050C2×C4C2×H(5,𝔽2)14yes—
1051C2×C4C2×H(5,𝔽2)12yes—
1052C2×C4C2×H(5,𝔽2)12yes—
1053C2×C4C2×H(5,𝔽2)12yes—
1054C2×C4C2×2−1+414yes—
1055C2×C4C2×2−1+412yes—
1056C2×C4C2×2−1+412yes—
1057C22—24no—
1058C22—24no—
1059C22—24no—
1060C22—24no—
1061C22—24no—
1062C22—24no—
1063C22C2×#55718yes—
1064C22C24×Q811yescharacteristic
1065C22C23×#4111yescharacteristic
1066C22C22×H(5,𝔽2)11yescharacteristic
1067C22C22×H(5,𝔽2)11yescharacteristic
1068C22C22×2−1+411yescharacteristic
1069C22C22×2−1+411yescharacteristic
1070C222−1+611yescharacteristic
1071C4—24no—
1072C4—28no—
1073C4—22no—
1074C4—22no—
1075C4—24no—
1076C4—24no—
1077C4—24no—
1078C4—24no—
1079C4—24no—
1080C4—22no—
1081C4—42no—
1082C4—44no—
1083C4—42no—
1084C4—41no—
1085C4—44no—
1086C4—44no—
1087C4—44no—
1088C4—48no—
1089C4—42no—
1090C4—42no—
1091C4—44no—
1092C4—42no—
1093C4C2×#55714yes—
1094C4#350314yes—
1095C4#351914yes—
1096C2—28no—
1097C2C22×#55711yescharacteristic
1098C2C2×#351911yescharacteristic
1099C2C2×#350311yescharacteristic
1100C2#6294211yescharacteristic
1101C2Q8×H(5,𝔽2)11yescharacteristic
1102C2#6300111yescharacteristic
1103C2#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. #59869C2semidirect
2. #59681C2semidirect
3. #59668C2semidirect
4. #59664C2semidirect
5. #59144C2semidirect
6. #59144C2semidirect
7. #45044C2semidirect
8. #43556C2semidirect
9. #39641C2semidirect
10. #39640C2semidirect
11. #39181C2semidirect
12. #39178C2semidirect
13. #36599C2semidirect
14. #36593C2semidirect
15. #36560C2semidirect
16. #36545C2semidirect
21. #34951C2semidirect
22. C2×#2546C2semidirect
203. #554Q8semidirect
567. C4⋊Q8C2×Q8semidirect
573. #125C2×Q8semidirect
578. C22⋊Q8C2×Q8semidirect
579. C22⋊Q8C2×Q8semidirect
596. C4×Q8C2×Q8semidirect
612. C2×C4⋊C4C2×Q8semidirect
973. D4#557semidirect

Maximal subgroups

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

subgroupindex
#598692
#596812
#596682
#596642
#591442
#450442
#435562
#396412
#396402
#391812
#391782
#365992
#365932
#365602
#365452
#362902
D4×C4⋊Q82
#358582
#349512
C2×#25462
#343342
#343322
C4×#5542
C4×D4×Q82