Finite Group Databasebeta

← #7688618

Subgroups — #7688618

Order 512.

4863 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59672C212yesmaximal, complemented
3#59445C212yesmaximal, complemented
4#59321C212yesmaximal, complemented
5#59321C214yesmaximal, complemented
6#59154C214yesmaximal, complemented
7#45223C214yesmaximal, complemented
8#43556C218yesmaximal, complemented
9#39642C212yesmaximal, complemented
10#39639C214yesmaximal, complemented
11#39183C212yesmaximal, complemented
12#39178C214yesmaximal, complemented
13#36599C212yesmaximal, complemented
14#36593C211yesmaximal, characteristic, complemented
15#36563C211yesmaximal, characteristic, complemented
16#36552C212yesmaximal, complemented
17#36180C212yesmaximal
18#36180C211yesmaximal, characteristic
19D4×#125C212yesmaximal
20#35858C214yesmaximal
21#34951C211yesmaximal, characteristic, complemented
22C2×#2552C212yesmaximal, complemented
23#34332C212yesmaximal
24#34332C212yesmaximal
25C4×#554C211yesmaximal, characteristic
26C4×#554C211yesmaximal, characteristic
27C2×#557C2212yes—
28C2×#554C2212yes—
29C2×#554C2211yescharacteristic
30C2×#554C2211yescharacteristic
31C22×#125C2214yes—
32#2868C2211yescharacteristic
33#2868C2212yes—
34#2859C2212yes—
35#2857C2212yes—
36#2857C2214yes—
37#2851C2214yes—
38#2809C2218yes—
39#2806C2214yes—
40#2802C2218yes—
41#2802C2218yes—
42#2791C2218yes—
43#2791C2218yes—
44#2791C2218yes—
45#2774C2218yes—
46#2726C2218yes—
47#2713C2218yes—
48#2713C2218yes—
49#2647C2214yes—
50#2646C2218yes—
51#2590C2218yes—
52#2585C2214yes—
53#2585C2218yes—
54#2584C2214yes—
55#2582C2211yescharacteristic
56#2582C2214yes—
57#2582C2212yes—
58#2570C2214yes—
59#2569C2218yes—
60#2568C2211yescharacteristic
61#2567C2212yes—
62#2567C2212yes—
63#2567C2212yes—
64#2565C2214yes—
65#2565C2218yes—
66#2552C2212yes—
67#2552C2212yes—
68#2552C2214yes—
69#2552C2212yes—
70#2552C2214yes—
71#2552C2214yes—
72#2552C2214yes—
73#2552C2214yes—
74#2552C2218yes—
75#2552C2214yes—
76#2552C2212yes—
77#2552C2211yescharacteristic
78#2552C2212yes—
79#2552C2212yes—
80#2552C2214yes—
81#2552C2212yes—
82#2552C2214yes—
83#2552C2214yes—
84#2550C2214yes—
85#2546C2212yes—
86#2546C2214yes—
87#2546C2211yescharacteristic
88#2511C2214yes—
89#2511C2212yes—
90#2511C2214yes—
91#2511C2214yes—
92#2509C2212yes—
93#2509C2214yes—
94#2508C2214yes—
95#2508C2214yes—
96#2507C2214yes—
97#2507C2214yes—
98#2506C2214yes—
99#2506C2214yes—
100#2506C2214yes—
101#2506C2214yes—
102#2506C2218yes—
103#2505C2218yes—
104#2502C2214yes—
105#2502C2214yes—
106#2502C2214yes—
107#2473C2218yes—
108#2473C2218yes—
109#2473C2218yes—
110#2473C2218yes—
111#2473C2218yes—
112#2462C2218yes—
113#2453C2214yes—
114#2453C2212yes—
115#2451C2214yes—
116#2446C2214yes—
117#2446C2212yes—
118#2442C2214yes—
119#2442C2214yes—
120#2442C2218yes—
121#2440C2214yes—
122#2440C2218yes—
123#2440C2218yes—
124#2440C2214yes—
125#2402C2214yes—
126C2×#398C2218yes—
127#2370C2214yes—
128#2370C2214yes—
129#2370C2214yes—
130#2370C2212yes—
131#2370C2212yes—
132#2369C2211yescharacteristic
133#2369C2212yes—
134#2369C2212yes—
135#2369C2211yescharacteristic
136#2368C2214yes—
137#2368C2214yes—
138#2365C2212yes—
139#2360C2212yes—
140#2360C2218yes—
141#2360C2214yes—
142#2360C2218yes—
143#2360C2214yes—
144#2360C2212yes—
145#2355C2211yescharacteristic
146#2355C2211yescharacteristic
147#2355C2214yes—
148#2355C2212yes—
149Q8×C4⋊C4C2212yes—
150Q8×C4⋊C4C2212yes—
151Q8×C4⋊C4C2212yes—
152Q8×C4⋊C4C2212yes—
153#2349C2212yes—
154#2349C2212yes—
155D4×C4⋊C4C2211yescharacteristic
156D4×C4⋊C4C2214yes—
157D4×C4⋊C4C2214yes—
158D4×C4⋊C4C2212yes—
159D4×C4⋊C4C2212yes—
160D4×C4⋊C4C2214yes—
161D4×C4⋊C4C2211yescharacteristic
162#2345C2212yes—
163#2345C2214yes—
164#2345C2214yes—
165#2345C2212yes—
166#2330C2214yes—
167#2330C2214yes—
168#2329C2218yes—
169#2329C2218yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2211yescharacteristic
176C4×#125C2212yes—
177C4×#125C2212yes—
178C4×#125C2212yes—
179C4×C22⋊Q8C2214yes—
180C4×C22⋊Q8C2214yes—
181C4×C22⋊Q8C2214yes—
182C4×C22⋊Q8C2212yes—
183C4×C22⋊Q8C2214yes—
184C4×C22⋊Q8C2212yes—
185#2295C2212yes—
186#2295C2212yes—
187C2×#389C2214yes—
188C2×#389C2214yes—
189C2×#384C2214yes—
190C2×#384C2212yes—
191#2275C2214yes—
192C42×Q8C2211yescharacteristic
193C42×Q8C2211yescharacteristic
194C42×D4C2212yes—
195C42×D4C2212yes—
196C42×D4C2211yescharacteristic
197C2×C4×C4⋊C4C2212yes—
198C2×C4×C4⋊C4C2212yes—
199#557—48no—
200#554—216no—
201#554—28no—
202#554Q8116yescomplemented
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2311yescharacteristic
212C2×#125—416no—
213C2×#125C2312yes—
214C2×#125C2312yes—
215C2×#125C2314yes—
216C2×#125C2314yes—
217C2×#125C2314yes—
218C2×#125C2314yes—
219C2×#125C2318yes—
220C2×#125C2318yes—
221C2×#125C2318yes—
222C2×#125C2318yes—
223C2×#125C2312yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4C2312yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2312yes—
250C2×C4×D4C2311yescharacteristic
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2314yes—
253C22×C4⋊C4C2312yes—
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2318yes—
256C22×C4⋊C4C2314yes—
257C22×C4⋊C4C2318yes—
258C22×C4⋊C4C2318yes—
259C22×C4⋊C4C2314yes—
260C22×C4⋊C4C2312yes—
261C22×C42C2312yes—
262C22×C42C2314yes—
263C22×C42C2314yes—
264#400C2314yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2314yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2314yes—
273#400C2314yes—
274#400C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2314yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2314yes—
286#398C2318yes—
287#398C2318yes—
288#398C2314yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2314yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#395C2318yes—
301#395C2318yes—
302#395C2318yes—
303#391C2312yes—
304#391C2312yes—
305#391C2314yes—
306#391C2312yes—
307#391C2314yes—
308#391C2312yes—
309#391C2312yes—
310#391C2312yes—
311#391C2312yes—
312#391C2314yes—
313#391C2318yes—
314#391C2314yes—
315#391C2314yes—
316#391C2314yes—
317#391C2312yes—
318#391C2312yes—
319#391C2318yes—
320#391C2312yes—
321#391C2314yes—
322#391C2312yes—
323#389C2312yes—
324#389C2312yes—
325#389C2312yes—
326#389C2312yes—
327#389C2312yes—
328#389C2312yes—
329#389C2314yes—
330#389C2312yes—
331#389C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2312yes—
338#389C2312yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2318yes—
347#389C2312yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2318yes—
352#389C2314yes—
353#389C2314yes—
354#389C2318yes—
355#389C2318yes—
356#389C2318yes—
357#389C2314yes—
358#389C2318yes—
359#389C2318yes—
360#389C2318yes—
361#389C2314yes—
362#389C2318yes—
363#389C2318yes—
364#389C2314yes—
365#389C2312yes—
366#389C2314yes—
367#389C2312yes—
368#389C2312yes—
369#389C2314yes—
370#389C2314yes—
371#389C2318yes—
372#389C2314yes—
373#389C2314yes—
374#389C2318yes—
375#389C2318yes—
376#389C2312yes—
377#389C2312yes—
378#387C2314yes—
379#387C2314yes—
380#387C2314yes—
381#387C2314yes—
382#387C2314yes—
383#387C2314yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2314yes—
393#387C2314yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2314yes—
400#387C2318yes—
401#387C2314yes—
402#387C2314yes—
403#387C2314yes—
404#387C2318yes—
405#387C2318yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#385C2314yes—
411#385C2318yes—
412#385C2314yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2314yes—
419#385C2318yes—
420#385C2318yes—
421#385C2314yes—
422#385C2314yes—
423#385C2314yes—
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2312yes—
428#384C2312yes—
429#384C2314yes—
430#384C2318yes—
431#384C2314yes—
432#384C2314yes—
433#384C2314yes—
434#384C2314yes—
435#384C2312yes—
436#384C2314yes—
437#384C2312yes—
438#384C2314yes—
439#384C2314yes—
440#384C2312yes—
441#384C2314yes—
442#384C2314yes—
443#384C2318yes—
444#382C2312yes—
445#382C2312yes—
446#382C2312yes—
447#382C2314yes—
448#382C2318yes—
449#380C2314yes—
450#380C2318yes—
451#380C2318yes—
452#380C2318yes—
453#380C2312yes—
454#380C2314yes—
455#380C2312yes—
456#380C2314yes—
457#380C2314yes—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2318yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2312yes—
517#376C2314yes—
518C2×#95C2314yes—
519C2×#95C2318yes—
520C2×#95C2314yes—
521C43C2312yes—
522C43C2312yes—
523C43C2311yescharacteristic
524C22×Q8C2411yescharacteristic
525C22×Q8C2412yes—
526C22×Q8C2411yescharacteristic
527C22×Q8C2412yes—
528C22×Q8C2414yes—
529C22×Q8C2412yes—
530C22×D4C2411yescharacteristic
531C23×C4C2414yes—
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2418yes—
536C23×C4C2414yes—
537C23×C4C2414yes—
538C23×C4C2414yes—
539C4⋊Q8—28no—
540C4⋊Q8—24no—
541C4⋊Q8—24no—
542C4⋊Q8—44no—
543C4⋊Q8—48no—
544C4⋊Q8—44no—
545C4⋊Q8—82no—
546C4⋊Q8—84no—
547C4⋊Q8C2×Q818yes—
548#125—28no—
549#125—216no—
550#125—28no—
551#125—216no—
552#125—48no—
553#125—48no—
554#125—416no—
555#125—416no—
556#125—416no—
557#125—88no—
558#125C2×Q8116yes—
559C22⋊Q8—216no—
560C22⋊Q8—28no—
561C22⋊Q8—232no—
562C22⋊Q8—216no—
563C22⋊Q8C2×Q8132yes—
564C22⋊Q8C2×Q8116yes—
565C4×Q8—24no—
566C4×Q8—28no—
567C4×Q8—24no—
568C4×Q8—24no—
569C4×Q8—24no—
570C4×Q8—44no—
571C4×Q8—44no—
572C4×Q8—48no—
573C4×Q8—48no—
574C4×Q8—42no—
575C4×Q8—48no—
576C4×Q8—84no—
577C4×Q8C2×Q818yes—
578C4×D4—216no—
579C4×D4—28no—
580C4×D4—28no—
581C4×D4—24no—
582C4×D4—28no—
583C4×D4C2×Q8116yes—
584C4×D4C2×Q818yes—
585C4×D4#4118yes—
586C2×C4⋊C4—28no—
587C2×C4⋊C4—216no—
588C2×C4⋊C4—28no—
589C2×C4⋊C4—44no—
590C2×C4⋊C4—416no—
591C2×C4⋊C4—48no—
592C2×C4⋊C4—416no—
593C2×C4⋊C4—88no—
594C2×C4⋊C4—84no—
595C2×C4⋊C4C2×Q8116yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C42—28no—
674C2×C42—48no—
675C2×C42—48no—
676C2×C42C2412yes—
677C2×C42C2414yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2412yes—
683C2×C42C2411yescharacteristic
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2418yes—
694C2×C42C2412yes—
695C2×C42C2418yes—
696C2×C42C2412yes—
697C2×C42C2418yes—
698C2×C42C2414yes—
699C2×C42C2414yes—
700C2×C42C2411yescharacteristic
701C2×C42C2412yes—
702C2×C42C2414yes—
703C2×C42C2414yes—
704C2×C42C2412yes—
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708#95C2414yes—
709#95C2412yes—
710#95C2412yes—
711#95C2418yes—
712#95C2418yes—
713#95C2418yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2412yes—
726#95C2412yes—
727#95C2412yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2412yes—
733#95C2412yes—
734#95C2414yes—
735#95C2414yes—
736#95C2412yes—
737#95C2412yes—
738#95C2414yes—
739#95C2418yes—
740#95C2418yes—
741#95C2414yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756C24C2512yes—
757C2×Q8—22no—
758C2×Q8—24no—
759C2×Q8—28no—
760C2×Q8—24no—
761C2×Q8—22no—
762C2×Q8—22no—
763C2×Q8—22no—
764C2×Q8—24no—
765C2×Q8—24no—
766C2×Q8—22no—
767C2×Q8—42no—
768C2×Q8—42no—
769C2×Q8—42no—
770C2×Q8—44no—
771C2×Q8—44no—
772C2×Q8—42no—
773C2×Q8C22×Q814yes—
774C2×Q8C22×Q818yes—
775C2×D4C22×Q814yes—
776C2×D4C2×#4114yes—
777C2×D42−1+414yes—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—28no—
783C22×C4—24no—
784C22×C4—216no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—28no—
788C22×C4—24no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—42no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—48no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—48no—
799C22×C4C22×Q818yes—
800C22×C4C22×Q8116yes—
801C22×C4C2×#4118yes—
802C22×C4C2512yes—
803C22×C4C2512yes—
804C22×C4C2512yes—
805C22×C4C2512yes—
806C22×C4C2514yes—
807C22×C4C2512yes—
808C22×C4C2514yes—
809C22×C4C2514yes—
810C22×C4C2511yescharacteristic
811C22×C4C2512yes—
812C22×C4C2514yes—
813C22×C4C2518yes—
814C22×C4C2514yes—
815C22×C4C2512yes—
816C22×C4C2511yescharacteristic
817C22×C4C2512yes—
818C22×C4C2514yes—
819C22×C4C2512yes—
820C22×C4C2511yescharacteristic
821C22×C4C2512yes—
822C22×C4C2512yes—
823C22×C4C2511yescharacteristic
824C22×C4C2511yescharacteristic
825C22×C4C2511yescharacteristic
826C22×C4C2511yescharacteristic
827C4⋊C4—22no—
828C4⋊C4—24no—
829C4⋊C4—28no—
830C4⋊C4—216no—
831C4⋊C4—24no—
832C4⋊C4—28no—
833C4⋊C4—28no—
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—28no—
837C4⋊C4—216no—
838C4⋊C4—28no—
839C4⋊C4—28no—
840C4⋊C4—24no—
841C4⋊C4—28no—
842C4⋊C4—28no—
843C4⋊C4—24no—
844C4⋊C4—216no—
845C4⋊C4—28no—
846C4⋊C4—216no—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—22no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—24no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—22no—
858C4⋊C4—24no—
859C4⋊C4—44no—
860C4⋊C4—48no—
861C4⋊C4—48no—
862C4⋊C4—48no—
863C4⋊C4—48no—
864C4⋊C4—48no—
865C4⋊C4—44no—
866C4⋊C4—42no—
867C4⋊C4—48no—
868C4⋊C4—48no—
869C4⋊C4—48no—
870C4⋊C4—44no—
871C4⋊C4—48no—
872C4⋊C4—44no—
873C4⋊C4—42no—
874C4⋊C4—48no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—44no—
878C4⋊C4—48no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—48no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4C22×Q814yes—
888C4⋊C4C22×Q8116yes—
889C4⋊C4C22×Q818yes—
890C4⋊C4C22×Q814yes—
891C4⋊C4C22×Q818yes—
892C4⋊C4C22×Q818yes—
893C4⋊C4C22×Q8116yes—
894C4⋊C4C2×#4114yes—
895C4⋊C4H(5,𝔽2)14yes—
896C22⋊C4—216no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—24no—
900C22⋊C4—28no—
901C22⋊C4C22×Q8116yes—
902C22⋊C4C22×Q818yes—
903C22⋊C4C2×#4118yes—
904C42—24no—
905C42—28no—
906C42—24no—
907C42—28no—
908C42—24no—
909C42—22no—
910C42—24no—
911C42—24no—
912C42—24no—
913C42—24no—
914C42—22no—
915C42—24no—
916C42—24no—
917C42—24no—
918C42—24no—
919C42—28no—
920C42—22no—
921C42—44no—
922C42—44no—
923C42—44no—
924C42—44no—
925C42—48no—
926C42—42no—
927C42—48no—
928C42—42no—
929C42—48no—
930C42—41no—
931C42—42no—
932C42C22×Q818yes—
933C42C22×Q814yes—
934C42C2×#4114yes—
935C422−1+414yes—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23C23×Q814yes—
941C23C22×#4114yes—
942C23C2×2−1+414yes—
943C23C2611yescharacteristic
944Q8—28no—
945Q8—48no—
946Q8—44no—
947Q8—48no—
948Q8—84no—
949Q8—88no—
950D4#557116yescomplemented
951C2×C4—21no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—21no—
959C2×C4—24no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—24no—
967C2×C4—22no—
968C2×C4—21no—
969C2×C4—216no—
970C2×C4—216no—
971C2×C4—22no—
972C2×C4—24no—
973C2×C4—22no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—28no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—24no—
981C2×C4—21no—
982C2×C4—28no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—21no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—21no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—28no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—416no—
1011C2×C4—416no—
1012C2×C4—48no—
1013C2×C4—88no—
1014C2×C4—816no—
1015C2×C4—88no—
1016C2×C4C23×Q814yes—
1017C2×C4C23×Q812yes—
1018C2×C4C23×Q814yes—
1019C2×C4C23×Q814yes—
1020C2×C4C23×Q818yes—
1021C2×C4C23×Q812yes—
1022C2×C4C23×Q812yes—
1023C2×C4C22×#4112yes—
1024C2×C4C22×#4114yes—
1025C2×C4C22×#4112yes—
1026C2×C4C22×#4112yes—
1027C2×C4C2×H(5,𝔽2)14yes—
1028C2×C4C2×H(5,𝔽2)12yes—
1029C2×C4C2×2−1+412yes—
1030C2×C4C2×2−1+412yes—
1031C2×C4C2×2−1+412yes—
1032C2×C4C2×2−1+412yes—
1033C2×C4#58512yes—
1034C22—24no—
1035C22—24no—
1036C22—24no—
1037C22—24no—
1038C22—24no—
1039C22—24no—
1040C22C2×#55718yes—
1041C22C24×Q811yescharacteristic
1042C22C23×#4111yescharacteristic
1043C22C22×H(5,𝔽2)11yescharacteristic
1044C22C22×2−1+411yescharacteristic
1045C22C22×2−1+411yescharacteristic
1046C22C2×#58511yescharacteristic
1047C22H(7,𝔽2)11yescharacteristic
1048C4—22no—
1049C4—24no—
1050C4—28no—
1051C4—22no—
1052C4—24no—
1053C4—24no—
1054C4—24no—
1055C4—24no—
1056C4—22no—
1057C4—42no—
1058C4—44no—
1059C4—44no—
1060C4—48no—
1061C4—41no—
1062C4—44no—
1063C4—44no—
1064C4—42no—
1065C4—42no—
1066C4—44no—
1067C4—42no—
1068C4—42no—
1069C4—42no—
1070C4C2×#55714yes—
1071C4#350314yes—
1072C4#351514yes—
1073C2—28no—
1074C2C22×#55711yescharacteristic
1075C2C2×#351511yescharacteristic
1076C2C2×#350311yescharacteristic
1077C2#6294511yescharacteristic
1078C2#6298611yescharacteristic
1079C2#6298911yescharacteristic
1080C2#6301311yescharacteristic
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. #59871C2semidirect
2. #59672C2semidirect
3. #59445C2semidirect
4. #59321C2semidirect
5. #59321C2semidirect
6. #59154C2semidirect
7. #45223C2semidirect
8. #43556C2semidirect
9. #39642C2semidirect
10. #39639C2semidirect
11. #39183C2semidirect
12. #39178C2semidirect
13. #36599C2semidirect
14. #36593C2semidirect
15. #36563C2semidirect
16. #36552C2semidirect
21. #34951C2semidirect
22. C2×#2552C2semidirect
202. #554Q8semidirect
950. D4#557semidirect

Maximal subgroups

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

subgroupindex
#598712
#596722
#594452
#593212
#591542
#452232
#435562
#396422
#396392
#391832
#391782
#365992
#365932
#365632
#365522
#361802
D4×#1252
#358582
#349512
C2×#25522
#343322
C4×#5542