Finite Group Databasebeta

← #7699918

Subgroups — #7699918

Order 512.

5221 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59867C214yesmaximal, complemented
3#59681C212yesmaximal, complemented
4#59673C212yesmaximal, complemented
5#59670C214yesmaximal, complemented
6#59663C214yesmaximal, complemented
7#59661C218yesmaximal, complemented
8#59144C212yesmaximal, complemented
9#36599C212yesmaximal, complemented
10#36598C211yesmaximal, characteristic, complemented
11#36560C211yesmaximal, characteristic, complemented
12#36556C212yesmaximal, complemented
13#36552C212yesmaximal, complemented
14#36545C214yesmaximal, complemented
15#36519C214yesmaximal, complemented
16#36497C212yesmaximal, complemented
17#36290C212yesmaximal
18#36276C212yesmaximal
19#36239C214yesmaximal
20D4×C4⋊Q8C211yesmaximal, characteristic
21C4×#557C211yesmaximal, characteristic, complemented
22C4×#554C212yesmaximal
23C4×#554C211yesmaximal, characteristic
24C4×#554C211yesmaximal, characteristic
25C4×D4×Q8C212yesmaximal
26C2×#2365C212yesmaximal, complemented
27C2×#557C2211yescharacteristic
28C2×#557C2212yes—
29C2×#554C2211yescharacteristic
30C2×#554C2211yescharacteristic
31C2×D4×Q8C2212yes—
32C22×C4⋊Q8C2212yes—
33C22×C4×Q8C2214yes—
34#2868C2211yescharacteristic
35#2864C2214yes—
36#2862C2212yes—
37#2859C2212yes—
38#2857C2212yes—
39#2857C2214yes—
40#2851C2218yes—
41#2851C2214yes—
42#2806C2214yes—
43#2802C2218yes—
44#2799C2218yes—
45#2755C2218yes—
46#2713C2218yes—
47#2590C2218yes—
48#2590C2218yes—
49#2588C2218yes—
50#2588C2218yes—
51#2585C2218yes—
52#2584C2218yes—
53#2584C2214yes—
54#2582C2212yes—
55#2582C2214yes—
56#2581C2218yes—
57#2571C2212yes—
58#2570C2214yes—
59#2570C2214yes—
60#2569C2218yes—
61#2569C2218yes—
62#2568C2212yes—
63#2568C2212yes—
64#2567C2212yes—
65#2565C2214yes—
66#2552C2212yes—
67#2552C2212yes—
68#2551C2212yes—
69#2551C2212yes—
70#2550C2214yes—
71#2550C2214yes—
72#2550C2214yes—
73#2549C2218yes—
74#2549C2218yes—
75#2546C2214yes—
76#2546C2212yes—
77#2546C2212yes—
78#2546C2212yes—
79#2520C2218yes—
80#2520C2218yes—
81#2511C2214yes—
82#2511C2214yes—
83#2511C2214yes—
84#2509C2214yes—
85#2509C2214yes—
86#2509C2214yes—
87#2508C2214yes—
88#2508C2214yes—
89#2507C2214yes—
90#2507C2214yes—
91#2506C2214yes—
92#2506C2214yes—
93#2505C2218yes—
94#2505C2218yes—
95#2505C2218yes—
96#2502C2214yes—
97#2473C2218yes—
98#2473C2218yes—
99#2473C2218yes—
100#2462C2218yes—
101#2462C2218yes—
102#2453C2214yes—
103#2451C2214yes—
104#2446C2214yes—
105#2446C2214yes—
106#2446C2214yes—
107#2442C2214yes—
108#2442C2214yes—
109#2440C2214yes—
110#2440C2214yes—
111#2434C2214yes—
112#2434C2214yes—
113#2370C2214yes—
114#2370C2212yes—
115#2370C2212yes—
116#2370C2214yes—
117#2370C2212yes—
118#2370C2214yes—
119#2369C2211yescharacteristic
120#2369C2212yes—
121#2369C2211yescharacteristic
122#2368C2214yes—
123#2368C2214yes—
124#2368C2218yes—
125#2365C2212yes—
126#2365C2218yes—
127#2365C2214yes—
128#2365C2214yes—
129#2365C2214yes—
130#2365C2211yescharacteristic
131#2365C2214yes—
132#2365C2214yes—
133#2365C2212yes—
134#2365C2212yes—
135#2365C2212yes—
136#2365C2212yes—
137#2360C2214yes—
138#2360C2218yes—
139#2360C2212yes—
140#2360C2214yes—
141#2360C2212yes—
142#2355C2211yescharacteristic
143#2355C2211yescharacteristic
144#2355C2212yes—
145#2355C2212yes—
146#2355C2211yescharacteristic
147#2355C2212yes—
148#2355C2214yes—
149#2351C2212yes—
150Q8×C4⋊C4C2212yes—
151Q8×C4⋊C4C2211yescharacteristic
152#2349C2212yes—
153#2349C2212yes—
154#2349C2214yes—
155#2349C2214yes—
156D4×C4⋊C4C2212yes—
157D4×C4⋊C4C2212yes—
158D4×C4⋊C4C2211yescharacteristic
159D4×C4⋊C4C2214yes—
160D4×C4⋊C4C2211yescharacteristic
161#2345C2212yes—
162#2345C2214yes—
163#2345C2212yes—
164Q8×C22⋊C4C2214yes—
165C4×C4⋊Q8C2214yes—
166C4×C4⋊Q8C2211yescharacteristic
167C4×C4⋊Q8C2212yes—
168C4×C4⋊Q8C2212yes—
169C4×C4⋊Q8C2212yes—
170C4×C4⋊Q8C2211yescharacteristic
171C4×C4⋊Q8C2211yescharacteristic
172C4×#125C2214yes—
173C4×#125C2214yes—
174C4×#125C2212yes—
175C4×#125C2212yes—
176C4×#125C2212yes—
177C4×C22⋊Q8C2212yes—
178C4×C22⋊Q8C2212yes—
179C4×C22⋊Q8C2218yes—
180C4×C22⋊Q8C2218yes—
181C4×C22⋊Q8C2214yes—
182C4×C22⋊Q8C2214yes—
183C4×C22⋊Q8C2214yes—
184C4×C22⋊Q8C2214yes—
185C2×#391C2214yes—
186C2×#389C2214yes—
187C2×#387C2218yes—
188C42×Q8C2212yes—
189C42×Q8C2212yes—
190C42×Q8C2211yescharacteristic
191C42×Q8C2211yescharacteristic
192C42×D4C2211yescharacteristic
193C42×D4C2214yes—
194C42×D4C2212yes—
195C42×D4C2212yes—
196C2×C4×C4⋊C4C2214yes—
197C2×C4×C4⋊C4C2212yes—
198C2×C4×C4⋊C4C2212yes—
199C23×Q8C2314yes—
200#557—28no—
201#557—48no—
202#554—28no—
203#554Q8116yescomplemented
204D4×Q8—216no—
205C2×C4⋊Q8—216no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#125C2312yes—
219C2×#125C2312yes—
220C2×#125C2314yes—
221C2×#125C2314yes—
222C2×#125C2314yes—
223C2×#125C2318yes—
224C2×#125C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2318yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2314yes—
231C2×C4×Q8—416no—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2318yes—
246C2×C4×Q8C2318yes—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×D4C2312yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2312yes—
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2312yes—
258C2×C4×D4C2311yescharacteristic
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2314yes—
263C22×C4⋊C4C2318yes—
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C42C2312yes—
267C22×C42C2318yes—
268C22×C42C2314yes—
269C22×C42C2314yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#395C2318yes—
293#395C2318yes—
294#395C2318yes—
295#395C2318yes—
296#395C2318yes—
297#391C2312yes—
298#391C2314yes—
299#391C2314yes—
300#391C2312yes—
301#391C2318yes—
302#391C2312yes—
303#391C2312yes—
304#391C2312yes—
305#391C2314yes—
306#391C2314yes—
307#391C2314yes—
308#391C2314yes—
309#391C2314yes—
310#391C2314yes—
311#391C2318yes—
312#391C2314yes—
313#391C2314yes—
314#391C2318yes—
315#391C2318yes—
316#391C2314yes—
317#391C2314yes—
318#391C2314yes—
319#391C2312yes—
320#391C2312yes—
321#391C2318yes—
322#389C2312yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2312yes—
327#389C2312yes—
328#389C2314yes—
329#389C2312yes—
330#389C2312yes—
331#389C2312yes—
332#389C2312yes—
333#389C2314yes—
334#389C2312yes—
335#389C2314yes—
336#389C2312yes—
337#389C2312yes—
338#389C2318yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2312yes—
343#389C2314yes—
344#389C2314yes—
345#389C2312yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2318yes—
351#389C2318yes—
352#389C2318yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2318yes—
357#389C2318yes—
358#389C2314yes—
359#389C2318yes—
360#389C2314yes—
361#389C2314yes—
362#389C2318yes—
363#389C2314yes—
364#389C2312yes—
365#389C2312yes—
366#389C2314yes—
367#389C2314yes—
368#389C2318yes—
369#387C2314yes—
370#387C2314yes—
371#387C2314yes—
372#387C2314yes—
373#387C2318yes—
374#387C2314yes—
375#387C2318yes—
376#387C2314yes—
377#387C2314yes—
378#387C2314yes—
379#387C2314yes—
380#387C2314yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2314yes—
391#387C2318yes—
392#387C2318yes—
393#387C2314yes—
394#387C2314yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2314yes—
399#387C2314yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2314yes—
405#387C2318yes—
406#387C2318yes—
407#385C2314yes—
408#385C2318yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2314yes—
413#385C2318yes—
414#385C2314yes—
415#385C2318yes—
416#385C2314yes—
417#385C2318yes—
418#385C2314yes—
419#385C2314yes—
420#385C2318yes—
421#384C2311yescharacteristic
422#384C2314yes—
423#384C2312yes—
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2312yes—
427#384C2312yes—
428#384C2314yes—
429#384C2312yes—
430#384C2312yes—
431#382C2312yes—
432#382C2312yes—
433#382C2314yes—
434#382C2312yes—
435#382C2314yes—
436#382C2314yes—
437#382C2314yes—
438#382C2314yes—
439#382C2318yes—
440#380C2314yes—
441#380C2314yes—
442#380C2314yes—
443#380C2318yes—
444#380C2318yes—
445#380C2318yes—
446#380C2312yes—
447#380C2314yes—
448#380C2312yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2318yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2318yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2318yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2314yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2318yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C2×#95C2314yes—
519C2×#95C2318yes—
520C2×#95C2314yes—
521C2×#95C2318yes—
522C43C2312yes—
523C43C2314yes—
524C43C2312yes—
525C43C2311yescharacteristic
526C22×Q8—216no—
527C22×Q8—216no—
528C22×Q8—48no—
529C22×Q8C2411yescharacteristic
530C22×Q8C2414yes—
531C22×Q8C2418yes—
532C22×Q8C2411yescharacteristic
533C22×Q8C2412yes—
534C22×Q8C2412yes—
535C22×Q8C2412yes—
536C22×D4C2411yescharacteristic
537C23×C4C2418yes—
538C23×C4C2414yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2414yes—
543C23×C4C2414yes—
544C23×C4C2414yes—
545C4⋊Q8—216no—
546C4⋊Q8—28no—
547C4⋊Q8—216no—
548C4⋊Q8—216no—
549C4⋊Q8—216no—
550C4⋊Q8—28no—
551C4⋊Q8—28no—
552C4⋊Q8—24no—
553C4⋊Q8—48no—
554C4⋊Q8—44no—
555C4⋊Q8C2×Q818yescomplemented
556C4⋊Q8#4118yes—
557#125—28no—
558#125—216no—
559#125—28no—
560#125—48no—
561#125—416no—
562#125—48no—
563#125C2×Q8116yescomplemented
564C22⋊Q8—216no—
565C22⋊Q8—28no—
566C22⋊Q8—232no—
567C22⋊Q8—216no—
568C22⋊Q8C2×Q8132yescomplemented
569C22⋊Q8C2×Q8116yescomplemented
570C4×Q8—28no—
571C4×Q8—28no—
572C4×Q8—28no—
573C4×Q8—216no—
574C4×Q8—24no—
575C4×Q8—28no—
576C4×Q8—24no—
577C4×Q8—24no—
578C4×Q8—24no—
579C4×Q8—44no—
580C4×Q8—48no—
581C4×Q8—44no—
582C4×Q8—416no—
583C4×Q8—416no—
584C4×Q8—48no—
585C4×Q8—48no—
586C4×Q8—44no—
587C4×Q8—42no—
588C4×Q8C2×Q818yescomplemented
589C4×D4—216no—
590C4×D4—28no—
591C4×D4—28no—
592C4×D4—24no—
593C4×D4—28no—
594C4×D4C2×Q8116yes—
595C4×D4C2×Q818yes—
596C4×D4#4118yes—
597C2×C4⋊C4—28no—
598C2×C4⋊C4—216no—
599C2×C4⋊C4—216no—
600C2×C4⋊C4—28no—
601C2×C4⋊C4—44no—
602C2×C4⋊C4—416no—
603C2×C4⋊C4C2×Q8116yescomplemented
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C42—28no—
677C2×C42—416no—
678C2×C42—48no—
679C2×C42—48no—
680C2×C42C2412yes—
681C2×C42C2414yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2411yescharacteristic
685C2×C42C2412yes—
686C2×C42C2418yes—
687C2×C42C2411yescharacteristic
688C2×C42C2414yes—
689C2×C42C2411yescharacteristic
690C2×C42C2414yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2414yes—
694C2×C42C2412yes—
695C2×C42C2414yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2418yes—
701C2×C42C2414yes—
702C2×C42C2418yes—
703C2×C42C2414yes—
704C2×C42C2414yes—
705C2×C42C2412yes—
706C2×C42C2414yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2411yescharacteristic
710C2×C42C2414yes—
711C2×C42C2414yes—
712C2×C42C2412yes—
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716#95C2412yes—
717#95C2412yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2418yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2414yes—
733#95C2412yes—
734#95C2412yes—
735#95C2412yes—
736#95C2414yes—
737#95C2414yes—
738#95C2418yes—
739#95C2414yes—
740#95C2418yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2412yes—
745#95C2412yes—
746#95C2412yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2412yes—
752#95C2414yes—
753#95C2414yes—
754#95C2418yes—
755#95C2418yes—
756#95C2414yes—
757#95C2418yes—
758#95C2414yes—
759#95C2414yes—
760#95C2418yes—
761#95C2414yes—
762#95C2418yes—
763#95C2418yes—
764C24C2512yes—
765C2×Q8—22no—
766C2×Q8—24no—
767C2×Q8—22no—
768C2×Q8—22no—
769C2×Q8—216no—
770C2×Q8—28no—
771C2×Q8—216no—
772C2×Q8—28no—
773C2×Q8—24no—
774C2×Q8—24no—
775C2×Q8—28no—
776C2×Q8—22no—
777C2×Q8—22no—
778C2×Q8—42no—
779C2×Q8—48no—
780C2×Q8—42no—
781C2×Q8—42no—
782C2×Q8—42no—
783C2×Q8—464no—
784C2×Q8C22×Q814yes—
785C2×Q8C22×Q818yes—
786C2×Q8C2×#4118yes—
787C2×D4C22×Q814yes—
788C2×D4C2×#4114yes—
789C2×D42−1+414yes—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—216no—
795C22×C4—28no—
796C22×C4—24no—
797C22×C4—28no—
798C22×C4—28no—
799C22×C4—24no—
800C22×C4—216no—
801C22×C4—28no—
802C22×C4—44no—
803C22×C4—48no—
804C22×C4—44no—
805C22×C4—44no—
806C22×C4—42no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4C22×Q818yes—
812C22×C4C22×Q8116yes—
813C22×C4C2×#4118yes—
814C22×C4C2512yes—
815C22×C4C2512yes—
816C22×C4C2512yes—
817C22×C4C2512yes—
818C22×C4C2514yes—
819C22×C4C2512yes—
820C22×C4C2514yes—
821C22×C4C2514yes—
822C22×C4C2514yes—
823C22×C4C2518yes—
824C22×C4C2511yescharacteristic
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2511yescharacteristic
829C22×C4C2512yes—
830C22×C4C2514yes—
831C22×C4C2511yescharacteristic
832C22×C4C2511yescharacteristic
833C22×C4C2512yes—
834C22×C4C2514yes—
835C22×C4C2512yes—
836C22×C4C2511yescharacteristic
837C22×C4C2511yescharacteristic
838C22×C4C2511yescharacteristic
839C4⋊C4—22no—
840C4⋊C4—28no—
841C4⋊C4—24no—
842C4⋊C4—216no—
843C4⋊C4—216no—
844C4⋊C4—28no—
845C4⋊C4—28no—
846C4⋊C4—24no—
847C4⋊C4—28no—
848C4⋊C4—22no—
849C4⋊C4—28no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—28no—
854C4⋊C4—24no—
855C4⋊C4—22no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—216no—
859C4⋊C4—28no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—24no—
863C4⋊C4—28no—
864C4⋊C4—216no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—22no—
868C4⋊C4—24no—
869C4⋊C4—22no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—44no—
873C4⋊C4—48no—
874C4⋊C4—48no—
875C4⋊C4—42no—
876C4⋊C4—44no—
877C4⋊C4—48no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—42no—
881C4⋊C4—44no—
882C4⋊C4—42no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—42no—
886C4⋊C4—48no—
887C4⋊C4—44no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4—48no—
891C4⋊C4—44no—
892C4⋊C4C22×Q814yes—
893C4⋊C4C22×Q8116yes—
894C4⋊C4C22×Q818yes—
895C4⋊C4C22×Q814yes—
896C4⋊C4C22×Q818yes—
897C4⋊C4C22×Q818yes—
898C4⋊C4C22×Q8116yes—
899C4⋊C4C2×#4118yes—
900C4⋊C4C2×#4118yes—
901C4⋊C4C2×#4114yes—
902C4⋊C4H(5,𝔽2)14yes—
903C22⋊C4—216no—
904C22⋊C4—28no—
905C22⋊C4—28no—
906C22⋊C4—28no—
907C22⋊C4—24no—
908C22⋊C4C22×Q8116yes—
909C22⋊C4C22×Q818yes—
910C22⋊C4C2×#4118yes—
911C42—24no—
912C42—24no—
913C42—24no—
914C42—24no—
915C42—28no—
916C42—28no—
917C42—24no—
918C42—24no—
919C42—28no—
920C42—24no—
921C42—216no—
922C42—28no—
923C42—24no—
924C42—22no—
925C42—24no—
926C42—22no—
927C42—24no—
928C42—24no—
929C42—28no—
930C42—22no—
931C42—44no—
932C42—44no—
933C42—44no—
934C42—48no—
935C42—48no—
936C42—44no—
937C42—42no—
938C42—44no—
939C42—41no—
940C42—42no—
941C42—44no—
942C42—42no—
943C42C22×Q818yes—
944C42C22×Q814yes—
945C42C2×#4114yes—
946C42C2×#4114yes—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23C23×Q814yes—
952C23C22×#4114yes—
953C23C2×2−1+414yes—
954C23C2611yescharacteristic
955Q8—28no—
956Q8—216no—
957Q8—48no—
958Q8—432no—
959Q8—44no—
960Q8—416no—
961Q8—84no—
962D4#557116yescomplemented
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—21no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—21no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—24no—
983C2×C4—216no—
984C2×C4—216no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—24no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—24no—
993C2×C4—28no—
994C2×C4—28no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—28no—
998C2×C4—21no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—21no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—416no—
1022C2×C4—48no—
1023C2×C4—416no—
1024C2×C4—432no—
1025C2×C4—88no—
1026C2×C4—88no—
1027C2×C4C23×Q814yes—
1028C2×C4C23×Q812yes—
1029C2×C4C23×Q814yes—
1030C2×C4C23×Q814yes—
1031C2×C4C23×Q818yes—
1032C2×C4C23×Q812yes—
1033C2×C4C23×Q812yes—
1034C2×C4C22×#4112yes—
1035C2×C4C22×#4118yes—
1036C2×C4C22×#4112yes—
1037C2×C4C22×#4114yes—
1038C2×C4C22×#4112yes—
1039C2×C4C22×#4112yes—
1040C2×C4C22×#4112yes—
1041C2×C4C22×#4112yes—
1042C2×C4C2×H(5,𝔽2)14yes—
1043C2×C4C2×H(5,𝔽2)12yes—
1044C2×C4C2×2−1+412yes—
1045C2×C4#58512yes—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—24no—
1050C22—24no—
1051C22—24no—
1052C22C2×#55718yes—
1053C22C24×Q811yescharacteristic
1054C22C23×#4111yescharacteristic
1055C22C23×#4111yescharacteristic
1056C22C22×H(5,𝔽2)11yescharacteristic
1057C22C22×2−1+411yescharacteristic
1058C22C2×#58511yescharacteristic
1059C222−1+611yescharacteristic
1060C4—24no—
1061C4—28no—
1062C4—22no—
1063C4—22no—
1064C4—22no—
1065C4—24no—
1066C4—24no—
1067C4—24no—
1068C4—24no—
1069C4—28no—
1070C4—44no—
1071C4—42no—
1072C4—44no—
1073C4—42no—
1074C4—42no—
1075C4—42no—
1076C4—41no—
1077C4—44no—
1078C4—44no—
1079C4—42no—
1080C4—48no—
1081C4—42no—
1082C4C2×#55714yes—
1083C4Q8×#4114yes—
1084C4#348114yes—
1085C2—28no—
1086C2C22×#55711yescharacteristic
1087C2C2×Q8×#4111yescharacteristic
1088C2C2×#348111yescharacteristic
1089C2Q8×H(5,𝔽2)11yescharacteristic
1090C2#6299511yescharacteristic
1091C2#6299811yescharacteristic
1092C2#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. #59867C2semidirect
3. #59681C2semidirect
4. #59673C2semidirect
5. #59670C2semidirect
6. #59663C2semidirect
7. #59661C2semidirect
8. #59144C2semidirect
9. #36599C2semidirect
10. #36598C2semidirect
11. #36560C2semidirect
12. #36556C2semidirect
13. #36552C2semidirect
14. #36545C2semidirect
15. #36519C2semidirect
16. #36497C2semidirect
21. C4×#557C2semidirect
26. C2×#2365C2semidirect
203. #554Q8semidirect
555. C4⋊Q8C2×Q8semidirect
563. #125C2×Q8semidirect
568. C22⋊Q8C2×Q8semidirect
569. C22⋊Q8C2×Q8semidirect
588. C4×Q8C2×Q8semidirect
603. C2×C4⋊C4C2×Q8semidirect
962. D4#557semidirect

Maximal subgroups

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

subgroupindex
#598712
#598672
#596812
#596732
#596702
#596632
#596612
#591442
#365992
#365982
#365602
#365562
#365522
#365452
#365192
#364972
#362902
#362762
#362392
D4×C4⋊Q82
C4×#5572
C4×#5542
C4×D4×Q82
C2×#23652