Finite Group Databasebeta

← #7688353

Subgroups — #7688353

Order 512.

4909 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic, complemented
2#59869C212yesmaximal, complemented
3#59867C214yesmaximal, complemented
4#59464C212yesmaximal, complemented
5#59325C214yesmaximal, complemented
6#59144C212yesmaximal, complemented
7#44954C214yesmaximal, complemented
8#43557C218yesmaximal, complemented
9#39643C212yesmaximal, complemented
10#39640C214yesmaximal, complemented
11#39182C212yesmaximal, complemented
12#39179C214yesmaximal, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36577C212yesmaximal, complemented
15#36560C211yesmaximal, characteristic, complemented
16#36552C212yesmaximal, complemented
17#36276C212yesmaximal
18#36165C212yesmaximal
19D4×C4⋊Q8C211yesmaximal, characteristic
20#35961C214yesmaximal
21#34951C211yesmaximal, characteristic, complemented
22C2×#2568C212yesmaximal, complemented
23#34334C212yesmaximal
24#34334C212yesmaximal
25C4×#554C211yesmaximal, characteristic
26C4×D4×Q8C211yesmaximal, characteristic
27C2×#557C2212yes—
28C2×#554C2211yescharacteristic
29C2×D4×Q8C2212yes—
30C2×D4×Q8C2211yescharacteristic
31C22×C4⋊Q8C2212yes—
32C22×C4×Q8C2212yes—
33#2868C2211yescharacteristic
34#2862C2212yes—
35#2859C2212yes—
36#2857C2212yes—
37#2857C2214yes—
38#2851C2214yes—
39#2809C2218yes—
40#2806C2218yes—
41#2805C2218yes—
42#2805C2214yes—
43#2799C2218yes—
44#2799C2218yes—
45#2774C2218yes—
46#2774C2218yes—
47#2755C2218yes—
48#2755C2218yes—
49#2713C2218yes—
50#2647C2214yes—
51#2646C2218yes—
52#2590C2218yes—
53#2588C2218yes—
54#2585C2214yes—
55#2582C2212yes—
56#2582C2211yescharacteristic
57#2582C2214yes—
58#2581C2214yes—
59#2571C2212yes—
60#2571C2214yes—
61#2571C2212yes—
62#2570C2214yes—
63#2569C2218yes—
64#2568C2212yes—
65#2568C2214yes—
66#2568C2218yes—
67#2568C2214yes—
68#2568C2211yescharacteristic
69#2568C2212yes—
70#2568C2214yes—
71#2568C2214yes—
72#2568C2212yes—
73#2568C2214yes—
74#2567C2212yes—
75#2565C2214yes—
76#2552C2211yescharacteristic
77#2551C2212yes—
78#2551C2212yes—
79#2550C2214yes—
80#2550C2214yes—
81#2550C2214yes—
82#2549C2218yes—
83#2549C2218yes—
84#2546C2211yescharacteristic
85#2546C2214yes—
86#2546C2212yes—
87#2546C2212yes—
88#2546C2212yes—
89#2520C2218yes—
90#2511C2214yes—
91#2511C2212yes—
92#2511C2214yes—
93#2511C2214yes—
94#2509C2214yes—
95#2509C2214yes—
96#2509C2212yes—
97#2508C2214yes—
98#2508C2218yes—
99#2508C2214yes—
100#2508C2214yes—
101#2508C2214yes—
102#2506C2214yes—
103#2506C2214yes—
104#2505C2218yes—
105#2505C2218yes—
106#2505C2218yes—
107#2505C2218yes—
108#2505C2218yes—
109#2502C2214yes—
110#2473C2218yes—
111#2453C2212yes—
112#2453C2214yes—
113#2453C2214yes—
114#2453C2218yes—
115#2451C2214yes—
116#2446C2214yes—
117#2446C2212yes—
118#2446C2214yes—
119#2442C2214yes—
120#2442C2218yes—
121#2442C2214yes—
122#2440C2214yes—
123#2440C2214yes—
124#2434C2214yes—
125#2434C2214yes—
126#2402C2214yes—
127C2×#400C2218yes—
128#2370C2212yes—
129#2369C2214yes—
130#2369C2214yes—
131#2369C2211yescharacteristic
132#2368C2218yes—
133#2368C2218yes—
134#2368C2214yes—
135#2365C2212yes—
136#2365C2212yes—
137#2365C2212yes—
138#2365C2211yescharacteristic
139#2365C2212yes—
140#2365C2212yes—
141#2360C2214yes—
142#2360C2214yes—
143#2360C2214yes—
144#2360C2212yes—
145#2360C2212yes—
146#2355C2212yes—
147#2355C2212yes—
148#2355C2211yescharacteristic
149#2355C2212yes—
150#2355C2214yes—
151#2351C2214yes—
152Q8×C4⋊C4C2211yescharacteristic
153Q8×C4⋊C4C2212yes—
154#2349C2214yes—
155#2349C2214yes—
156#2349C2214yes—
157#2349C2212yes—
158D4×C4⋊C4C2212yes—
159D4×C4⋊C4C2212yes—
160D4×C4⋊C4C2211yescharacteristic
161D4×C4⋊C4C2211yescharacteristic
162D4×C4⋊C4C2212yes—
163#2345C2212yes—
164Q8×C22⋊C4C2214yes—
165Q8×C22⋊C4C2212yes—
166Q8×C22⋊C4C2214yes—
167#2331C2214yes—
168#2331C2214yes—
169#2329C2218yes—
170#2329C2218yes—
171C4×C4⋊Q8C2211yescharacteristic
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2211yescharacteristic
177C4×C4⋊Q8C2212yes—
178C4×#125C2212yes—
179C4×#125C2212yes—
180C4×C22⋊Q8C2212yes—
181C4×C22⋊Q8C2212yes—
182C4×C22⋊Q8C2214yes—
183C4×C22⋊Q8C2214yes—
184C4×C22⋊Q8C2214yes—
185C4×C22⋊Q8C2214yes—
186#2295C2212yes—
187#2295C2212yes—
188C2×#391C2214yes—
189C2×#391C2214yes—
190C2×#391C2214yes—
191C2×#382C2214yes—
192#2275C2214yes—
193C42×Q8C2211yescharacteristic
194C42×Q8C2211yescharacteristic
195C42×D4C2211yescharacteristic
196C42×D4C2212yes—
197C42×D4C2212yes—
198C2×C4×C4⋊C4C2212yes—
199C23×Q8C2314yes—
200C23×Q8C2312yes—
201#557—48no—
202#554—28no—
203D4×Q8—216no—
204D4×Q8Q8116yescomplemented
205C2×C4⋊Q8—48no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2312yes—
219C2×#125C2312yes—
220C2×#125C2312yes—
221C2×#125C2314yes—
222C2×#125C2318yes—
223C2×C22⋊Q8C2318yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2312yes—
229C2×C4×Q8—48no—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2312yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2312yes—
254C2×C4×D4C2311yescharacteristic
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2314yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2314yes—
260C22×C4⋊C4C2314yes—
261C22×C42C2312yes—
262C22×C42C2314yes—
263C22×C42C2314yes—
264#400C2314yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2314yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2314yes—
281#400C2314yes—
282#400C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2314yes—
288#398C2318yes—
289#398C2314yes—
290#398C2314yes—
291#398C2318yes—
292#398C2318yes—
293#398C2314yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#395C2318yes—
299#395C2318yes—
300#395C2318yes—
301#395C2318yes—
302#395C2318yes—
303#391C2312yes—
304#391C2314yes—
305#391C2314yes—
306#391C2312yes—
307#391C2312yes—
308#391C2314yes—
309#391C2312yes—
310#391C2312yes—
311#391C2314yes—
312#391C2312yes—
313#391C2312yes—
314#391C2314yes—
315#391C2314yes—
316#391C2314yes—
317#391C2318yes—
318#391C2318yes—
319#391C2318yes—
320#391C2314yes—
321#391C2312yes—
322#391C2314yes—
323#391C2314yes—
324#391C2318yes—
325#391C2318yes—
326#391C2318yes—
327#391C2314yes—
328#391C2318yes—
329#391C2318yes—
330#391C2312yes—
331#391C2314yes—
332#391C2318yes—
333#391C2318yes—
334#391C2312yes—
335#391C2312yes—
336#391C2314yes—
337#391C2314yes—
338#391C2314yes—
339#391C2314yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2312yes—
345#389C2314yes—
346#389C2312yes—
347#389C2314yes—
348#389C2314yes—
349#389C2312yes—
350#389C2314yes—
351#389C2314yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2314yes—
357#389C2314yes—
358#389C2312yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2318yes—
366#389C2312yes—
367#389C2312yes—
368#389C2318yes—
369#389C2318yes—
370#389C2318yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2318yes—
375#389C2314yes—
376#389C2318yes—
377#389C2318yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2312yes—
382#389C2312yes—
383#389C2312yes—
384#389C2314yes—
385#389C2312yes—
386#387C2314yes—
387#387C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2314yes—
399#387C2314yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2314yes—
405#387C2314yes—
406#387C2318yes—
407#387C2318yes—
408#387C2314yes—
409#387C2314yes—
410#387C2318yes—
411#387C2318yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#385C2318yes—
417#385C2318yes—
418#385C2314yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2314yes—
423#385C2314yes—
424#385C2314yes—
425#385C2314yes—
426#385C2314yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2312yes—
433#384C2312yes—
434#384C2311yescharacteristic
435#384C2312yes—
436#384C2312yes—
437#384C2314yes—
438#384C2312yes—
439#384C2312yes—
440#382C2312yes—
441#382C2312yes—
442#382C2314yes—
443#382C2314yes—
444#382C2314yes—
445#382C2318yes—
446#382C2318yes—
447#382C2318yes—
448#382C2314yes—
449#382C2314yes—
450#382C2314yes—
451#382C2318yes—
452#380C2314yes—
453#380C2314yes—
454#380C2318yes—
455#380C2318yes—
456#380C2312yes—
457#380C2314yes—
458#380C2312yes—
459#380C2314yes—
460#380C2318yes—
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2318yes—
492C4×C4⋊C4C2318yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C22⋊C4C2318yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516#376C2314yes—
517C2×#95C2318yes—
518C2×#95C2318yes—
519C2×#95C2314yes—
520C2×#95C2318yes—
521C2×#95C2318yes—
522C43C2312yes—
523C43C2312yes—
524C43C2311yescharacteristic
525C22×Q8—216no—
526C22×Q8—44no—
527C22×Q8—44no—
528C22×Q8—48no—
529C22×Q8—48no—
530C22×Q8C2×Q8116yescomplemented
531C22×Q8C2411yescharacteristic
532C22×Q8C2414yes—
533C22×Q8C2412yes—
534C22×Q8C2412yes—
535C22×Q8C2411yescharacteristic
536C22×Q8C2412yes—
537C22×Q8C2418yes—
538C22×Q8C2414yes—
539C22×D4C2411yescharacteristic
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2418yes—
544C23×C4C2414yes—
545C23×C4C2414yes—
546C23×C4C2414yes—
547C23×C4C2414yes—
548C4⋊Q8—216no—
549C4⋊Q8—28no—
550C4⋊Q8—24no—
551C4⋊Q8—24no—
552C4⋊Q8—28no—
553C4⋊Q8—48no—
554C4⋊Q8—48no—
555C4⋊Q8—48no—
556C4⋊Q8—44no—
557C4⋊Q8—44no—
558C4⋊Q8—48no—
559C4⋊Q8C2×Q818yescomplemented
560C4⋊Q8C2×Q8116yescomplemented
561#125—28no—
562#125—44no—
563#125—48no—
564#125—416no—
565C22⋊Q8—216no—
566C22⋊Q8—28no—
567C22⋊Q8—232no—
568C22⋊Q8—216no—
569C22⋊Q8C2×Q8116yescomplemented
570C22⋊Q8C2×Q8132yescomplemented
571C4×Q8—28no—
572C4×Q8—24no—
573C4×Q8—24no—
574C4×Q8—28no—
575C4×Q8—24no—
576C4×Q8—48no—
577C4×Q8—44no—
578C4×Q8—48no—
579C4×Q8—44no—
580C4×Q8—44no—
581C4×Q8—48no—
582C4×Q8—42no—
583C4×Q8—48no—
584C4×Q8—42no—
585C4×Q8—48no—
586C4×Q8—48no—
587C4×Q8C2×Q818yescomplemented
588C4×D4—216no—
589C4×D4—28no—
590C4×D4—24no—
591C4×D4—28no—
592C4×D4—28no—
593C4×D4C2×Q818yes—
594C4×D4C2×Q8116yes—
595C4×D4#4118yes—
596C2×C4⋊C4—28no—
597C2×C4⋊C4—44no—
598C2×C4⋊C4—44no—
599C2×C4⋊C4—48no—
600C2×C4⋊C4—48no—
601C2×C4⋊C4—48no—
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2411yescharacteristic
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2412yes—
673C2×C42—28no—
674C2×C42—48no—
675C2×C42—48no—
676C2×C42C2412yes—
677C2×C42C2414yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2411yescharacteristic
681C2×C42C2412yes—
682C2×C42C2414yes—
683C2×C42C2411yescharacteristic
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2412yes—
689C2×C42C2414yes—
690C2×C42C2411yescharacteristic
691C2×C42C2412yes—
692C2×C42C2418yes—
693C2×C42C2414yes—
694C2×C42C2414yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2418yes—
698C2×C42C2418yes—
699C2×C42C2411yescharacteristic
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2414yes—
703C2×C42C2414yes—
704C2×C42C2411yescharacteristic
705C2×C42C2412yes—
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708#95C2414yes—
709#95C2412yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2414yes—
717#95C2418yes—
718#95C2414yes—
719#95C2418yes—
720#95C2414yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2412yes—
732#95C2414yes—
733#95C2412yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2412yes—
740#95C2412yes—
741#95C2414yes—
742#95C2412yes—
743#95C2412yes—
744#95C2412yes—
745#95C2412yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2418yes—
753#95C2414yes—
754#95C2418yes—
755#95C2418yes—
756#95C2414yes—
757#95C2414yes—
758#95C2418yes—
759#95C2418yes—
760C24C2512yes—
761C2×Q8—22no—
762C2×Q8—24no—
763C2×Q8—28no—
764C2×Q8—24no—
765C2×Q8—216no—
766C2×Q8—24no—
767C2×Q8—22no—
768C2×Q8—22no—
769C2×Q8—28no—
770C2×Q8—24no—
771C2×Q8—24no—
772C2×Q8—22no—
773C2×Q8—22no—
774C2×Q8—28no—
775C2×Q8—24no—
776C2×Q8—44no—
777C2×Q8—44no—
778C2×Q8—42no—
779C2×Q8—48no—
780C2×Q8—48no—
781C2×Q8—42no—
782C2×Q8—432no—
783C2×Q8—832no—
784C2×Q8C22×Q814yes—
785C2×Q8C22×Q818yes—
786C2×Q8C22×Q8116yes—
787C2×D4C22×Q814yes—
788C2×D4C2×#4114yes—
789C2×D42−1+414yes—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—28no—
796C22×C4—216no—
797C22×C4—28no—
798C22×C4—28no—
799C22×C4—24no—
800C22×C4—44no—
801C22×C4—42no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—44no—
806C22×C4—48no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—48no—
811C22×C4C22×Q818yes—
812C22×C4C22×Q8116yes—
813C22×C4C2×#4118yes—
814C22×C4C2512yes—
815C22×C4C2514yes—
816C22×C4C2512yes—
817C22×C4C2512yes—
818C22×C4C2514yes—
819C22×C4C2514yes—
820C22×C4C2511yescharacteristic
821C22×C4C2512yes—
822C22×C4C2512yes—
823C22×C4C2514yes—
824C22×C4C2512yes—
825C22×C4C2514yes—
826C22×C4C2518yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2512yes—
830C22×C4C2511yescharacteristic
831C22×C4C2512yes—
832C22×C4C2514yes—
833C22×C4C2511yescharacteristic
834C22×C4C2512yes—
835C22×C4C2511yescharacteristic
836C22×C4C2511yescharacteristic
837C22×C4C2511yescharacteristic
838C22×C4C2511yescharacteristic
839C4⋊C4—22no—
840C4⋊C4—28no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—28no—
844C4⋊C4—24no—
845C4⋊C4—28no—
846C4⋊C4—24no—
847C4⋊C4—28no—
848C4⋊C4—216no—
849C4⋊C4—28no—
850C4⋊C4—24no—
851C4⋊C4—22no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—28no—
855C4⋊C4—24no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—22no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—22no—
862C4⋊C4—24no—
863C4⋊C4—22no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—22no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—48no—
872C4⋊C4—48no—
873C4⋊C4—42no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—42no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—48no—
880C4⋊C4—42no—
881C4⋊C4—48no—
882C4⋊C4—42no—
883C4⋊C4—44no—
884C4⋊C4—48no—
885C4⋊C4—42no—
886C4⋊C4—48no—
887C4⋊C4—48no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—48no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4C22×Q814yes—
896C4⋊C4C22×Q818yes—
897C4⋊C4C22×Q818yes—
898C4⋊C4C22×Q814yes—
899C4⋊C4C22×Q8116yes—
900C4⋊C4C22×Q818yes—
901C4⋊C4C2×#4114yes—
902C22⋊C4—216no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—24no—
906C22⋊C4—28no—
907C22⋊C4C22×Q818yes—
908C22⋊C4C22×Q8116yes—
909C22⋊C4C2×#4118yes—
910C42—24no—
911C42—28no—
912C42—24no—
913C42—24no—
914C42—24no—
915C42—24no—
916C42—28no—
917C42—24no—
918C42—22no—
919C42—24no—
920C42—24no—
921C42—24no—
922C42—28no—
923C42—22no—
924C42—24no—
925C42—22no—
926C42—44no—
927C42—44no—
928C42—44no—
929C42—44no—
930C42—41no—
931C42—42no—
932C42—42no—
933C42—48no—
934C42—42no—
935C42—42no—
936C42—48no—
937C42—48no—
938C42C22×Q818yes—
939C42C22×Q814yes—
940C42C2×#4114yes—
941C42H(5,𝔽2)14yes—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23C23×Q814yes—
947C23C22×#4114yes—
948C23C2×2−1+414yes—
949C23C2611yescharacteristic
950Q8—28no—
951Q8—216no—
952Q8—416no—
953Q8—44no—
954Q8—416no—
955Q8—48no—
956Q8—84no—
957Q8—816no—
958D4#557116yescomplemented
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—22no—
963C2×C4—21no—
964C2×C4—22no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—22no—
974C2×C4—21no—
975C2×C4—216no—
976C2×C4—216no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—28no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—24no—
987C2×C4—22no—
988C2×C4—28no—
989C2×C4—24no—
990C2×C4—21no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—21no—
1003C2×C4—22no—
1004C2×C4—21no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—28no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—416no—
1020C2×C4—48no—
1021C2×C4—88no—
1022C2×C4—88no—
1023C2×C4—88no—
1024C2×C4—816no—
1025C2×C4C23×Q814yes—
1026C2×C4C23×Q812yes—
1027C2×C4C23×Q814yes—
1028C2×C4C23×Q814yes—
1029C2×C4C23×Q818yes—
1030C2×C4C23×Q812yes—
1031C2×C4C23×Q812yes—
1032C2×C4C22×#4112yes—
1033C2×C4C22×#4114yes—
1034C2×C4C22×#4112yes—
1035C2×C4C22×#4112yes—
1036C2×C4C2×H(5,𝔽2)12yes—
1037C2×C4C2×H(5,𝔽2)12yes—
1038C2×C4C2×H(5,𝔽2)12yes—
1039C2×C4C2×2−1+412yes—
1040C2×C4#58512yes—
1041C2×C4#58512yes—
1042C22—24no—
1043C22—24no—
1044C22—24no—
1045C22—24no—
1046C22—24no—
1047C22—24no—
1048C22C2×#55718yes—
1049C22C24×Q811yescharacteristic
1050C22C23×#4111yescharacteristic
1051C22C22×H(5,𝔽2)11yescharacteristic
1052C22C22×2−1+411yescharacteristic
1053C22C2×#58511yescharacteristic
1054C22C2×#58511yescharacteristic
1055C222−1+611yescharacteristic
1056C4—22no—
1057C4—24no—
1058C4—22no—
1059C4—24no—
1060C4—24no—
1061C4—28no—
1062C4—24no—
1063C4—22no—
1064C4—44no—
1065C4—42no—
1066C4—44no—
1067C4—41no—
1068C4—42no—
1069C4—44no—
1070C4—42no—
1071C4—44no—
1072C4—48no—
1073C4—42no—
1074C4—42no—
1075C4—42no—
1076C4—44no—
1077C4—42no—
1078C4C2×#55714yes—
1079C4#350114yes—
1080C4#351414yes—
1081C2—28no—
1082C2C22×#55711yescharacteristic
1083C2C2×#350111yescharacteristic
1084C2C2×#351411yescharacteristic
1085C2#6294211yescharacteristic
1086C2#6299511yescharacteristic
1087C2#6300411yescharacteristic
1088C2#6302511yescharacteristic
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. #59870C2semidirect
2. #59869C2semidirect
3. #59867C2semidirect
4. #59464C2semidirect
5. #59325C2semidirect
6. #59144C2semidirect
7. #44954C2semidirect
8. #43557C2semidirect
9. #39643C2semidirect
10. #39640C2semidirect
11. #39182C2semidirect
12. #39179C2semidirect
13. #36598C2semidirect
14. #36577C2semidirect
15. #36560C2semidirect
16. #36552C2semidirect
21. #34951C2semidirect
22. C2×#2568C2semidirect
204. D4×Q8Q8semidirect
530. C22×Q8C2×Q8semidirect
559. C4⋊Q8C2×Q8semidirect
560. C4⋊Q8C2×Q8semidirect
569. C22⋊Q8C2×Q8semidirect
570. C22⋊Q8C2×Q8semidirect
587. C4×Q8C2×Q8semidirect
958. D4#557semidirect

Maximal subgroups

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

subgroupindex
#598702
#598692
#598672
#594642
#593252
#591442
#449542
#435572
#396432
#396402
#391822
#391792
#365982
#365772
#365602
#365522
#362762
#361652
D4×C4⋊Q82
#359612
#349512
C2×#25682
#343342
C4×#5542
C4×D4×Q82