Finite Group Databasebeta

← #7688278

Subgroups — #7688278

Order 512.

5223 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59924C212yesmaximal, complemented
2#59918C214yesmaximal, complemented
3#59871C211yesmaximal, characteristic, complemented
4#59459C212yesmaximal, complemented
5#59322C214yesmaximal, complemented
6#59151C212yesmaximal, complemented
7#44950C214yesmaximal, complemented
8#43553C218yesmaximal, complemented
9#39626C212yesmaximal, complemented
10#39625C212yesmaximal, complemented
11#39624C214yesmaximal, complemented
12#39623C214yesmaximal, complemented
13#36564C212yesmaximal, complemented
14#36563C211yesmaximal, characteristic, complemented
15Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
16Q8×C22⋊Q8C212yesmaximal, complemented
17#36261C212yesmaximal
18#36180C212yesmaximal
19D4×C4⋊Q8C211yesmaximal, characteristic
20#35928C214yesmaximal
21#34950C211yesmaximal, characteristic, complemented
22C2×#2567C212yesmaximal, complemented
23#34334C212yesmaximal
24#34332C212yesmaximal
25C4×#554C211yesmaximal, characteristic
26C4×D4×Q8C211yesmaximal, characteristic
27C2×Q82C2212yes—
28C2×#554C2214yes—
29C2×#554C2211yescharacteristic
30C2×D4×Q8C2212yes—
31C2×D4×Q8C2211yescharacteristic
32C22×C4⋊Q8C2212yes—
33C22×C4×Q8C2212yes—
34#2868C2211yescharacteristic
35#2868C2212yes—
36#2859C2212yes—
37#2857C2212yes—
38#2857C2214yes—
39#2857C2214yes—
40#2811C2218yes—
41#2806C2218yes—
42#2806C2214yes—
43#2806C2218yes—
44#2806C2218yes—
45#2792C2218yes—
46#2792C2218yes—
47#2792C2218yes—
48#2792C2218yes—
49#2734C2218yes—
50#2734C2218yes—
51#2660C2214yes—
52#2659C2218yes—
53#2586C2218yes—
54#2586C2214yes—
55#2586C2218yes—
56#2584C2214yes—
57#2584C2214yes—
58#2583C2218yes—
59#2583C2218yes—
60#2582C2214yes—
61#2582C2211yescharacteristic
62#2582C2214yes—
63#2582C2212yes—
64#2567C2214yes—
65#2567C2211yescharacteristic
66#2567C2212yes—
67#2567C2218yes—
68#2567C2214yes—
69#2567C2214yes—
70#2567C2214yes—
71#2567C2218yes—
72#2567C2214yes—
73#2567C2211yescharacteristic
74#2567C2212yes—
75#2567C2214yes—
76#2567C2214yes—
77#2567C2212yes—
78#2567C2214yes—
79#2552C2212yes—
80#2552C2214yes—
81#2552C2212yes—
82#2552C2212yes—
83#2551C2214yes—
84#2551C2214yes—
85#2551C2212yes—
86#2551C2214yes—
87#2551C2212yes—
88#2551C2212yes—
89#2551C2214yes—
90#2551C2214yes—
91#2551C2211yescharacteristic
92#2551C2212yes—
93#2550C2214yes—
94#2550C2214yes—
95#2550C2214yes—
96#2549C2218yes—
97#2549C2218yes—
98#2549C2218yes—
99#2546C2212yes—
100#2507C2218yes—
101#2507C2214yes—
102#2507C2214yes—
103#2507C2212yes—
104#2507C2212yes—
105#2507C2214yes—
106#2507C2214yes—
107#2502C2218yes—
108#2451C2212yes—
109#2451C2214yes—
110#2451C2214yes—
111#2451C2214yes—
112#2451C2218yes—
113#2451C2214yes—
114#2451C2212yes—
115#2451C2214yes—
116#2440C2214yes—
117#2440C2214yes—
118#2440C2214yes—
119#2440C2214yes—
120#2440C2214yes—
121#2440C2218yes—
122#2440C2218yes—
123#2440C2214yes—
124#2440C2218yes—
125#2434C2218yes—
126#2434C2214yes—
127#2399C2214yes—
128C2×#395C2218yes—
129#2370C2214yes—
130#2370C2212yes—
131#2369C2214yes—
132#2369C2212yes—
133#2369C2211yescharacteristic
134#2369C2212yes—
135#2369C2214yes—
136#2368C2218yes—
137#2368C2214yes—
138#2365C2212yes—
139#2365C2211yescharacteristic
140#2365C2212yes—
141#2360C2212yes—
142#2360C2214yes—
143#2360C2214yes—
144#2360C2218yes—
145#2360C2214yes—
146#2360C2212yes—
147#2355C2212yes—
148#2355C2211yescharacteristic
149Q8×C4⋊C4C2212yes—
150Q8×C4⋊C4C2212yes—
151Q8×C4⋊C4C2214yes—
152Q8×C4⋊C4C2211yescharacteristic
153Q8×C4⋊C4C2212yes—
154Q8×C4⋊C4C2212yes—
155#2349C2214yes—
156#2349C2212yes—
157D4×C4⋊C4C2212yes—
158D4×C4⋊C4C2212yes—
159D4×C4⋊C4C2214yes—
160D4×C4⋊C4C2211yescharacteristic
161D4×C4⋊C4C2212yes—
162D4×C4⋊C4C2211yescharacteristic
163#2345C2214yes—
164#2345C2212yes—
165Q8×C22⋊C4C2214yes—
166Q8×C22⋊C4C2212yes—
167#2331C2214yes—
168#2330C2214yes—
169#2329C2218yes—
170#2329C2218yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2211yescharacteristic
178C4×C4⋊Q8C2211yescharacteristic
179C4×#125C2212yes—
180C4×C22⋊Q8C2214yes—
181C4×C22⋊Q8C2214yes—
182C4×C22⋊Q8C2212yes—
183C4×C22⋊Q8C2212yes—
184C4×C22⋊Q8C2214yes—
185C4×C22⋊Q8C2214yes—
186#2295C2212yes—
187#2295C2212yes—
188C2×#391C2214yes—
189C2×#389C2214yes—
190C2×#389C2214yes—
191C2×#384C2214yes—
192#2275C2214yes—
193C42×Q8C2211yescharacteristic
194C42×Q8C2211yescharacteristic
195C42×D4C2211yescharacteristic
196C42×D4C2212yes—
197C42×D4C2212yes—
198C2×C4×C4⋊C4C2212yes—
199C23×Q8C2314yes—
200C23×Q8C2312yes—
201Q82—48no—
202#554—416no—
203#554Q8116yescomplemented
204D4×Q8—48no—
205D4×Q8Q8116yescomplemented
206C2×C4⋊Q8—48no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2312yes—
219C2×C4⋊Q8C2318yes—
220C2×C4⋊Q8C2318yes—
221C2×C4⋊Q8C2312yes—
222C2×C4⋊Q8C2314yes—
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2312yes—
226C2×#125C2314yes—
227C2×#125C2314yes—
228C2×#125C2312yes—
229C2×C22⋊Q8C2318yes—
230C2×C22⋊Q8C2318yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2318yes—
233C2×C22⋊Q8C2318yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2312yes—
238C2×C4×Q8—48no—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×D4C2312yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2312yes—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2312yes—
264C2×C4×D4C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2318yes—
267C22×C4⋊C4C2314yes—
268C22×C4⋊C4C2312yes—
269C22×C4⋊C4C2314yes—
270C22×C4⋊C4C2314yes—
271C22×C4⋊C4C2318yes—
272C22×C4⋊C4C2312yes—
273C22×C42C2312yes—
274C22×C42C2314yes—
275C22×C42C2314yes—
276#398C2318yes—
277#398C2318yes—
278#398C2314yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2314yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2314yes—
287#398C2314yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#395C2318yes—
294#395C2314yes—
295#395C2318yes—
296#395C2318yes—
297#395C2318yes—
298#395C2318yes—
299#395C2318yes—
300#395C2318yes—
301#395C2318yes—
302#395C2318yes—
303#395C2314yes—
304#395C2318yes—
305#395C2318yes—
306#395C2318yes—
307#395C2318yes—
308#395C2318yes—
309#395C2318yes—
310#395C2318yes—
311#395C2318yes—
312#395C2314yes—
313#395C2318yes—
314#395C2314yes—
315#391C2314yes—
316#391C2312yes—
317#391C2314yes—
318#391C2314yes—
319#391C2312yes—
320#391C2314yes—
321#391C2314yes—
322#391C2312yes—
323#391C2312yes—
324#391C2314yes—
325#391C2314yes—
326#391C2318yes—
327#391C2318yes—
328#391C2314yes—
329#391C2318yes—
330#391C2318yes—
331#391C2318yes—
332#391C2318yes—
333#391C2312yes—
334#391C2312yes—
335#391C2312yes—
336#391C2318yes—
337#391C2312yes—
338#391C2314yes—
339#391C2318yes—
340#391C2318yes—
341#391C2312yes—
342#391C2314yes—
343#391C2318yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2314yes—
348#389C2312yes—
349#389C2314yes—
350#389C2312yes—
351#389C2312yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2314yes—
361#389C2314yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2314yes—
367#389C2318yes—
368#389C2318yes—
369#389C2314yes—
370#389C2312yes—
371#389C2314yes—
372#389C2314yes—
373#389C2318yes—
374#389C2314yes—
375#389C2318yes—
376#389C2314yes—
377#389C2318yes—
378#389C2318yes—
379#389C2314yes—
380#389C2318yes—
381#389C2318yes—
382#389C2314yes—
383#389C2312yes—
384#389C2318yes—
385#389C2318yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2318yes—
391#389C2318yes—
392#389C2314yes—
393#389C2314yes—
394#389C2318yes—
395#389C2318yes—
396#389C2318yes—
397#389C2312yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2312yes—
402#389C2314yes—
403#389C2312yes—
404#387C2314yes—
405#387C2314yes—
406#387C2314yes—
407#387C2314yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2318yes—
420#387C2314yes—
421#387C2314yes—
422#387C2314yes—
423#387C2314yes—
424#385C2314yes—
425#385C2314yes—
426#385C2314yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2314yes—
434#385C2314yes—
435#385C2314yes—
436#384C2312yes—
437#384C2312yes—
438#384C2311yescharacteristic
439#384C2311yescharacteristic
440#384C2312yes—
441#384C2311yescharacteristic
442#384C2312yes—
443#384C2312yes—
444#384C2318yes—
445#384C2314yes—
446#384C2318yes—
447#384C2312yes—
448#384C2314yes—
449#384C2314yes—
450#384C2318yes—
451#384C2314yes—
452#384C2314yes—
453#384C2312yes—
454#384C2314yes—
455#382C2312yes—
456#382C2314yes—
457#380C2318yes—
458#380C2318yes—
459#380C2312yes—
460#380C2314yes—
461#380C2314yes—
462#380C2314yes—
463#380C2312yes—
464#380C2314yes—
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2318yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2318yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2312yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519#376C2314yes—
520C2×#95C2318yes—
521C2×#95C2314yes—
522C2×#95C2318yes—
523C43C2312yes—
524C43C2312yes—
525C43C2311yescharacteristic
526C22×Q8—48no—
527C22×Q8—44no—
528C22×Q8—44no—
529C22×Q8—48no—
530C22×Q8—84no—
531C22×Q8C2×Q8116yescomplemented
532C22×Q8C2411yescharacteristic
533C22×Q8C2412yes—
534C22×Q8C2411yescharacteristic
535C22×Q8C2414yes—
536C22×Q8C2412yes—
537C22×Q8C2414yes—
538C22×Q8C2418yes—
539C22×Q8C2418yes—
540C22×Q8C2412yes—
541C22×Q8C2414yes—
542C22×D4C2411yescharacteristic
543C23×C4C2414yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2414yes—
548C23×C4C2418yes—
549C23×C4C2414yes—
550C23×C4C2414yes—
551C4⋊Q8—28no—
552C4⋊Q8—24no—
553C4⋊Q8—28no—
554C4⋊Q8—48no—
555C4⋊Q8—48no—
556C4⋊Q8—44no—
557C4⋊Q8—48no—
558C4⋊Q8—44no—
559C4⋊Q8—48no—
560C4⋊Q8—48no—
561C4⋊Q8—48no—
562C4⋊Q8—48no—
563C4⋊Q8—416no—
564C4⋊Q8—88no—
565C4⋊Q8—84no—
566C4⋊Q8—82no—
567C4⋊Q8C2×Q818yescomplemented
568C4⋊Q8C2×Q8116yescomplemented
569C4⋊Q8C2×Q818yescomplemented
570#125—48no—
571#125—48no—
572#125C2×Q8116yescomplemented
573C22⋊Q8—48no—
574C22⋊Q8—416no—
575C22⋊Q8—416no—
576C22⋊Q8—416no—
577C22⋊Q8—416no—
578C22⋊Q8C2×Q8116yescomplemented
579C22⋊Q8C2×Q8132yescomplemented
580C22⋊Q8C2×Q8132yescomplemented
581C22⋊Q8C2×Q8116yescomplemented
582C4×Q8—24no—
583C4×Q8—24no—
584C4×Q8—28no—
585C4×Q8—24no—
586C4×Q8—48no—
587C4×Q8—44no—
588C4×Q8—44no—
589C4×Q8—48no—
590C4×Q8—48no—
591C4×Q8—44no—
592C4×Q8—44no—
593C4×Q8—48no—
594C4×Q8—42no—
595C4×Q8—48no—
596C4×Q8—48no—
597C4×Q8—84no—
598C4×Q8C2×Q818yescomplemented
599C4×Q8C2×Q818yescomplemented
600C4×D4—24no—
601C4×D4—216no—
602C4×D4—28no—
603C4×D4—28no—
604C4×D4C2×Q818yes—
605C4×D4C2×Q8116yes—
606C4×D4C2×Q8116yes—
607C4×D4C2×Q818yes—
608C2×C4⋊C4—28no—
609C2×C4⋊C4—44no—
610C2×C4⋊C4—48no—
611C2×C4⋊C4—48no—
612C2×C4⋊C4—48no—
613C2×C4⋊C4—416no—
614C2×C4⋊C4—88no—
615C2×C4⋊C4C2×Q8116yescomplemented
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2412yes—
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⋊C4C2411yescharacteristic
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2411yescharacteristic
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2412yes—
693C2×C42—28no—
694C2×C42—48no—
695C2×C42—48no—
696C2×C42C2412yes—
697C2×C42C2414yes—
698C2×C42C2411yescharacteristic
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2414yes—
702C2×C42C2411yescharacteristic
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2414yes—
708C2×C42C2411yescharacteristic
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2418yes—
713C2×C42C2412yes—
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2418yes—
717C2×C42C2412yes—
718C2×C42C2418yes—
719C2×C42C2411yescharacteristic
720C2×C42C2412yes—
721C2×C42C2414yes—
722C2×C42C2414yes—
723C2×C42C2412yes—
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2412yes—
727C2×C42C2411yescharacteristic
728#95C2414yes—
729#95C2412yes—
730#95C2414yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2412yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2412yes—
748#95C2414yes—
749#95C2414yes—
750#95C2412yes—
751#95C2414yes—
752#95C2412yes—
753#95C2412yes—
754#95C2412yes—
755#95C2412yes—
756#95C2414yes—
757#95C2412yes—
758#95C2414yes—
759#95C2418yes—
760#95C2414yes—
761#95C2418yes—
762#95C2418yes—
763#95C2414yes—
764#95C2414yes—
765#95C2418yes—
766#95C2414yes—
767#95C2418yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772C24C2512yes—
773C2×Q8—22no—
774C2×Q8—24no—
775C2×Q8—22no—
776C2×Q8—24no—
777C2×Q8—28no—
778C2×Q8—22no—
779C2×Q8—28no—
780C2×Q8—24no—
781C2×Q8—22no—
782C2×Q8—44no—
783C2×Q8—42no—
784C2×Q8—42no—
785C2×Q8—42no—
786C2×Q8—44no—
787C2×Q8—42no—
788C2×Q8—44no—
789C2×Q8—44no—
790C2×Q8—48no—
791C2×Q8—48no—
792C2×Q8—44no—
793C2×Q8—44no—
794C2×Q8—48no—
795C2×Q8—48no—
796C2×Q8—48no—
797C2×Q8—48no—
798C2×Q8—432no—
799C2×Q8—832no—
800C2×Q8C22×Q814yes—
801C2×Q8C22×Q814yes—
802C2×Q8C22×Q818yes—
803C2×Q8C22×Q818yes—
804C2×Q8C22×Q8116yes—
805C2×D4C22×Q814yes—
806C2×D4C22×Q814yes—
807C2×D4H(5,𝔽2)14yes—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—28no—
813C22×C4—24no—
814C22×C4—28no—
815C22×C4—216no—
816C22×C4—24no—
817C22×C4—28no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—42no—
824C22×C4—44no—
825C22×C4—48no—
826C22×C4—44no—
827C22×C4—48no—
828C22×C4C22×Q818yes—
829C22×C4C22×Q818yes—
830C22×C4C22×Q8116yes—
831C22×C4C22×Q8116yes—
832C22×C4C2512yes—
833C22×C4C2514yes—
834C22×C4C2514yes—
835C22×C4C2511yescharacteristic
836C22×C4C2512yes—
837C22×C4C2514yes—
838C22×C4C2512yes—
839C22×C4C2518yes—
840C22×C4C2514yes—
841C22×C4C2512yes—
842C22×C4C2512yes—
843C22×C4C2511yescharacteristic
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2511yescharacteristic
847C22×C4C2512yes—
848C22×C4C2514yes—
849C22×C4C2512yes—
850C22×C4C2514yes—
851C22×C4C2512yes—
852C22×C4C2511yescharacteristic
853C22×C4C2512yes—
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C4⋊C4—24no—
858C4⋊C4—22no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—28no—
862C4⋊C4—24no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—28no—
868C4⋊C4—22no—
869C4⋊C4—24no—
870C4⋊C4—22no—
871C4⋊C4—28no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—28no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—22no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—48no—
883C4⋊C4—48no—
884C4⋊C4—48no—
885C4⋊C4—48no—
886C4⋊C4—48no—
887C4⋊C4—44no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4—48no—
891C4⋊C4—44no—
892C4⋊C4—42no—
893C4⋊C4—48no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—48no—
900C4⋊C4—48no—
901C4⋊C4—44no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—44no—
905C4⋊C4—48no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—42no—
911C4⋊C4—44no—
912C4⋊C4C22×Q814yes—
913C4⋊C4C22×Q8116yes—
914C4⋊C4C22×Q818yes—
915C4⋊C4C22×Q814yes—
916C4⋊C4C22×Q818yes—
917C4⋊C4C22×Q814yes—
918C4⋊C4C22×Q818yes—
919C4⋊C4C22×Q818yes—
920C4⋊C4C22×Q814yes—
921C4⋊C4C22×Q818yes—
922C4⋊C4C22×Q8116yes—
923C4⋊C4C22×Q8116yes—
924C4⋊C4C22×Q818yes—
925C4⋊C42−1+414yes—
926C22⋊C4—24no—
927C22⋊C4—216no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4C22×Q818yes—
931C22⋊C4C22×Q8116yes—
932C22⋊C4C22×Q8116yes—
933C22⋊C4C22×Q818yes—
934C42—24no—
935C42—24no—
936C42—24no—
937C42—24no—
938C42—28no—
939C42—24no—
940C42—28no—
941C42—24no—
942C42—22no—
943C42—24no—
944C42—24no—
945C42—22no—
946C42—24no—
947C42—24no—
948C42—28no—
949C42—22no—
950C42—44no—
951C42—44no—
952C42—44no—
953C42—44no—
954C42—48no—
955C42—42no—
956C42—48no—
957C42—42no—
958C42—48no—
959C42—41no—
960C42—42no—
961C42C22×Q818yes—
962C42C22×Q818yes—
963C42C22×Q814yes—
964C42C22×Q814yes—
965C42H(5,𝔽2)14yes—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23C23×Q814yes—
971C23C23×Q814yes—
972C23C2×H(5,𝔽2)14yes—
973C23C2611yescharacteristic
974Q8—28no—
975Q8—216no—
976Q8—28no—
977Q8—416no—
978Q8—48no—
979Q8—48no—
980Q8—88no—
981Q8—88no—
982Q8—816no—
983Q8—168no—
984D4Q82116yescomplemented
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—22no—
998C2×C4—21no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—216no—
1010C2×C4—216no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—21no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—28no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—28no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—21no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—21no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—28no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—416no—
1042C2×C4—416no—
1043C2×C4—416no—
1044C2×C4—48no—
1045C2×C4—88no—
1046C2×C4—816no—
1047C2×C4C23×Q812yes—
1048C2×C4C23×Q814yes—
1049C2×C4C23×Q814yes—
1050C2×C4C23×Q812yes—
1051C2×C4C23×Q814yes—
1052C2×C4C23×Q814yes—
1053C2×C4C23×Q814yes—
1054C2×C4C23×Q818yes—
1055C2×C4C23×Q814yes—
1056C2×C4C23×Q818yes—
1057C2×C4C23×Q812yes—
1058C2×C4C23×Q812yes—
1059C2×C4C23×Q812yes—
1060C2×C4C23×Q812yes—
1061C2×C4C2×H(5,𝔽2)12yes—
1062C2×C4C2×H(5,𝔽2)12yes—
1063C2×C4C2×H(5,𝔽2)12yes—
1064C2×C4C2×H(5,𝔽2)12yes—
1065C2×C4C2×2−1+414yes—
1066C2×C4C2×2−1+412yes—
1067C2×C4#58512yes—
1068C22—24no—
1069C22—24no—
1070C22—24no—
1071C22—24no—
1072C22—24no—
1073C22—24no—
1074C22C2×Q8218yes—
1075C22C24×Q811yescharacteristic
1076C22C24×Q811yescharacteristic
1077C22C22×H(5,𝔽2)11yescharacteristic
1078C22C22×H(5,𝔽2)11yescharacteristic
1079C22C22×2−1+411yescharacteristic
1080C22C2×#58511yescharacteristic
1081C22H(7,𝔽2)11yescharacteristic
1082C4—24no—
1083C4—28no—
1084C4—22no—
1085C4—22no—
1086C4—24no—
1087C4—24no—
1088C4—24no—
1089C4—24no—
1090C4—28no—
1091C4—24no—
1092C4—24no—
1093C4—22no—
1094C4—41no—
1095C4—44no—
1096C4—44no—
1097C4—42no—
1098C4—42no—
1099C4—42no—
1100C4—44no—
1101C4—48no—
1102C4—44no—
1103C4—42no—
1104C4C2×Q8214yes—
1105C4#350114yes—
1106C4#350314yes—
1107C2—28no—
1108C2C22×Q8211yescharacteristic
1109C2C2×#350111yescharacteristic
1110C2C2×#350311yescharacteristic
1111C2#6291211yescharacteristic
1112C2#6298911yescharacteristic
1113C2Q8×2−1+411yescharacteristic
1114C2#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. #59924C2semidirect
2. #59918C2semidirect
3. #59871C2semidirect
4. #59459C2semidirect
5. #59322C2semidirect
6. #59151C2semidirect
7. #44950C2semidirect
8. #43553C2semidirect
9. #39626C2semidirect
10. #39625C2semidirect
11. #39624C2semidirect
12. #39623C2semidirect
13. #36564C2semidirect
14. #36563C2semidirect
15. Q8×C4⋊Q8C2semidirect
16. Q8×C22⋊Q8C2semidirect
21. #34950C2semidirect
22. C2×#2567C2semidirect
203. #554Q8semidirect
205. D4×Q8Q8semidirect
531. C22×Q8C2×Q8semidirect
567. C4⋊Q8C2×Q8semidirect
568. C4⋊Q8C2×Q8semidirect
569. C4⋊Q8C2×Q8semidirect
572. #125C2×Q8semidirect
578. C22⋊Q8C2×Q8semidirect
579. C22⋊Q8C2×Q8semidirect
580. C22⋊Q8C2×Q8semidirect
581. C22⋊Q8C2×Q8semidirect
598. C4×Q8C2×Q8semidirect
599. C4×Q8C2×Q8semidirect
615. C2×C4⋊C4C2×Q8semidirect
984. D4Q82semidirect

Maximal subgroups

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

subgroupindex
#599242
#599182
#598712
#594592
#593222
#591512
#449502
#435532
#396262
#396252
#396242
#396232
#365642
#365632
Q8×C4⋊Q82
Q8×C22⋊Q82
#362612
#361802
D4×C4⋊Q82
#359282
#349502
C2×#25672
#343342
#343322
C4×#5542
C4×D4×Q82