Finite Group Databasebeta

← #7708742

Subgroups — #7708742

Order 512.

5048 conjugacy classes of subgroups.

The subgroup lattice has 1157 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59664C214yesmaximal, complemented
2#59321C212yesmaximal, complemented
3#59151C212yesmaximal, complemented
4#45794C214yesmaximal, complemented
5#45499C214yesmaximal, complemented
6#39752C212yesmaximal, complemented
7#39689C214yesmaximal, complemented
8#39676C214yesmaximal, complemented
9#39639C212yesmaximal, complemented
10#39623C212yesmaximal, complemented
11#39607C212yesmaximal, complemented
12#39597C212yesmaximal, complemented
13#39368C212yesmaximal, complemented
14#37685C214yesmaximal
15#37477C212yesmaximal
16#36752C214yesmaximal, complemented
17#36625C211yesmaximal, characteristic
18C2×#2857C211yesmaximal, characteristic
19Q8×C22⋊Q8C212yesmaximal, complemented
20#36193C212yesmaximal, complemented
21#36190C214yesmaximal
22#35167C212yesmaximal, complemented
23#35015C212yesmaximal, complemented
24#34380C212yesmaximal
25C2×C4×C22⋊Q8C211yesmaximal, characteristic
26C2×Q82C2212yescomplemented
27C2×#544C2214yes—
28C2×#533C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2212yes—
31C22×C22⋊Q8C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C23×C42C2211yescharacteristic
34#2857C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2857C2212yes—
40#2857C2212yes—
41#2857C2212yes—
42#2857C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2214yes—
47#2855C2212yes—
48#2855C2212yes—
49#2855C2214yes—
50#2851C2212yes—
51#2851C2212yes—
52#2848C2212yes—
53#2848C2212yes—
54#2841C2218yes—
55#2809C2214yescomplemented
56#2806C2214yescomplemented
57#2805C2218yescomplemented
58#2802C2218yescomplemented
59#2799C2218yescomplemented
60#2792C2218yescomplemented
61#2791C2218yescomplemented
62#2791C2218yescomplemented
63#2755C2218yescomplemented
64#2734C2218yescomplemented
65#2734C2214yescomplemented
66#2729C2218yes—
67#2726C2214yescomplemented
68#2720C2218yes—
69#2713C2218yescomplemented
70#2713C2218yescomplemented
71#2704C2218yes—
72#2677C2218yes—
73#2659C2214yes—
74#2659C2214yes—
75#2659C2214yes—
76#2646C2214yes—
77#2646C2214yes—
78#2629C2214yes—
79#2628C2214yes—
80#2627C2214yes—
81#2590C2218yescomplemented
82#2588C2218yescomplemented
83#2582C2212yescomplemented
84#2582C2214yescomplemented
85#2581C2214yescomplemented
86#2574C2218yes—
87#2569C2218yes—
88#2567C2212yescomplemented
89#2567C2212yescomplemented
90#2567C2214yescomplemented
91#2565C2214yescomplemented
92#2552C2214yescomplemented
93#2552C2214yescomplemented
94#2552C2212yescomplemented
95#2551C2214yescomplemented
96#2551C2214yescomplemented
97#2551C2214yescomplemented
98#2550C2218yescomplemented
99#2550C2218yescomplemented
100#2546C2214yescomplemented
101#2522C2218yes—
102#2520C2218yescomplemented
103#2511C2214yescomplemented
104#2511C2214yescomplemented
105#2508C2214yescomplemented
106#2507C2214yescomplemented
107#2507C2214yescomplemented
108#2506C2214yescomplemented
109#2506C2214yescomplemented
110#2505C2218yes—
111#2502C2214yes—
112#2497C2214yes—
113#2497C2214yes—
114#2492C2214yes—
115#2473C2218yes—
116#2473C2218yes—
117#2453C2214yescomplemented
118#2451C2214yescomplemented
119#2451C2214yescomplemented
120#2451C2214yescomplemented
121#2451C2218yescomplemented
122#2446C2214yescomplemented
123#2442C2214yes—
124#2442C2214yes—
125#2440C2214yes—
126#2440C2214yes—
127#2440C2218yes—
128#2440C2218yes—
129#2440C2214yes—
130#2438C2218yes—
131#2438C2218yes—
132#2437C2218yes—
133#2434C2218yes—
134#2423C2214yes—
135#2378C2218yes—
136#2370C2214yescomplemented
137#2369C2212yescomplemented
138#2368C2218yes—
139#2360C2214yes—
140#2360C2214yes—
141#2360C2214yes—
142#2355C2212yescomplemented
143Q8×C4⋊C4C2214yescomplemented
144Q8×C4⋊C4C2212yescomplemented
145#2345C2214yes—
146#2344C2214yes—
147#2342C2218yes—
148Q8×C22⋊C4C2214yes—
149#2329C2214yes—
150#2329C2214yes—
151#2329C2214yes—
152#2323C2214yes—
153#2323C2214yes—
154#2316C2214yes—
155#2313C2214yes—
156C4×C22⋊Q8C2212yes—
157C4×C22⋊Q8C2212yes—
158C4×C22⋊Q8C2212yes—
159C4×C22⋊Q8C2212yes—
160C4×C22⋊Q8C2212yes—
161C4×C22⋊Q8C2212yes—
162C4×C22⋊Q8C2212yes—
163C4×C22⋊Q8C2214yes—
164C4×C22⋊Q8C2212yes—
165C4×C22⋊Q8C2212yes—
166C4×C22⋊Q8C2212yes—
167C4×C22⋊Q8C2212yes—
168C4×C22⋊Q8C2212yes—
169#2296C2212yes—
170C2×#391C2212yes—
171C2×#391C2211yescharacteristic
172C2×#389C2212yes—
173C2×#389C2212yes—
174C2×#389C2211yescharacteristic
175C2×#387C2212yes—
176C2×#385C2212yes—
177#2285C2211yescharacteristic
178#2285C2214yes—
179C2×#384C2211yescharacteristic
180#2280C2212yes—
181C2×#380C2212yes—
182C2×#380C2212yes—
183C2×#380C2211yescharacteristic
184C2×C4×C4⋊C4C2212yes—
185C2×C4×C4⋊C4C2211yescharacteristic
186C2×C4×C22⋊C4C2212yes—
187C23×Q8C2312yes—
188C23×Q8C2311yescharacteristic
189C24×C4C2311yescharacteristic
190C24×C4C2311yescharacteristic
191C24×C4C2311yescharacteristic
192Q82—48no—
193#544—416no—
194#533—44no—
195C2×C4⋊Q8—44no—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2314yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2311yescharacteristic
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2314yes—
204C2×C4⋊Q8C2318yes—
205C2×C4⋊Q8C2318yes—
206C2×C4⋊Q8C2318yes—
207C2×#125C2314yes—
208C2×#125C2312yes—
209C2×#125C2318yes—
210C2×#125C2318yes—
211C2×C22⋊Q8—48no—
212C2×C22⋊Q8Q8116yescomplemented
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2318yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C4×Q8—44no—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2312yes—
239C2×#117C2318yes—
240C2×#117C2312yes—
241C2×#117C2312yes—
242C22×C4⋊C4C2312yes—
243C22×C4⋊C4C2312yes—
244C22×C4⋊C4C2312yes—
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2314yes—
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2311yescharacteristic
254C22×C22⋊C4C2314yes—
255C22×C22⋊C4C2312yes—
256C22×C22⋊C4C2312yes—
257C22×C42—44no—
258C22×C42C2312yes—
259C22×C42C2311yescharacteristic
260C22×C42C2311yescharacteristic
261C22×C42C2311yescharacteristic
262C22×C42C2311yescharacteristic
263C22×C42C2311yescharacteristic
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268C22×C42C2311yescharacteristic
269C22×C42C2311yescharacteristic
270C22×C42C2312yes—
271C22×C42C2311yescharacteristic
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#399C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#396C2318yes—
300#396C2318yes—
301#395C2318yes—
302#395C2318yes—
303#395C2318yes—
304#395C2318yes—
305#395C2318yes—
306#395C2318yes—
307#395C2318yes—
308#395C2318yes—
309#395C2318yes—
310#395C2318yes—
311#393C2318yes—
312#391C2312yes—
313#391C2314yes—
314#391C2314yes—
315#391C2318yes—
316#391C2314yes—
317#391C2318yes—
318#391C2312yes—
319#391C2312yes—
320#391C2314yes—
321#391C2318yes—
322#391C2318yes—
323#391C2314yes—
324#391C2312yes—
325#391C2312yes—
326#391C2312yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2318yes—
332#391C2318yes—
333#391C2312yes—
334#391C2312yes—
335#389C2312yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2318yes—
343#389C2318yes—
344#389C2318yes—
345#389C2318yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2318yes—
350#389C2318yes—
351#389C2312yes—
352#389C2312yes—
353#389C2314yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2314yes—
358#389C2312yes—
359#389C2312yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2318yes—
367#389C2314yes—
368#389C2318yes—
369#389C2318yes—
370#389C2314yes—
371#389C2318yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2312yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2314yes—
396#387C2314yes—
397#387C2314yes—
398#387C2314yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2314yes—
404#387C2314yes—
405#387C2314yes—
406#387C2314yes—
407#385C2314yes—
408#385C2318yes—
409#385C2314yes—
410#385C2318yes—
411#385C2318yes—
412#385C2314yes—
413#385C2314yes—
414#385C2314yes—
415#385C2314yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2314yes—
420#385C2314yes—
421#385C2314yes—
422#385C2314yes—
423#384C2312yes—
424#384C2314yes—
425#384C2318yes—
426#384C2314yes—
427#384C2312yes—
428#384C2314yes—
429#384C2311yescharacteristic
430#384C2312yes—
431#384C2312yes—
432#384C2311yescharacteristic
433#384C2314yes—
434#382C2314yes—
435#382C2318yes—
436#382C2312yes—
437#381C2318yes—
438#381C2314yes—
439#380C2312yes—
440#380C2314yes—
441#380C2314yes—
442#380C2318yes—
443#380C2318yes—
444#380C2312yes—
445#380C2314yes—
446#380C2314yes—
447#380C2312yes—
448#380C2312yes—
449#380C2312yes—
450#380C2312yes—
451#380C2314yes—
452#380C2312yes—
453#380C2312yes—
454#380C2312yes—
455#380C2312yes—
456#380C2312yes—
457#380C2314yes—
458#380C2314yes—
459#380C2318yes—
460#380C2314yes—
461#380C2312yes—
462#380C2312yes—
463#380C2312yes—
464#379C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2318yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C22⋊C4C2318yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2318yes—
487C4×C22⋊C4C2318yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C2×#95C2312yes—
494C2×#95C2314yes—
495C2×#95C2312yes—
496C2×#95C2314yes—
497C2×#95C2312yes—
498C2×#95C2312yes—
499C2×#95C2312yes—
500C25C2411yescharacteristic
501C22×Q8—44no—
502C22×Q8—42no—
503C22×Q8—42no—
504C22×Q8—44no—
505C22×Q8—44no—
506C22×Q8C2×Q818yescomplemented
507C22×Q8C2412yes—
508C22×Q8C2412yes—
509C22×Q8C2412yes—
510C22×Q8C2414yes—
511C22×Q8C2414yes—
512C22×Q8C2418yes—
513C22×Q8C2412yes—
514C23×C4—24no—
515C23×C4—24no—
516C23×C4—24no—
517C23×C4—42no—
518C23×C4—42no—
519C23×C4—42no—
520C23×C4—42no—
521C23×C4—42no—
522C23×C4C2×Q818yes—
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2412yes—
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2414yes—
538C23×C4C2412yes—
539C23×C4C2414yes—
540C23×C4C2412yes—
541C23×C4C2411yescharacteristic
542C23×C4C2412yes—
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546C23×C4C2411yescharacteristic
547C4⋊Q8—28no—
548C4⋊Q8—44no—
549C4⋊Q8—44no—
550C4⋊Q8—42no—
551C4⋊Q8—48no—
552C4⋊Q8—48no—
553C4⋊Q8—44no—
554C4⋊Q8—42no—
555C4⋊Q8—416no—
556C4⋊Q8—416no—
557C4⋊Q8—416no—
558#125—48no—
559#125—44no—
560#125—416no—
561#125—416no—
562C22⋊Q8—216no—
563C22⋊Q8—28no—
564C22⋊Q8—28no—
565C22⋊Q8—28no—
566C22⋊Q8—48no—
567C22⋊Q8—416no—
568C22⋊Q8—44no—
569C22⋊Q8—416no—
570C22⋊Q8—48no—
571C22⋊Q8—44no—
572C22⋊Q8—48no—
573C22⋊Q8—44no—
574C22⋊Q8C2×Q8116yes—
575C22⋊Q8C2×Q8116yes—
576C22⋊Q8C2×Q8116yescomplemented
577C22⋊Q8C2×Q8116yescomplemented
578C4×Q8—28no—
579C4×Q8—28no—
580C4×Q8—44no—
581C4×Q8—44no—
582C4×Q8—44no—
583C4×Q8—44no—
584C4×Q8—48no—
585C4×Q8—48no—
586C4×Q8—48no—
587#117—44no—
588#117—44no—
589#117—416no—
590C2×C4⋊C4—28no—
591C2×C4⋊C4—28no—
592C2×C4⋊C4—44no—
593C2×C4⋊C4—42no—
594C2×C4⋊C4—42no—
595C2×C4⋊C4—44no—
596C2×C4⋊C4—44no—
597C2×C4⋊C4—48no—
598C2×C4⋊C4—44no—
599C2×C4⋊C4—44no—
600C2×C4⋊C4C2×Q818yescomplemented
601C2×C4⋊C4C2×Q8116yescomplemented
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C22⋊C4—44no—
656C2×C22⋊C4—48no—
657C2×C22⋊C4C2×Q8116yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C42—28no—
671C2×C42—24no—
672C2×C42—24no—
673C2×C42—24no—
674C2×C42—44no—
675C2×C42—42no—
676C2×C42—42no—
677C2×C42—42no—
678C2×C42—42no—
679C2×C42—42no—
680C2×C42—42no—
681C2×C42—42no—
682C2×C42—42no—
683C2×C42—42no—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2414yes—
697C2×C42C2414yes—
698C2×C42C2418yes—
699C2×C42C2418yes—
700C2×C42C2418yes—
701C2×C42C2414yes—
702C2×C42C2418yes—
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2418yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734#95C2414yes—
735#95C2418yes—
736#95C2414yes—
737#95C2414yes—
738#95C2418yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748C24—22no—
749C24—22no—
750C24—22no—
751C24—22no—
752C24—41no—
753C24—41no—
754C24C22×Q814yes—
755C24C2511yescharacteristic
756C24C2511yescharacteristic
757C24C2511yescharacteristic
758C2×Q8—24no—
759C2×Q8—24no—
760C2×Q8—28no—
761C2×Q8—24no—
762C2×Q8—28no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—24no—
766C2×Q8—42no—
767C2×Q8—42no—
768C2×Q8—42no—
769C2×Q8—44no—
770C2×Q8—42no—
771C2×Q8—44no—
772C2×Q8—44no—
773C2×Q8—44no—
774C2×Q8—48no—
775C2×Q8—48no—
776C2×Q8—48no—
777C2×Q8—416no—
778C2×Q8—816no—
779C2×Q8C22×Q818yes—
780C2×Q8C22×Q818yes—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—28no—
803C22×C4—28no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—416no—
817C22×C4—41no—
818C22×C4—41no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—42no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—41no—
832C22×C4—41no—
833C22×C4—41no—
834C22×C4—42no—
835C22×C4—416no—
836C22×C4—42no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—42no—
840C22×C4—42no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—42no—
844C22×C4—416no—
845C22×C4C22×Q818yes—
846C22×C4C22×Q814yes—
847C22×C4C22×Q814yes—
848C22×C4C22×Q814yes—
849C22×C4C22×Q818yes—
850C22×C4C22×Q814yes—
851C22×C4C22×Q814yes—
852C22×C4C22×Q814yes—
853C22×C4H(5,𝔽2)14yes—
854C22×C42−1+414yes—
855C22×C42−1+414yes—
856C22×C4C2511yescharacteristic
857C22×C4C2514yes—
858C22×C4C2514yes—
859C22×C4C2514yes—
860C22×C4C2518yes—
861C22×C4C2514yes—
862C22×C4C2518yes—
863C22×C4C2511yescharacteristic
864C22×C4C2514yes—
865C22×C4C2514yes—
866C22×C4C2511yescharacteristic
867C22×C4C2514yes—
868C22×C4C2514yes—
869C22×C4C2511yescharacteristic
870C22×C4C2511yescharacteristic
871C22×C4C2511yescharacteristic
872C22×C4C2511yescharacteristic
873C22×C4C2511yescharacteristic
874C22×C4C2511yescharacteristic
875C22×C4C2511yescharacteristic
876C22×C4C2511yescharacteristic
877C22×C4C2511yescharacteristic
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—24no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—216no—
886C4⋊C4—28no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—28no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—28no—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—24no—
898C4⋊C4—44no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—48no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—48no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—44no—
914C4⋊C4—42no—
915C4⋊C4—48no—
916C4⋊C4—48no—
917C4⋊C4—42no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—48no—
921C4⋊C4—44no—
922C4⋊C4—48no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—48no—
926C4⋊C4—48no—
927C4⋊C4C22×Q818yes—
928C4⋊C4C22×Q818yes—
929C4⋊C4C22×Q8116yes—
930C4⋊C4C22×Q8116yes—
931C22⋊C4—216no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—44no—
938C22⋊C4—48no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4C22×Q8116yes—
942C22⋊C4C22×Q8116yes—
943C42—22no—
944C42—22no—
945C42—22no—
946C42—22no—
947C42—22no—
948C42—22no—
949C42—22no—
950C42—22no—
951C42—22no—
952C42—28no—
953C42—28no—
954C42—28no—
955C42—28no—
956C42—28no—
957C42—41no—
958C42—41no—
959C42—41no—
960C42—41no—
961C42—41no—
962C42—41no—
963C42—44no—
964C42—48no—
965C42—48no—
966C42—48no—
967C42—48no—
968C42H(5,𝔽2)14yes—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—21no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—21no—
983C23—28no—
984C23—28no—
985C23—44no—
986C23—44no—
987C23—44no—
988C23—44no—
989C23—44no—
990C23C23×Q812yes—
991C23C23×Q812yes—
992C23C23×Q812yes—
993C23C2×H(5,𝔽2)12yes—
994C23C2×2−1+412yes—
995C23C2×2−1+412yes—
996C23#58512yes—
997C23C2611yescharacteristic
998Q8—216no—
999Q8—48no—
1000Q8—48no—
1001Q8—84no—
1002Q8—88no—
1003Q8—88no—
1004Q8—168no—
1005C2×C4—28no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—21no—
1016C2×C4—24no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—24no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—216no—
1027C2×C4—28no—
1028C2×C4—28no—
1029C2×C4—28no—
1030C2×C4—28no—
1031C2×C4—28no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—28no—
1040C2×C4—28no—
1041C2×C4—28no—
1042C2×C4—24no—
1043C2×C4—21no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—28no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—28no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—21no—
1061C2×C4—28no—
1062C2×C4—44no—
1063C2×C4—44no—
1064C2×C4—44no—
1065C2×C4—44no—
1066C2×C4—48no—
1067C2×C4—44no—
1068C2×C4—44no—
1069C2×C4—44no—
1070C2×C4—44no—
1071C2×C4—44no—
1072C2×C4—44no—
1073C2×C4—44no—
1074C2×C4—44no—
1075C2×C4—84no—
1076C2×C4—84no—
1077C2×C4—88no—
1078C2×C4—88no—
1079C2×C4C23×Q818yes—
1080C2×C4C23×Q818yes—
1081C2×C4C23×Q812yes—
1082C2×C4C23×Q812yes—
1083C2×C4C23×Q812yes—
1084C2×C4C23×Q812yes—
1085C2×C4C2×H(5,𝔽2)12yes—
1086C2×C4C2×H(5,𝔽2)12yes—
1087C2×C4C2×H(5,𝔽2)12yes—
1088C2×C4C2×H(5,𝔽2)12yes—
1089C2×C4C2×H(5,𝔽2)12yes—
1090C2×C4C2×2−1+412yes—
1091C2×C4C2×2−1+412yes—
1092C2×C4C2×2−1+412yes—
1093C2×C4C2×2−1+412yes—
1094C2×C4#58512yes—
1095C22—22no—
1096C22—22no—
1097C22—22no—
1098C22—22no—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—22no—
1103C22—22no—
1104C22—22no—
1105C22—22no—
1106C22—22no—
1107C22—22no—
1108C22—22no—
1109C22—22no—
1110C22—416no—
1111C22—41no—
1112C22—41no—
1113C22—41no—
1114C22—41no—
1115C22#350214yes—
1116C22#350314yes—
1117C22C24×Q811yescharacteristic
1118C22C22×H(5,𝔽2)11yescharacteristic
1119C22C22×H(5,𝔽2)11yescharacteristic
1120C22C22×2−1+411yescharacteristic
1121C22C22×2−1+411yescharacteristic
1122C22C2×#58511yescharacteristic
1123C22C2×#58511yescharacteristic
1124C4—22no—
1125C4—22no—
1126C4—22no—
1127C4—22no—
1128C4—22no—
1129C4—28no—
1130C4—28no—
1131C4—22no—
1132C4—22no—
1133C4—22no—
1134C4—41no—
1135C4—44no—
1136C4—44no—
1137C4—44no—
1138C4—41no—
1139C4—48no—
1140C4—44no—
1141C4—44no—
1142C4—44no—
1143C4—48no—
1144C4#350114yes—
1145C4#353814yes—
1146C2—24no—
1147C2—24no—
1148C2—42no—
1149C2C2×#353811yescharacteristic
1150C2#6275211yescharacteristic
1151C2C2×#350111yescharacteristic
1152C2C2×#350211yescharacteristic
1153C2C2×#350311yescharacteristic
1154C2#6281811yescharacteristic
1155C2#6283511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59664C2semidirect
2. #59321C2semidirect
3. #59151C2semidirect
4. #45794C2semidirect
5. #45499C2semidirect
6. #39752C2semidirect
7. #39689C2semidirect
8. #39676C2semidirect
9. #39639C2semidirect
10. #39623C2semidirect
11. #39607C2semidirect
12. #39597C2semidirect
13. #39368C2semidirect
16. #36752C2semidirect
19. Q8×C22⋊Q8C2semidirect
20. #36193C2semidirect
22. #35167C2semidirect
23. #35015C2semidirect
26. C2×Q82C22semidirect
55. #2809C22semidirect
56. #2806C22semidirect
57. #2805C22semidirect
58. #2802C22semidirect
59. #2799C22semidirect
60. #2792C22semidirect
61. #2791C22semidirect
62. #2791C22semidirect
63. #2755C22semidirect
64. #2734C22semidirect
65. #2734C22semidirect
67. #2726C22semidirect
69. #2713C22semidirect
70. #2713C22semidirect
81. #2590C22semidirect
82. #2588C22semidirect
83. #2582C22semidirect
84. #2582C22semidirect
85. #2581C22semidirect
88. #2567C22semidirect
89. #2567C22semidirect
90. #2567C22semidirect
91. #2565C22semidirect
92. #2552C22semidirect
93. #2552C22semidirect
94. #2552C22semidirect
95. #2551C22semidirect
96. #2551C22semidirect
97. #2551C22semidirect
98. #2550C22semidirect
99. #2550C22semidirect
100. #2546C22semidirect
102. #2520C22semidirect
103. #2511C22semidirect
104. #2511C22semidirect
105. #2508C22semidirect
106. #2507C22semidirect
107. #2507C22semidirect
108. #2506C22semidirect
109. #2506C22semidirect
117. #2453C22semidirect
118. #2451C22semidirect
119. #2451C22semidirect
120. #2451C22semidirect
121. #2451C22semidirect
122. #2446C22semidirect
136. #2370C22semidirect
137. #2369C22semidirect
142. #2355C22semidirect
143. Q8×C4⋊C4C22semidirect
144. Q8×C4⋊C4C22semidirect
212. C2×C22⋊Q8Q8semidirect
506. C22×Q8C2×Q8semidirect
576. C22⋊Q8C2×Q8semidirect
577. C22⋊Q8C2×Q8semidirect
600. C2×C4⋊C4C2×Q8semidirect
601. C2×C4⋊C4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#596642
#593212
#591512
#457942
#454992
#397522
#396892
#396762
#396392
#396232
#396072
#395972
#393682
#376852
#374772
#367522
#366252
C2×#28572
Q8×C22⋊Q82
#361932
#361902
#351672
#350152
#343802
C2×C4×C22⋊Q82