Finite Group Databasebeta

← #7667049

Subgroups — #7667049

Order 512.

4882 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#59872C214yesmaximal, complemented
2#59871C211yesmaximal, characteristic, complemented
3#59870C211yesmaximal, characteristic, complemented
4#59869C211yesmaximal, characteristic, complemented
5#59868C214yesmaximal
6#59867C214yesmaximal
7#59866C214yesmaximal
8#59828C211yesmaximal, characteristic, complemented
9#59681C212yesmaximal, complemented
10#59665C212yesmaximal, complemented
11#59456C212yesmaximal, complemented
12#59445C212yesmaximal, complemented
13#59321C212yesmaximal
14#59144C212yesmaximal
15#52274C214yesmaximal, complemented
16#34953C212yesmaximal
17#34951C212yesmaximal, complemented
18#34951C214yesmaximal, complemented
19#34948C212yesmaximal
20#34920C214yesmaximal, complemented
21#34815C214yesmaximal
22C4×#557C212yesmaximal, complemented
23#34145C212yesmaximal
24Q8×#117C212yesmaximal
25C4×#533C211yesmaximal, characteristic
26C4×#533C211yesmaximal, characteristic
27C2×C4×C4⋊Q8C211yesmaximal, characteristic
28C2×#557C2212yes—
29C2×#533C2211yescharacteristic
30C2×#533C2211yescharacteristic
31C22×C4⋊Q8C2211yescharacteristic
32C22×C4×Q8C2212yes—
33#2809C2214yes—
34#2806C2214yes—
35#2805C2214yes—
36#2802C2218yes—
37#2799C2218yes—
38#2791C2218yes—
39#2774C2218yes—
40#2755C2218yes—
41#2726C2214yes—
42#2713C2218yes—
43#2590C2218yes—
44#2588C2218yes—
45#2585C2218yes—
46#2585C2218yes—
47#2585C2218yes—
48#2584C2214yes—
49#2584C2214yes—
50#2584C2214yes—
51#2583C2218yes—
52#2582C2212yes—
53#2582C2214yes—
54#2581C2214yes—
55#2571C2212yes—
56#2571C2212yes—
57#2570C2214yes—
58#2570C2214yes—
59#2569C2218yes—
60#2568C2212yes—
61#2568C2214yes—
62#2567C2212yes—
63#2567C2212yes—
64#2565C2214yes—
65#2552C2212yes—
66#2552C2214yes—
67#2552C2212yes—
68#2552C2212yes—
69#2550C2214yes—
70#2546C2214yes—
71#2546C2212yes—
72#2546C2212yes—
73#2546C2212yes—
74#2520C2218yes—
75#2511C2214yes—
76#2511C2214yes—
77#2511C2214yes—
78#2509C2214yes—
79#2509C2214yes—
80#2509C2218yes—
81#2509C2214yes—
82#2508C2214yes—
83#2508C2214yes—
84#2508C2214yes—
85#2507C2214yes—
86#2507C2214yes—
87#2506C2214yes—
88#2506C2214yes—
89#2506C2214yes—
90#2505C2218yes—
91#2505C2218yes—
92#2502C2214yes—
93#2473C2218yes—
94#2473C2218yes—
95#2462C2218yes—
96#2453C2218yes—
97#2453C2214yes—
98#2453C2214yes—
99#2451C2214yes—
100#2446C2214yes—
101#2446C2214yes—
102#2446C2214yes—
103#2442C2214yes—
104#2442C2214yes—
105#2434C2214yes—
106#2402C2218yes—
107#2402C2218yes—
108#2402C2218yes—
109#2399C2218yes—
110#2370C2214yes—
111#2370C2214yes—
112#2370C2214yes—
113#2370C2218yes—
114#2369C2212yes—
115#2369C2212yes—
116#2368C2218yes—
117#2365C2212yes—
118#2365C2214yes—
119#2365C2212yes—
120#2365C2212yes—
121#2360C2214yes—
122#2360C2214yes—
123#2355C2214yes—
124#2355C2212yes—
125#2355C2212yes—
126#2355C2214yes—
127#2355C2214yes—
128#2355C2212yes—
129#2351C2214yes—
130Q8×C4⋊C4C2212yes—
131Q8×C4⋊C4C2212yes—
132Q8×C4⋊C4C2212yes—
133#2345C2214yes—
134#2345C2218yes—
135Q8×C22⋊C4C2214yes—
136C4×C4⋊Q8C2211yescharacteristic
137C4×C4⋊Q8C2212yes—
138C4×C4⋊Q8C2211yescharacteristic
139C4×C4⋊Q8C2212yes—
140C4×C4⋊Q8C2212yes—
141C4×C4⋊Q8C2211yescharacteristic
142C4×C4⋊Q8C2211yescharacteristic
143C4×C4⋊Q8C2212yes—
144C4×C4⋊Q8C2211yescharacteristic
145C4×C4⋊Q8C2214yes—
146C4×C4⋊Q8C2214yes—
147C4×C4⋊Q8C2212yes—
148C4×C4⋊Q8C2211yescharacteristic
149C4×C4⋊Q8C2211yescharacteristic
150C4×C4⋊Q8C2211yescharacteristic
151C4×C4⋊Q8C2211yescharacteristic
152C4×C4⋊Q8C2211yescharacteristic
153C4×C4⋊Q8C2211yescharacteristic
154C4×C4⋊Q8C2211yescharacteristic
155C4×C4⋊Q8C2212yes—
156C4×#125C2212yes—
157C4×#125C2212yes—
158C4×#125C2218yes—
159C4×#125C2214yes—
160C4×#125C2214yes—
161C4×#125C2218yes—
162C4×#125C2212yes—
163C4×#125C2212yes—
164C4×C22⋊Q8C2212yes—
165C4×C22⋊Q8C2212yes—
166C4×C22⋊Q8C2212yes—
167C4×C22⋊Q8C2212yes—
168C4×C22⋊Q8C2212yes—
169C4×C22⋊Q8C2212yes—
170C4×C22⋊Q8C2212yes—
171C4×C22⋊Q8C2212yes—
172#2296C2214yes—
173#2296C2214yes—
174#2296C2212yes—
175#2296C2212yes—
176#2295C2212yes—
177#2295C2212yes—
178#2295C2218yes—
179#2295C2218yes—
180#2295C2214yes—
181#2295C2214yes—
182#2295C2212yes—
183#2295C2212yes—
184C2×#391C2212yes—
185C2×#389C2212yes—
186C2×#389C2212yes—
187#2285C2211yescharacteristic
188#2285C2214yes—
189#2285C2211yescharacteristic
190C2×#384C2211yescharacteristic
191C42×Q8C2214yes—
192C42×Q8C2214yes—
193C42×Q8C2212yes—
194C42×Q8C2212yes—
195C42×Q8C2212yes—
196C42×Q8C2212yes—
197C4×#117C2214yes—
198C4×#117C2212yes—
199C4×#117C2212yes—
200C2×C4×C4⋊C4C2212yes—
201C2×C4×C4⋊C4C2212yes—
202C2×C43C2211yescharacteristic
203C23×Q8C2312yes—
204#557—216no—
205#533—28no—
206#533Q8116yescomplemented
207C2×C4⋊Q8—28no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#125C2312yes—
220C2×#125C2314yes—
221C2×#125C2318yes—
222C2×#125C2314yes—
223C2×#125C2318yes—
224C2×#125C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C4×Q8—216no—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2312yes—
252C2×#117C2312yes—
253C2×#117C2312yes—
254C2×#117C2312yes—
255C2×#117C2312yes—
256C22×C4⋊C4C2314yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C42C2314yes—
263C22×C42C2311yescharacteristic
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268C22×C42C2311yescharacteristic
269C22×C42C2311yescharacteristic
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
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#395C2318yes—
299#395C2318yes—
300#395C2318yes—
301#395C2318yes—
302#391C2312yes—
303#391C2312yes—
304#391C2314yes—
305#391C2312yes—
306#391C2312yes—
307#391C2314yes—
308#391C2312yes—
309#391C2314yes—
310#391C2314yes—
311#391C2312yes—
312#391C2314yes—
313#391C2312yes—
314#391C2314yes—
315#391C2312yes—
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2318yes—
325#391C2318yes—
326#391C2318yes—
327#391C2318yes—
328#389C2312yes—
329#389C2312yes—
330#389C2312yes—
331#389C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2312yes—
335#389C2312yes—
336#389C2314yes—
337#389C2314yes—
338#389C2318yes—
339#389C2314yes—
340#389C2314yes—
341#389C2318yes—
342#389C2318yes—
343#389C2318yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2314yes—
355#389C2312yes—
356#389C2312yes—
357#389C2318yes—
358#389C2318yes—
359#389C2318yes—
360#389C2318yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2318yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2318yes—
381#389C2314yes—
382#389C2318yes—
383#389C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2314yes—
391#387C2314yes—
392#387C2318yes—
393#387C2318yes—
394#387C2314yes—
395#387C2314yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2314yes—
401#387C2314yes—
402#387C2314yes—
403#387C2314yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2314yes—
421#385C2314yes—
422#385C2314yes—
423#385C2314yes—
424#384C2312yes—
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#384C2312yes—
432#384C2312yes—
433#384C2314yes—
434#384C2314yes—
435#384C2314yes—
436#384C2314yes—
437#382C2312yes—
438#382C2312yes—
439#382C2314yes—
440#382C2314yes—
441#382C2318yes—
442#382C2318yes—
443#382C2314yes—
444#382C2314yes—
445#380C2312yes—
446#380C2318yes—
447#380C2318yes—
448#380C2312yes—
449#380C2312yes—
450#380C2312yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2318yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2318yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2318yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2318yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2318yes—
501C4×C4⋊C4C2318yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2318yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2314yes—
509C4×C4⋊C4C2318yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2318yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2318yes—
518C4×C22⋊C4C2314yes—
519#376C2314yes—
520#376C2314yes—
521#376C2318yes—
522C2×#95C2314yes—
523C2×#95C2314yes—
524C43C2311yescharacteristic
525C43C2311yescharacteristic
526C43C2311yescharacteristic
527C43C2314yes—
528C43C2318yes—
529C43C2311yescharacteristic
530C43C2311yescharacteristic
531C43C2311yescharacteristic
532C43C2311yescharacteristic
533C43C2311yescharacteristic
534C43C2314yes—
535C22×Q8—28no—
536C22×Q8—28no—
537C22×Q8—44no—
538C22×Q8C2412yes—
539C22×Q8C2412yes—
540C22×Q8C2414yes—
541C22×Q8C2412yes—
542C22×Q8C2412yes—
543C22×Q8C2412yes—
544C22×Q8C2412yes—
545C23×C4C2411yescharacteristic
546C23×C4C2414yes—
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C23×C4C2414yes—
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C23×C4C2411yescharacteristic
553C23×C4C2411yescharacteristic
554C4⋊Q8—28no—
555C4⋊Q8—216no—
556C4⋊Q8—28no—
557C4⋊Q8—28no—
558C4⋊Q8—24no—
559C4⋊Q8—24no—
560C4⋊Q8—24no—
561C4⋊Q8—48no—
562C4⋊Q8C2×Q818yescomplemented
563C4⋊Q8C2×Q818yescomplemented
564C4⋊Q8#4118yes—
565#125—232no—
566#125—216no—
567#125—28no—
568#125—48no—
569#125—416no—
570#125C2×Q8116yescomplemented
571C22⋊Q8—28no—
572C22⋊Q8—28no—
573C22⋊Q8C2×Q8116yes—
574C22⋊Q8C2×Q8116yes—
575C4×Q8—216no—
576C4×Q8—216no—
577C4×Q8—28no—
578C4×Q8—28no—
579C4×Q8—216no—
580C4×Q8—216no—
581C4×Q8—28no—
582C4×Q8—28no—
583C4×Q8—28no—
584C4×Q8—28no—
585C4×Q8—28no—
586C4×Q8—28no—
587C4×Q8—44no—
588C4×Q8—44no—
589C4×Q8—44no—
590C4×Q8—44no—
591C4×Q8—44no—
592C4×Q8—44no—
593C4×Q8—48no—
594C4×Q8—48no—
595C4×Q8C2×Q8116yescomplemented
596C4×Q8C2×Q8116yescomplemented
597#117—28no—
598#117—28no—
599#117—28no—
600#117C2×Q8116yes—
601C2×C4⋊C4—216no—
602C2×C4⋊C4—28no—
603C2×C4⋊C4—28no—
604C2×C4⋊C4—28no—
605C2×C4⋊C4—44no—
606C2×C4⋊C4—44no—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2412yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C42—216no—
675C2×C42—24no—
676C2×C42—24no—
677C2×C42—42no—
678C2×C42—42no—
679C2×C42—42no—
680C2×C42C2×Q818yes—
681C2×C42#4118yes—
682C2×C42C2414yes—
683C2×C42C2414yes—
684C2×C42C2418yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2414yes—
694C2×C42C2414yes—
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2414yes—
701C2×C42C2414yes—
702C2×C42C2414yes—
703C2×C42C2414yes—
704C2×C42C2414yes—
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2414yes—
708C2×C42C2414yes—
709C2×C42C2414yes—
710C2×C42C2414yes—
711C2×C42C2418yes—
712C2×C42C2418yes—
713C2×C42C2418yes—
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2414yes—
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2418yes—
743#95C2418yes—
744#95C2414yes—
745#95C2414yes—
746#95C2418yes—
747#95C2418yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752#95C2414yes—
753#95C2414yes—
754#95C2418yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2418yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773#95C2418yes—
774C24C2511yescharacteristic
775C2×Q8—24no—
776C2×Q8—24no—
777C2×Q8—28no—
778C2×Q8—24no—
779C2×Q8—24no—
780C2×Q8—24no—
781C2×Q8—24no—
782C2×Q8—28no—
783C2×Q8—24no—
784C2×Q8—24no—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—42no—
789C2×Q8—42no—
790C2×Q8—42no—
791C2×Q8—42no—
792C2×Q8—44no—
793C2×Q8—432no—
794C2×Q8C22×Q818yes—
795C2×Q8C22×Q818yes—
796C2×Q8C2×#4118yes—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—28no—
805C22×C4—22no—
806C22×C4—28no—
807C22×C4—28no—
808C22×C4—41no—
809C22×C4—41no—
810C22×C4—41no—
811C22×C4—41no—
812C22×C4—41no—
813C22×C4—41no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4C22×Q814yes—
818C22×C4C22×Q814yes—
819C22×C4C22×Q814yes—
820C22×C4C2×#4114yes—
821C22×C4C2×#4114yes—
822C22×C4C2×#4114yes—
823C22×C42−1+414yes—
824C22×C4C2511yescharacteristic
825C22×C4C2511yescharacteristic
826C22×C4C2514yes—
827C22×C4C2514yes—
828C22×C4C2514yes—
829C22×C4C2514yes—
830C22×C4C2514yes—
831C22×C4C2514yes—
832C22×C4C2514yes—
833C22×C4C2514yes—
834C22×C4C2514yes—
835C22×C4C2511yescharacteristic
836C22×C4C2511yescharacteristic
837C22×C4C2514yes—
838C22×C4C2514yes—
839C22×C4C2511yescharacteristic
840C22×C4C2511yescharacteristic
841C22×C4C2511yescharacteristic
842C22×C4C2514yes—
843C22×C4C2511yescharacteristic
844C22×C4C2511yescharacteristic
845C22×C4C2511yescharacteristic
846C22×C4C2511yescharacteristic
847C22×C4C2511yescharacteristic
848C22×C4C2511yescharacteristic
849C22×C4C2511yescharacteristic
850C4⋊C4—28no—
851C4⋊C4—28no—
852C4⋊C4—28no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—28no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—28no—
869C4⋊C4—216no—
870C4⋊C4—28no—
871C4⋊C4—24no—
872C4⋊C4—216no—
873C4⋊C4—216no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—28no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—24no—
885C4⋊C4—42no—
886C4⋊C4—44no—
887C4⋊C4—42no—
888C4⋊C4—44no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—44no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—48no—
899C4⋊C4—48no—
900C4⋊C4—48no—
901C4⋊C4—48no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4C22×Q818yes—
906C4⋊C4C22×Q818yes—
907C4⋊C4C22×Q8116yes—
908C4⋊C4C22×Q8116yes—
909C4⋊C4C22×Q818yes—
910C4⋊C4C22×Q818yes—
911C4⋊C4C2×#4118yes—
912C4⋊C4C2×#4118yes—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4C22×Q8116yes—
917C42—28no—
918C42—28no—
919C42—28no—
920C42—28no—
921C42—22no—
922C42—22no—
923C42—22no—
924C42—28no—
925C42—216no—
926C42—28no—
927C42—28no—
928C42—22no—
929C42—22no—
930C42—22no—
931C42—22no—
932C42—28no—
933C42—28no—
934C42—22no—
935C42—22no—
936C42—22no—
937C42—22no—
938C42—22no—
939C42—22no—
940C42—28no—
941C42—28no—
942C42—41no—
943C42—41no—
944C42—41no—
945C42—41no—
946C42—41no—
947C42—41no—
948C42—44no—
949C42—44no—
950C42—44no—
951C42—44no—
952C42—48no—
953C42—48no—
954C42—48no—
955C42C22×Q814yes—
956C42C22×Q814yes—
957C42C22×Q814yes—
958C42C22×Q814yes—
959C42C22×Q8116yes—
960C42C2×#4114yes—
961C42C2×#4114yes—
962C42C2×#4114yes—
963C42C2×#4114yes—
964C42C2×#4114yes—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—21no—
969C23C23×Q812yes—
970C23C22×#4112yes—
971C23C2×2−1+412yes—
972C23C2611yescharacteristic
973Q8—216no—
974Q8—216no—
975Q8—48no—
976Q8—416no—
977Q8—48no—
978Q8—48no—
979Q8—48no—
980C2×C4—28no—
981C2×C4—24no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—24no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—24no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—24no—
1002C2×C4—21no—
1003C2×C4—28no—
1004C2×C4—28no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—44no—
1039C2×C4—44no—
1040C2×C4—416no—
1041C2×C4—44no—
1042C2×C4—88no—
1043C2×C4#557116yescomplemented
1044C2×C4C23×Q812yes—
1045C2×C4C23×Q812yes—
1046C2×C4C23×Q812yes—
1047C2×C4C23×Q818yes—
1048C2×C4C23×Q818yes—
1049C2×C4C23×Q812yes—
1050C2×C4C23×Q812yes—
1051C2×C4C23×Q812yes—
1052C2×C4C22×#4118yes—
1053C2×C4C22×#4112yes—
1054C2×C4C22×#4112yes—
1055C2×C4C22×#4112yes—
1056C2×C4C22×#4112yes—
1057C2×C4C22×#4112yes—
1058C2×C4C22×#4112yes—
1059C2×C4C22×#4112yes—
1060C2×C4C22×#4112yes—
1061C2×C4C22×#4112yes—
1062C2×C4C2×2−1+412yes—
1063C2×C4C2×2−1+412yes—
1064C2×C4#58512yes—
1065C2×C4#58512yes—
1066C2×C4#58512yes—
1067C22—22no—
1068C22—22no—
1069C22—22no—
1070C22—22no—
1071C22—22no—
1072C22—22no—
1073C22C2×#55714yes—
1074C22C24×Q811yescharacteristic
1075C22C23×#4111yescharacteristic
1076C22C23×#4111yescharacteristic
1077C22C22×2−1+411yescharacteristic
1078C22C2×#58511yescharacteristic
1079C22C2×#58511yescharacteristic
1080C22C2×#58511yescharacteristic
1081C4—22no—
1082C4—22no—
1083C4—22no—
1084C4—22no—
1085C4—28no—
1086C4—22no—
1087C4—22no—
1088C4—22no—
1089C4—28no—
1090C4—22no—
1091C4—28no—
1092C4—44no—
1093C4—44no—
1094C4—41no—
1095C4—41no—
1096C4—44no—
1097C4—44no—
1098C4—44no—
1099C4—44no—
1100C4—44no—
1101C4—44no—
1102C4—44no—
1103C4#347514yes—
1104C4C2×#55714yes—
1105C4C2×#55714yes—
1106C4Q8×#4114yes—
1107C2—24no—
1108C2C2×#347511yescharacteristic
1109C2C22×#55711yescharacteristic
1110C2C2×Q8×#4111yescharacteristic
1111C2#6276111yescharacteristic
1112C2#6278811yescharacteristic
1113C2#6281311yescharacteristic
1114C2#6281511yescharacteristic
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59872C2semidirect
2. #59871C2semidirect
3. #59870C2semidirect
4. #59869C2semidirect
8. #59828C2semidirect
9. #59681C2semidirect
10. #59665C2semidirect
11. #59456C2semidirect
12. #59445C2semidirect
15. #52274C2semidirect
17. #34951C2semidirect
18. #34951C2semidirect
20. #34920C2semidirect
22. C4×#557C2semidirect
206. #533Q8semidirect
562. C4⋊Q8C2×Q8semidirect
563. C4⋊Q8C2×Q8semidirect
570. #125C2×Q8semidirect
595. C4×Q8C2×Q8semidirect
596. C4×Q8C2×Q8semidirect
1043. C2×C4#557semidirect

Maximal subgroups

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

subgroupindex
#598722
#598712
#598702
#598692
#598682
#598672
#598662
#598282
#596812
#596652
#594562
#594452
#593212
#591442
#522742
#349532
#349512
#349482
#349202
#348152
C4×#5572
#341452
Q8×#1172
C4×#5332
C2×C4×C4⋊Q82