Finite Group Databasebeta

← #7671977

Subgroups — #7671977

Order 512.

4850 conjugacy classes of subgroups.

The subgroup lattice has 1115 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59670C214yesmaximal, complemented
2#59669C214yesmaximal, complemented
3#59668C212yesmaximal, complemented
4#59667C212yesmaximal, complemented
5#59666C212yesmaximal, complemented
6#59665C212yesmaximal, complemented
7#39677C214yesmaximal
8#39676C214yesmaximal
9#39181C212yesmaximal, complemented
10#39180C212yesmaximal, complemented
11#39176C214yesmaximal, complemented
12#36640C211yesmaximal, characteristic
13#36571C214yesmaximal
14#36545C214yesmaximal
15#36535C212yesmaximal, complemented
16#36497C214yesmaximal, complemented
17#36466C212yesmaximal, complemented
18#35576C212yesmaximal
19#35555C212yesmaximal
20#35265C212yesmaximal
21#35181C211yesmaximal, characteristic
22#35167C211yesmaximal, characteristic
23#34272C212yesmaximal
24#34213C211yesmaximal, characteristic
25#34213C211yesmaximal, characteristic
26C4×#533C211yesmaximal, characteristic
27C2×C4×C4⋊Q8C211yesmaximal, characteristic
28C2×#557C2214yes—
29C2×#544C2212yes—
30C2×#533C2211yescharacteristic
31C22×C4⋊Q8C2211yescharacteristic
32C22×C4×Q8C2212yes—
33#2864C2212yes—
34#2864C2212yes—
35#2864C2214yes—
36#2859C2211yescharacteristic
37#2859C2211yescharacteristic
38#2859C2211yescharacteristic
39#2859C2211yescharacteristic
40#2859C2214yes—
41#2857C2214yes—
42#2851C2212yes—
43#2851C2212yes—
44#2851C2212yes—
45#2851C2212yes—
46#2851C2214yes—
47#2806C2218yes—
48#2802C2218yes—
49#2799C2218yes—
50#2774C2218yes—
51#2755C2218yes—
52#2726C2218yes—
53#2713C2218yes—
54#2713C2218yes—
55#2659C2214yes—
56#2647C2214yes—
57#2647C2214yes—
58#2646C2214yes—
59#2590C2218yes—
60#2588C2218yes—
61#2588C2218yes—
62#2585C2218yes—
63#2584C2214yes—
64#2584C2214yes—
65#2584C2218yes—
66#2583C2218yes—
67#2582C2214yes—
68#2581C2214yes—
69#2581C2214yes—
70#2571C2212yes—
71#2571C2212yes—
72#2570C2214yes—
73#2570C2214yes—
74#2570C2214yes—
75#2570C2214yes—
76#2565C2214yes—
77#2552C2214yes—
78#2552C2212yes—
79#2552C2212yes—
80#2552C2214yes—
81#2552C2212yes—
82#2552C2212yes—
83#2551C2214yes—
84#2551C2212yes—
85#2551C2214yes—
86#2551C2212yes—
87#2551C2214yes—
88#2551C2214yes—
89#2550C2214yes—
90#2550C2214yes—
91#2550C2214yes—
92#2550C2214yes—
93#2550C2214yes—
94#2550C2214yes—
95#2550C2214yes—
96#2550C2218yes—
97#2546C2214yes—
98#2520C2218yes—
99#2520C2218yes—
100#2509C2214yes—
101#2509C2214yes—
102#2508C2214yes—
103#2507C2214yes—
104#2507C2214yes—
105#2507C2214yes—
106#2506C2214yes—
107#2506C2214yes—
108#2506C2214yes—
109#2506C2214yes—
110#2505C2218yes—
111#2473C2218yes—
112#2473C2218yes—
113#2473C2218yes—
114#2462C2218yes—
115#2462C2218yes—
116#2462C2218yes—
117#2453C2214yes—
118#2453C2218yes—
119#2451C2214yes—
120#2451C2218yes—
121#2446C2218yes—
122#2434C2218yes—
123#2370C2214yes—
124#2370C2214yes—
125#2370C2214yes—
126#2370C2214yes—
127#2370C2214yes—
128#2370C2218yes—
129#2369C2212yes—
130#2369C2212yes—
131#2369C2214yes—
132#2368C2218yes—
133#2365C2212yes—
134#2365C2212yes—
135#2365C2214yes—
136#2365C2218yes—
137#2360C2218yes—
138#2355C2214yes—
139#2355C2214yes—
140#2355C2212yes—
141#2355C2212yes—
142#2355C2214yes—
143#2351C2214yes—
144Q8×C4⋊C4C2212yes—
145Q8×C4⋊C4C2212yes—
146#2331C2214yes—
147#2330C2214yes—
148#2329C2214yes—
149#2329C2214yes—
150#2317C2212yes—
151#2317C2212yes—
152#2317C2212yes—
153#2317C2212yes—
154#2316C2212yes—
155C4×C4⋊Q8C2212yes—
156C4×C4⋊Q8C2212yes—
157C4×C4⋊Q8C2211yescharacteristic
158C4×C4⋊Q8C2212yes—
159C4×C4⋊Q8C2211yescharacteristic
160C4×C4⋊Q8C2212yes—
161C4×C4⋊Q8C2211yescharacteristic
162C4×C4⋊Q8C2211yescharacteristic
163C4×C4⋊Q8C2212yes—
164C4×C4⋊Q8C2212yes—
165C4×C4⋊Q8C2214yes—
166C4×C4⋊Q8C2212yes—
167C4×C4⋊Q8C2212yes—
168C4×#125C2212yes—
169C4×#125C2212yes—
170C4×#125C2212yes—
171C4×#125C2212yes—
172C4×#125C2212yes—
173C4×#125C2212yes—
174C4×#125C2214yes—
175C4×C22⋊Q8C2214yes—
176C4×C22⋊Q8C2214yes—
177C4×C22⋊Q8C2212yes—
178C4×C22⋊Q8C2212yes—
179C4×C22⋊Q8C2212yes—
180C4×C22⋊Q8C2212yes—
181#2296C2212yes—
182#2296C2212yes—
183#2296C2212yes—
184#2295C2212yes—
185#2295C2212yes—
186C2×#391C2212yes—
187C2×#389C2211yescharacteristic
188C2×#389C2211yescharacteristic
189C2×#389C2212yes—
190#2285C2211yescharacteristic
191#2285C2211yescharacteristic
192#2285C2211yescharacteristic
193C2×#384C2211yescharacteristic
194#2274C2212yes—
195#2274C2212yes—
196C42×Q8C2212yes—
197C42×Q8C2212yes—
198C4×#117C2212yes—
199C2×C4×C4⋊C4C2211yescharacteristic
200C2×C4×C4⋊C4C2211yescharacteristic
201C2×C4×C4⋊C4C2212yes—
202C2×C43C2211yescharacteristic
203C23×Q8C2312yes—
204#557—416no—
205#544—216no—
206#533Q8116yescomplemented
207C2×C4⋊Q8—28no—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2318yes—
216C2×C4⋊Q8C2318yes—
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#125C2312yes—
220C2×#125C2312yes—
221C2×#125C2314yes—
222C2×#125C2314yes—
223C2×#125C2312yes—
224C2×#125C2312yes—
225C2×#125C2314yes—
226C2×#125C2318yes—
227C2×#125C2318yes—
228C2×#125C2318yes—
229C2×#125C2312yes—
230C2×C22⋊Q8C2318yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2312yes—
233C2×C4×Q8—48no—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2318yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2312yes—
247C2×#117C2312yes—
248C2×#117C2312yes—
249C2×#117C2312yes—
250C2×#117C2312yes—
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2311yescharacteristic
260C22×C42C2311yescharacteristic
261C22×C42C2311yescharacteristic
262C22×C42C2311yescharacteristic
263C22×C42C2311yescharacteristic
264C22×C42C2312yes—
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267C22×C42C2312yes—
268C22×C42C2311yescharacteristic
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#395C2318yes—
294#395C2318yes—
295#395C2318yes—
296#395C2318yes—
297#395C2318yes—
298#395C2318yes—
299#395C2318yes—
300#395C2318yes—
301#391C2314yes—
302#391C2314yes—
303#391C2314yes—
304#391C2314yes—
305#391C2312yes—
306#391C2318yes—
307#391C2312yes—
308#391C2312yes—
309#391C2312yes—
310#391C2314yes—
311#391C2314yes—
312#391C2318yes—
313#391C2318yes—
314#391C2318yes—
315#391C2318yes—
316#391C2318yes—
317#391C2318yes—
318#391C2318yes—
319#389C2312yes—
320#389C2312yes—
321#389C2312yes—
322#389C2312yes—
323#389C2312yes—
324#389C2312yes—
325#389C2312yes—
326#389C2312yes—
327#389C2312yes—
328#389C2312yes—
329#389C2312yes—
330#389C2312yes—
331#389C2312yes—
332#389C2312yes—
333#389C2314yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2314yes—
341#389C2314yes—
342#389C2312yes—
343#389C2312yes—
344#389C2314yes—
345#389C2318yes—
346#389C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2318yes—
369#389C2318yes—
370#389C2318yes—
371#389C2318yes—
372#389C2318yes—
373#389C2318yes—
374#389C2314yes—
375#389C2318yes—
376#389C2318yes—
377#389C2318yes—
378#389C2318yes—
379#389C2314yes—
380#389C2318yes—
381#389C2318yes—
382#389C2312yes—
383#389C2312yes—
384#389C2312yes—
385#389C2312yes—
386#389C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2314yes—
390#387C2314yes—
391#387C2314yes—
392#387C2314yes—
393#387C2314yes—
394#387C2314yes—
395#387C2314yes—
396#387C2314yes—
397#387C2314yes—
398#387C2314yes—
399#387C2314yes—
400#387C2314yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
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#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2314yes—
426#385C2314yes—
427#385C2314yes—
428#385C2314yes—
429#385C2314yes—
430#385C2314yes—
431#384C2312yes—
432#384C2312yes—
433#384C2311yescharacteristic
434#384C2312yes—
435#384C2312yes—
436#384C2311yescharacteristic
437#384C2314yes—
438#384C2314yes—
439#384C2314yes—
440#384C2311yescharacteristic
441#384C2314yes—
442#384C2314yes—
443#384C2311yescharacteristic
444#384C2311yescharacteristic
445#384C2311yescharacteristic
446#382C2312yes—
447#382C2314yes—
448#382C2312yes—
449#382C2312yes—
450#382C2312yes—
451#382C2312yes—
452#382C2314yes—
453#382C2314yes—
454#382C2312yes—
455#382C2314yes—
456#382C2314yes—
457#382C2318yes—
458#382C2312yes—
459#380C2318yes—
460#380C2312yes—
461#380C2312yes—
462#380C2312yes—
463#380C2312yes—
464#380C2312yes—
465#380C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2318yes—
483C4×C4⋊C4C2318yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2318yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2318yes—
511C4×C4⋊C4C2318yes—
512C4×C4⋊C4C2314yes—
513C4×C4⋊C4C2314yes—
514C4×C4⋊C4C2314yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2314yes—
517C4×C22⋊C4C2318yes—
518C4×C22⋊C4C2318yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521#376C2314yes—
522C2×#95C2312yes—
523C2×#95C2312yes—
524C2×#95C2312yes—
525C2×#95C2312yes—
526C43C2311yescharacteristic
527C43C2311yescharacteristic
528C43C2311yescharacteristic
529C43C2311yescharacteristic
530C43C2314yes—
531C43C2311yescharacteristic
532C43C2311yescharacteristic
533C43C2311yescharacteristic
534C43C2311yescharacteristic
535C22×Q8—28no—
536C22×Q8—44no—
537C22×Q8—44no—
538C22×Q8C2414yes—
539C22×Q8C2414yes—
540C22×Q8C2412yes—
541C22×Q8C2418yes—
542C22×Q8C2412yes—
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2411yescharacteristic
552C23×C4C2412yes—
553C23×C4C2411yescharacteristic
554C4⋊Q8—28no—
555C4⋊Q8—28no—
556C4⋊Q8—28no—
557C4⋊Q8—28no—
558C4⋊Q8—216no—
559C4⋊Q8—216no—
560C4⋊Q8—48no—
561C4⋊Q8—416no—
562C4⋊Q8—416no—
563C4⋊Q8C2×Q818yescomplemented
564C4⋊Q8C2×Q818yescomplemented
565#125—216no—
566#125—216no—
567#125—28no—
568#125—28no—
569#125—44no—
570#125—44no—
571#125—48no—
572#125—416no—
573#125—416no—
574#125—416no—
575#125C2×Q8116yescomplemented
576C22⋊Q8—232no—
577C22⋊Q8C2×Q8116yes—
578C22⋊Q8C2×Q8116yes—
579C4×Q8—216no—
580C4×Q8—28no—
581C4×Q8—28no—
582C4×Q8—48no—
583C4×Q8—48no—
584C4×Q8—44no—
585C4×Q8—44no—
586C4×Q8—416no—
587C4×Q8—48no—
588C4×Q8—48no—
589C4×Q8—48no—
590C4×Q8C2×Q8116yescomplemented
591C4×Q8C2×Q8116yescomplemented
592#117—28no—
593#117—28no—
594#117—28no—
595#117C2×Q8116yes—
596C2×C4⋊C4—28no—
597C2×C4⋊C4—24no—
598C2×C4⋊C4—24no—
599C2×C4⋊C4—24no—
600C2×C4⋊C4—44no—
601C2×C4⋊C4—44no—
602C2×C4⋊C4—44no—
603C2×C4⋊C4—44no—
604C2×C4⋊C4#4118yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C42—24no—
677C2×C42—24no—
678C2×C42—24no—
679C2×C42—24no—
680C2×C42—44no—
681C2×C42—44no—
682C2×C42—42no—
683C2×C42—42no—
684C2×C42C2×Q818yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2414yes—
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2414yes—
692C2×C42C2414yes—
693C2×C42C2414yes—
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2414yes—
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2418yes—
711C2×C42C2418yes—
712C2×C42C2414yes—
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2418yes—
717C2×C42C2418yes—
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2414yes—
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2418yes—
758#95C2414yes—
759#95C2418yes—
760#95C2418yes—
761#95C2414yes—
762#95C2414yes—
763#95C2418yes—
764#95C2418yes—
765#95C2414yes—
766#95C2418yes—
767#95C2414yes—
768#95C2414yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773C24C2511yescharacteristic
774C2×Q8—28no—
775C2×Q8—28no—
776C2×Q8—216no—
777C2×Q8—24no—
778C2×Q8—28no—
779C2×Q8—24no—
780C2×Q8—28no—
781C2×Q8—44no—
782C2×Q8—42no—
783C2×Q8—42no—
784C2×Q8—44no—
785C2×Q8—48no—
786C2×Q8—48no—
787C2×Q8—432no—
788C2×Q8C22×Q818yes—
789C2×Q8C22×Q818yes—
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—24no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—41no—
808C22×C4—41no—
809C22×C4—41no—
810C22×C4—41no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4C22×Q814yes—
818C22×C4C22×Q814yes—
819C22×C4C22×Q814yes—
820C22×C4C2×#4118yes—
821C22×C4C2×#4114yes—
822C22×C42−1+414yes—
823C22×C4C2511yescharacteristic
824C22×C4C2514yes—
825C22×C4C2514yes—
826C22×C4C2514yes—
827C22×C4C2511yescharacteristic
828C22×C4C2514yes—
829C22×C4C2514yes—
830C22×C4C2514yes—
831C22×C4C2514yes—
832C22×C4C2514yes—
833C22×C4C2514yes—
834C22×C4C2511yescharacteristic
835C22×C4C2511yescharacteristic
836C22×C4C2514yes—
837C22×C4C2514yes—
838C22×C4C2511yescharacteristic
839C22×C4C2514yes—
840C22×C4C2511yescharacteristic
841C22×C4C2511yescharacteristic
842C22×C4C2511yescharacteristic
843C22×C4C2511yescharacteristic
844C22×C4C2511yescharacteristic
845C22×C4C2511yescharacteristic
846C22×C4C2511yescharacteristic
847C22×C4C2511yescharacteristic
848C22×C4C2511yescharacteristic
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—216no—
858C4⋊C4—216no—
859C4⋊C4—216no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—28no—
867C4⋊C4—24no—
868C4⋊C4—28no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—28no—
876C4⋊C4—24no—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—48no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4—48no—
906C4⋊C4—48no—
907C4⋊C4—48no—
908C4⋊C4C22×Q818yes—
909C4⋊C4C22×Q818yes—
910C4⋊C4C22×Q8116yes—
911C4⋊C4C22×Q8116yes—
912C4⋊C4C22×Q818yes—
913C4⋊C4C22×Q818yes—
914C4⋊C4C2×#4118yes—
915C4⋊C4C2×#4118yes—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4C22×Q8116yes—
920C42—22no—
921C42—22no—
922C42—22no—
923C42—22no—
924C42—28no—
925C42—28no—
926C42—22no—
927C42—22no—
928C42—22no—
929C42—28no—
930C42—28no—
931C42—28no—
932C42—22no—
933C42—22no—
934C42—22no—
935C42—22no—
936C42—22no—
937C42—22no—
938C42—22no—
939C42—28no—
940C42—28no—
941C42—22no—
942C42—22no—
943C42—22no—
944C42—22no—
945C42—41no—
946C42—41no—
947C42—41no—
948C42—41no—
949C42—44no—
950C42—44no—
951C42—44no—
952C42—44no—
953C42—48no—
954C42—48no—
955C42—48no—
956C42—48no—
957C42C22×Q814yes—
958C42C22×Q814yes—
959C42C22×Q814yes—
960C42C22×Q814yes—
961C42C22×Q8116yes—
962C42H(5,𝔽2)14yes—
963C422−1+414yes—
964C23—21no—
965C23—21no—
966C23—21no—
967C23—21no—
968C23C23×Q812yes—
969C23C22×#4112yes—
970C23C2×2−1+412yes—
971C23C2611yescharacteristic
972Q8—216no—
973Q8—48no—
974Q8—416no—
975Q8—416no—
976Q8—816no—
977C2×C4—28no—
978C2×C4—28no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—24no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—24no—
1003C2×C4—28no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—21no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—21no—
1027C2×C4—21no—
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—44no—
1038C2×C4—48no—
1039C2×C4—44no—
1040C2×C4—44no—
1041C2×C4—48no—
1042C2×C4—84no—
1043C2×C4—84no—
1044C2×C4#557116yescomplemented
1045C2×C4C23×Q812yes—
1046C2×C4C23×Q812yes—
1047C2×C4C23×Q812yes—
1048C2×C4C23×Q818yes—
1049C2×C4C23×Q818yes—
1050C2×C4C23×Q812yes—
1051C2×C4C23×Q812yes—
1052C2×C4C23×Q812yes—
1053C2×C4C22×#4118yes—
1054C2×C4C22×#4112yes—
1055C2×C4C22×#4112yes—
1056C2×C4C2×H(5,𝔽2)12yes—
1057C2×C4C2×H(5,𝔽2)12yes—
1058C2×C4C2×H(5,𝔽2)12yes—
1059C2×C4C2×2−1+412yes—
1060C2×C4C2×2−1+412yes—
1061C2×C4C2×2−1+412yes—
1062C2×C4C2×2−1+412yes—
1063C2×C4C2×2−1+412yes—
1064C2×C4#58512yes—
1065C2×C4#58512yes—
1066C22—22no—
1067C22—22no—
1068C22—22no—
1069C22—22no—
1070C22—22no—
1071C22—22no—
1072C22C2×#55714yes—
1073C22C24×Q811yescharacteristic
1074C22C23×#4111yescharacteristic
1075C22C22×H(5,𝔽2)11yescharacteristic
1076C22C22×2−1+411yescharacteristic
1077C22C22×2−1+411yescharacteristic
1078C22C2×#58511yescharacteristic
1079C22C2×#58511yescharacteristic
1080C4—22no—
1081C4—22no—
1082C4—28no—
1083C4—22no—
1084C4—22no—
1085C4—22no—
1086C4—28no—
1087C4—22no—
1088C4—22no—
1089C4—28no—
1090C4—22no—
1091C4—22no—
1092C4—44no—
1093C4—44no—
1094C4—44no—
1095C4—44no—
1096C4—44no—
1097C4—44no—
1098C4—41no—
1099C4—44no—
1100C4—44no—
1101C4—44no—
1102C4—41no—
1103C4C2×#55714yes—
1104C4C2×#55714yes—
1105C4#350314yes—
1106C2—24no—
1107C2C22×#55711yescharacteristic
1108C2#6277311yescharacteristic
1109C2#6278811yescharacteristic
1110C2C2×#350311yescharacteristic
1111C2#6281311yescharacteristic
1112C2#6283511yescharacteristic
1113C2#6283711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59670C2semidirect
2. #59669C2semidirect
3. #59668C2semidirect
4. #59667C2semidirect
5. #59666C2semidirect
6. #59665C2semidirect
9. #39181C2semidirect
10. #39180C2semidirect
11. #39176C2semidirect
15. #36535C2semidirect
16. #36497C2semidirect
17. #36466C2semidirect
206. #533Q8semidirect
563. C4⋊Q8C2×Q8semidirect
564. C4⋊Q8C2×Q8semidirect
575. #125C2×Q8semidirect
590. C4×Q8C2×Q8semidirect
591. C4×Q8C2×Q8semidirect
1044. C2×C4#557semidirect

Maximal subgroups

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

subgroupindex
#596702
#596692
#596682
#596672
#596662
#596652
#396772
#396762
#391812
#391802
#391762
#366402
#365712
#365452
#365352
#364972
#364662
#355762
#355552
#352652
#351812
#351672
#342722
#342132
C4×#5332
C2×C4×C4⋊Q82