Finite Group Databasebeta

← #7643143

Subgroups — #7643143

Order 512.

4526 conjugacy classes of subgroups.

The subgroup lattice has 1031 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39753C212yesmaximal, complemented
2#39752C212yesmaximal
3#39749C212yesmaximal, complemented
4#39625C212yesmaximal, complemented
5#39624C212yesmaximal
6#39621C212yesmaximal, complemented
7#39496C212yesmaximal
8#39368C212yesmaximal
9#39181C212yesmaximal, complemented
10#39180C212yesmaximal, complemented
11#39176C214yesmaximal, complemented
12#37877C214yesmaximal
13#37689C214yesmaximal
14#37196C214yesmaximal, complemented
15#37195C214yesmaximal, complemented
16#36645C211yesmaximal, characteristic
17#36635C211yesmaximal, characteristic
18#35583C214yesmaximal, complemented
19#35582C214yesmaximal, complemented
20#35304C214yesmaximal
21#35239C212yesmaximal
22#35167C212yesmaximal
23#35104C212yesmaximal
24#34196C212yesmaximal
25C2×#2295C211yesmaximal, characteristic
26C2×#544C2214yes—
27C2×#533C2212yes—
28C22×C4×Q8C2211yescharacteristic
29#2868C2211yescharacteristic
30#2868C2211yescharacteristic
31#2864C2212yes—
32#2863C2212yes—
33#2863C2212yes—
34#2862C2211yescharacteristic
35#2862C2212yes—
36#2859C2212yes—
37#2859C2211yescharacteristic
38#2859C2212yes—
39#2857C2211yescharacteristic
40#2857C2211yescharacteristic
41#2857C2212yes—
42#2857C2212yes—
43#2857C2212yes—
44#2857C2212yes—
45#2857C2214yes—
46#2855C2212yes—
47#2855C2212yes—
48#2851C2212yes—
49#2851C2214yes—
50#2811C2214yes—
51#2809C2214yes—
52#2806C2218yes—
53#2806C2214yes—
54#2806C2214yes—
55#2806C2214yes—
56#2805C2214yes—
57#2802C2218yes—
58#2799C2218yes—
59#2792C2218yes—
60#2791C2218yes—
61#2774C2218yes—
62#2755C2218yes—
63#2734C2218yes—
64#2734C2214yes—
65#2726C2218yes—
66#2726C2214yes—
67#2713C2218yes—
68#2713C2218yes—
69#2713C2218yes—
70#2666C2218yes—
71#2660C2214yes—
72#2660C2214yes—
73#2659C2214yes—
74#2659C2214yes—
75#2647C2214yes—
76#2647C2214yes—
77#2627C2214yes—
78#2627C2214yes—
79#2612C2218yes—
80#2612C2218yes—
81#2606C2218yes—
82#2606C2218yes—
83#2605C2218yes—
84#2605C2218yes—
85#2590C2218yes—
86#2588C2218yes—
87#2586C2218yes—
88#2585C2218yes—
89#2584C2214yes—
90#2582C2214yes—
91#2581C2214yes—
92#2571C2212yes—
93#2570C2214yes—
94#2570C2214yes—
95#2570C2214yes—
96#2569C2218yes—
97#2567C2214yes—
98#2565C2214yes—
99#2552C2214yes—
100#2552C2214yes—
101#2552C2212yes—
102#2552C2212yes—
103#2551C2214yes—
104#2551C2214yes—
105#2551C2212yes—
106#2551C2214yes—
107#2550C2214yes—
108#2550C2214yes—
109#2550C2214yes—
110#2550C2214yes—
111#2550C2218yes—
112#2550C2218yes—
113#2549C2218yes—
114#2546C2214yes—
115#2509C2214yes—
116#2507C2214yes—
117#2506C2214yes—
118#2506C2214yes—
119#2462C2218yes—
120#2462C2218yes—
121#2453C2214yes—
122#2451C2214yes—
123#2451C2218yes—
124#2451C2214yes—
125#2451C2214yes—
126#2446C2218yes—
127#2442C2214yes—
128#2440C2214yes—
129#2438C2218yes—
130#2438C2218yes—
131#2438C2218yes—
132#2355C2214yes—
133#2355C2214yes—
134#2355C2212yes—
135#2355C2212yes—
136Q8×C4⋊C4C2212yes—
137Q8×C4⋊C4C2212yes—
138#2344C2218yes—
139#2344C2214yes—
140Q8×C22⋊C4C2214yes—
141#2331C2214yes—
142#2331C2214yes—
143#2331C2214yes—
144#2330C2214yes—
145#2330C2214yes—
146#2330C2214yes—
147#2329C2214yes—
148#2329C2214yes—
149#2320C2218yes—
150#2320C2214yes—
151#2316C2214yes—
152C4×C4⋊Q8C2212yes—
153C4×C4⋊Q8C2211yescharacteristic
154C4×C4⋊Q8C2211yescharacteristic
155C4×C4⋊Q8C2212yes—
156C4×C4⋊Q8C2212yes—
157C4×C4⋊Q8C2212yes—
158C4×#125C2212yes—
159C4×C22⋊Q8C2212yes—
160C4×C22⋊Q8C2212yes—
161#2295C2212yes—
162#2295C2212yes—
163#2295C2212yes—
164#2295C2212yes—
165#2295C2212yes—
166#2295C2212yes—
167#2295C2212yes—
168#2295C2212yes—
169#2295C2212yes—
170#2295C2212yes—
171C2×#391C2211yescharacteristic
172C2×#391C2211yescharacteristic
173C2×#389C2211yescharacteristic
174C2×#389C2211yescharacteristic
175C2×#387C2212yes—
176C2×#387C2212yes—
177#2285C2212yes—
178#2285C2212yes—
179#2285C2214yes—
180#2283C2212yes—
181#2283C2214yes—
182#2276C2214yes—
183C2×C4×C4⋊C4C2212yes—
184C2×C4×C4⋊C4C2211yescharacteristic
185C2×#376C2212yes—
186C2×C43C2211yescharacteristic
187C23×Q8C2311yescharacteristic
188#544—416no—
189#533—48no—
190C2×C4⋊Q8C2312yes—
191C2×C4⋊Q8C2311yescharacteristic
192C2×C4⋊Q8C2311yescharacteristic
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2314yes—
197C2×C4⋊Q8C2314yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2318yes—
201C2×C4⋊Q8C2318yes—
202C2×#125C2312yes—
203C2×#125C2314yes—
204C2×#125C2314yes—
205C2×#125C2314yes—
206C2×#125C2318yes—
207C2×#125C2318yes—
208C2×C22⋊Q8C2312yes—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2312yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2318yes—
213C2×C4×Q8Q8116yescomplemented
214C2×C4×Q8C2314yes—
215C2×C4×Q8C2314yes—
216C2×C4×Q8C2312yes—
217C2×C4×Q8C2312yes—
218C2×C4×Q8C2314yes—
219C2×C4×Q8C2314yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×#117C2318yes—
225C2×#117C2314yes—
226C22×C4⋊C4C2312yes—
227C22×C4⋊C4C2312yes—
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2312yes—
231C22×C4⋊C4C2311yescharacteristic
232C22×C42C2311yescharacteristic
233C22×C42C2311yescharacteristic
234C22×C42C2311yescharacteristic
235C22×C42C2312yes—
236C22×C42C2311yescharacteristic
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239C22×C42C2311yescharacteristic
240C22×C42C2312yes—
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#400C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2318yes—
265#398C2318yes—
266#398C2318yes—
267#398C2318yes—
268#398C2318yes—
269#395C2318yes—
270#395C2318yes—
271#395C2318yes—
272#395C2318yes—
273#395C2318yes—
274#395C2318yes—
275#395C2318yes—
276#395C2318yes—
277#395C2318yes—
278#395C2318yes—
279#395C2318yes—
280#395C2318yes—
281#391C2312yes—
282#391C2312yes—
283#391C2314yes—
284#391C2314yes—
285#391C2314yes—
286#391C2314yes—
287#391C2312yes—
288#391C2314yes—
289#391C2312yes—
290#391C2314yes—
291#391C2318yes—
292#391C2318yes—
293#391C2312yes—
294#391C2312yes—
295#391C2318yes—
296#391C2318yes—
297#391C2312yes—
298#391C2318yes—
299#391C2318yes—
300#391C2318yes—
301#391C2318yes—
302#391C2318yes—
303#391C2318yes—
304#391C2312yes—
305#391C2312yes—
306#391C2312yes—
307#391C2312yes—
308#391C2312yes—
309#391C2312yes—
310#391C2312yes—
311#391C2312yes—
312#391C2312yes—
313#389C2312yes—
314#389C2312yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#389C2312yes—
319#389C2314yes—
320#389C2312yes—
321#389C2312yes—
322#389C2312yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2318yes—
328#389C2318yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2318yes—
335#389C2318yes—
336#389C2318yes—
337#389C2318yes—
338#389C2314yes—
339#389C2318yes—
340#389C2318yes—
341#389C2314yes—
342#389C2314yes—
343#389C2318yes—
344#389C2314yes—
345#389C2312yes—
346#389C2318yes—
347#389C2314yes—
348#389C2318yes—
349#389C2318yes—
350#389C2318yes—
351#389C2318yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#387C2314yes—
366#387C2314yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2314yes—
384#387C2314yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2314yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2314yes—
393#387C2314yes—
394#387C2314yes—
395#387C2314yes—
396#387C2314yes—
397#387C2314yes—
398#387C2314yes—
399#387C2314yes—
400#387C2314yes—
401#387C2314yes—
402#387C2314yes—
403#385C2314yes—
404#385C2318yes—
405#385C2318yes—
406#385C2314yes—
407#384C2312yes—
408#384C2312yes—
409#384C2311yescharacteristic
410#384C2312yes—
411#384C2312yes—
412#384C2311yescharacteristic
413#384C2314yes—
414#384C2314yes—
415#384C2312yes—
416#384C2312yes—
417#384C2312yes—
418#384C2312yes—
419#384C2314yes—
420#384C2314yes—
421#383C2318yes—
422#383C2314yes—
423#382C2312yes—
424#382C2314yes—
425#382C2314yes—
426#382C2312yes—
427#382C2314yes—
428#382C2314yes—
429#382C2318yes—
430#382C2314yes—
431#382C2312yes—
432#382C2314yes—
433#381C2314yes—
434#381C2318yes—
435#380C2314yes—
436#380C2318yes—
437#380C2318yes—
438#380C2312yes—
439#380C2314yes—
440#380C2312yes—
441#380C2312yes—
442#380C2314yes—
443#380C2312yes—
444#380C2314yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2318yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2318yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2318yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2312yes—
472C4×C22⋊C4C2318yes—
473C4×C22⋊C4C2314yes—
474#376C2314yes—
475#376C2318yes—
476#376C2314yes—
477#376C2314yes—
478#376C2314yes—
479#376C2314yes—
480C2×#95C2312yes—
481C2×#95C2312yes—
482C2×#95C2312yes—
483C2×#95C2312yes—
484C2×#95C2312yes—
485C2×#95C2312yes—
486C2×#95C2312yes—
487C43C2311yescharacteristic
488C43C2311yescharacteristic
489C43C2311yescharacteristic
490C43C2311yescharacteristic
491C43C2311yescharacteristic
492C43C2311yescharacteristic
493C43C2311yescharacteristic
494C43C2311yescharacteristic
495C22×Q8—42no—
496C22×Q8—42no—
497C22×Q8C2×Q818yes—
498C22×Q8C2412yes—
499C22×Q8C2412yes—
500C22×Q8C2414yes—
501C22×Q8C2414yes—
502C22×Q8C2412yes—
503C22×Q8C2418yes—
504C22×Q8C2412yes—
505C23×C4C2411yescharacteristic
506C23×C4C2411yescharacteristic
507C23×C4C2412yes—
508C23×C4C2411yescharacteristic
509C23×C4C2411yescharacteristic
510C23×C4C2411yescharacteristic
511C23×C4C2412yes—
512C23×C4C2412yes—
513C23×C4C2412yes—
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C4⋊Q8—28no—
517C4⋊Q8—48no—
518C4⋊Q8—44no—
519C4⋊Q8—44no—
520C4⋊Q8—42no—
521C4⋊Q8—44no—
522C4⋊Q8—42no—
523C4⋊Q8—48no—
524C4⋊Q8—44no—
525C4⋊Q8—44no—
526C4⋊Q8—416no—
527C4⋊Q8—416no—
528#125—28no—
529#125—48no—
530#125—48no—
531#125—48no—
532#125—416no—
533#125—416no—
534C22⋊Q8—216no—
535C22⋊Q8—28no—
536C22⋊Q8—28no—
537C22⋊Q8—48no—
538C22⋊Q8—416no—
539C4×Q8—44no—
540C4×Q8—44no—
541C4×Q8—48no—
542C4×Q8—48no—
543C4×Q8—48no—
544C4×Q8—48no—
545C4×Q8C2×Q8116yes—
546C4×Q8C2×Q8116yes—
547C4×Q8C2×Q8116yes—
548C4×Q8C2×Q8116yes—
549#117—48no—
550#117—416no—
551C2×C4⋊C4—28no—
552C2×C4⋊C4—28no—
553C2×C4⋊C4—42no—
554C2×C4⋊C4—42no—
555C2×C4⋊C4C2×Q818yes—
556C2×C4⋊C4C2×Q8116yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2412yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C42—24no—
616C2×C42—24no—
617C2×C42—24no—
618C2×C42—42no—
619C2×C42—42no—
620C2×C42—44no—
621C2×C42—42no—
622C2×C42C2×Q818yes—
623C2×C42C2×Q8116yes—
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626C2×C42C2414yes—
627C2×C42C2414yes—
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2414yes—
632C2×C42C2411yescharacteristic
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2418yes—
645C2×C42C2418yes—
646C2×C42C2418yes—
647C2×C42C2418yes—
648C2×C42C2418yes—
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2414yes—
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2414yes—
661C2×C42C2414yes—
662C2×C42C2411yescharacteristic
663#95C2414yes—
664#95C2414yes—
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2414yes—
671#95C2414yes—
672#95C2414yes—
673#95C2414yes—
674#95C2414yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2418yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2418yes—
683#95C2418yes—
684#95C2418yes—
685#95C2414yes—
686#95C2414yes—
687#95C2418yes—
688#95C2418yes—
689#95C2418yes—
690#95C2418yes—
691#95C2418yes—
692#95C2418yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2418yes—
697#95C2418yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709C24C2511yescharacteristic
710C2×Q8—28no—
711C2×Q8—24no—
712C2×Q8—24no—
713C2×Q8—28no—
714C2×Q8—24no—
715C2×Q8—24no—
716C2×Q8—42no—
717C2×Q8—42no—
718C2×Q8—44no—
719C2×Q8—42no—
720C2×Q8—42no—
721C2×Q8—42no—
722C2×Q8—42no—
723C2×Q8—44no—
724C2×Q8—44no—
725C2×Q8—44no—
726C2×Q8—48no—
727C2×Q8—48no—
728C2×Q8—48no—
729C2×Q8—416no—
730C2×Q8C22×Q818yes—
731C2×Q8C22×Q818yes—
732C22×C4—22no—
733C22×C4—24no—
734C22×C4—22no—
735C22×C4—24no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—24no—
743C22×C4—24no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—41no—
747C22×C4—41no—
748C22×C4—41no—
749C22×C4—41no—
750C22×C4—41no—
751C22×C4—41no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4C22×Q814yes—
759C22×C4C22×Q818yes—
760C22×C4C22×Q814yes—
761C22×C4C22×Q814yes—
762C22×C4C22×Q818yes—
763C22×C4H(5,𝔽2)14yes—
764C22×C42−1+414yes—
765C22×C4C2511yescharacteristic
766C22×C4C2514yes—
767C22×C4C2514yes—
768C22×C4C2514yes—
769C22×C4C2511yescharacteristic
770C22×C4C2518yes—
771C22×C4C2514yes—
772C22×C4C2514yes—
773C22×C4C2514yes—
774C22×C4C2518yes—
775C22×C4C2511yescharacteristic
776C22×C4C2511yescharacteristic
777C22×C4C2514yes—
778C22×C4C2511yescharacteristic
779C22×C4C2511yescharacteristic
780C22×C4C2514yes—
781C22×C4C2511yescharacteristic
782C22×C4C2511yescharacteristic
783C22×C4C2511yescharacteristic
784C22×C4C2511yescharacteristic
785C22×C4C2511yescharacteristic
786C22×C4C2511yescharacteristic
787C22×C4C2511yescharacteristic
788C22×C4C2511yescharacteristic
789C4⋊C4—28no—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—216no—
793C4⋊C4—24no—
794C4⋊C4—28no—
795C4⋊C4—28no—
796C4⋊C4—28no—
797C4⋊C4—24no—
798C4⋊C4—28no—
799C4⋊C4—28no—
800C4⋊C4—28no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—28no—
804C4⋊C4—28no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—28no—
808C4⋊C4—28no—
809C4⋊C4—24no—
810C4⋊C4—28no—
811C4⋊C4—24no—
812C4⋊C4—42no—
813C4⋊C4—42no—
814C4⋊C4—48no—
815C4⋊C4—44no—
816C4⋊C4—44no—
817C4⋊C4—48no—
818C4⋊C4—42no—
819C4⋊C4—42no—
820C4⋊C4—48no—
821C4⋊C4—48no—
822C4⋊C4—44no—
823C4⋊C4—44no—
824C4⋊C4—48no—
825C4⋊C4—44no—
826C4⋊C4—48no—
827C4⋊C4—48no—
828C4⋊C4—48no—
829C4⋊C4—48no—
830C4⋊C4—48no—
831C4⋊C4—48no—
832C4⋊C4—48no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—42no—
837C4⋊C4—42no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C4⋊C4C22×Q8116yes—
841C4⋊C4C22×Q818yes—
842C4⋊C4C22×Q8116yes—
843C4⋊C4C22×Q818yes—
844C22⋊C4—28no—
845C22⋊C4—216no—
846C22⋊C4—28no—
847C42—22no—
848C42—22no—
849C42—22no—
850C42—22no—
851C42—22no—
852C42—22no—
853C42—22no—
854C42—22no—
855C42—22no—
856C42—22no—
857C42—22no—
858C42—22no—
859C42—22no—
860C42—28no—
861C42—22no—
862C42—22no—
863C42—22no—
864C42—22no—
865C42—28no—
866C42—28no—
867C42—41no—
868C42—41no—
869C42—41no—
870C42—41no—
871C42—41no—
872C42—41no—
873C42—44no—
874C42—48no—
875C42—48no—
876C42—48no—
877C42—48no—
878C42—48no—
879C42C22×Q814yes—
880C42C22×Q8116yes—
881C42C22×Q814yes—
882C42C22×Q814yes—
883C42C22×Q8116yes—
884C42C22×Q814yes—
885C422−1+414yes—
886C23—21no—
887C23—21no—
888C23—21no—
889C23—21no—
890C23C23×Q812yes—
891C23C2×H(5,𝔽2)12yes—
892C23C2×2−1+412yes—
893C23C2611yescharacteristic
894Q8—216no—
895Q8—48no—
896Q8—84no—
897Q8—88no—
898Q8—84no—
899Q8—88no—
900Q8—168no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—24no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—24no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—28no—
926C2×C4—216no—
927C2×C4—28no—
928C2×C4—28no—
929C2×C4—21no—
930C2×C4—24no—
931C2×C4—28no—
932C2×C4—28no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—28no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—28no—
953C2×C4—28no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—28no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—48no—
960C2×C4—44no—
961C2×C4—44no—
962C2×C4—44no—
963C2×C4—44no—
964C2×C4—84no—
965C2×C4—84no—
966C2×C4C23×Q812yes—
967C2×C4C23×Q812yes—
968C2×C4C23×Q812yes—
969C2×C4C23×Q818yes—
970C2×C4C23×Q812yes—
971C2×C4C23×Q818yes—
972C2×C4C23×Q812yes—
973C2×C4C23×Q812yes—
974C2×C4C2×H(5,𝔽2)12yes—
975C2×C4C2×H(5,𝔽2)12yes—
976C2×C4C2×2−1+412yes—
977C2×C4C2×2−1+412yes—
978C2×C4C2×2−1+412yes—
979C2×C4C2×2−1+412yes—
980C2×C4C2×2−1+412yes—
981C2×C4#58512yes—
982C2×C4#58512yes—
983C2×C4#58512yes—
984C22—22no—
985C22—22no—
986C22—22no—
987C22—22no—
988C22—22no—
989C22—22no—
990C22#350314yes—
991C22C24×Q811yescharacteristic
992C22C22×H(5,𝔽2)11yescharacteristic
993C22C22×2−1+411yescharacteristic
994C22C22×2−1+411yescharacteristic
995C22C2×#58511yescharacteristic
996C22C2×#58511yescharacteristic
997C22C2×#58511yescharacteristic
998C4—22no—
999C4—22no—
1000C4—22no—
1001C4—28no—
1002C4—22no—
1003C4—22no—
1004C4—22no—
1005C4—22no—
1006C4—22no—
1007C4—22no—
1008C4—22no—
1009C4—28no—
1010C4—44no—
1011C4—48no—
1012C4—44no—
1013C4—44no—
1014C4—44no—
1015C4—44no—
1016C4—41no—
1017C4—48no—
1018C4—44no—
1019C4—41no—
1020C4#345814yes—
1021C4#350214yes—
1022C2—24no—
1023C2C2×#345811yescharacteristic
1024C2C2×#350211yescharacteristic
1025C2C2×#350311yescharacteristic
1026C2#6282211yescharacteristic
1027C2#6282311yescharacteristic
1028C2#6283511yescharacteristic
1029C2#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. #39753C2semidirect
3. #39749C2semidirect
4. #39625C2semidirect
6. #39621C2semidirect
9. #39181C2semidirect
10. #39180C2semidirect
11. #39176C2semidirect
14. #37196C2semidirect
15. #37195C2semidirect
18. #35583C2semidirect
19. #35582C2semidirect
213. C2×C4×Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#397532
#397522
#397492
#396252
#396242
#396212
#394962
#393682
#391812
#391802
#391762
#378772
#376892
#371962
#371952
#366452
#366352
#355832
#355822
#353042
#352392
#351672
#351042
#341962
C2×#22952