Finite Group Databasebeta

← #7712557

Subgroups — #7712557

Order 512.

4990 conjugacy classes of subgroups.

The subgroup lattice has 1167 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59274C214yesmaximal, complemented
2#59096C214yesmaximal, complemented
3#46007C212yesmaximal, complemented
4#46006C212yesmaximal, complemented
5#46005C212yesmaximal, complemented
6#46004C212yesmaximal, complemented
7#39663C214yesmaximal, complemented
8#39660C214yesmaximal, complemented
9#39640C212yesmaximal, complemented
10#39632C212yesmaximal
11#39624C212yesmaximal, complemented
12#39621C212yesmaximal, complemented
13#39615C212yesmaximal
14#39493C212yesmaximal, complemented
15#37875C214yesmaximal, complemented
16#37561C212yesmaximal, complemented
17#37314C214yesmaximal, complemented
18#36645C211yesmaximal, characteristic, complemented
19C2×#2862C211yesmaximal, characteristic, complemented
20#36598C212yesmaximal, complemented
21#36129C212yesmaximal, complemented
22#36129C212yesmaximal, complemented
23D4×C4⋊Q8C212yesmaximal, complemented
24#35283C212yesmaximal, complemented
25#35281C212yesmaximal, complemented
26#34382C212yesmaximal
27C4×#529C211yesmaximal, characteristic
28C2×D4×Q8C2214yes—
29C2×#533C2212yes—
30C2×#533C2212yes—
31C22×C4⋊Q8C2211yescharacteristic
32C22×C4⋊Q8C2212yes—
33C22×C4⋊Q8C2211yescharacteristic
34C2×#529C2211yescharacteristic
35#2868C2212yes—
36#2868C2211yescharacteristic
37#2868C2211yescharacteristic
38#2862C2212yes—
39#2862C2212yes—
40#2862C2212yes—
41#2862C2212yes—
42#2862C2212yes—
43#2862C2212yes—
44#2862C2212yes—
45#2862C2212yes—
46#2862C2212yes—
47#2862C2212yes—
48#2859C2212yes—
49#2859C2212yes—
50#2857C2212yes—
51#2857C2212yes—
52#2857C2212yes—
53#2857C2212yes—
54#2857C2212yes—
55#2857C2212yes—
56#2845C2214yes—
57#2844C2214yes—
58#2811C2214yes—
59#2806C2214yes—
60#2806C2214yes—
61#2806C2214yes—
62#2806C2218yes—
63#2805C2214yes—
64#2804C2214yes—
65#2788C2218yes—
66#2774C2218yes—
67#2774C2218yes—
68#2768C2218yes—
69#2763C2218yes—
70#2763C2218yes—
71#2755C2218yes—
72#2755C2218yes—
73#2734C2214yes—
74#2732C2214yes—
75#2729C2218yes—
76#2713C2218yes—
77#2704C2218yes—
78#2666C2218yes—
79#2660C2214yes—
80#2660C2214yes—
81#2659C2214yes—
82#2647C2214yes—
83#2646C2214yes—
84#2628C2214yes—
85#2589C2218yes—
86#2586C2218yes—
87#2582C2214yes—
88#2571C2214yes—
89#2570C2214yes—
90#2570C2214yes—
91#2568C2214yes—
92#2567C2214yes—
93#2567C2214yes—
94#2564C2218yes—
95#2551C2214yes—
96#2551C2214yes—
97#2550C2214yes—
98#2550C2214yes—
99#2549C2218yes—
100#2546C2214yes—
101#2546C2214yes—
102#2546C2214yes—
103#2511C2214yes—
104#2511C2214yes—
105#2511C2214yes—
106#2511C2214yes—
107#2505C2218yes—
108#2502C2214yes—
109#2502C2214yes—
110#2492C2214yes—
111#2492C2214yes—
112#2492C2214yes—
113#2492C2214yes—
114#2465C2218yes—
115#2451C2214yes—
116#2451C2214yes—
117#2451C2214yes—
118#2451C2218yes—
119#2451C2214yes—
120#2450C2218yes—
121#2446C2214yes—
122#2446C2214yes—
123#2446C2214yes—
124#2446C2214yes—
125#2442C2214yes—
126#2442C2214yes—
127#2440C2214yes—
128#2440C2214yes—
129#2440C2214yes—
130#2440C2214yes—
131#2439C2214yes—
132#2439C2214yes—
133#2438C2218yes—
134#2434C2214yes—
135#2434C2214yes—
136#2434C2214yes—
137#2434C2214yes—
138#2429C2214yes—
139#2429C2214yes—
140#2423C2214yes—
141#2423C2214yes—
142#2417C2214yes—
143#2417C2214yes—
144#2409C2214yes—
145#2409C2214yes—
146#2382C2214yes—
147#2379C2214yes—
148#2365C2214yes—
149#2360C2214yes—
150#2360C2214yes—
151#2359C2218yes—
152#2355C2214yes—
153#2355C2214yes—
154#2352C2214yes—
155#2352C2214yes—
156D4×C4⋊C4C2214yes—
157D4×C4⋊C4C2214yes—
158Q8×C22⋊C4C2214yes—
159Q8×C22⋊C4C2214yes—
160#2334C2218yes—
161#2331C2214yes—
162#2329C2214yes—
163#2325C2214yes—
164#2317C2214yes—
165#2317C2214yes—
166#2314C2214yes—
167C4×C4⋊Q8C2212yes—
168C4×C4⋊Q8C2212yes—
169C4×C4⋊Q8C2212yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×#125C2211yescharacteristic
174C4×#125C2211yescharacteristic
175C4×#126C2212yes—
176C4×#126C2212yes—
177C4×#124C2211yescharacteristic
178C4×#124C2211yescharacteristic
179C4×C22⋊Q8C2211yescharacteristic
180C4×C22⋊Q8C2211yescharacteristic
181C4×#123C2212yes—
182C4×#123C2212yes—
183C4×#121C2211yescharacteristic
184C4×#121C2211yescharacteristic
185#2298C2212yes—
186#2295C2211yescharacteristic
187C2×#391C2212yes—
188C2×#391C2212yes—
189C2×#391C2212yes—
190C2×#391C2212yes—
191#2293C2211yescharacteristic
192#2290C2212yes—
193#2285C2212yes—
194#2285C2212yes—
195#2283C2211yescharacteristic
196C2×#382C2212yes—
197C2×#382C2212yes—
198C42×Q8C2211yescharacteristic
199C42×D4C2212yes—
200C42×D4C2211yescharacteristic
201C4×#117C2212yes—
202C2×C43C2211yescharacteristic
203C23×Q8C2312yes—
204C23×Q8C2312yes—
205C23×Q8C2314yes—
206D4×Q8—416no—
207#533—48no—
208#533—48no—
209C2×C4⋊Q8—44no—
210C2×C4⋊Q8—44no—
211C2×C4⋊Q8—48no—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2312yes—
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×C4⋊Q8C2312yes—
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2314yes—
229C2×C4⋊Q8C2314yes—
230C2×C4⋊Q8C2314yes—
231C2×C4⋊Q8C2318yes—
232#529Q8116yescomplemented
233C2×#126C2312yes—
234C2×#125C2314yes—
235C2×#125C2314yes—
236C2×#125C2311yescharacteristic
237C2×#124C2311yescharacteristic
238C2×#123C2312yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2318yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2318yes—
247C2×C22⋊Q8C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2311yescharacteristic
258C2×C4×D4C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2318yes—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2312yes—
264C2×C4×D4C2311yescharacteristic
265C2×#117C2312yes—
266C2×#117C2314yes—
267C2×#117C2314yes—
268C2×#117C2312yes—
269C22×C4⋊C4C2314yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2312yes—
272C22×C4⋊C4C2314yes—
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2312yes—
275C22×C42C2311yescharacteristic
276C22×C42C2312yes—
277C22×C42C2311yescharacteristic
278C22×C42C2311yescharacteristic
279C22×C42C2311yescharacteristic
280C22×C42C2311yescharacteristic
281C22×C42C2311yescharacteristic
282C22×C42C2311yescharacteristic
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#400C2318yes—
291#400C2318yes—
292#399C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2318yes—
306#398C2318yes—
307#396C2318yes—
308#396C2318yes—
309#395C2318yes—
310#395C2318yes—
311#395C2318yes—
312#395C2318yes—
313#395C2318yes—
314#395C2318yes—
315#395C2318yes—
316#395C2318yes—
317#395C2318yes—
318#395C2318yes—
319#395C2318yes—
320#393C2318yes—
321#393C2318yes—
322#393C2318yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2318yes—
334#391C2314yes—
335#391C2314yes—
336#391C2314yes—
337#391C2314yes—
338#391C2318yes—
339#391C2318yes—
340#391C2318yes—
341#391C2318yes—
342#391C2318yes—
343#391C2314yes—
344#391C2314yes—
345#391C2314yes—
346#391C2318yes—
347#391C2314yes—
348#391C2314yes—
349#391C2314yes—
350#391C2314yes—
351#391C2314yes—
352#391C2314yes—
353#391C2314yes—
354#391C2314yes—
355#391C2314yes—
356#391C2314yes—
357#391C2314yes—
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2318yes—
379#389C2318yes—
380#389C2318yes—
381#389C2318yes—
382#389C2318yes—
383#389C2318yes—
384#389C2318yes—
385#389C2314yes—
386#389C2314yes—
387#389C2318yes—
388#389C2314yes—
389#389C2314yes—
390#389C2318yes—
391#388C2312yes—
392#388C2312yes—
393#388C2312yes—
394#388C2312yes—
395#388C2312yes—
396#388C2312yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2312yes—
402#388C2312yes—
403#387C2312yes—
404#387C2312yes—
405#387C2312yes—
406#387C2312yes—
407#387C2312yes—
408#387C2312yes—
409#387C2312yes—
410#387C2312yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#386C2312yes—
426#386C2318yes—
427#386C2318yes—
428#386C2312yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2318yes—
438#385C2318yes—
439#385C2312yes—
440#385C2312yes—
441#384C2312yes—
442#384C2312yes—
443#384C2312yes—
444#384C2312yes—
445#384C2312yes—
446#384C2314yes—
447#384C2314yes—
448#384C2312yes—
449#384C2314yes—
450#384C2314yes—
451#384C2312yes—
452#384C2312yes—
453#383C2312yes—
454#382C2311yescharacteristic
455#382C2311yescharacteristic
456#382C2318yes—
457#382C2314yes—
458#382C2314yes—
459#382C2314yes—
460#382C2314yes—
461#382C2314yes—
462#382C2314yes—
463#382C2314yes—
464#382C2314yes—
465#382C2314yes—
466#382C2314yes—
467#382C2314yes—
468#382C2314yes—
469#381C2312yes—
470#380C2314yes—
471#380C2318yes—
472#380C2314yes—
473#380C2314yes—
474#380C2314yes—
475#380C2314yes—
476#380C2314yes—
477#380C2318yes—
478#380C2314yes—
479#380C2314yes—
480#380C2311yescharacteristic
481#380C2311yescharacteristic
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2318yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2312yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2318yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2312yes—
522#376C2312yes—
523#376C2312yes—
524C2×#95C2314yes—
525C2×#95C2314yes—
526C2×#95C2314yes—
527C2×#95C2314yes—
528C43C2311yescharacteristic
529C43C2311yescharacteristic
530C43C2311yescharacteristic
531C43C2311yescharacteristic
532C43C2311yescharacteristic
533C43C2311yescharacteristic
534C43C2312yes—
535C43C2311yescharacteristic
536C43C2311yescharacteristic
537C22×Q8—28no—
538C22×Q8—28no—
539C22×Q8—44no—
540C22×Q8—44no—
541C22×Q8—48no—
542C22×Q8—48no—
543C22×Q8—44no—
544C22×Q8—44no—
545C22×Q8—48no—
546C22×Q8C2414yes—
547C22×Q8C2414yes—
548C22×Q8C2414yes—
549C22×Q8C2414yes—
550C22×Q8C2414yes—
551C22×Q8C2414yes—
552C22×Q8C2418yes—
553C22×Q8C2411yescharacteristic
554C22×D4C2412yes—
555C22×D4C2411yescharacteristic
556C23×C4C2412yes—
557C23×C4C2412yes—
558C23×C4C2411yescharacteristic
559C23×C4C2411yescharacteristic
560C23×C4C2411yescharacteristic
561C23×C4C2412yes—
562C23×C4C2411yescharacteristic
563C23×C4C2411yescharacteristic
564C23×C4C2411yescharacteristic
565C23×C4C2414yes—
566C23×C4C2414yes—
567C23×C4C2418yes—
568C23×C4C2411yescharacteristic
569C4⋊Q8—28no—
570C4⋊Q8—28no—
571C4⋊Q8—28no—
572C4⋊Q8—28no—
573C4⋊Q8—48no—
574C4⋊Q8—48no—
575C4⋊Q8—44no—
576C4⋊Q8—44no—
577C4⋊Q8—44no—
578C4⋊Q8—44no—
579C4⋊Q8—44no—
580C4⋊Q8—44no—
581C4⋊Q8—48no—
582C4⋊Q8—44no—
583C4⋊Q8—44no—
584C4⋊Q8—44no—
585C4⋊Q8—48no—
586C4⋊Q8—44no—
587C4⋊Q8—48no—
588C4⋊Q8—416no—
589#126C2×Q8116yescomplemented
590#125—48no—
591#125—48no—
592#125C2×Q818yescomplemented
593#124C2×Q818yescomplemented
594#123C2×Q8116yescomplemented
595C22⋊Q8—216no—
596C22⋊Q8—48no—
597C22⋊Q8—416no—
598C22⋊Q8—416no—
599C22⋊Q8—48no—
600C22⋊Q8—48no—
601C22⋊Q8—48no—
602C22⋊Q8—48no—
603C22⋊Q8C2×Q818yescomplemented
604#121C2×Q818yes—
605C4×Q8—42no—
606C4×Q8—42no—
607C4×Q8—48no—
608C4×Q8—48no—
609C4×Q8—48no—
610C4×Q8—48no—
611C4×Q8—48no—
612C4×Q8—48no—
613C4×Q8C2×Q818yescomplemented
614C4×D4—28no—
615C4×D4—28no—
616C4×D4—42no—
617C4×D4—42no—
618C4×D4—416no—
619C4×D4C2×Q818yescomplemented
620C4×D4C2×Q8116yescomplemented
621#117—28no—
622#117—48no—
623#117—48no—
624#117C2×Q8116yescomplemented
625C2×C4⋊C4—44no—
626C2×C4⋊C4—44no—
627C2×C4⋊C4—48no—
628C2×C4⋊C4—48no—
629C2×C4⋊C4—44no—
630C2×C4⋊C4—44no—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2412yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2412yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2412yes—
694C2×C22⋊C4C2412yes—
695C2×C22⋊C4C2412yes—
696C2×C22⋊C4C2412yes—
697C2×C22⋊C4C2412yes—
698C2×C42—24no—
699C2×C42—24no—
700C2×C42—24no—
701C2×C42—28no—
702C2×C42—24no—
703C2×C42—42no—
704C2×C42—42no—
705C2×C42C2×Q818yescomplemented
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2412yes—
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2411yescharacteristic
718C2×C42C2412yes—
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2418yes—
733C2×C42C2418yes—
734C2×C42C2418yes—
735C2×C42C2418yes—
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2412yes—
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753#95C2418yes—
754#95C2418yes—
755#95C2412yes—
756#95C2412yes—
757#95C2412yes—
758#95C2412yes—
759#95C2412yes—
760#95C2412yes—
761#95C2412yes—
762#95C2412yes—
763#95C2412yes—
764#95C2412yes—
765#95C2412yes—
766#95C2412yes—
767#95C2412yes—
768#95C2412yes—
769#95C2412yes—
770#95C2412yes—
771#95C2412yes—
772#95C2418yes—
773#95C2418yes—
774#95C2418yes—
775#95C2412yes—
776#95C2412yes—
777#95C2412yes—
778#95C2418yes—
779#95C2418yes—
780#95C2418yes—
781#95C2418yes—
782#95C2418yes—
783#95C2418yes—
784#95C2418yes—
785#95C2418yes—
786#95C2418yes—
787#95C2418yes—
788#95C2418yes—
789#95C2418yes—
790#95C2418yes—
791C24C2512yes—
792C24C2511yescharacteristic
793C2×Q8—28no—
794C2×Q8—28no—
795C2×Q8—28no—
796C2×Q8—28no—
797C2×Q8—28no—
798C2×Q8—28no—
799C2×Q8—28no—
800C2×Q8—28no—
801C2×Q8—28no—
802C2×Q8—28no—
803C2×Q8—28no—
804C2×Q8—28no—
805C2×Q8—41no—
806C2×Q8—41no—
807C2×Q8—44no—
808C2×Q8—48no—
809C2×Q8—44no—
810C2×Q8—44no—
811C2×Q8—48no—
812C2×Q8—44no—
813C2×Q8—44no—
814C2×Q8—44no—
815C2×Q8—48no—
816C2×Q8—816no—
817C2×Q8—816no—
818C2×Q8—832no—
819C2×Q8C22×Q814yes—
820C2×D4—24no—
821C2×D4—24no—
822C2×D4—41no—
823C2×D4—41no—
824C2×D4C22×Q818yes—
825C2×D4C22×Q814yes—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—24no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—24no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—28no—
839C22×C4—28no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—24no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—41no—
849C22×C4—41no—
850C22×C4—41no—
851C22×C4—41no—
852C22×C4—44no—
853C22×C4—48no—
854C22×C4—44no—
855C22×C4—48no—
856C22×C4—44no—
857C22×C4—48no—
858C22×C4—44no—
859C22×C4C22×Q814yes—
860C22×C4C22×Q814yes—
861C22×C4C22×Q818yes—
862C22×C4C22×Q814yes—
863C22×C4H(5,𝔽2)14yes—
864C22×C42−1+414yes—
865C22×C4C2511yescharacteristic
866C22×C4C2512yes—
867C22×C4C2518yes—
868C22×C4C2511yescharacteristic
869C22×C4C2518yes—
870C22×C4C2512yes—
871C22×C4C2512yes—
872C22×C4C2518yes—
873C22×C4C2512yes—
874C22×C4C2518yes—
875C22×C4C2511yescharacteristic
876C22×C4C2511yescharacteristic
877C22×C4C2512yes—
878C22×C4C2512yes—
879C22×C4C2512yes—
880C22×C4C2511yescharacteristic
881C22×C4C2511yescharacteristic
882C22×C4C2511yescharacteristic
883C22×C4C2511yescharacteristic
884C22×C4C2511yescharacteristic
885C22×C4C2511yescharacteristic
886C22×C4C2511yescharacteristic
887C22×C4C2511yescharacteristic
888C22×C4C2511yescharacteristic
889C22×C4C2511yescharacteristic
890C4⋊C4—28no—
891C4⋊C4—28no—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—28no—
895C4⋊C4—28no—
896C4⋊C4—24no—
897C4⋊C4—28no—
898C4⋊C4—216no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—28no—
903C4⋊C4—28no—
904C4⋊C4—28no—
905C4⋊C4—48no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—48no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—41no—
914C4⋊C4—41no—
915C4⋊C4—48no—
916C4⋊C4—42no—
917C4⋊C4—41no—
918C4⋊C4—41no—
919C4⋊C4—42no—
920C4⋊C4—48no—
921C4⋊C4—48no—
922C4⋊C4—48no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—44no—
926C4⋊C4—48no—
927C4⋊C4—48no—
928C4⋊C4—48no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—48no—
933C4⋊C4—48no—
934C4⋊C4C22×Q818yes—
935C4⋊C4C22×Q818yes—
936C4⋊C4C22×Q814yes—
937C4⋊C4C22×Q818yes—
938C4⋊C4C22×Q814yes—
939C4⋊C4C22×Q818yes—
940C22⋊C4—216no—
941C22⋊C4—24no—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—24no—
945C22⋊C4—24no—
946C22⋊C4—24no—
947C22⋊C4—48no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4C22×Q818yes—
953C22⋊C4C22×Q818yes—
954C22⋊C4C22×Q818yes—
955C22⋊C4C22×Q818yes—
956C22⋊C4C22×Q818yes—
957C42—22no—
958C42—22no—
959C42—24no—
960C42—24no—
961C42—22no—
962C42—24no—
963C42—22no—
964C42—22no—
965C42—22no—
966C42—22no—
967C42—24no—
968C42—22no—
969C42—22no—
970C42—22no—
971C42—22no—
972C42—22no—
973C42—22no—
974C42—22no—
975C42—24no—
976C42—24no—
977C42—22no—
978C42—22no—
979C42—22no—
980C42—22no—
981C42—24no—
982C42—24no—
983C42—41no—
984C42—41no—
985C42—41no—
986C42—41no—
987C42—48no—
988C42—48no—
989C42—48no—
990C42—48no—
991C42C22×Q814yes—
992C42C22×Q814yes—
993C42C22×Q814yes—
994C42C22×Q814yes—
995C42C22×Q818yes—
996C42H(5,𝔽2)14yes—
997C422−1+414yes—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23C23×Q814yes—
1009C23C23×Q812yes—
1010C23C2×H(5,𝔽2)12yes—
1011C23C2×2−1+412yes—
1012C23C2611yescharacteristic
1013Q8—44no—
1014Q8—416no—
1015Q8—416no—
1016Q8—416no—
1017Q8—88no—
1018Q8—88no—
1019Q8—88no—
1020Q8—816no—
1021D4—216no—
1022D4—44no—
1023C2×C4—21no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—28no—
1048C2×C4—28no—
1049C2×C4—216no—
1050C2×C4—28no—
1051C2×C4—28no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—28no—
1057C2×C4—28no—
1058C2×C4—28no—
1059C2×C4—28no—
1060C2×C4—28no—
1061C2×C4—22no—
1062C2×C4—28no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—28no—
1071C2×C4—28no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—28no—
1077C2×C4—28no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—28no—
1081C2×C4—28no—
1082C2×C4—44no—
1083C2×C4—44no—
1084C2×C4—44no—
1085C2×C4—48no—
1086C2×C4—48no—
1087C2×C4—88no—
1088C2×C4—88no—
1089C2×C4—816no—
1090C2×C4C23×Q812yes—
1091C2×C4C23×Q812yes—
1092C2×C4C23×Q812yes—
1093C2×C4C23×Q812yes—
1094C2×C4C23×Q812yes—
1095C2×C4C23×Q814yes—
1096C2×C4C23×Q814yes—
1097C2×C4C23×Q814yes—
1098C2×C4C23×Q812yes—
1099C2×C4C2×H(5,𝔽2)12yes—
1100C2×C4C2×H(5,𝔽2)12yes—
1101C2×C4C2×H(5,𝔽2)12yes—
1102C2×C4C2×H(5,𝔽2)12yes—
1103C2×C4C2×H(5,𝔽2)12yes—
1104C2×C4C2×2−1+412yes—
1105C2×C4C2×2−1+412yes—
1106C2×C4C2×2−1+412yes—
1107C2×C4C2×2−1+412yes—
1108C2×C4C2×2−1+412yes—
1109C2×C4#58512yes—
1110C2×C4#58512yes—
1111C22—22no—
1112C22—22no—
1113C22—22no—
1114C22—22no—
1115C22—22no—
1116C22—22no—
1117C22—24no—
1118C22—24no—
1119C22—24no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22#350314yes—
1125C22C24×Q811yescharacteristic
1126C22C22×H(5,𝔽2)11yescharacteristic
1127C22C22×H(5,𝔽2)11yescharacteristic
1128C22C22×2−1+411yescharacteristic
1129C22C22×2−1+411yescharacteristic
1130C22C2×#58511yescharacteristic
1131C22C2×#58511yescharacteristic
1132C4—22no—
1133C4—22no—
1134C4—22no—
1135C4—22no—
1136C4—24no—
1137C4—22no—
1138C4—24no—
1139C4—22no—
1140C4—22no—
1141C4—24no—
1142C4—22no—
1143C4—22no—
1144C4—42no—
1145C4—48no—
1146C4—48no—
1147C4—42no—
1148C4—48no—
1149C4—42no—
1150C4—41no—
1151C4—48no—
1152C4—42no—
1153C4—41no—
1154C4#350314yes—
1155C4#355814yes—
1156C4#356114yes—
1157C2—24no—
1158C2—44no—
1159C2C2×#355811yescharacteristic
1160C2C2×#356111yescharacteristic
1161C2C2×#350311yescharacteristic
1162C2C2×#350311yescharacteristic
1163C2#6281311yescharacteristic
1164C2#6283511yescharacteristic
1165C2#6283711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59274C2semidirect
2. #59096C2semidirect
3. #46007C2semidirect
4. #46006C2semidirect
5. #46005C2semidirect
6. #46004C2semidirect
7. #39663C2semidirect
8. #39660C2semidirect
9. #39640C2semidirect
11. #39624C2semidirect
12. #39621C2semidirect
14. #39493C2semidirect
15. #37875C2semidirect
16. #37561C2semidirect
17. #37314C2semidirect
18. #36645C2semidirect
19. C2×#2862C2semidirect
20. #36598C2semidirect
21. #36129C2semidirect
22. #36129C2semidirect
23. D4×C4⋊Q8C2semidirect
24. #35283C2semidirect
25. #35281C2semidirect
232. #529Q8semidirect
589. #126C2×Q8semidirect
592. #125C2×Q8semidirect
593. #124C2×Q8semidirect
594. #123C2×Q8semidirect
603. C22⋊Q8C2×Q8semidirect
613. C4×Q8C2×Q8semidirect
619. C4×D4C2×Q8semidirect
620. C4×D4C2×Q8semidirect
624. #117C2×Q8semidirect
705. C2×C42C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#592742
#590962
#460072
#460062
#460052
#460042
#396632
#396602
#396402
#396322
#396242
#396212
#396152
#394932
#378752
#375612
#373142
#366452
C2×#28622
#365982
#361292
D4×C4⋊Q82
#352832
#352812
#343822
C4×#5292