Finite Group Databasebeta

← #7711442

Subgroups — #7711442

Order 512.

4558 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59325C214yesmaximal
2#59151C212yesmaximal
3#59144C212yesmaximal
4#46155C214yesmaximal, complemented
5#46007C212yesmaximal, complemented
6#46006C212yesmaximal, complemented
7#39978C214yesmaximal, complemented
8#39676C214yesmaximal
9#39643C212yesmaximal, complemented
10#39640C212yesmaximal
11#39629C212yesmaximal, complemented
12#39624C212yesmaximal
13#39621C212yesmaximal, complemented
14#39619C212yesmaximal, complemented
15#38446C214yesmaximal
16#37561C212yesmaximal
17#37195C214yesmaximal, complemented
18#36635C211yesmaximal, characteristic
19C2×#2862C211yesmaximal, characteristic
20#36474C212yesmaximal, complemented
21#36286C212yesmaximal, complemented
22#36279C214yesmaximal
23#35199C214yesmaximal, complemented
24#34399C212yesmaximal
25C4×#533C211yesmaximal, characteristic
26C2×Q82C2212yes—
27C2×#557C2212yes—
28C2×#533C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C22×C4⋊Q8C2211yescharacteristic
31#2864C2212yes—
32#2863C2212yes—
33#2863C2212yes—
34#2863C2214yes—
35#2862C2212yes—
36#2862C2212yes—
37#2862C2212yes—
38#2862C2212yes—
39#2862C2212yes—
40#2862C2212yes—
41#2862C2212yes—
42#2862C2212yes—
43#2862C2211yescharacteristic
44#2862C2214yes—
45#2859C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2855C2212yes—
49#2855C2212yes—
50#2851C2212yes—
51#2845C2214yes—
52#2844C2214yes—
53#2811C2214yes—
54#2806C2218yes—
55#2806C2214yes—
56#2806C2214yes—
57#2806C2214yes—
58#2806C2214yes—
59#2805C2214yes—
60#2805C2214yes—
61#2799C2218yes—
62#2774C2218yes—
63#2774C2218yes—
64#2755C2218yes—
65#2755C2218yes—
66#2755C2218yes—
67#2734C2218yes—
68#2734C2214yes—
69#2713C2218yes—
70#2713C2218yes—
71#2713C2218yes—
72#2713C2218yes—
73#2666C2218yes—
74#2666C2218yes—
75#2660C2214yes—
76#2659C2214yes—
77#2647C2214yes—
78#2646C2214yes—
79#2612C2218yes—
80#2605C2218yes—
81#2605C2218yes—
82#2588C2218yes—
83#2586C2218yes—
84#2582C2214yes—
85#2581C2214yes—
86#2570C2214yes—
87#2568C2212yes—
88#2568C2214yes—
89#2568C2214yes—
90#2567C2212yes—
91#2567C2212yes—
92#2567C2214yes—
93#2565C2214yes—
94#2551C2214yes—
95#2551C2214yes—
96#2550C2214yes—
97#2550C2214yes—
98#2550C2218yes—
99#2550C2218yes—
100#2550C2214yes—
101#2549C2218yes—
102#2546C2212yes—
103#2546C2214yes—
104#2546C2214yes—
105#2520C2218yes—
106#2520C2218yes—
107#2520C2218yes—
108#2511C2214yes—
109#2511C2214yes—
110#2509C2214yes—
111#2508C2214yes—
112#2508C2218yes—
113#2505C2218yes—
114#2505C2218yes—
115#2473C2218yes—
116#2451C2214yes—
117#2451C2214yes—
118#2451C2214yes—
119#2451C2214yes—
120#2451C2218yes—
121#2451C2214yes—
122#2451C2214yes—
123#2446C2214yes—
124#2446C2214yes—
125#2446C2214yes—
126#2446C2214yes—
127#2442C2214yes—
128#2440C2214yes—
129#2440C2214yes—
130#2438C2218yes—
131#2434C2214yes—
132#2434C2218yes—
133#2382C2214yes—
134#2382C2214yes—
135#2369C2212yes—
136#2368C2218yes—
137#2365C2212yes—
138#2360C2214yes—
139#2360C2214yes—
140#2360C2214yes—
141#2356C2214yes—
142#2355C2214yes—
143#2351C2214yes—
144#2351C2214yes—
145#2343C2218yes—
146Q8×C22⋊C4C2214yes—
147#2331C2218yes—
148#2331C2214yes—
149#2329C2214yes—
150#2329C2214yes—
151#2327C2214yes—
152#2320C2218yes—
153C4×C4⋊Q8C2211yescharacteristic
154C4×C4⋊Q8C2211yescharacteristic
155C4×C4⋊Q8C2214yes—
156C4×C4⋊Q8C2211yescharacteristic
157C4×C4⋊Q8C2211yescharacteristic
158C4×C4⋊Q8C2211yescharacteristic
159C4×C4⋊Q8C2211yescharacteristic
160C4×#125C2212yes—
161C4×#125C2212yes—
162C4×#125C2212yes—
163C4×C22⋊Q8C2212yes—
164C4×C22⋊Q8C2212yes—
165C4×C22⋊Q8C2212yes—
166C4×C22⋊Q8C2212yes—
167C4×C22⋊Q8C2212yes—
168C4×C22⋊Q8C2212yes—
169#2296C2212yes—
170#2295C2212yes—
171#2295C2212yes—
172#2295C2212yes—
173#2295C2212yes—
174#2295C2214yes—
175C2×#391C2212yes—
176C2×#391C2212yes—
177C2×#391C2212yes—
178C2×#391C2212yes—
179#2285C2211yescharacteristic
180#2283C2212yes—
181C2×#382C2212yes—
182C2×#382C2212yes—
183C42×Q8C2212yes—
184C42×Q8C2212yes—
185C4×#117C2212yes—
186C2×C43C2211yescharacteristic
187C23×Q8C2312yes—
188C23×Q8C2312yes—
189Q82—48no—
190#557—48no—
191#533Q8116yescomplemented
192C2×C4⋊Q8—44no—
193C2×C4⋊Q8—44no—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2314yes—
197C2×C4⋊Q8C2311yescharacteristic
198C2×C4⋊Q8C2311yescharacteristic
199C2×C4⋊Q8C2314yes—
200C2×C4⋊Q8C2314yes—
201C2×C4⋊Q8C2318yes—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2318yes—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#125C2312yes—
213C2×#125C2314yes—
214C2×#125C2318yes—
215C2×#125C2312yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2318yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×#117C2312yes—
235C2×#117C2312yes—
236C22×C4⋊C4C2312yes—
237C22×C4⋊C4C2312yes—
238C22×C4⋊C4C2312yes—
239C22×C4⋊C4C2312yes—
240C22×C42C2311yescharacteristic
241C22×C42C2311yescharacteristic
242C22×C42C2311yescharacteristic
243C22×C42C2311yescharacteristic
244C22×C42C2311yescharacteristic
245C22×C42C2311yescharacteristic
246C22×C42C2311yescharacteristic
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#400C2318yes—
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2318yes—
265#398C2318yes—
266#398C2318yes—
267#398C2318yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2318yes—
274#395C2318yes—
275#395C2318yes—
276#395C2318yes—
277#395C2318yes—
278#395C2318yes—
279#395C2318yes—
280#395C2318yes—
281#395C2318yes—
282#395C2318yes—
283#395C2318yes—
284#395C2318yes—
285#395C2318yes—
286#395C2318yes—
287#391C2312yes—
288#391C2312yes—
289#391C2312yes—
290#391C2314yes—
291#391C2312yes—
292#391C2312yes—
293#391C2312yes—
294#391C2314yes—
295#391C2314yes—
296#391C2314yes—
297#391C2314yes—
298#391C2314yes—
299#391C2312yes—
300#391C2318yes—
301#391C2314yes—
302#391C2318yes—
303#391C2314yes—
304#391C2318yes—
305#391C2314yes—
306#391C2314yes—
307#391C2318yes—
308#391C2314yes—
309#391C2318yes—
310#391C2318yes—
311#391C2314yes—
312#391C2318yes—
313#391C2318yes—
314#391C2314yes—
315#391C2318yes—
316#391C2318yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2314yes—
321#391C2314yes—
322#391C2318yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2312yes—
332#391C2312yes—
333#389C2312yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2312yes—
339#389C2318yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2318yes—
345#389C2312yes—
346#389C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2318yes—
350#389C2314yes—
351#389C2314yes—
352#389C2318yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2318yes—
358#389C2318yes—
359#389C2312yes—
360#389C2318yes—
361#389C2314yes—
362#389C2318yes—
363#389C2318yes—
364#389C2314yes—
365#389C2318yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2314yes—
372#389C2318yes—
373#387C2314yes—
374#387C2314yes—
375#387C2314yes—
376#387C2314yes—
377#387C2314yes—
378#387C2314yes—
379#387C2318yes—
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#387C2314yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2314yes—
400#387C2314yes—
401#387C2314yes—
402#387C2318yes—
403#387C2318yes—
404#387C2314yes—
405#387C2314yes—
406#387C2318yes—
407#387C2318yes—
408#385C2318yes—
409#385C2318yes—
410#385C2314yes—
411#385C2314yes—
412#385C2318yes—
413#385C2318yes—
414#385C2314yes—
415#385C2314yes—
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2314yes—
420#384C2311yescharacteristic
421#384C2314yes—
422#383C2314yes—
423#383C2318yes—
424#382C2312yes—
425#382C2312yes—
426#382C2314yes—
427#382C2314yes—
428#382C2318yes—
429#382C2314yes—
430#382C2314yes—
431#382C2318yes—
432#382C2314yes—
433#382C2314yes—
434#382C2312yes—
435#382C2314yes—
436#382C2312yes—
437#382C2314yes—
438#382C2314yes—
439#382C2318yes—
440#381C2314yes—
441#380C2312yes—
442#380C2312yes—
443#380C2312yes—
444#380C2318yes—
445#380C2312yes—
446#380C2312yes—
447#380C2312yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2318yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2318yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2318yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C22⋊C4C2318yes—
477C4×C22⋊C4C2318yes—
478C4×C22⋊C4C2314yes—
479C4×C22⋊C4C2314yes—
480C4×C22⋊C4C2314yes—
481#376C2318yes—
482#376C2314yes—
483#376C2314yes—
484C2×#95C2314yes—
485C2×#95C2314yes—
486C2×#95C2314yes—
487C2×#95C2314yes—
488C43C2311yescharacteristic
489C43C2311yescharacteristic
490C43C2311yescharacteristic
491C43C2311yescharacteristic
492C43C2311yescharacteristic
493C43C2311yescharacteristic
494C43C2314yes—
495C43C2311yescharacteristic
496C43C2311yescharacteristic
497C22×Q8—28no—
498C22×Q8—44no—
499C22×Q8—44no—
500C22×Q8—44no—
501C22×Q8—44no—
502C22×Q8—44no—
503C22×Q8C2412yes—
504C22×Q8C2414yes—
505C22×Q8C2412yes—
506C22×Q8C2412yes—
507C22×Q8C2414yes—
508C22×Q8C2414yes—
509C22×Q8C2414yes—
510C22×Q8C2418yes—
511C22×Q8C2412yes—
512C23×C4C2411yescharacteristic
513C23×C4C2411yescharacteristic
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C23×C4C2414yes—
519C23×C4C2414yes—
520C23×C4C2411yescharacteristic
521C4⋊Q8—28no—
522C4⋊Q8—28no—
523C4⋊Q8—44no—
524C4⋊Q8—44no—
525C4⋊Q8—44no—
526C4⋊Q8—44no—
527C4⋊Q8—42no—
528C4⋊Q8—48no—
529C4⋊Q8—48no—
530C4⋊Q8—44no—
531C4⋊Q8—44no—
532C4⋊Q8—42no—
533C4⋊Q8—48no—
534C4⋊Q8—48no—
535C4⋊Q8—416no—
536C4⋊Q8—416no—
537C4⋊Q8C2×Q818yescomplemented
538C4⋊Q8C2×Q818yescomplemented
539#125—44no—
540#125—48no—
541#125—416no—
542#125C2×Q8116yescomplemented
543C22⋊Q8—28no—
544C22⋊Q8—416no—
545C22⋊Q8—44no—
546C22⋊Q8C2×Q8116yes—
547C22⋊Q8C2×Q8116yes—
548C4×Q8—28no—
549C4×Q8—28no—
550C4×Q8—28no—
551C4×Q8—28no—
552C4×Q8—44no—
553C4×Q8—44no—
554C4×Q8—48no—
555C4×Q8—48no—
556C4×Q8—48no—
557C4×Q8—48no—
558C4×Q8—48no—
559C4×Q8C2×Q8116yescomplemented
560C4×Q8C2×Q8116yescomplemented
561#117—44no—
562#117C2×Q8116yes—
563C2×C4⋊C4—44no—
564C2×C4⋊C4—44no—
565C2×C4⋊C4—44no—
566C2×C4⋊C4—44no—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C42—24no—
625C2×C42—24no—
626C2×C42—24no—
627C2×C42—42no—
628C2×C42—42no—
629C2×C42—42no—
630C2×C42C2×Q818yes—
631C2×C42C2414yes—
632C2×C42C2414yes—
633C2×C42C2414yes—
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2414yes—
637C2×C42C2414yes—
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2414yes—
651C2×C42C2418yes—
652C2×C42C2418yes—
653C2×C42C2414yes—
654C2×C42C2418yes—
655C2×C42C2418yes—
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2414yes—
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671#95C2418yes—
672#95C2418yes—
673#95C2418yes—
674#95C2418yes—
675#95C2418yes—
676#95C2418yes—
677#95C2418yes—
678#95C2418yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2418yes—
689#95C2418yes—
690#95C2414yes—
691#95C2414yes—
692#95C2418yes—
693#95C2418yes—
694#95C2418yes—
695#95C2418yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2414yes—
712#95C2418yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717C24C2511yescharacteristic
718C2×Q8—24no—
719C2×Q8—24no—
720C2×Q8—28no—
721C2×Q8—28no—
722C2×Q8—24no—
723C2×Q8—24no—
724C2×Q8—28no—
725C2×Q8—24no—
726C2×Q8—28no—
727C2×Q8—28no—
728C2×Q8—24no—
729C2×Q8—28no—
730C2×Q8—42no—
731C2×Q8—42no—
732C2×Q8—42no—
733C2×Q8—44no—
734C2×Q8—44no—
735C2×Q8—42no—
736C2×Q8—44no—
737C2×Q8—44no—
738C2×Q8—44no—
739C2×Q8—44no—
740C2×Q8—48no—
741C2×Q8—48no—
742C2×Q8—48no—
743C2×Q8—816no—
744C2×Q8—816no—
745C2×Q8C22×Q818yes—
746C2×Q8C22×Q818yes—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—28no—
759C22×C4—28no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—41no—
763C22×C4—41no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4C22×Q814yes—
771C22×C4C22×Q814yes—
772C22×C4C22×Q814yes—
773C22×C42−1+414yes—
774C22×C4C2511yescharacteristic
775C22×C4C2514yes—
776C22×C4C2511yescharacteristic
777C22×C4C2514yes—
778C22×C4C2518yes—
779C22×C4C2514yes—
780C22×C4C2518yes—
781C22×C4C2514yes—
782C22×C4C2514yes—
783C22×C4C2514yes—
784C22×C4C2511yescharacteristic
785C22×C4C2511yescharacteristic
786C22×C4C2511yescharacteristic
787C22×C4C2514yes—
788C22×C4C2514yes—
789C22×C4C2511yescharacteristic
790C22×C4C2511yescharacteristic
791C22×C4C2511yescharacteristic
792C22×C4C2511yescharacteristic
793C22×C4C2511yescharacteristic
794C22×C4C2511yescharacteristic
795C22×C4C2511yescharacteristic
796C22×C4C2511yescharacteristic
797C22×C4C2511yescharacteristic
798C4⋊C4—28no—
799C4⋊C4—28no—
800C4⋊C4—28no—
801C4⋊C4—28no—
802C4⋊C4—24no—
803C4⋊C4—28no—
804C4⋊C4—28no—
805C4⋊C4—24no—
806C4⋊C4—28no—
807C4⋊C4—24no—
808C4⋊C4—24no—
809C4⋊C4—28no—
810C4⋊C4—24no—
811C4⋊C4—28no—
812C4⋊C4—24no—
813C4⋊C4—28no—
814C4⋊C4—28no—
815C4⋊C4—44no—
816C4⋊C4—44no—
817C4⋊C4—44no—
818C4⋊C4—44no—
819C4⋊C4—42no—
820C4⋊C4—42no—
821C4⋊C4—44no—
822C4⋊C4—42no—
823C4⋊C4—42no—
824C4⋊C4—48no—
825C4⋊C4—48no—
826C4⋊C4—48no—
827C4⋊C4—48no—
828C4⋊C4—48no—
829C4⋊C4—42no—
830C4⋊C4—44no—
831C4⋊C4—48no—
832C4⋊C4—48no—
833C4⋊C4—48no—
834C4⋊C4—42no—
835C4⋊C4—42no—
836C4⋊C4—44no—
837C4⋊C4—48no—
838C4⋊C4—48no—
839C4⋊C4—42no—
840C4⋊C4—42no—
841C4⋊C4—42no—
842C4⋊C4—48no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C4⋊C4C22×Q818yes—
846C4⋊C4C22×Q818yes—
847C4⋊C4C22×Q8116yes—
848C4⋊C4C22×Q8116yes—
849C4⋊C4C22×Q818yes—
850C4⋊C4C22×Q818yes—
851C22⋊C4—28no—
852C22⋊C4—28no—
853C22⋊C4—28no—
854C22⋊C4C22×Q8116yes—
855C42—22no—
856C42—22no—
857C42—22no—
858C42—28no—
859C42—28no—
860C42—22no—
861C42—22no—
862C42—22no—
863C42—22no—
864C42—22no—
865C42—22no—
866C42—22no—
867C42—28no—
868C42—28no—
869C42—22no—
870C42—22no—
871C42—22no—
872C42—22no—
873C42—28no—
874C42—41no—
875C42—41no—
876C42—41no—
877C42—41no—
878C42—41no—
879C42—41no—
880C42—41no—
881C42—41no—
882C42—44no—
883C42—44no—
884C42—48no—
885C42—48no—
886C42—48no—
887C42—48no—
888C42C22×Q814yes—
889C42C22×Q814yes—
890C42C22×Q814yes—
891C42C22×Q814yes—
892C42C22×Q8116yes—
893C42H(5,𝔽2)14yes—
894C422−1+414yes—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23C23×Q812yes—
900C23C2×2−1+412yes—
901C23#58512yes—
902C23C2611yescharacteristic
903Q8—216no—
904Q8—48no—
905Q8—48no—
906Q8—416no—
907Q8—84no—
908Q8—88no—
909Q8—88no—
910Q8—88no—
911Q8—168no—
912C2×C4—28no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—24no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—24no—
922C2×C4—21no—
923C2×C4—24no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—24no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—28no—
938C2×C4—28no—
939C2×C4—28no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—28no—
944C2×C4—28no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—28no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—21no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—28no—
964C2×C4—28no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—28no—
970C2×C4—44no—
971C2×C4—44no—
972C2×C4—44no—
973C2×C4—88no—
974C2×C4—88no—
975C2×C4C23×Q812yes—
976C2×C4C23×Q812yes—
977C2×C4C23×Q812yes—
978C2×C4C23×Q812yes—
979C2×C4C23×Q812yes—
980C2×C4C23×Q818yes—
981C2×C4C23×Q818yes—
982C2×C4C23×Q812yes—
983C2×C4C2×H(5,𝔽2)12yes—
984C2×C4C2×H(5,𝔽2)12yes—
985C2×C4C2×H(5,𝔽2)12yes—
986C2×C4C2×2−1+412yes—
987C2×C4C2×2−1+412yes—
988C2×C4C2×2−1+412yes—
989C2×C4C2×2−1+412yes—
990C2×C4C2×2−1+412yes—
991C2×C4#58512yes—
992C2×C4#58512yes—
993C22—22no—
994C22—22no—
995C22—22no—
996C22—22no—
997C22—22no—
998C22—22no—
999C22#350214yes—
1000C22C24×Q811yescharacteristic
1001C22C22×H(5,𝔽2)11yescharacteristic
1002C22C22×2−1+411yescharacteristic
1003C22C22×2−1+411yescharacteristic
1004C22C2×#58511yescharacteristic
1005C22C2×#58511yescharacteristic
1006C22C2×#58511yescharacteristic
1007C4—22no—
1008C4—22no—
1009C4—22no—
1010C4—22no—
1011C4—22no—
1012C4—28no—
1013C4—22no—
1014C4—22no—
1015C4—28no—
1016C4—22no—
1017C4—22no—
1018C4—22no—
1019C4—48no—
1020C4—44no—
1021C4—44no—
1022C4—41no—
1023C4—44no—
1024C4—48no—
1025C4—44no—
1026C4—44no—
1027C4—44no—
1028C4—41no—
1029C4#350314yes—
1030C4#356114yes—
1031C2—24no—
1032C2C2×#356111yescharacteristic
1033C2#6275211yescharacteristic
1034C2C2×#350211yescharacteristic
1035C2C2×#350311yescharacteristic
1036C2#6281311yescharacteristic
1037C2#6282411yescharacteristic
1038C2#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
4. #46155C2semidirect
5. #46007C2semidirect
6. #46006C2semidirect
7. #39978C2semidirect
9. #39643C2semidirect
11. #39629C2semidirect
13. #39621C2semidirect
14. #39619C2semidirect
17. #37195C2semidirect
20. #36474C2semidirect
21. #36286C2semidirect
23. #35199C2semidirect
191. #533Q8semidirect
537. C4⋊Q8C2×Q8semidirect
538. C4⋊Q8C2×Q8semidirect
542. #125C2×Q8semidirect
559. C4×Q8C2×Q8semidirect
560. C4×Q8C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#593252
#591512
#591442
#461552
#460072
#460062
#399782
#396762
#396432
#396402
#396292
#396242
#396212
#396192
#384462
#375612
#371952
#366352
C2×#28622
#364742
#362862
#362792
#351992
#343992
C4×#5332