Finite Group Databasebeta

← #7710049

Subgroups — #7710049

Order 512.

4490 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59669C214yesmaximal, complemented
2#59668C212yesmaximal, complemented
3#59445C212yesmaximal, complemented
4#46155C214yesmaximal, complemented
5#46153C212yesmaximal, complemented
6#46006C212yesmaximal, complemented
7#39751C212yesmaximal
8#39701C214yesmaximal, complemented
9#39682C214yesmaximal, complemented
10#39653C214yesmaximal, complemented
11#39642C212yesmaximal, complemented
12#39625C212yesmaximal, complemented
13#39368C212yesmaximal
14#37689C214yesmaximal
15#37561C212yesmaximal
16#36751C214yesmaximal
17#36645C211yesmaximal, characteristic
18#36635C211yesmaximal, characteristic
19#36564C212yesmaximal
20#36193C212yesmaximal
21#36193C214yesmaximal
22#35167C212yesmaximal
23#35015C212yesmaximal
24#34378C212yesmaximal
25C2×C4×#125C211yesmaximal, characteristic
26C2×#544C2214yes—
27C2×#533C2212yes—
28C22×#125C2211yescharacteristic
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#2855C2214yes—
49#2851C2212yes—
50#2845C2214yes—
51#2844C2214yes—
52#2806C2218yes—
53#2805C2214yes—
54#2802C2218yes—
55#2792C2218yes—
56#2774C2218yes—
57#2774C2218yes—
58#2755C2218yes—
59#2755C2218yes—
60#2734C2214yes—
61#2734C2218yes—
62#2726C2218yes—
63#2726C2214yes—
64#2726C2214yes—
65#2726C2218yes—
66#2713C2218yes—
67#2713C2218yes—
68#2713C2218yes—
69#2713C2218yes—
70#2666C2218yes—
71#2660C2214yes—
72#2659C2214yes—
73#2659C2214yes—
74#2647C2214yes—
75#2646C2214yes—
76#2627C2214yes—
77#2590C2218yes—
78#2588C2218yes—
79#2586C2218yes—
80#2584C2214yes—
81#2570C2214yes—
82#2567C2212yes—
83#2567C2212yes—
84#2567C2214yes—
85#2552C2212yes—
86#2552C2214yes—
87#2552C2214yes—
88#2552C2214yes—
89#2551C2214yes—
90#2551C2212yes—
91#2551C2214yes—
92#2551C2214yes—
93#2550C2218yes—
94#2550C2214yes—
95#2550C2214yes—
96#2550C2218yes—
97#2549C2218yes—
98#2546C2214yes—
99#2520C2218yes—
100#2520C2218yes—
101#2520C2218yes—
102#2511C2214yes—
103#2511C2214yes—
104#2511C2214yes—
105#2511C2214yes—
106#2508C2214yes—
107#2508C2214yes—
108#2508C2218yes—
109#2507C2214yes—
110#2507C2214yes—
111#2507C2214yes—
112#2507C2214yes—
113#2507C2214yes—
114#2507C2214yes—
115#2506C2214yes—
116#2506C2214yes—
117#2506C2214yes—
118#2462C2218yes—
119#2462C2218yes—
120#2451C2218yes—
121#2451C2214yes—
122#2451C2214yes—
123#2446C2218yes—
124#2446C2214yes—
125#2442C2218yes—
126#2442C2214yes—
127#2440C2214yes—
128#2438C2218yes—
129#2438C2218yes—
130#2438C2218yes—
131#2382C2214yes—
132#2382C2214yes—
133#2370C2214yes—
134#2370C2214yes—
135#2370C2218yes—
136#2370C2214yes—
137#2369C2214yes—
138#2369C2212yes—
139#2369C2214yes—
140#2369C2212yes—
141#2355C2212yes—
142#2355C2214yes—
143Q8×C4⋊C4C2212yes—
144#2345C2214yes—
145#2344C2218yes—
146#2344C2214yes—
147#2336C2218yes—
148#2330C2214yes—
149#2330C2214yes—
150#2329C2214yes—
151#2316C2214yes—
152#2313C2214yes—
153C4×C4⋊Q8C2211yescharacteristic
154C4×C4⋊Q8C2212yes—
155C4×C4⋊Q8C2212yes—
156C4×C4⋊Q8C2212yes—
157C4×C4⋊Q8C2211yescharacteristic
158C4×C4⋊Q8C2212yes—
159C4×#125C2212yes—
160C4×#125C2212yes—
161C4×#125C2212yes—
162C4×#125C2212yes—
163C4×#125C2212yes—
164C4×#125C2212yes—
165C4×#125C2212yes—
166C4×#125C2212yes—
167C4×#125C2212yes—
168C4×C22⋊Q8C2212yes—
169C4×C22⋊Q8C2212yes—
170C4×C22⋊Q8C2214yes—
171#2295C2212yes—
172#2295C2212yes—
173C2×#389C2211yescharacteristic
174C2×#389C2211yescharacteristic
175C2×#387C2212yes—
176C2×#387C2212yes—
177#2285C2212yes—
178#2285C2212yes—
179#2285C2214yes—
180#2283C2212yes—
181C2×#382C2211yescharacteristic
182C2×C4×C4⋊C4C2212yes—
183C2×C4×C4⋊C4C2211yescharacteristic
184C2×C4×C4⋊C4C2212yes—
185C2×C4×C4⋊C4C2211yescharacteristic
186C2×C43C2211yescharacteristic
187#544—416no—
188#533—48no—
189C2×C4⋊Q8C2312yes—
190C2×C4⋊Q8C2311yescharacteristic
191C2×C4⋊Q8C2311yescharacteristic
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2314yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2314yes—
199C2×C4⋊Q8C2318yes—
200C2×C4⋊Q8C2318yes—
201C2×#125Q8116yescomplemented
202C2×#125C2312yes—
203C2×#125C2314yes—
204C2×#125C2314yes—
205C2×#125C2318yes—
206C2×#125C2318yes—
207C2×#125C2318yes—
208C2×#125C2312yes—
209C2×#125C2312yes—
210C2×#125C2312yes—
211C2×#125C2312yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2312yes—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2318yes—
217C2×C4×Q8C2312yes—
218C2×C4×Q8C2314yes—
219C2×C4×Q8C2314yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2314yes—
222C2×#117C2318yes—
223C2×#117C2314yes—
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2312yes—
228C22×C4⋊C4C2312yes—
229C22×C4⋊C4C2312yes—
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C42C2311yescharacteristic
233C22×C42C2311yescharacteristic
234C22×C42C2312yes—
235C22×C42C2311yescharacteristic
236C22×C42C2311yescharacteristic
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239C22×C42C2312yes—
240C22×C42C2311yescharacteristic
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
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#398C2318yes—
270#395C2318yes—
271#395C2318yes—
272#395C2318yes—
273#395C2318yes—
274#395C2318yes—
275#395C2318yes—
276#395C2318yes—
277#395C2318yes—
278#395C2318yes—
279#395C2318yes—
280#395C2318yes—
281#391C2314yes—
282#391C2314yes—
283#391C2312yes—
284#391C2312yes—
285#391C2314yes—
286#391C2314yes—
287#391C2312yes—
288#391C2314yes—
289#391C2314yes—
290#391C2314yes—
291#391C2318yes—
292#391C2318yes—
293#391C2318yes—
294#391C2312yes—
295#391C2312yes—
296#391C2312yes—
297#391C2312yes—
298#391C2312yes—
299#391C2318yes—
300#391C2318yes—
301#391C2318yes—
302#391C2318yes—
303#389C2312yes—
304#389C2312yes—
305#389C2312yes—
306#389C2312yes—
307#389C2312yes—
308#389C2312yes—
309#389C2312yes—
310#389C2312yes—
311#389C2312yes—
312#389C2312yes—
313#389C2314yes—
314#389C2314yes—
315#389C2312yes—
316#389C2312yes—
317#389C2312yes—
318#389C2312yes—
319#389C2314yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2318yes—
329#389C2314yes—
330#389C2318yes—
331#389C2318yes—
332#389C2318yes—
333#389C2318yes—
334#389C2318yes—
335#389C2318yes—
336#389C2314yes—
337#389C2314yes—
338#389C2318yes—
339#389C2314yes—
340#389C2318yes—
341#389C2318yes—
342#389C2318yes—
343#389C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2312yes—
350#389C2314yes—
351#389C2312yes—
352#389C2312yes—
353#389C2314yes—
354#389C2318yes—
355#389C2318yes—
356#389C2318yes—
357#389C2318yes—
358#389C2314yes—
359#387C2314yes—
360#387C2314yes—
361#387C2314yes—
362#387C2314yes—
363#387C2314yes—
364#387C2314yes—
365#387C2314yes—
366#387C2314yes—
367#387C2314yes—
368#387C2314yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2314yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2314yes—
390#387C2314yes—
391#387C2314yes—
392#387C2314yes—
393#387C2314yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#385C2318yes—
399#385C2314yes—
400#385C2314yes—
401#385C2318yes—
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2312yes—
405#384C2312yes—
406#384C2312yes—
407#384C2312yes—
408#384C2312yes—
409#384C2314yes—
410#384C2314yes—
411#384C2314yes—
412#384C2314yes—
413#384C2312yes—
414#384C2312yes—
415#384C2312yes—
416#383C2314yes—
417#382C2312yes—
418#382C2312yes—
419#382C2312yes—
420#382C2312yes—
421#382C2312yes—
422#382C2314yes—
423#382C2312yes—
424#382C2314yes—
425#382C2312yes—
426#382C2314yes—
427#382C2318yes—
428#382C2318yes—
429#381C2318yes—
430#381C2314yes—
431#380C2312yes—
432#380C2314yes—
433#380C2312yes—
434#380C2318yes—
435#380C2312yes—
436#380C2314yes—
437#380C2312yes—
438#380C2314yes—
439#380C2314yes—
440#380C2318yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2318yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2318yes—
478C4×C22⋊C4C2318yes—
479C4×C22⋊C4C2314yes—
480#376C2314yes—
481C2×#95C2312yes—
482C2×#95C2312yes—
483C2×#95C2312yes—
484C2×#95C2312yes—
485C2×#95C2312yes—
486C2×#95C2312yes—
487C43C2311yescharacteristic
488C43C2311yescharacteristic
489C43C2311yescharacteristic
490C43C2311yescharacteristic
491C43C2311yescharacteristic
492C43C2311yescharacteristic
493C43C2311yescharacteristic
494C43C2311yescharacteristic
495C22×Q8C2412yes—
496C22×Q8C2412yes—
497C22×Q8C2414yes—
498C22×Q8C2414yes—
499C22×Q8C2418yes—
500C23×C4C2411yescharacteristic
501C23×C4C2411yescharacteristic
502C23×C4C2412yes—
503C23×C4C2411yescharacteristic
504C23×C4C2411yescharacteristic
505C23×C4C2411yescharacteristic
506C23×C4C2412yes—
507C23×C4C2412yes—
508C23×C4C2412yes—
509C23×C4C2411yescharacteristic
510C23×C4C2411yescharacteristic
511C4⋊Q8—28no—
512C4⋊Q8—48no—
513C4⋊Q8—44no—
514C4⋊Q8—44no—
515C4⋊Q8—44no—
516C4⋊Q8—42no—
517C4⋊Q8—48no—
518C4⋊Q8—44no—
519C4⋊Q8—42no—
520C4⋊Q8—44no—
521C4⋊Q8—416no—
522C4⋊Q8—416no—
523#125—44no—
524#125—48no—
525#125—48no—
526#125—416no—
527#125—416no—
528#125—416no—
529#125C2×Q8116yes—
530#125C2×Q8116yes—
531#125C2×Q8116yes—
532#125C2×Q8116yes—
533C22⋊Q8—216no—
534C22⋊Q8—28no—
535C22⋊Q8—28no—
536C22⋊Q8—48no—
537C22⋊Q8—416no—
538C4×Q8—28no—
539C4×Q8—44no—
540C4×Q8—48no—
541C4×Q8—48no—
542C4×Q8—48no—
543#117—48no—
544#117—416no—
545C2×C4⋊C4—28no—
546C2×C4⋊C4—42no—
547C2×C4⋊C4—44no—
548C2×C4⋊C4—42no—
549C2×C4⋊C4C2×Q818yes—
550C2×C4⋊C4C2×Q8116yes—
551C2×C4⋊C4C2×Q818yes—
552C2×C4⋊C4C2×Q8116yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C42—24no—
616C2×C42—24no—
617C2×C42—28no—
618C2×C42—24no—
619C2×C42—42no—
620C2×C42—44no—
621C2×C42—42no—
622C2×C42—42no—
623C2×C42C2×Q818yes—
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626C2×C42C2411yescharacteristic
627C2×C42C2414yes—
628C2×C42C2414yes—
629C2×C42C2414yes—
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
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×C42C2414yes—
645C2×C42C2414yes—
646C2×C42C2418yes—
647C2×C42C2418yes—
648C2×C42C2418yes—
649C2×C42C2418yes—
650C2×C42C2418yes—
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2414yes—
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
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#95C2414yes—
679#95C2414yes—
680#95C2414yes—
681#95C2418yes—
682#95C2418yes—
683#95C2418yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2418yes—
688#95C2418yes—
689#95C2418yes—
690#95C2418yes—
691#95C2418yes—
692#95C2414yes—
693#95C2418yes—
694#95C2418yes—
695#95C2418yes—
696#95C2418yes—
697#95C2418yes—
698#95C2418yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707C24C2511yescharacteristic
708C2×Q8—28no—
709C2×Q8—24no—
710C2×Q8—24no—
711C2×Q8—24no—
712C2×Q8—28no—
713C2×Q8—24no—
714C2×Q8—44no—
715C2×Q8—42no—
716C2×Q8—42no—
717C2×Q8—44no—
718C2×Q8—44no—
719C2×Q8—44no—
720C2×Q8—48no—
721C2×Q8—48no—
722C2×Q8—48no—
723C22×C4—22no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—42no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4—41no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4C22×Q814yes—
750C22×C4C22×Q814yes—
751C22×C4C22×Q818yes—
752C22×C4C22×Q814yes—
753C22×C4C22×Q818yes—
754C22×C4H(5,𝔽2)14yes—
755C22×C42−1+414yes—
756C22×C4C2514yes—
757C22×C4C2511yescharacteristic
758C22×C4C2514yes—
759C22×C4C2514yes—
760C22×C4C2511yescharacteristic
761C22×C4C2518yes—
762C22×C4C2514yes—
763C22×C4C2514yes—
764C22×C4C2514yes—
765C22×C4C2518yes—
766C22×C4C2511yescharacteristic
767C22×C4C2511yescharacteristic
768C22×C4C2511yescharacteristic
769C22×C4C2514yes—
770C22×C4C2514yes—
771C22×C4C2511yescharacteristic
772C22×C4C2511yescharacteristic
773C22×C4C2511yescharacteristic
774C22×C4C2511yescharacteristic
775C22×C4C2511yescharacteristic
776C22×C4C2511yescharacteristic
777C22×C4C2511yescharacteristic
778C22×C4C2511yescharacteristic
779C22×C4C2511yescharacteristic
780C4⋊C4—28no—
781C4⋊C4—28no—
782C4⋊C4—28no—
783C4⋊C4—216no—
784C4⋊C4—24no—
785C4⋊C4—28no—
786C4⋊C4—24no—
787C4⋊C4—28no—
788C4⋊C4—24no—
789C4⋊C4—28no—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—28no—
793C4⋊C4—24no—
794C4⋊C4—24no—
795C4⋊C4—28no—
796C4⋊C4—28no—
797C4⋊C4—28no—
798C4⋊C4—28no—
799C4⋊C4—24no—
800C4⋊C4—44no—
801C4⋊C4—42no—
802C4⋊C4—42no—
803C4⋊C4—48no—
804C4⋊C4—44no—
805C4⋊C4—44no—
806C4⋊C4—48no—
807C4⋊C4—42no—
808C4⋊C4—44no—
809C4⋊C4—48no—
810C4⋊C4—48no—
811C4⋊C4—44no—
812C4⋊C4—48no—
813C4⋊C4—48no—
814C4⋊C4—48no—
815C4⋊C4—42no—
816C4⋊C4—42no—
817C4⋊C4—48no—
818C4⋊C4—44no—
819C4⋊C4—48no—
820C4⋊C4—48no—
821C4⋊C4—48no—
822C4⋊C4—48no—
823C4⋊C4—48no—
824C4⋊C4—42no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—42no—
829C4⋊C4—42no—
830C4⋊C4—48no—
831C4⋊C4C22×Q8116yes—
832C4⋊C4C22×Q818yes—
833C4⋊C4C22×Q818yes—
834C4⋊C4C22×Q8116yes—
835C4⋊C4C22×Q8116yes—
836C4⋊C4C22×Q8116yes—
837C4⋊C4C22×Q818yes—
838C4⋊C4C22×Q818yes—
839C22⋊C4—28no—
840C22⋊C4—216no—
841C22⋊C4—28no—
842C42—22no—
843C42—22no—
844C42—22no—
845C42—22no—
846C42—22no—
847C42—22no—
848C42—22no—
849C42—22no—
850C42—28no—
851C42—22no—
852C42—22no—
853C42—28no—
854C42—22no—
855C42—28no—
856C42—22no—
857C42—28no—
858C42—22no—
859C42—22no—
860C42—22no—
861C42—22no—
862C42—22no—
863C42—28no—
864C42—44no—
865C42—41no—
866C42—41no—
867C42—41no—
868C42—41no—
869C42—41no—
870C42—41no—
871C42—48no—
872C42—48no—
873C42—48no—
874C42—48no—
875C42—48no—
876C42C22×Q814yes—
877C42C22×Q814yes—
878C42C22×Q814yes—
879C42C22×Q814yes—
880C422−1+414yes—
881C23—21no—
882C23—21no—
883C23—21no—
884C23—21no—
885C23C23×Q812yes—
886C23C2×H(5,𝔽2)12yes—
887C23C2×2−1+412yes—
888C23C2611yescharacteristic
889Q8—48no—
890Q8—84no—
891Q8—88no—
892Q8—88no—
893Q8—168no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—24no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—24no—
917C2×C4—21no—
918C2×C4—28no—
919C2×C4—216no—
920C2×C4—28no—
921C2×C4—28no—
922C2×C4—21no—
923C2×C4—24no—
924C2×C4—28no—
925C2×C4—28no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—21no—
929C2×C4—24no—
930C2×C4—21no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—28no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—21no—
943C2×C4—24no—
944C2×C4—28no—
945C2×C4—28no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—28no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—44no—
953C2×C4—48no—
954C2×C4—44no—
955C2×C4—44no—
956C2×C4—44no—
957C2×C4—84no—
958C2×C4—84no—
959C2×C4C23×Q812yes—
960C2×C4C23×Q812yes—
961C2×C4C23×Q812yes—
962C2×C4C23×Q812yes—
963C2×C4C23×Q812yes—
964C2×C4C23×Q818yes—
965C2×C4C23×Q818yes—
966C2×C4C23×Q812yes—
967C2×C4C2×H(5,𝔽2)12yes—
968C2×C4C2×H(5,𝔽2)12yes—
969C2×C4C2×2−1+412yes—
970C2×C4C2×2−1+412yes—
971C2×C4C2×2−1+412yes—
972C2×C4C2×2−1+412yes—
973C2×C4C2×2−1+412yes—
974C2×C4#58512yes—
975C2×C4#58512yes—
976C2×C4#58512yes—
977C22—22no—
978C22—22no—
979C22—22no—
980C22—22no—
981C22—22no—
982C22—22no—
983C22#350314yes—
984C22C24×Q811yescharacteristic
985C22C22×H(5,𝔽2)11yescharacteristic
986C22C22×2−1+411yescharacteristic
987C22C22×2−1+411yescharacteristic
988C22C2×#58511yescharacteristic
989C22C2×#58511yescharacteristic
990C22C2×#58511yescharacteristic
991C4—22no—
992C4—22no—
993C4—22no—
994C4—22no—
995C4—22no—
996C4—28no—
997C4—28no—
998C4—22no—
999C4—22no—
1000C4—22no—
1001C4—22no—
1002C4—22no—
1003C4—44no—
1004C4—44no—
1005C4—41no—
1006C4—44no—
1007C4—44no—
1008C4—48no—
1009C4—44no—
1010C4—44no—
1011C4—41no—
1012C4—48no—
1013C4#350214yes—
1014C4#356314yes—
1015C2—24no—
1016C2C2×#356311yescharacteristic
1017C2#6275211yescharacteristic
1018C2C2×#350211yescharacteristic
1019C2C2×#350311yescharacteristic
1020C2#6281311yescharacteristic
1021C2#6282211yescharacteristic
1022C2#6283511yescharacteristic
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. #59669C2semidirect
2. #59668C2semidirect
3. #59445C2semidirect
4. #46155C2semidirect
5. #46153C2semidirect
6. #46006C2semidirect
8. #39701C2semidirect
9. #39682C2semidirect
10. #39653C2semidirect
11. #39642C2semidirect
12. #39625C2semidirect
201. C2×#125Q8semidirect

Maximal subgroups

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

subgroupindex
#596692
#596682
#594452
#461552
#461532
#460062
#397512
#397012
#396822
#396532
#396422
#396252
#393682
#376892
#375612
#367512
#366452
#366352
#365642
#361932
#351672
#350152
#343782
C2×C4×#1252