Finite Group Databasebeta

← #7710067

Subgroups — #7710067

Order 512.

4506 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59681C212yesmaximal, complemented
2#59670C214yesmaximal, complemented
3#59459C212yesmaximal, complemented
4#46009C214yesmaximal, complemented
5#46007C212yesmaximal, complemented
6#46006C212yesmaximal, complemented
7#39703C214yesmaximal, complemented
8#39683C214yesmaximal, complemented
9#39655C214yesmaximal, complemented
10#39641C212yesmaximal, complemented
11#39625C212yesmaximal, complemented
12#39623C212yesmaximal
13#39496C212yesmaximal
14#37877C214yesmaximal
15#37561C212yesmaximal
16#36752C214yesmaximal
17#36645C211yesmaximal, characteristic
18#36635C211yesmaximal, characteristic
19#36599C212yesmaximal
20#36133C214yesmaximal
21#36133C212yesmaximal
22#35173C212yesmaximal
23#35015C212yesmaximal
24#34378C212yesmaximal
25C2×C4×#125C211yesmaximal, characteristic
26C2×#533C2212yes—
27C2×#533C2214yes—
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#2857C2214yes—
43#2857C2212yes—
44#2857C2212yes—
45#2857C2212yes—
46#2855C2212yes—
47#2855C2212yes—
48#2855C2214yes—
49#2851C2212yes—
50#2845C2214yes—
51#2844C2214yes—
52#2806C2214yes—
53#2806C2214yes—
54#2805C2218yes—
55#2805C2214yes—
56#2802C2218yes—
57#2802C2218yes—
58#2792C2218yes—
59#2792C2218yes—
60#2792C2218yes—
61#2791C2218yes—
62#2791C2218yes—
63#2791C2218yes—
64#2774C2218yes—
65#2755C2218yes—
66#2755C2218yes—
67#2734C2218yes—
68#2734C2214yes—
69#2713C2218yes—
70#2666C2218yes—
71#2660C2214yes—
72#2659C2214yes—
73#2659C2214yes—
74#2647C2214yes—
75#2646C2214yes—
76#2627C2214yes—
77#2590C2218yes—
78#2590C2218yes—
79#2588C2218yes—
80#2588C2218yes—
81#2586C2218yes—
82#2585C2218yes—
83#2585C2218yes—
84#2584C2218yes—
85#2584C2214yes—
86#2584C2218yes—
87#2570C2214yes—
88#2569C2218yes—
89#2567C2214yes—
90#2567C2214yes—
91#2567C2214yes—
92#2552C2212yes—
93#2551C2214yes—
94#2551C2212yes—
95#2551C2214yes—
96#2550C2214yes—
97#2550C2214yes—
98#2546C2212yes—
99#2546C2214yes—
100#2546C2212yes—
101#2546C2214yes—
102#2546C2214yes—
103#2511C2214yes—
104#2511C2214yes—
105#2509C2214yes—
106#2509C2214yes—
107#2507C2214yes—
108#2507C2214yes—
109#2507C2214yes—
110#2507C2214yes—
111#2506C2214yes—
112#2506C2218yes—
113#2462C2218yes—
114#2462C2218yes—
115#2462C2218yes—
116#2451C2214yes—
117#2451C2214yes—
118#2451C2214yes—
119#2451C2214yes—
120#2446C2214yes—
121#2446C2214yes—
122#2446C2214yes—
123#2446C2214yes—
124#2446C2214yes—
125#2442C2214yes—
126#2440C2218yes—
127#2440C2214yes—
128#2438C2218yes—
129#2438C2218yes—
130#2438C2218yes—
131#2382C2214yes—
132#2382C2214yes—
133#2370C2214yes—
134#2370C2214yes—
135#2370C2214yes—
136#2365C2214yes—
137#2365C2218yes—
138#2365C2214yes—
139#2365C2212yes—
140#2365C2212yes—
141#2355C2212yes—
142Q8×C4⋊C4C2212yes—
143Q8×C4⋊C4C2214yes—
144#2345C2214yes—
145#2344C2214yes—
146#2344C2218yes—
147#2336C2218yes—
148#2330C2214yes—
149#2330C2214yes—
150#2329C2214yes—
151#2316C2214yes—
152#2316C2214yes—
153#2313C2214yes—
154C4×C4⋊Q8C2212yes—
155C4×C4⋊Q8C2212yes—
156C4×C4⋊Q8C2211yescharacteristic
157C4×C4⋊Q8C2211yescharacteristic
158C4×C4⋊Q8C2212yes—
159C4×C4⋊Q8C2212yes—
160C4×#125C2212yes—
161C4×#125C2212yes—
162C4×#125C2212yes—
163C4×#125C2212yes—
164C4×#125C2212yes—
165C4×#125C2212yes—
166C4×#125C2212yes—
167C4×#125C2212yes—
168C4×#125C2212yes—
169C4×C22⋊Q8C2212yes—
170C4×C22⋊Q8C2212yes—
171C4×C22⋊Q8C2214yes—
172#2295C2212yes—
173#2295C2212yes—
174C2×#389C2211yescharacteristic
175C2×#389C2211yescharacteristic
176C2×#387C2212yes—
177C2×#387C2212yes—
178#2285C2212yes—
179#2285C2212yes—
180#2283C2212yes—
181C2×#382C2211yescharacteristic
182C2×C4×C4⋊C4C2211yescharacteristic
183C2×C4×C4⋊C4C2212yes—
184C2×C4×C4⋊C4C2212yes—
185C2×C4×C4⋊C4C2211yescharacteristic
186C2×C43C2211yescharacteristic
187#533—48no—
188#533—416no—
189C2×C4⋊Q8C2312yes—
190C2×C4⋊Q8C2311yescharacteristic
191C2×C4⋊Q8C2311yescharacteristic
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2314yes—
196C2×C4⋊Q8C2314yes—
197C2×C4⋊Q8C2314yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2318yes—
201C2×C4⋊Q8C2314yes—
202C2×#125Q8116yescomplemented
203C2×#125C2312yes—
204C2×#125C2318yes—
205C2×#125C2314yes—
206C2×#125C2314yes—
207C2×#125C2312yes—
208C2×#125C2312yes—
209C2×#125C2312yes—
210C2×#125C2312yes—
211C2×C22⋊Q8C2312yes—
212C2×C22⋊Q8C2312yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2318yes—
216C2×C4×Q8C2312yes—
217C2×C4×Q8C2314yes—
218C2×C4×Q8C2314yes—
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2314yes—
221C2×C4×Q8C2314yes—
222C2×C4×Q8C2318yes—
223C2×C4×Q8C2314yes—
224C2×#117C2318yes—
225C2×#117C2314yes—
226C22×C4⋊C4C2312yes—
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2312yes—
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2312yes—
231C22×C4⋊C4C2312yes—
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C42C2311yescharacteristic
235C22×C42C2312yes—
236C22×C42C2311yescharacteristic
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239C22×C42C2311yescharacteristic
240C22×C42C2311yescharacteristic
241C22×C42C2312yes—
242C22×C42C2311yescharacteristic
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#400C2318yes—
251#400C2318yes—
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#398C2318yes—
271#398C2318yes—
272#395C2318yes—
273#395C2318yes—
274#395C2318yes—
275#395C2318yes—
276#395C2318yes—
277#395C2318yes—
278#395C2318yes—
279#395C2318yes—
280#395C2318yes—
281#395C2318yes—
282#395C2318yes—
283#391C2314yes—
284#391C2312yes—
285#391C2312yes—
286#391C2314yes—
287#391C2314yes—
288#391C2314yes—
289#391C2312yes—
290#391C2318yes—
291#391C2314yes—
292#391C2314yes—
293#391C2318yes—
294#391C2312yes—
295#391C2318yes—
296#391C2312yes—
297#391C2312yes—
298#391C2314yes—
299#391C2314yes—
300#391C2312yes—
301#391C2312yes—
302#391C2318yes—
303#391C2314yes—
304#389C2312yes—
305#389C2312yes—
306#389C2312yes—
307#389C2312yes—
308#389C2312yes—
309#389C2312yes—
310#389C2312yes—
311#389C2312yes—
312#389C2312yes—
313#389C2312yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#389C2312yes—
319#389C2312yes—
320#389C2312yes—
321#389C2312yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2318yes—
327#389C2318yes—
328#389C2318yes—
329#389C2318yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2318yes—
335#389C2318yes—
336#389C2318yes—
337#389C2318yes—
338#389C2312yes—
339#389C2318yes—
340#389C2318yes—
341#389C2314yes—
342#389C2318yes—
343#389C2314yes—
344#389C2318yes—
345#389C2318yes—
346#389C2314yes—
347#389C2318yes—
348#389C2318yes—
349#389C2314yes—
350#389C2318yes—
351#389C2312yes—
352#389C2312yes—
353#389C2314yes—
354#389C2314yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2318yes—
359#389C2318yes—
360#389C2314yes—
361#387C2314yes—
362#387C2314yes—
363#387C2314yes—
364#387C2314yes—
365#387C2314yes—
366#387C2314yes—
367#387C2314yes—
368#387C2314yes—
369#387C2314yes—
370#387C2314yes—
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#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2314yes—
398#387C2314yes—
399#387C2314yes—
400#387C2314yes—
401#387C2314yes—
402#387C2318yes—
403#387C2318yes—
404#385C2314yes—
405#385C2318yes—
406#385C2318yes—
407#385C2314yes—
408#384C2311yescharacteristic
409#384C2312yes—
410#384C2311yescharacteristic
411#384C2312yes—
412#384C2312yes—
413#384C2312yes—
414#384C2314yes—
415#384C2318yes—
416#384C2314yes—
417#384C2312yes—
418#384C2312yes—
419#384C2312yes—
420#384C2312yes—
421#383C2314yes—
422#382C2312yes—
423#382C2312yes—
424#382C2312yes—
425#382C2312yes—
426#382C2312yes—
427#382C2314yes—
428#382C2312yes—
429#382C2314yes—
430#382C2312yes—
431#382C2314yes—
432#381C2318yes—
433#381C2314yes—
434#380C2312yes—
435#380C2314yes—
436#380C2314yes—
437#380C2318yes—
438#380C2318yes—
439#380C2312yes—
440#380C2312yes—
441#380C2314yes—
442#380C2312yes—
443#380C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2318yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2318yes—
477C4×C4⋊C4C2314yes—
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×Q8C2414yes—
497C22×Q8C2414yes—
498C22×Q8C2412yes—
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—42no—
513C4⋊Q8—44no—
514C4⋊Q8—48no—
515C4⋊Q8—48no—
516C4⋊Q8—44no—
517C4⋊Q8—48no—
518C4⋊Q8—44no—
519C4⋊Q8—42no—
520C4⋊Q8—44no—
521C4⋊Q8—48no—
522C4⋊Q8—44no—
523C4⋊Q8—416no—
524#125—44no—
525#125—48no—
526#125—416no—
527#125—48no—
528#125C2×Q8116yes—
529#125C2×Q8116yes—
530#125C2×Q8116yes—
531#125C2×Q8116yes—
532C22⋊Q8—28no—
533C22⋊Q8—216no—
534C22⋊Q8—28no—
535C22⋊Q8—48no—
536C22⋊Q8—416no—
537C4×Q8—28no—
538C4×Q8—44no—
539C4×Q8—48no—
540C4×Q8—416no—
541C4×Q8—48no—
542C4×Q8—48no—
543C4×Q8—48no—
544C4×Q8—48no—
545#117—416no—
546#117—48no—
547C2×C4⋊C4—28no—
548C2×C4⋊C4—42no—
549C2×C4⋊C4—42no—
550C2×C4⋊C4—44no—
551C2×C4⋊C4C2×Q818yes—
552C2×C4⋊C4C2×Q8116yes—
553C2×C4⋊C4C2×Q818yes—
554C2×C4⋊C4C2×Q8116yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2414yes—
617C2×C42—24no—
618C2×C42—28no—
619C2×C42—24no—
620C2×C42—24no—
621C2×C42—42no—
622C2×C42—44no—
623C2×C42—42no—
624C2×C42—42no—
625C2×C42C2×Q818yes—
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628C2×C42C2414yes—
629C2×C42C2414yes—
630C2×C42C2411yescharacteristic
631C2×C42C2414yes—
632C2×C42C2414yes—
633C2×C42C2414yes—
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648C2×C42C2418yes—
649C2×C42C2418yes—
650C2×C42C2418yes—
651C2×C42C2418yes—
652C2×C42C2418yes—
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2414yes—
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
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#95C2414yes—
682#95C2414yes—
683#95C2418yes—
684#95C2418yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2418yes—
689#95C2418yes—
690#95C2418yes—
691#95C2418yes—
692#95C2418yes—
693#95C2418yes—
694#95C2414yes—
695#95C2418yes—
696#95C2418yes—
697#95C2418yes—
698#95C2418yes—
699#95C2414yes—
700#95C2418yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709C24C2511yescharacteristic
710C2×Q8—24no—
711C2×Q8—28no—
712C2×Q8—24no—
713C2×Q8—28no—
714C2×Q8—24no—
715C2×Q8—28no—
716C2×Q8—24no—
717C2×Q8—28no—
718C2×Q8—44no—
719C2×Q8—48no—
720C2×Q8—42no—
721C2×Q8—42no—
722C2×Q8—44no—
723C2×Q8—48no—
724C2×Q8—48no—
725C22×C4—22no—
726C22×C4—24no—
727C22×C4—22no—
728C22×C4—24no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—42no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4—41no—
744C22×C4—41no—
745C22×C4—41no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4C22×Q814yes—
752C22×C4C22×Q814yes—
753C22×C4C22×Q818yes—
754C22×C4C22×Q814yes—
755C22×C4C22×Q818yes—
756C22×C4H(5,𝔽2)14yes—
757C22×C42−1+414yes—
758C22×C4C2511yescharacteristic
759C22×C4C2514yes—
760C22×C4C2514yes—
761C22×C4C2514yes—
762C22×C4C2514yes—
763C22×C4C2518yes—
764C22×C4C2514yes—
765C22×C4C2514yes—
766C22×C4C2518yes—
767C22×C4C2511yescharacteristic
768C22×C4C2511yescharacteristic
769C22×C4C2511yescharacteristic
770C22×C4C2514yes—
771C22×C4C2511yescharacteristic
772C22×C4C2514yes—
773C22×C4C2511yescharacteristic
774C22×C4C2511yescharacteristic
775C22×C4C2511yescharacteristic
776C22×C4C2511yescharacteristic
777C22×C4C2511yescharacteristic
778C22×C4C2511yescharacteristic
779C22×C4C2511yescharacteristic
780C22×C4C2511yescharacteristic
781C22×C4C2511yescharacteristic
782C4⋊C4—216no—
783C4⋊C4—28no—
784C4⋊C4—28no—
785C4⋊C4—24no—
786C4⋊C4—28no—
787C4⋊C4—28no—
788C4⋊C4—24no—
789C4⋊C4—28no—
790C4⋊C4—24no—
791C4⋊C4—28no—
792C4⋊C4—28no—
793C4⋊C4—28no—
794C4⋊C4—24no—
795C4⋊C4—28no—
796C4⋊C4—24no—
797C4⋊C4—24no—
798C4⋊C4—28no—
799C4⋊C4—28no—
800C4⋊C4—44no—
801C4⋊C4—42no—
802C4⋊C4—42no—
803C4⋊C4—48no—
804C4⋊C4—48no—
805C4⋊C4—44no—
806C4⋊C4—44no—
807C4⋊C4—42no—
808C4⋊C4—44no—
809C4⋊C4—48no—
810C4⋊C4—48no—
811C4⋊C4—48no—
812C4⋊C4—48no—
813C4⋊C4—44no—
814C4⋊C4—48no—
815C4⋊C4—42no—
816C4⋊C4—42no—
817C4⋊C4—44no—
818C4⋊C4—48no—
819C4⋊C4—48no—
820C4⋊C4—48no—
821C4⋊C4—42no—
822C4⋊C4—44no—
823C4⋊C4—44no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—42no—
828C4⋊C4—42no—
829C4⋊C4—48no—
830C4⋊C4—48no—
831C4⋊C4—48no—
832C4⋊C4—48no—
833C4⋊C4C22×Q8116yes—
834C4⋊C4C22×Q818yes—
835C4⋊C4C22×Q818yes—
836C4⋊C4C22×Q8116yes—
837C4⋊C4C22×Q8116yes—
838C4⋊C4C22×Q8116yes—
839C4⋊C4C22×Q818yes—
840C4⋊C4C22×Q818yes—
841C22⋊C4—28no—
842C22⋊C4—216no—
843C22⋊C4—28no—
844C42—22no—
845C42—22no—
846C42—28no—
847C42—28no—
848C42—22no—
849C42—22no—
850C42—22no—
851C42—22no—
852C42—22no—
853C42—22no—
854C42—22no—
855C42—22no—
856C42—22no—
857C42—28no—
858C42—22no—
859C42—28no—
860C42—22no—
861C42—22no—
862C42—22no—
863C42—22no—
864C42—22no—
865C42—28no—
866C42—44no—
867C42—41no—
868C42—41no—
869C42—41no—
870C42—41no—
871C42—41no—
872C42—41no—
873C42—48no—
874C42—48no—
875C42—48no—
876C42—48no—
877C42—48no—
878C42C22×Q814yes—
879C42C22×Q814yes—
880C42C22×Q814yes—
881C42C22×Q814yes—
882C422−1+414yes—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23C23×Q812yes—
888C23C2×H(5,𝔽2)12yes—
889C23C2×2−1+412yes—
890C23C2611yescharacteristic
891Q8—48no—
892Q8—416no—
893Q8—88no—
894Q8—84no—
895Q8—816no—
896C2×C4—21no—
897C2×C4—24no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—24no—
906C2×C4—24no—
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—21no—
917C2×C4—21no—
918C2×C4—24no—
919C2×C4—21no—
920C2×C4—28no—
921C2×C4—216no—
922C2×C4—28no—
923C2×C4—28no—
924C2×C4—21no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—28no—
928C2×C4—24no—
929C2×C4—28no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—28no—
938C2×C4—21no—
939C2×C4—24no—
940C2×C4—21no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—21no—
946C2×C4—28no—
947C2×C4—28no—
948C2×C4—24no—
949C2×C4—28no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—44no—
955C2×C4—48no—
956C2×C4—44no—
957C2×C4—44no—
958C2×C4—44no—
959C2×C4—84no—
960C2×C4—84no—
961C2×C4C23×Q812yes—
962C2×C4C23×Q812yes—
963C2×C4C23×Q812yes—
964C2×C4C23×Q812yes—
965C2×C4C23×Q812yes—
966C2×C4C23×Q818yes—
967C2×C4C23×Q818yes—
968C2×C4C23×Q812yes—
969C2×C4C2×H(5,𝔽2)12yes—
970C2×C4C2×H(5,𝔽2)12yes—
971C2×C4C2×2−1+412yes—
972C2×C4C2×2−1+412yes—
973C2×C4C2×2−1+412yes—
974C2×C4C2×2−1+412yes—
975C2×C4C2×2−1+412yes—
976C2×C4#58512yes—
977C2×C4#58512yes—
978C2×C4#58512yes—
979C22—22no—
980C22—22no—
981C22—22no—
982C22—22no—
983C22—22no—
984C22—22no—
985C22#350314yes—
986C22C24×Q811yescharacteristic
987C22C22×H(5,𝔽2)11yescharacteristic
988C22C22×2−1+411yescharacteristic
989C22C22×2−1+411yescharacteristic
990C22C2×#58511yescharacteristic
991C22C2×#58511yescharacteristic
992C22C2×#58511yescharacteristic
993C4—22no—
994C4—22no—
995C4—22no—
996C4—22no—
997C4—28no—
998C4—22no—
999C4—28no—
1000C4—22no—
1001C4—22no—
1002C4—22no—
1003C4—22no—
1004C4—22no—
1005C4—44no—
1006C4—48no—
1007C4—41no—
1008C4—44no—
1009C4—44no—
1010C4—48no—
1011C4—44no—
1012C4—44no—
1013C4—44no—
1014C4—41no—
1015C4#350214yes—
1016C4#355914yes—
1017C2—24no—
1018C2C2×#355911yescharacteristic
1019C2#6274811yescharacteristic
1020C2C2×#350211yescharacteristic
1021C2C2×#350311yescharacteristic
1022C2#6281311yescharacteristic
1023C2#6282311yescharacteristic
1024C2#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. #59681C2semidirect
2. #59670C2semidirect
3. #59459C2semidirect
4. #46009C2semidirect
5. #46007C2semidirect
6. #46006C2semidirect
7. #39703C2semidirect
8. #39683C2semidirect
9. #39655C2semidirect
10. #39641C2semidirect
11. #39625C2semidirect
202. C2×#125Q8semidirect

Maximal subgroups

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

subgroupindex
#596812
#596702
#594592
#460092
#460072
#460062
#397032
#396832
#396552
#396412
#396252
#396232
#394962
#378772
#375612
#367522
#366452
#366352
#365992
#361332
#351732
#350152
#343782
C2×C4×#1252