Finite Group Databasebeta

← #7673889

Subgroups — #7673889

Order 512.

4978 conjugacy classes of subgroups.

The subgroup lattice has 1027 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45279C214yesmaximal, complemented
2#45213C214yesmaximal, complemented
3#45059C214yesmaximal, complemented
4#44952C214yesmaximal, complemented
5#39671C214yesmaximal, complemented
6#39668C214yesmaximal, complemented
7#39632C214yesmaximal, complemented
8#39627C214yesmaximal, complemented
9#38106C214yesmaximal, complemented
10#38105C214yesmaximal, complemented
11#38100C214yesmaximal, complemented
12#38099C214yesmaximal, complemented
13#35620C212yesmaximal, complemented
14#35574C212yesmaximal, complemented
15#35257C212yesmaximal, complemented
16#35181C211yesmaximal, characteristic, complemented
17#35167C211yesmaximal, characteristic, complemented
18#34638C211yesmaximal, characteristic, complemented
19#34250C212yesmaximal, complemented
20#34206C211yesmaximal, characteristic
21#34206C211yesmaximal, characteristic
22C2×#2331C211yesmaximal, characteristic, complemented
23#34070C211yesmaximal, characteristic
24C2×#544C2212yes—
25C2×#532C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C2×#520C2212yes—
28C2×#520C2212yes—
29C2×C4×#41C2212yes—
30#2857C2214yes—
31#2857C2214yes—
32#2851C2214yes—
33#2851C2214yes—
34#2806C2218yes—
35#2804C2218yes—
36#2802C2218yes—
37#2791C2218yes—
38#2790C2218yes—
39#2790C2218yes—
40#2788C2218yes—
41#2788C2218yes—
42#2788C2218yes—
43#2784C2218yes—
44#2780C2218yes—
45#2763C2218yes—
46#2755C2218yes—
47#2729C2218yes—
48#2704C2218yes—
49#2692C2218yes—
50#2659C2214yes—
51#2647C2212yes—
52#2647C2212yes—
53#2647C2212yes—
54#2647C2212yes—
55#2646C2212yes—
56#2646C2212yes—
57#2646C2212yes—
58#2646C2212yes—
59#2646C2214yes—
60#2629C2214yes—
61#2628C2214yes—
62#2589C2218yes—
63#2588C2218yes—
64#2586C2218yes—
65#2579C2218yes—
66#2579C2218yes—
67#2574C2218yes—
68#2571C2212yes—
69#2571C2212yes—
70#2570C2214yes—
71#2570C2214yes—
72#2568C2214yes—
73#2566C2214yes—
74#2565C2214yes—
75#2563C2214yes—
76#2552C2212yes—
77#2552C2212yes—
78#2552C2212yes—
79#2552C2212yes—
80#2551C2212yes—
81#2551C2212yes—
82#2550C2214yes—
83#2550C2214yes—
84#2549C2218yes—
85#2522C2218yes—
86#2520C2218yes—
87#2511C2218yes—
88#2505C2218yes—
89#2502C2218yes—
90#2492C2218yes—
91#2473C2218yes—
92#2454C2214yes—
93#2453C2214yes—
94#2452C2214yes—
95#2452C2214yes—
96#2452C2214yes—
97#2451C2214yes—
98#2451C2214yes—
99#2451C2214yes—
100#2450C2218yes—
101#2450C2218yes—
102#2450C2218yes—
103#2450C2218yes—
104#2450C2218yes—
105#2449C2218yes—
106#2442C2214yes—
107#2442C2214yes—
108#2440C2214yes—
109#2440C2214yes—
110#2439C2214yes—
111#2439C2214yes—
112#2439C2214yes—
113#2439C2214yes—
114#2417C2218yes—
115#2409C2218yes—
116#2402C2214yes—
117#2402C2214yes—
118#2367C2214yes—
119#2367C2214yes—
120#2366C2212yes—
121#2366C2212yes—
122#2365C2212yes—
123#2365C2212yes—
124#2354C2212yes—
125#2354C2212yes—
126#2352C2214yes—
127#2352C2214yes—
128#2351C2214yes—
129Q8×C4⋊C4C2214yes—
130#2349C2214yes—
131#2349C2218yes—
132D4×C4⋊C4C2214yes—
133D4×C4⋊C4C2212yes—
134D4×C4⋊C4C2212yes—
135D4×C4⋊C4C2218yes—
136#2331C2214yes—
137#2331C2214yes—
138#2331C2214yes—
139#2331C2214yes—
140#2328C2212yes—
141#2327C2212yes—
142#2326C2212yes—
143#2326C2212yes—
144#2325C2212yes—
145#2325C2212yes—
146#2325C2212yes—
147#2325C2212yes—
148#2325C2214yes—
149#2325C2214yes—
150#2317C2212yes—
151#2317C2212yes—
152#2317C2214yes—
153#2316C2212yes—
154#2316C2214yes—
155#2311C2212yes—
156#2311C2212yes—
157C4×#121C2214yes—
158C4×#121C2214yes—
159#2297C2212yes—
160#2296C2212yes—
161#2296C2212yes—
162#2296C2214yes—
163C2×#391C2212yes—
164C2×#391C2212yes—
165C2×#389C2211yescharacteristic
166C2×#389C2211yescharacteristic
167C2×#389C2214yes—
168#2290C2214yes—
169#2290C2214yes—
170C2×#387C2212yes—
171C2×#387C2212yes—
172#2285C2211yescharacteristic
173#2285C2211yescharacteristic
174#2285C2211yescharacteristic
175C2×#382C2211yescharacteristic
176C2×C4×C4⋊C4C2211yescharacteristic
177C2×C4×C4⋊C4C2211yescharacteristic
178C2×#376C2211yescharacteristic
179C22×#41C2312yes—
180C23×Q8C2312yes—
181#544—48no—
182#532Q8116yescomplemented
183C2×C4⋊Q8—28no—
184C2×C4⋊Q8C2314yes—
185C2×C4⋊Q8C2314yes—
186C2×C4⋊Q8C2314yes—
187C2×C4⋊Q8C2314yes—
188C2×C4⋊Q8C2314yes—
189C2×C4⋊Q8C2311yescharacteristic
190C2×#127C2311yescharacteristic
191C2×#125C2314yes—
192C2×#125C2314yes—
193C2×#125C2314yes—
194C2×#124C2312yes—
195C2×C22⋊Q8C2318yes—
196C2×C22⋊Q8C2318yes—
197C2×C22⋊Q8C2318yes—
198C2×C22⋊Q8C2318yes—
199C2×#121C2312yes—
200C2×#121C2312yes—
201#520—216no—
202#520—48no—
203C4×#41—48no—
204C2×C4×Q8C2314yes—
205C2×C4×Q8C2314yes—
206C2×C4×Q8C2312yes—
207C2×C4×Q8C2312yes—
208C2×C4×D4C2318yes—
209C2×C4×D4C2314yes—
210C2×C4×D4C2314yes—
211C2×C4×D4C2314yes—
212C2×C4×D4C2314yes—
213C2×C4×D4C2318yes—
214C2×C4×D4C2312yes—
215C2×C4×D4C2312yes—
216C2×C4×D4C2314yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2312yes—
219C2×C4×D4C2312yes—
220C2×#117C2312yes—
221C2×#117C2312yes—
222C2×#117C2312yes—
223C2×#117C2314yes—
224C2×#117C2314yes—
225C2×#117C2314yes—
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2314yes—
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2312yes—
231C22×C4⋊C4C2314yes—
232C22×C4⋊C4C2318yes—
233C22×C4⋊C4C2312yes—
234C22×C4⋊C4C2312yes—
235C22×C4⋊C4C2311yescharacteristic
236C22×C42C2311yescharacteristic
237C22×C42C2311yescharacteristic
238C22×C42C2314yes—
239C22×C42C2312yes—
240C22×C42C2312yes—
241C22×C42C2311yescharacteristic
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2314yes—
247#400C2318yes—
248#400C2314yes—
249#400C2314yes—
250#400C2314yes—
251#400C2314yes—
252#400C2314yes—
253#400C2314yes—
254#400C2314yes—
255#399C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2314yes—
261#398C2314yes—
262#398C2318yes—
263#398C2318yes—
264#398C2318yes—
265#398C2314yes—
266#398C2318yes—
267#398C2318yes—
268#398C2318yes—
269#398C2314yes—
270#398C2314yes—
271#398C2314yes—
272#398C2314yes—
273#398C2314yes—
274#396C2318yes—
275#396C2318yes—
276#396C2318yes—
277#396C2318yes—
278#396C2318yes—
279#396C2318yes—
280#395C2318yes—
281#395C2318yes—
282#395C2318yes—
283#395C2318yes—
284#395C2318yes—
285#393C2318yes—
286#393C2318yes—
287#393C2318yes—
288#393C2318yes—
289#393C2318yes—
290#391C2312yes—
291#391C2314yes—
292#391C2314yes—
293#391C2312yes—
294#391C2318yes—
295#391C2318yes—
296#391C2318yes—
297#391C2318yes—
298#391C2318yes—
299#391C2318yes—
300#391C2318yes—
301#391C2318yes—
302#391C2318yes—
303#391C2318yes—
304#390C2312yes—
305#390C2314yes—
306#390C2312yes—
307#390C2314yes—
308#390C2314yes—
309#390C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2314yes—
316#389C2312yes—
317#389C2314yes—
318#389C2314yes—
319#389C2314yes—
320#389C2318yes—
321#389C2318yes—
322#389C2314yes—
323#389C2314yes—
324#389C2312yes—
325#389C2318yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2318yes—
330#389C2314yes—
331#389C2314yes—
332#389C2318yes—
333#389C2314yes—
334#389C2314yes—
335#389C2318yes—
336#389C2312yes—
337#389C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#388C2314yes—
343#388C2318yes—
344#388C2314yes—
345#388C2314yes—
346#388C2314yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2314yes—
360#387C2314yes—
361#387C2314yes—
362#387C2314yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#386C2318yes—
369#386C2318yes—
370#386C2314yes—
371#386C2314yes—
372#386C2318yes—
373#386C2314yes—
374#386C2314yes—
375#386C2314yes—
376#386C2314yes—
377#386C2318yes—
378#385C2318yes—
379#385C2318yes—
380#385C2318yes—
381#385C2318yes—
382#385C2318yes—
383#385C2318yes—
384#385C2314yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#385C2314yes—
389#385C2314yes—
390#385C2314yes—
391#385C2314yes—
392#385C2318yes—
393#385C2318yes—
394#385C2318yes—
395#385C2314yes—
396#385C2318yes—
397#385C2314yes—
398#385C2318yes—
399#385C2314yes—
400#384C2314yes—
401#384C2314yes—
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2318yes—
405#384C2311yescharacteristic
406#384C2314yes—
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#382C2314yes—
411#382C2314yes—
412#382C2312yes—
413#382C2312yes—
414#382C2314yes—
415#382C2314yes—
416#382C2318yes—
417#382C2314yes—
418#382C2312yes—
419#380C2318yes—
420#380C2318yes—
421#380C2314yes—
422#380C2314yes—
423#380C2314yes—
424#380C2314yes—
425#380C2318yes—
426#380C2318yes—
427#380C2318yes—
428#380C2312yes—
429#380C2312yes—
430#380C2312yes—
431#380C2312yes—
432#380C2318yes—
433#380C2312yes—
434#380C2312yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2312yes—
440C4×C4⋊C4C2312yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2318yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2318yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2312yes—
457C4×C22⋊C4C2318yes—
458C4×C22⋊C4C2318yes—
459C4×C22⋊C4C2314yes—
460C4×C22⋊C4C2314yes—
461#376C2312yes—
462#376C2312yes—
463#376C2312yes—
464#376C2312yes—
465C2×#95C2311yescharacteristic
466C2×#95C2311yescharacteristic
467C2×#95C2311yescharacteristic
468C2×#95C2311yescharacteristic
469C2×#95C2312yes—
470C2×#95C2312yes—
471C2×#95C2312yes—
472C2×#95C2318yes—
473C2×#95C2312yes—
474C2×#95C2312yes—
475C2×#95C2312yes—
476C2×#41—28no—
477C2×#41—28no—
478C2×#41C2×Q8116yes—
479C22×Q8—28no—
480C22×Q8—82no—
481C22×Q8—82no—
482C22×Q8C2412yes—
483C22×Q8C2418yes—
484C22×Q8C2418yes—
485C22×D4C2414yes—
486C22×D4C2412yes—
487C22×D4C2412yes—
488C22×D4C2412yes—
489C23×C4C2414yes—
490C23×C4C2412yes—
491C23×C4C2411yescharacteristic
492C23×C4C2411yescharacteristic
493C23×C4C2412yes—
494C23×C4C2418yes—
495C23×C4C2412yes—
496C23×C4C2411yescharacteristic
497C23×C4C2411yescharacteristic
498C23×C4C2418yes—
499C23×C4C2414yes—
500C23×C4C2414yes—
501C23×C4C2411yescharacteristic
502C23×C4C2411yescharacteristic
503C23×C4C2412yes—
504C23×C4C2411yescharacteristic
505C4⋊Q8—216no—
506C4⋊Q8—216no—
507C4⋊Q8—48no—
508C4⋊Q8—48no—
509C4⋊Q8—84no—
510C4⋊Q8C2×Q818yescomplemented
511#127C2×Q818yescomplemented
512#125—48no—
513#125—48no—
514#125—84no—
515#124C2×Q8116yescomplemented
516C22⋊Q8—416no—
517C22⋊Q8—88no—
518C22⋊Q8—88no—
519C22⋊Q8—88no—
520#121C2×Q8116yes—
521#121C2×Q8116yes—
522C4×Q8—216no—
523C4×Q8—44no—
524C4×Q8—44no—
525C4×Q8—48no—
526C4×D4—232no—
527C4×D4—216no—
528C4×D4—44no—
529C4×D4—44no—
530C4×D4—48no—
531C4×D4—48no—
532C4×D4—48no—
533C4×D4—416no—
534C4×D4—84no—
535C4×D4—84no—
536C4×D4C2×Q8116yescomplemented
537C4×D4C2×Q8116yescomplemented
538#117—28no—
539#117—28no—
540#117—28no—
541#117—216no—
542#117—48no—
543#117—48no—
544C2×C4⋊C4—28no—
545C2×C4⋊C4—24no—
546C2×C4⋊C4—24no—
547C2×C4⋊C4—24no—
548C2×C4⋊C4—216no—
549C2×C4⋊C4—48no—
550C2×C4⋊C4—82no—
551C2×C4⋊C4—88no—
552C2×C4⋊C4—82no—
553C2×C4⋊C4#4118yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C42—24no—
624C2×C42—24no—
625C2×C42—48no—
626C2×C42—82no—
627C2×C42—82no—
628C2×C42C2×Q818yes—
629C2×C42C2414yes—
630C2×C42C2412yes—
631C2×C42C2414yes—
632C2×C42C2418yes—
633C2×C42C2414yes—
634C2×C42C2412yes—
635C2×C42C2412yes—
636C2×C42C2412yes—
637C2×C42C2418yes—
638C2×C42C2414yes—
639C2×C42C2414yes—
640C2×C42C2414yes—
641C2×C42C2414yes—
642C2×C42C2414yes—
643C2×C42C2414yes—
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648#95C2418yes—
649#95C2414yes—
650#95C2412yes—
651#95C2412yes—
652#95C2412yes—
653#95C2412yes—
654#95C2412yes—
655#95C2412yes—
656#95C2412yes—
657#95C2412yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2414yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665#95C2418yes—
666#95C2418yes—
667#95C2414yes—
668#95C2414yes—
669#95C2418yes—
670#95C2418yes—
671#95C2414yes—
672#95C2414yes—
673#95C2414yes—
674#95C2414yes—
675#95C2414yes—
676#95C2414yes—
677#95C2418yes—
678#95C2418yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2418yes—
684#95C2418yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2418yes—
691#95C2418yes—
692C24C2514yes—
693C24C2511yescharacteristic
694#41—264no—
695C2×Q8—24no—
696C2×Q8—216no—
697C2×Q8—24no—
698C2×Q8—48no—
699C2×Q8—48no—
700C2×Q8—48no—
701C2×Q8—48no—
702C2×Q8—48no—
703C2×Q8—816no—
704C2×Q8C22×Q818yes—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—42no—
713C2×D4C22×Q8116yes—
714C2×D4C22×Q818yes—
715C2×D4C22×Q818yes—
716C2×D4C22×Q818yes—
717C22×C4—28no—
718C22×C4—28no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—24no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—216no—
727C22×C4—41no—
728C22×C4—41no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—41no—
734C22×C4—41no—
735C22×C4—41no—
736C22×C4—41no—
737C22×C4—41no—
738C22×C4—41no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—44no—
744C22×C4—41no—
745C22×C4—41no—
746C22×C4—48no—
747C22×C4—48no—
748C22×C4—44no—
749C22×C4—42no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—41no—
753C22×C4—41no—
754C22×C4—42no—
755C22×C4—48no—
756C22×C4—48no—
757C22×C4—48no—
758C22×C4C22×Q8116yes—
759C22×C4C22×Q814yes—
760C22×C4C22×Q814yes—
761C22×C4C22×Q814yes—
762C22×C4C2×#4118yes—
763C22×C4C2×#4114yes—
764C22×C4H(5,𝔽2)14yes—
765C22×C4C2512yes—
766C22×C4C2512yes—
767C22×C4C2514yes—
768C22×C4C2512yes—
769C22×C4C2512yes—
770C22×C4C2514yes—
771C22×C4C2514yes—
772C22×C4C2514yes—
773C22×C4C2514yes—
774C22×C4C2514yes—
775C22×C4C2514yes—
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2511yescharacteristic
779C22×C4C2511yescharacteristic
780C22×C4C2511yescharacteristic
781C22×C4C2511yescharacteristic
782C22×C4C2514yes—
783C22×C4C2514yes—
784C22×C4C2511yescharacteristic
785C22×C4C2511yescharacteristic
786C4⋊C4—24no—
787C4⋊C4—216no—
788C4⋊C4—216no—
789C4⋊C4—24no—
790C4⋊C4—24no—
791C4⋊C4—24no—
792C4⋊C4—24no—
793C4⋊C4—24no—
794C4⋊C4—24no—
795C4⋊C4—24no—
796C4⋊C4—24no—
797C4⋊C4—24no—
798C4⋊C4—24no—
799C4⋊C4—24no—
800C4⋊C4—48no—
801C4⋊C4—48no—
802C4⋊C4—44no—
803C4⋊C4—48no—
804C4⋊C4—48no—
805C4⋊C4—48no—
806C4⋊C4—42no—
807C4⋊C4—42no—
808C4⋊C4—42no—
809C4⋊C4—42no—
810C4⋊C4—42no—
811C4⋊C4—42no—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—44no—
815C4⋊C4—48no—
816C4⋊C4—44no—
817C4⋊C4—44no—
818C4⋊C4—44no—
819C4⋊C4—42no—
820C4⋊C4—42no—
821C4⋊C4—48no—
822C4⋊C4—48no—
823C4⋊C4—48no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—48no—
827C4⋊C4—44no—
828C4⋊C4—48no—
829C4⋊C4—48no—
830C4⋊C4—42no—
831C4⋊C4—42no—
832C4⋊C4—42no—
833C4⋊C4—42no—
834C4⋊C4C22×Q818yes—
835C4⋊C4C22×Q818yes—
836C4⋊C4C2×#4118yes—
837C4⋊C4C2×#4118yes—
838C22⋊C4—28no—
839C22⋊C4—28no—
840C22⋊C4—28no—
841C22⋊C4—216no—
842C22⋊C4—48no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—48no—
848C22⋊C4—48no—
849C22⋊C4—48no—
850C22⋊C4—48no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4C22×Q8116yes—
854C22⋊C4C22×Q8116yes—
855C42—24no—
856C42—24no—
857C42—216no—
858C42—28no—
859C42—24no—
860C42—24no—
861C42—28no—
862C42—28no—
863C42—44no—
864C42—44no—
865C42—44no—
866C42—44no—
867C42—44no—
868C42—44no—
869C42—48no—
870C42C22×Q814yes—
871C42C22×Q814yes—
872C42C22×Q814yes—
873C42C22×Q814yes—
874C23—21no—
875C23—21no—
876C23—21no—
877C23—21no—
878C23—24no—
879C23—24no—
880C23—24no—
881C23—24no—
882C23—24no—
883C23—24no—
884C23C23×Q818yes—
885C23C23×Q812yes—
886C23C22×#4112yes—
887C23C2×H(5,𝔽2)12yes—
888C23C2611yescharacteristic
889Q8—216no—
890Q8—816no—
891Q8—168no—
892D4—232no—
893D4—216no—
894D4—48no—
895D4—48no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—232no—
909C2×C4—24no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—44no—
949C2×C4—44no—
950C2×C4—48no—
951C2×C4—44no—
952C2×C4—48no—
953C2×C4—44no—
954C2×C4—816no—
955C2×C4—82no—
956C2×C4—82no—
957C2×C4—84no—
958C2×C4—84no—
959C2×C4—88no—
960C2×C4—88no—
961C2×C4—168no—
962C2×C4#554116yes—
963C2×C4C23×Q812yes—
964C2×C4C23×Q812yes—
965C2×C4C23×Q812yes—
966C2×C4C23×Q812yes—
967C2×C4C23×Q818yes—
968C2×C4C23×Q812yes—
969C2×C4C23×Q812yes—
970C2×C4C22×#4118yes—
971C2×C4C22×#4112yes—
972C2×C4C22×#4112yes—
973C2×C4C2×H(5,𝔽2)12yes—
974C2×C4C2×H(5,𝔽2)12yes—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—22no—
979C22—22no—
980C22—22no—
981C22—28no—
982C22—28no—
983C22—28no—
984C22—44no—
985C22—44no—
986C22—44no—
987C22—44no—
988C22C2×#55414yes—
989C22C24×Q811yescharacteristic
990C22C23×#4111yescharacteristic
991C22C22×H(5,𝔽2)11yescharacteristic
992C22H(7,𝔽2)11yescharacteristic
993C22H(7,𝔽2)11yescharacteristic
994C222−1+611yescharacteristic
995C222−1+611yescharacteristic
996C4—28no—
997C4—22no—
998C4—22no—
999C4—22no—
1000C4—22no—
1001C4—28no—
1002C4—44no—
1003C4—42no—
1004C4—44no—
1005C4—44no—
1006C4—42no—
1007C4—44no—
1008C4—42no—
1009C4—42no—
1010C4—44no—
1011C4—44no—
1012C4—44no—
1013C4—44no—
1014C4—44no—
1015C4C2×#55414yes—
1016C4C2×#55414yes—
1017C2—24no—
1018C2—48no—
1019C2C22×#55411yescharacteristic
1020C2#6284611yescharacteristic
1021C2#6285011yescharacteristic
1022C2#6285411yescharacteristic
1023C2#6285411yescharacteristic
1024C2#6287811yescharacteristic
1025C2#6287811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45279C2semidirect
2. #45213C2semidirect
3. #45059C2semidirect
4. #44952C2semidirect
5. #39671C2semidirect
6. #39668C2semidirect
7. #39632C2semidirect
8. #39627C2semidirect
9. #38106C2semidirect
10. #38105C2semidirect
11. #38100C2semidirect
12. #38099C2semidirect
13. #35620C2semidirect
14. #35574C2semidirect
15. #35257C2semidirect
16. #35181C2semidirect
17. #35167C2semidirect
18. #34638C2semidirect
19. #34250C2semidirect
22. C2×#2331C2semidirect
182. #532Q8semidirect
510. C4⋊Q8C2×Q8semidirect
511. #127C2×Q8semidirect
515. #124C2×Q8semidirect
536. C4×D4C2×Q8semidirect
537. C4×D4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#452792
#452132
#450592
#449522
#396712
#396682
#396322
#396272
#381062
#381052
#381002
#380992
#356202
#355742
#352572
#351812
#351672
#346382
#342502
#342062
C2×#23312
#340702