Finite Group Databasebeta

← #7673892

Subgroups — #7673892

Order 512.

4946 conjugacy classes of subgroups.

The subgroup lattice has 1025 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45278C214yesmaximal, complemented
2#45233C214yesmaximal, complemented
3#45086C214yesmaximal, complemented
4#44951C214yesmaximal, complemented
5#39670C214yesmaximal, complemented
6#39669C214yesmaximal, complemented
7#39631C214yesmaximal, complemented
8#39627C214yesmaximal, complemented
9#38107C214yesmaximal, complemented
10#38104C214yesmaximal, complemented
11#38101C214yesmaximal, complemented
12#38098C214yesmaximal, complemented
13#35639C212yesmaximal, complemented
14#35532C212yesmaximal, 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×#2330C211yesmaximal, characteristic, complemented
23#34070C211yesmaximal, characteristic
24C2×#544C2212yes—
25C2×#532C2211yescharacteristic
26C22×#125C2211yescharacteristic
27C2×#520C2212yes—
28C2×#520C2212yes—
29C2×C4×#41C2212yes—
30#2857C2214yes—
31#2857C2214yes—
32#2851C2214yes—
33#2851C2214yes—
34#2807C2218yes—
35#2807C2218yes—
36#2805C2218yes—
37#2802C2218yes—
38#2792C2218yes—
39#2790C2218yes—
40#2780C2218yes—
41#2780C2218yes—
42#2774C2218yes—
43#2768C2218yes—
44#2768C2218yes—
45#2748C2218yes—
46#2742C2218yes—
47#2732C2218yes—
48#2729C2218yes—
49#2720C2218yes—
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#2590C2218yes—
63#2587C2218yes—
64#2585C2218yes—
65#2583C2218yes—
66#2579C2218yes—
67#2571C2212yes—
68#2571C2212yes—
69#2570C2214yes—
70#2570C2214yes—
71#2567C2214yes—
72#2566C2214yes—
73#2565C2214yes—
74#2564C2218yes—
75#2556C2218yes—
76#2552C2212yes—
77#2552C2212yes—
78#2552C2212yes—
79#2552C2212yes—
80#2551C2212yes—
81#2551C2212yes—
82#2550C2214yes—
83#2550C2214yes—
84#2542C2214yes—
85#2522C2218yes—
86#2520C2218yes—
87#2507C2218yes—
88#2505C2218yes—
89#2505C2218yes—
90#2497C2218yes—
91#2487C2218yes—
92#2487C2218yes—
93#2454C2214yes—
94#2454C2214yes—
95#2454C2214yes—
96#2453C2214yes—
97#2453C2214yes—
98#2453C2214yes—
99#2452C2214yes—
100#2451C2214yes—
101#2450C2218yes—
102#2450C2218yes—
103#2449C2218yes—
104#2449C2218yes—
105#2449C2218yes—
106#2449C2218yes—
107#2442C2214yes—
108#2442C2214yes—
109#2441C2214yes—
110#2441C2214yes—
111#2441C2214yes—
112#2441C2214yes—
113#2440C2218yes—
114#2440C2214yes—
115#2440C2214yes—
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#2330C2214yes—
137#2330C2214yes—
138#2330C2214yes—
139#2330C2214yes—
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×#389C2211yescharacteristic
164C2×#389C2211yescharacteristic
165C2×#389C2212yes—
166C2×#389C2212yes—
167C2×#389C2214yes—
168#2290C2214yes—
169#2290C2214yes—
170C2×#387C2212yes—
171C2×#387C2212yes—
172#2285C2211yescharacteristic
173#2285C2211yescharacteristic
174#2285C2211yescharacteristic
175C2×#384C2211yescharacteristic
176C2×C4×C4⋊C4C2211yescharacteristic
177C2×C4×C4⋊C4C2211yescharacteristic
178C2×#376C2211yescharacteristic
179C22×#41C2312yes—
180#544—48no—
181#532Q8116yescomplemented
182C2×C4⋊Q8C2314yes—
183C2×C4⋊Q8C2314yes—
184C2×C4⋊Q8C2314yes—
185C2×C4⋊Q8C2311yescharacteristic
186C2×#127C2311yescharacteristic
187C2×#125—28no—
188C2×#125C2314yes—
189C2×#125C2314yes—
190C2×#125C2314yes—
191C2×#125C2314yes—
192C2×#125C2314yes—
193C2×#124C2312yes—
194C2×C22⋊Q8C2318yes—
195C2×C22⋊Q8C2318yes—
196C2×C22⋊Q8C2318yes—
197C2×C22⋊Q8C2318yes—
198C2×#121C2312yes—
199C2×#121C2312yes—
200#520—216no—
201#520—48no—
202C4×#41—48no—
203C2×C4×Q8C2314yes—
204C2×C4×Q8C2314yes—
205C2×C4×Q8C2312yes—
206C2×C4×Q8C2312yes—
207C2×C4×D4C2318yes—
208C2×C4×D4C2314yes—
209C2×C4×D4C2314yes—
210C2×C4×D4C2314yes—
211C2×C4×D4C2314yes—
212C2×C4×D4C2318yes—
213C2×C4×D4C2312yes—
214C2×C4×D4C2312yes—
215C2×C4×D4C2314yes—
216C2×C4×D4C2314yes—
217C2×C4×D4C2312yes—
218C2×C4×D4C2312yes—
219C2×#117C2312yes—
220C2×#117C2312yes—
221C2×#117C2312yes—
222C2×#117C2314yes—
223C2×#117C2314yes—
224C2×#117C2314yes—
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2314yes—
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2312yes—
230C22×C4⋊C4C2312yes—
231C22×C4⋊C4C2314yes—
232C22×C4⋊C4C2318yes—
233C22×C4⋊C4C2312yes—
234C22×C4⋊C4C2312yes—
235C22×C4⋊C4C2312yes—
236C22×C4⋊C4C2312yes—
237C22×C4⋊C4C2311yescharacteristic
238C22×C42C2311yescharacteristic
239C22×C42C2311yescharacteristic
240C22×C42C2314yes—
241C22×C42C2312yes—
242C22×C42C2312yes—
243C22×C42C2311yescharacteristic
244#400C2314yes—
245#400C2318yes—
246#400C2318yes—
247#400C2314yes—
248#400C2314yes—
249#400C2318yes—
250#400C2318yes—
251#400C2314yes—
252#400C2314yes—
253#400C2314yes—
254#400C2314yes—
255#400C2314yes—
256#400C2318yes—
257#399C2318yes—
258#399C2318yes—
259#399C2318yes—
260#399C2318yes—
261#399C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2318yes—
265#398C2318yes—
266#398C2318yes—
267#398C2318yes—
268#398C2314yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2314yes—
273#398C2318yes—
274#398C2314yes—
275#398C2314yes—
276#398C2314yes—
277#398C2314yes—
278#398C2314yes—
279#398C2314yes—
280#396C2318yes—
281#396C2318yes—
282#396C2318yes—
283#396C2318yes—
284#396C2318yes—
285#396C2318yes—
286#395C2318yes—
287#395C2318yes—
288#395C2318yes—
289#395C2318yes—
290#395C2318yes—
291#393C2318yes—
292#391C2312yes—
293#391C2314yes—
294#391C2314yes—
295#391C2312yes—
296#391C2318yes—
297#391C2318yes—
298#390C2312yes—
299#390C2314yes—
300#390C2314yes—
301#390C2312yes—
302#390C2314yes—
303#390C2314yes—
304#389C2318yes—
305#389C2318yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2312yes—
313#389C2314yes—
314#389C2314yes—
315#389C2314yes—
316#389C2318yes—
317#389C2318yes—
318#389C2314yes—
319#389C2314yes—
320#389C2312yes—
321#389C2318yes—
322#389C2318yes—
323#389C2314yes—
324#389C2314yes—
325#389C2318yes—
326#389C2314yes—
327#389C2318yes—
328#389C2318yes—
329#389C2318yes—
330#389C2318yes—
331#389C2314yes—
332#389C2314yes—
333#389C2318yes—
334#389C2314yes—
335#389C2314yes—
336#389C2318yes—
337#389C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2318yes—
344#388C2314yes—
345#388C2314yes—
346#388C2314yes—
347#388C2314yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
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#387C2318yes—
369#387C2318yes—
370#386C2314yes—
371#386C2318yes—
372#386C2318yes—
373#386C2318yes—
374#386C2314yes—
375#386C2314yes—
376#386C2314yes—
377#386C2314yes—
378#386C2314yes—
379#386C2318yes—
380#385C2318yes—
381#385C2318yes—
382#385C2318yes—
383#385C2318yes—
384#385C2318yes—
385#385C2318yes—
386#385C2314yes—
387#385C2318yes—
388#385C2318yes—
389#385C2314yes—
390#385C2314yes—
391#385C2314yes—
392#385C2314yes—
393#385C2318yes—
394#385C2318yes—
395#385C2318yes—
396#385C2318yes—
397#385C2314yes—
398#385C2318yes—
399#385C2314yes—
400#385C2318yes—
401#385C2314yes—
402#384C2314yes—
403#384C2314yes—
404#384C2314yes—
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2318yes—
408#384C2311yescharacteristic
409#384C2314yes—
410#384C2314yes—
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#382C2314yes—
415#382C2312yes—
416#382C2312yes—
417#382C2314yes—
418#382C2314yes—
419#382C2318yes—
420#382C2312yes—
421#380C2318yes—
422#380C2318yes—
423#380C2314yes—
424#380C2314yes—
425#380C2314yes—
426#380C2314yes—
427#380C2318yes—
428#380C2318yes—
429#380C2318yes—
430#380C2312yes—
431#380C2312yes—
432#380C2312yes—
433#380C2312yes—
434#380C2312yes—
435#380C2312yes—
436#380C2318yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2312yes—
440C4×C4⋊C4C2312yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2318yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2318yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2312yes—
459C4×C22⋊C4C2318yes—
460C4×C22⋊C4C2318yes—
461C4×C22⋊C4C2314yes—
462C4×C22⋊C4C2314yes—
463#376C2312yes—
464#376C2312yes—
465#376C2312yes—
466#376C2312yes—
467C2×#95C2318yes—
468C2×#95C2311yescharacteristic
469C2×#95C2311yescharacteristic
470C2×#95C2311yescharacteristic
471C2×#95C2311yescharacteristic
472C2×#95C2312yes—
473C2×#95C2312yes—
474C2×#95C2312yes—
475C2×#95C2312yes—
476C2×#41—28no—
477C2×#41—28no—
478C2×#41C2×Q8116yes—
479C22×Q8C2412yes—
480C22×Q8C2418yes—
481C22×D4C2414yes—
482C22×D4C2412yes—
483C22×D4C2412yes—
484C22×D4C2412yes—
485C23×C4C2414yes—
486C23×C4C2411yescharacteristic
487C23×C4C2412yes—
488C23×C4C2412yes—
489C23×C4C2411yescharacteristic
490C23×C4C2411yescharacteristic
491C23×C4C2412yes—
492C23×C4C2418yes—
493C23×C4C2411yescharacteristic
494C23×C4C2418yes—
495C23×C4C2414yes—
496C23×C4C2414yes—
497C23×C4C2411yescharacteristic
498C23×C4C2411yescharacteristic
499C23×C4C2412yes—
500C23×C4C2411yescharacteristic
501C4⋊Q8—48no—
502C4⋊Q8—48no—
503C4⋊Q8—84no—
504C4⋊Q8C2×Q818yes—
505#127C2×Q818yes—
506#125—216no—
507#125—216no—
508#125—48no—
509#125—48no—
510#125—84no—
511#124C2×Q8116yes—
512C22⋊Q8—416no—
513C22⋊Q8—88no—
514C22⋊Q8—88no—
515C22⋊Q8—88no—
516#121C2×Q8116yes—
517#121C2×Q8116yes—
518C4×Q8—216no—
519C4×Q8—44no—
520C4×Q8—44no—
521C4×Q8—48no—
522C4×D4—232no—
523C4×D4—216no—
524C4×D4—44no—
525C4×D4—44no—
526C4×D4—48no—
527C4×D4—48no—
528C4×D4—48no—
529C4×D4—416no—
530C4×D4—84no—
531C4×D4—84no—
532C4×D4C2×Q8116yes—
533C4×D4C2×Q8116yes—
534#117—28no—
535#117—28no—
536#117—28no—
537#117—216no—
538#117—48no—
539#117—48no—
540C2×C4⋊C4—28no—
541C2×C4⋊C4—28no—
542C2×C4⋊C4—24no—
543C2×C4⋊C4—24no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—216no—
546C2×C4⋊C4—48no—
547C2×C4⋊C4—82no—
548C2×C4⋊C4—88no—
549C2×C4⋊C4—82no—
550C2×C4⋊C4—82no—
551C2×C4⋊C4—82no—
552C2×C4⋊C4#4118yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2418yes—
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⋊C4C2418yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C42—24no—
626C2×C42—24no—
627C2×C42—48no—
628C2×C42—82no—
629C2×C42—82no—
630C2×C42C2×Q818yes—
631C2×C42C2414yes—
632C2×C42C2412yes—
633C2×C42C2414yes—
634C2×C42C2418yes—
635C2×C42C2414yes—
636C2×C42C2412yes—
637C2×C42C2412yes—
638C2×C42C2412yes—
639C2×C42C2418yes—
640C2×C42C2414yes—
641C2×C42C2414yes—
642C2×C42C2414yes—
643C2×C42C2414yes—
644C2×C42C2414yes—
645C2×C42C2414yes—
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650#95C2418yes—
651#95C2414yes—
652#95C2412yes—
653#95C2412yes—
654#95C2412yes—
655#95C2412yes—
656#95C2412yes—
657#95C2412yes—
658#95C2412yes—
659#95C2412yes—
660#95C2414yes—
661#95C2414yes—
662#95C2414yes—
663#95C2414yes—
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#95C2414yes—
678#95C2414yes—
679#95C2418yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C2418yes—
686#95C2418yes—
687#95C2418yes—
688#95C2414yes—
689#95C2414yes—
690#95C2418yes—
691#95C2418yes—
692C24C2514yes—
693C24C2511yescharacteristic
694#41—264no—
695C2×Q8—24no—
696C2×Q8—24no—
697C2×Q8—48no—
698C2×Q8—48no—
699C2×Q8—48no—
700C2×Q8C22×Q818yes—
701C2×D4—28no—
702C2×D4—28no—
703C2×D4—24no—
704C2×D4—24no—
705C2×D4—42no—
706C2×D4—42no—
707C2×D4—42no—
708C2×D4—42no—
709C2×D4C22×Q8116yes—
710C2×D4C22×Q818yes—
711C2×D4C22×Q818yes—
712C2×D4C22×Q818yes—
713C22×C4—28no—
714C22×C4—28no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—24no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—216no—
723C22×C4—41no—
724C22×C4—41no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—41no—
728C22×C4—41no—
729C22×C4—41no—
730C22×C4—41no—
731C22×C4—42no—
732C22×C4—41no—
733C22×C4—41no—
734C22×C4—42no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—42no—
738C22×C4—42no—
739C22×C4—42no—
740C22×C4—44no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4—42no—
744C22×C4—48no—
745C22×C4—44no—
746C22×C4—48no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—41no—
750C22×C4—41no—
751C22×C4—48no—
752C22×C4—48no—
753C22×C4—48no—
754C22×C4C22×Q8116yes—
755C22×C4C22×Q814yes—
756C22×C4C22×Q814yes—
757C22×C4C22×Q814yes—
758C22×C4C2×#4118yes—
759C22×C4C2×#4114yes—
760C22×C4H(5,𝔽2)14yes—
761C22×C4C2512yes—
762C22×C4C2514yes—
763C22×C4C2512yes—
764C22×C4C2512yes—
765C22×C4C2514yes—
766C22×C4C2514yes—
767C22×C4C2514yes—
768C22×C4C2514yes—
769C22×C4C2514yes—
770C22×C4C2512yes—
771C22×C4C2514yes—
772C22×C4C2514yes—
773C22×C4C2514yes—
774C22×C4C2511yescharacteristic
775C22×C4C2511yescharacteristic
776C22×C4C2511yescharacteristic
777C22×C4C2511yescharacteristic
778C22×C4C2514yes—
779C22×C4C2514yes—
780C22×C4C2511yescharacteristic
781C22×C4C2511yescharacteristic
782C4⋊C4—24no—
783C4⋊C4—216no—
784C4⋊C4—216no—
785C4⋊C4—216no—
786C4⋊C4—24no—
787C4⋊C4—24no—
788C4⋊C4—24no—
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—48no—
798C4⋊C4—48no—
799C4⋊C4—44no—
800C4⋊C4—48no—
801C4⋊C4—48no—
802C4⋊C4—48no—
803C4⋊C4—48no—
804C4⋊C4—48no—
805C4⋊C4—42no—
806C4⋊C4—42no—
807C4⋊C4—42no—
808C4⋊C4—42no—
809C4⋊C4—48no—
810C4⋊C4—42no—
811C4⋊C4—42no—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—48no—
815C4⋊C4—44no—
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—44no—
827C4⋊C4—48no—
828C4⋊C4—48no—
829C4⋊C4—42no—
830C4⋊C4—42no—
831C4⋊C4—42no—
832C4⋊C4—42no—
833C4⋊C4C22×Q818yes—
834C4⋊C4C22×Q818yes—
835C4⋊C4C2×#4118yes—
836C4⋊C4C2×#4118yes—
837C22⋊C4—28no—
838C22⋊C4—28no—
839C22⋊C4—28no—
840C22⋊C4—216no—
841C22⋊C4—48no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—48no—
847C22⋊C4—48no—
848C22⋊C4—48no—
849C22⋊C4—48no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4C22×Q8116yes—
853C22⋊C4C22×Q8116yes—
854C42—24no—
855C42—24no—
856C42—216no—
857C42—28no—
858C42—24no—
859C42—24no—
860C42—28no—
861C42—28no—
862C42—44no—
863C42—44no—
864C42—44no—
865C42—44no—
866C42—44no—
867C42—44no—
868C42—48no—
869C42C22×Q814yes—
870C42C22×Q814yes—
871C42C22×Q814yes—
872C42C22×Q814yes—
873C23—21no—
874C23—21no—
875C23—21no—
876C23—21no—
877C23—24no—
878C23—24no—
879C23—24no—
880C23—24no—
881C23—24no—
882C23—24no—
883C23C23×Q818yes—
884C23C23×Q812yes—
885C23C22×#4112yes—
886C23C2×H(5,𝔽2)12yes—
887C23C2611yescharacteristic
888Q8—216no—
889Q8—168no—
890D4—232no—
891D4—216no—
892D4—48no—
893D4—48no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—24no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—24no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—232no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—24no—
915C2×C4—24no—
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—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—44no—
947C2×C4—44no—
948C2×C4—48no—
949C2×C4—44no—
950C2×C4—44no—
951C2×C4—48no—
952C2×C4—816no—
953C2×C4—82no—
954C2×C4—84no—
955C2×C4—84no—
956C2×C4—82no—
957C2×C4—88no—
958C2×C4—88no—
959C2×C4—168no—
960C2×C4#554116yes—
961C2×C4C23×Q812yes—
962C2×C4C23×Q812yes—
963C2×C4C23×Q812yes—
964C2×C4C23×Q812yes—
965C2×C4C23×Q818yes—
966C2×C4C23×Q812yes—
967C2×C4C23×Q812yes—
968C2×C4C22×#4118yes—
969C2×C4C22×#4112yes—
970C2×C4C22×#4112yes—
971C2×C4C2×H(5,𝔽2)12yes—
972C2×C4C2×H(5,𝔽2)12yes—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—22no—
979C22—28no—
980C22—28no—
981C22—28no—
982C22—44no—
983C22—44no—
984C22—44no—
985C22—44no—
986C22C2×#55414yes—
987C22C24×Q811yescharacteristic
988C22C23×#4111yescharacteristic
989C22C22×H(5,𝔽2)11yescharacteristic
990C22H(7,𝔽2)11yescharacteristic
991C22H(7,𝔽2)11yescharacteristic
992C222−1+611yescharacteristic
993C222−1+611yescharacteristic
994C4—28no—
995C4—22no—
996C4—22no—
997C4—22no—
998C4—22no—
999C4—28no—
1000C4—42no—
1001C4—44no—
1002C4—44no—
1003C4—42no—
1004C4—44no—
1005C4—42no—
1006C4—44no—
1007C4—44no—
1008C4—44no—
1009C4—44no—
1010C4—44no—
1011C4—44no—
1012C4—42no—
1013C4C2×#55414yes—
1014C4C2×#55414yes—
1015C2—24no—
1016C2—48no—
1017C2C22×#55411yescharacteristic
1018C2#6284711yescharacteristic
1019C2#6285111yescharacteristic
1020C2#6285411yescharacteristic
1021C2#6285411yescharacteristic
1022C2#6288011yescharacteristic
1023C2#6288811yescharacteristic
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. #45278C2semidirect
2. #45233C2semidirect
3. #45086C2semidirect
4. #44951C2semidirect
5. #39670C2semidirect
6. #39669C2semidirect
7. #39631C2semidirect
8. #39627C2semidirect
9. #38107C2semidirect
10. #38104C2semidirect
11. #38101C2semidirect
12. #38098C2semidirect
13. #35639C2semidirect
14. #35532C2semidirect
15. #35257C2semidirect
16. #35181C2semidirect
17. #35167C2semidirect
18. #34638C2semidirect
19. #34250C2semidirect
22. C2×#2330C2semidirect
181. #532Q8semidirect

Maximal subgroups

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

subgroupindex
#452782
#452332
#450862
#449512
#396702
#396692
#396312
#396272
#381072
#381042
#381012
#380982
#356392
#355322
#352572
#351812
#351672
#346382
#342502
#342062
C2×#23302
#340702