Finite Group Databasebeta

← #7712517

Subgroups — #7712517

Order 512.

4564 conjugacy classes of subgroups.

The subgroup lattice has 983 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59712C214yesmaximal, complemented
2#59499C214yesmaximal, complemented
3#45499C214yesmaximal, complemented
4#45498C214yesmaximal
5#39750C212yesmaximal, complemented
6#39658C214yesmaximal, complemented
7#39657C214yesmaximal, complemented
8#39653C214yesmaximal, complemented
9#39652C214yesmaximal, complemented
10#39366C212yesmaximal, complemented
11#37691C214yesmaximal, complemented
12#37567C212yesmaximal, complemented
13#37429C214yesmaximal, complemented
14#36645C211yesmaximal, characteristic, complemented
15#36635C211yesmaximal, characteristic, complemented
16#36563C212yesmaximal, complemented
17#36194C212yesmaximal, complemented
18#36189C212yesmaximal, complemented
19#36189C212yesmaximal, complemented
20#35283C212yesmaximal, complemented
21#35275C212yesmaximal, complemented
22#34385C212yesmaximal
23C4×#529C211yesmaximal, characteristic
24C2×#544C2214yes—
25C2×#533C2212yes—
26C2×#529C2211yescharacteristic
27#2868C2212yes—
28#2868C2212yes—
29#2864C2212yes—
30#2863C2214yes—
31#2862C2211yescharacteristic
32#2862C2212yes—
33#2859C2211yescharacteristic
34#2859C2212yes—
35#2859C2212yes—
36#2859C2212yes—
37#2857C2212yes—
38#2857C2214yes—
39#2857C2214yes—
40#2857C2212yes—
41#2857C2212yes—
42#2855C2214yes—
43#2851C2212yes—
44#2841C2218yes—
45#2805C2218yes—
46#2802C2218yes—
47#2799C2218yes—
48#2791C2218yes—
49#2790C2218yes—
50#2788C2218yes—
51#2768C2218yes—
52#2755C2218yes—
53#2755C2218yes—
54#2742C2218yes—
55#2732C2218yes—
56#2729C2218yes—
57#2720C2218yes—
58#2713C2218yes—
59#2692C2218yes—
60#2692C2218yes—
61#2667C2214yes—
62#2666C2218yes—
63#2665C2214yes—
64#2660C2214yes—
65#2660C2214yes—
66#2647C2214yes—
67#2628C2214yes—
68#2606C2214yes—
69#2605C2214yes—
70#2588C2218yes—
71#2582C2214yes—
72#2571C2214yes—
73#2570C2214yes—
74#2570C2214yes—
75#2567C2214yes—
76#2563C2214yes—
77#2556C2218yes—
78#2552C2214yes—
79#2552C2214yes—
80#2552C2214yes—
81#2551C2214yes—
82#2551C2214yes—
83#2550C2214yes—
84#2550C2214yes—
85#2538C2214yes—
86#2520C2218yes—
87#2511C2214yes—
88#2511C2214yes—
89#2511C2214yes—
90#2511C2214yes—
91#2507C2214yes—
92#2507C2214yes—
93#2507C2214yes—
94#2507C2214yes—
95#2497C2214yes—
96#2497C2214yes—
97#2497C2214yes—
98#2497C2214yes—
99#2492C2214yes—
100#2492C2214yes—
101#2492C2218yes—
102#2492C2214yes—
103#2492C2214yes—
104#2487C2214yes—
105#2487C2214yes—
106#2465C2218yes—
107#2462C2218yes—
108#2451C2214yes—
109#2451C2214yes—
110#2451C2214yes—
111#2451C2214yes—
112#2446C2218yes—
113#2442C2214yes—
114#2442C2214yes—
115#2441C2214yes—
116#2441C2214yes—
117#2440C2214yes—
118#2440C2214yes—
119#2440C2214yes—
120#2440C2214yes—
121#2439C2214yes—
122#2439C2214yes—
123#2423C2218yes—
124#2423C2214yes—
125#2423C2214yes—
126#2423C2214yes—
127#2423C2214yes—
128#2417C2214yes—
129#2417C2214yes—
130#2378C2214yes—
131#2377C2214yes—
132#2373C2218yes—
133#2369C2214yes—
134#2369C2214yes—
135#2360C2214yes—
136#2360C2214yes—
137#2355C2214yes—
138#2355C2214yes—
139#2354C2214yes—
140#2352C2214yes—
141#2352C2214yes—
142Q8×C4⋊C4C2214yes—
143#2345C2214yes—
144#2345C2214yes—
145#2337C2214yes—
146#2336C2214yes—
147#2335C2218yes—
148#2331C2214yes—
149#2317C2214yes—
150#2314C2214yes—
151C4×C4⋊Q8C2212yes—
152C4×C4⋊Q8C2214yes—
153C4×C4⋊Q8C2214yes—
154C4×C4⋊Q8C2212yes—
155C4×C4⋊Q8C2212yes—
156C4×#125C2212yes—
157C4×#125C2212yes—
158C4×#126C2212yes—
159C4×#126C2212yes—
160C4×#124C2212yes—
161C4×C22⋊Q8C2214yes—
162C4×C22⋊Q8C2212yes—
163C4×#123C2212yes—
164C4×#123C2212yes—
165C4×#121C2212yes—
166#2298C2212yes—
167#2295C2214yes—
168#2295C2211yescharacteristic
169#2293C2211yescharacteristic
170#2290C2212yes—
171#2285C2212yes—
172#2285C2211yescharacteristic
173#2285C2211yescharacteristic
174#2285C2212yes—
175C2×#384C2212yes—
176#2283C2212yes—
177#2283C2211yescharacteristic
178C42×Q8C2211yescharacteristic
179C42×D4C2211yescharacteristic
180C42×D4C2212yes—
181C4×#117C2212yes—
182C2×C43C2211yescharacteristic
183#544—416no—
184#533—48no—
185C2×C4⋊Q8C2312yes—
186C2×C4⋊Q8C2314yes—
187C2×C4⋊Q8C2314yes—
188C2×C4⋊Q8C2314yes—
189C2×C4⋊Q8C2314yes—
190C2×C4⋊Q8C2314yes—
191C2×C4⋊Q8C2314yes—
192C2×C4⋊Q8C2318yes—
193#529Q8116yescomplemented
194C2×#126C2312yes—
195C2×#125C2312yes—
196C2×#125C2314yes—
197C2×#125C2314yes—
198C2×#125C2318yes—
199C2×#125C2311yescharacteristic
200C2×#124C2311yescharacteristic
201C2×#123C2312yes—
202C2×C22⋊Q8C2314yes—
203C2×C22⋊Q8C2318yes—
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2314yes—
206C2×C22⋊Q8C2318yes—
207C2×C22⋊Q8C2318yes—
208C2×C22⋊Q8C2311yescharacteristic
209C2×#121C2311yescharacteristic
210C2×C4×Q8C2318yes—
211C2×C4×Q8C2314yes—
212C2×C4×Q8C2314yes—
213C2×C4×Q8C2314yes—
214C2×C4×Q8C2312yes—
215C2×C4×Q8C2311yescharacteristic
216C2×C4×D4C2312yes—
217C2×C4×D4C2312yes—
218C2×C4×D4C2312yes—
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2312yes—
221C2×#117C2312yes—
222C2×#117C2314yes—
223C2×#117C2312yes—
224C2×#117C2312yes—
225C2×#117C2312yes—
226C22×C4⋊C4C2314yes—
227C22×C4⋊C4C2314yes—
228C22×C4⋊C4C2314yes—
229C22×C42C2311yescharacteristic
230C22×C42C2311yescharacteristic
231C22×C42C2312yes—
232C22×C42C2312yes—
233C22×C42C2312yes—
234C22×C42C2311yescharacteristic
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#399C2318yes—
245#399C2318yes—
246#399C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#396C2318yes—
262#396C2318yes—
263#396C2318yes—
264#396C2318yes—
265#395C2318yes—
266#395C2318yes—
267#395C2318yes—
268#395C2318yes—
269#395C2318yes—
270#395C2318yes—
271#395C2318yes—
272#393C2318yes—
273#393C2318yes—
274#393C2318yes—
275#391C2314yes—
276#391C2314yes—
277#391C2318yes—
278#391C2318yes—
279#391C2314yes—
280#391C2318yes—
281#391C2318yes—
282#391C2318yes—
283#391C2314yes—
284#391C2314yes—
285#391C2314yes—
286#391C2314yes—
287#391C2318yes—
288#391C2318yes—
289#391C2314yes—
290#391C2318yes—
291#391C2318yes—
292#391C2312yes—
293#390C2318yes—
294#390C2312yes—
295#389C2314yes—
296#389C2312yes—
297#389C2312yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2318yes—
306#389C2318yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2318yes—
314#389C2318yes—
315#389C2318yes—
316#389C2314yes—
317#389C2318yes—
318#389C2314yes—
319#389C2314yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2318yes—
326#389C2318yes—
327#389C2318yes—
328#389C2318yes—
329#388C2312yes—
330#388C2312yes—
331#388C2312yes—
332#388C2312yes—
333#388C2312yes—
334#388C2312yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2312yes—
342#388C2312yes—
343#387C2312yes—
344#387C2312yes—
345#387C2312yes—
346#387C2312yes—
347#387C2312yes—
348#387C2312yes—
349#387C2318yes—
350#387C2312yes—
351#387C2312yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#386C2318yes—
372#386C2318yes—
373#386C2312yes—
374#386C2312yes—
375#385C2318yes—
376#385C2318yes—
377#385C2318yes—
378#385C2318yes—
379#385C2318yes—
380#385C2312yes—
381#385C2312yes—
382#384C2312yes—
383#384C2312yes—
384#384C2312yes—
385#384C2314yes—
386#384C2314yes—
387#384C2318yes—
388#384C2314yes—
389#384C2314yes—
390#384C2314yes—
391#384C2314yes—
392#384C2314yes—
393#384C2314yes—
394#384C2314yes—
395#383C2311yescharacteristic
396#383C2311yescharacteristic
397#383C2314yes—
398#382C2312yes—
399#382C2312yes—
400#382C2318yes—
401#382C2312yes—
402#382C2312yes—
403#382C2314yes—
404#382C2314yes—
405#382C2314yes—
406#382C2312yes—
407#382C2312yes—
408#381C2314yes—
409#381C2311yescharacteristic
410#381C2311yescharacteristic
411#380C2314yes—
412#380C2314yes—
413#380C2314yes—
414#380C2314yes—
415#380C2314yes—
416#380C2314yes—
417#380C2312yes—
418#380C2314yes—
419#380C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2318yes—
423#380C2318yes—
424#380C2314yes—
425#380C2314yes—
426C4×C4⋊C4C2312yes—
427C4×C4⋊C4C2312yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2312yes—
430C4×C4⋊C4C2312yes—
431C4×C4⋊C4C2312yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2318yes—
434C4×C4⋊C4C2312yes—
435C4×C4⋊C4C2312yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2318yes—
450C4×C4⋊C4C2318yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2312yes—
455C4×C22⋊C4C2312yes—
456C4×C22⋊C4C2312yes—
457C4×C22⋊C4C2312yes—
458C4×C22⋊C4C2312yes—
459C4×C22⋊C4C2312yes—
460C4×C22⋊C4C2312yes—
461C4×C22⋊C4C2314yes—
462C4×C22⋊C4C2318yes—
463C4×C22⋊C4C2318yes—
464C4×C22⋊C4C2312yes—
465C4×C22⋊C4C2312yes—
466C4×C22⋊C4C2312yes—
467C4×C22⋊C4C2312yes—
468C4×C22⋊C4C2312yes—
469C4×C22⋊C4C2312yes—
470C4×C22⋊C4C2312yes—
471#376C2312yes—
472#376C2314yes—
473#376C2312yes—
474C43C2312yes—
475C43C2311yescharacteristic
476C43C2312yes—
477C43C2311yescharacteristic
478C43C2312yes—
479C43C2311yescharacteristic
480C43C2311yescharacteristic
481C22×Q8C2414yes—
482C22×Q8C2418yes—
483C22×Q8C2418yes—
484C22×Q8C2411yescharacteristic
485C22×D4C2412yes—
486C22×D4C2411yescharacteristic
487C23×C4C2412yes—
488C23×C4C2412yes—
489C23×C4C2412yes—
490C23×C4C2412yes—
491C23×C4C2411yescharacteristic
492C23×C4C2412yes—
493C23×C4C2418yes—
494C23×C4C2411yescharacteristic
495C23×C4C2411yescharacteristic
496C4⋊Q8—216no—
497C4⋊Q8—28no—
498C4⋊Q8—48no—
499C4⋊Q8—48no—
500C4⋊Q8—48no—
501C4⋊Q8—48no—
502C4⋊Q8—48no—
503C4⋊Q8—416no—
504#126C2×Q8116yes—
505#125—28no—
506#125—48no—
507#125—48no—
508#125—416no—
509#125C2×Q818yes—
510#124C2×Q818yes—
511#123C2×Q8116yes—
512C22⋊Q8—416no—
513C22⋊Q8—416no—
514C22⋊Q8—48no—
515C22⋊Q8—48no—
516C22⋊Q8—48no—
517C22⋊Q8—416no—
518C22⋊Q8C2×Q818yes—
519#121C2×Q818yes—
520C4×Q8—44no—
521C4×Q8—48no—
522C4×Q8—48no—
523C4×Q8—48no—
524C4×Q8—416no—
525C4×Q8C2×Q818yes—
526C4×D4—44no—
527C4×D4—44no—
528C4×D4—44no—
529C4×D4C2×Q818yes—
530C4×D4C2×Q8116yes—
531#117—28no—
532#117—44no—
533#117—44no—
534#117—48no—
535#117C2×Q8116yes—
536C2×C4⋊C4—48no—
537C2×C4⋊C4—48no—
538C2×C4⋊C4—48no—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2412yes—
584C2×C22⋊C4C2412yes—
585C2×C22⋊C4C2412yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2412yes—
590C2×C22⋊C4C2412yes—
591C2×C22⋊C4C2412yes—
592C2×C22⋊C4C2412yes—
593C2×C22⋊C4C2412yes—
594C2×C22⋊C4C2412yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2412yes—
599C2×C22⋊C4C2412yes—
600C2×C22⋊C4C2412yes—
601C2×C22⋊C4C2412yes—
602C2×C22⋊C4C2412yes—
603C2×C42—24no—
604C2×C42—24no—
605C2×C42—28no—
606C2×C42—44no—
607C2×C42—44no—
608C2×C42C2×Q818yes—
609C2×C42C2412yes—
610C2×C42C2412yes—
611C2×C42C2412yes—
612C2×C42C2412yes—
613C2×C42C2412yes—
614C2×C42C2412yes—
615C2×C42C2412yes—
616C2×C42C2412yes—
617C2×C42C2411yescharacteristic
618C2×C42C2412yes—
619C2×C42C2412yes—
620C2×C42C2412yes—
621C2×C42C2411yescharacteristic
622C2×C42C2412yes—
623C2×C42C2412yes—
624C2×C42C2412yes—
625C2×C42C2414yes—
626C2×C42C2414yes—
627C2×C42C2418yes—
628C2×C42C2418yes—
629C2×C42C2418yes—
630C2×C42C2418yes—
631C2×C42C2412yes—
632C2×C42C2412yes—
633C2×C42C2412yes—
634C2×C42C2412yes—
635C2×C42C2411yescharacteristic
636C2×C42C2412yes—
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642#95C2418yes—
643#95C2412yes—
644#95C2412yes—
645#95C2412yes—
646#95C2412yes—
647#95C2412yes—
648#95C2412yes—
649#95C2412yes—
650#95C2412yes—
651#95C2414yes—
652#95C2414yes—
653#95C2411yescharacteristic
654#95C2411yescharacteristic
655#95C2412yes—
656#95C2412yes—
657#95C2412yes—
658#95C2412yes—
659#95C2412yes—
660#95C2412yes—
661#95C2412yes—
662#95C2412yes—
663#95C2418yes—
664#95C2418yes—
665#95C2414yes—
666#95C2414yes—
667#95C2418yes—
668#95C2411yescharacteristic
669#95C2411yescharacteristic
670#95C2412yes—
671#95C2412yes—
672#95C2418yes—
673#95C2418yes—
674#95C2418yes—
675#95C2418yes—
676#95C2418yes—
677#95C2418yes—
678#95C2418yes—
679#95C2418yes—
680#95C2418yes—
681#95C2418yes—
682#95C2418yes—
683#95C2418yes—
684#95C2418yes—
685#95C2418yes—
686#95C2418yes—
687#95C2418yes—
688#95C2418yes—
689C24C2512yes—
690C24C2511yescharacteristic
691C2×Q8—216no—
692C2×Q8—28no—
693C2×Q8—28no—
694C2×Q8—28no—
695C2×Q8—42no—
696C2×Q8—48no—
697C2×Q8—48no—
698C2×Q8—48no—
699C2×Q8—48no—
700C2×Q8—48no—
701C2×Q8C22×Q814yes—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4C22×Q818yes—
706C2×D4C22×Q814yes—
707C22×C4—22no—
708C22×C4—24no—
709C22×C4—24no—
710C22×C4—22no—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—24no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—24no—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—24no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—48no—
726C22×C4—48no—
727C22×C4—48no—
728C22×C4C22×Q814yes—
729C22×C4C22×Q818yes—
730C22×C4C22×Q814yes—
731C22×C4C22×Q814yes—
732C22×C4C2512yes—
733C22×C4C2518yes—
734C22×C4C2512yes—
735C22×C4C2512yes—
736C22×C4C2512yes—
737C22×C4C2518yes—
738C22×C4C2518yes—
739C22×C4C2518yes—
740C22×C4C2512yes—
741C22×C4C2512yes—
742C22×C4C2511yescharacteristic
743C22×C4C2511yescharacteristic
744C22×C4C2511yescharacteristic
745C22×C4C2512yes—
746C22×C4C2512yes—
747C22×C4C2512yes—
748C22×C4C2511yescharacteristic
749C22×C4C2511yescharacteristic
750C22×C4C2512yes—
751C22×C4C2511yescharacteristic
752C22×C4C2512yes—
753C4⋊C4—28no—
754C4⋊C4—28no—
755C4⋊C4—24no—
756C4⋊C4—24no—
757C4⋊C4—28no—
758C4⋊C4—216no—
759C4⋊C4—216no—
760C4⋊C4—28no—
761C4⋊C4—28no—
762C4⋊C4—28no—
763C4⋊C4—28no—
764C4⋊C4—28no—
765C4⋊C4—28no—
766C4⋊C4—28no—
767C4⋊C4—28no—
768C4⋊C4—48no—
769C4⋊C4—48no—
770C4⋊C4—48no—
771C4⋊C4—42no—
772C4⋊C4—42no—
773C4⋊C4—42no—
774C4⋊C4—42no—
775C4⋊C4—42no—
776C4⋊C4—42no—
777C4⋊C4—48no—
778C4⋊C4—48no—
779C4⋊C4—48no—
780C4⋊C4—48no—
781C4⋊C4—48no—
782C4⋊C4—48no—
783C4⋊C4—48no—
784C4⋊C4—48no—
785C4⋊C4—48no—
786C4⋊C4—48no—
787C4⋊C4—48no—
788C4⋊C4—48no—
789C4⋊C4—48no—
790C4⋊C4—48no—
791C4⋊C4—48no—
792C4⋊C4C22×Q818yes—
793C4⋊C4C22×Q818yes—
794C4⋊C4C22×Q814yes—
795C4⋊C4C22×Q818yes—
796C4⋊C4C22×Q814yes—
797C4⋊C4C22×Q818yes—
798C22⋊C4—24no—
799C22⋊C4—24no—
800C22⋊C4—44no—
801C22⋊C4—48no—
802C22⋊C4—44no—
803C22⋊C4—42no—
804C22⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—42no—
807C22⋊C4—42no—
808C22⋊C4—42no—
809C22⋊C4—48no—
810C22⋊C4—48no—
811C22⋊C4—48no—
812C22⋊C4C22×Q818yes—
813C22⋊C4C22×Q818yes—
814C22⋊C4C22×Q818yes—
815C22⋊C4C22×Q818yes—
816C22⋊C4C22×Q818yes—
817C42—24no—
818C42—22no—
819C42—24no—
820C42—24no—
821C42—24no—
822C42—24no—
823C42—22no—
824C42—24no—
825C42—24no—
826C42—24no—
827C42—24no—
828C42—24no—
829C42—24no—
830C42—24no—
831C42—24no—
832C42—24no—
833C42—42no—
834C42—42no—
835C42—42no—
836C42—42no—
837C42—44no—
838C42—44no—
839C42—48no—
840C42—48no—
841C42—48no—
842C42—48no—
843C42C22×Q814yes—
844C42C22×Q814yes—
845C42C22×Q814yes—
846C42C22×Q814yes—
847C42C22×Q818yes—
848C42H(5,𝔽2)14yes—
849C422−1+414yes—
850C23—22no—
851C23—21no—
852C23—22no—
853C23—21no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23C23×Q814yes—
861C23C23×Q812yes—
862C23C2611yescharacteristic
863Q8—44no—
864Q8—416no—
865Q8—816no—
866Q8—168no—
867D4—44no—
868D4—48no—
869C2×C4—21no—
870C2×C4—22no—
871C2×C4—21no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—28no—
884C2×C4—216no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—28no—
889C2×C4—28no—
890C2×C4—28no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—28no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—28no—
903C2×C4—22no—
904C2×C4—28no—
905C2×C4—28no—
906C2×C4—28no—
907C2×C4—28no—
908C2×C4—28no—
909C2×C4—28no—
910C2×C4—28no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—44no—
916C2×C4—44no—
917C2×C4—48no—
918C2×C4—48no—
919C2×C4—48no—
920C2×C4—48no—
921C2×C4—168no—
922C2×C4C23×Q812yes—
923C2×C4C23×Q812yes—
924C2×C4C23×Q812yes—
925C2×C4C23×Q812yes—
926C2×C4C23×Q812yes—
927C2×C4C23×Q814yes—
928C2×C4C23×Q814yes—
929C2×C4C23×Q814yes—
930C2×C4C23×Q812yes—
931C2×C4C2×H(5,𝔽2)14yes—
932C2×C4C2×H(5,𝔽2)12yes—
933C2×C4C2×2−1+412yes—
934C2×C4C2×2−1+414yes—
935C2×C4#58514yes—
936C2×C4#58514yes—
937C22—24no—
938C22—22no—
939C22—22no—
940C22—22no—
941C22—24no—
942C22—24no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22C24×Q811yescharacteristic
950C22C22×H(5,𝔽2)11yescharacteristic
951C22C22×2−1+411yescharacteristic
952C22C2×#58512yes—
953C22C2×#58512yes—
954C4—22no—
955C4—24no—
956C4—22no—
957C4—22no—
958C4—22no—
959C4—22no—
960C4—24no—
961C4—24no—
962C4—24no—
963C4—42no—
964C4—42no—
965C4—42no—
966C4—48no—
967C4—42no—
968C4—42no—
969C4—48no—
970C4—48no—
971C4—48no—
972C4—42no—
973C4#350314yes—
974C4#356518yes—
975C2—42no—
976C2—44no—
977C2C2×#356512yes—
978C2C2×#350311yescharacteristic
979C2#6281311yescharacteristic
980C2#6281311yescharacteristic
981C2#6283612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59712C2semidirect
2. #59499C2semidirect
3. #45499C2semidirect
5. #39750C2semidirect
6. #39658C2semidirect
7. #39657C2semidirect
8. #39653C2semidirect
9. #39652C2semidirect
10. #39366C2semidirect
11. #37691C2semidirect
12. #37567C2semidirect
13. #37429C2semidirect
14. #36645C2semidirect
15. #36635C2semidirect
16. #36563C2semidirect
17. #36194C2semidirect
18. #36189C2semidirect
19. #36189C2semidirect
20. #35283C2semidirect
21. #35275C2semidirect
193. #529Q8semidirect

Maximal subgroups

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

subgroupindex
#597122
#594992
#454992
#454982
#397502
#396582
#396572
#396532
#396522
#393662
#376912
#375672
#374292
#366452
#366352
#365632
#361942
#361892
#352832
#352752
#343852
C4×#5292