Finite Group Databasebeta

← #7720071

Subgroups — #7720071

Order 512.

4928 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#50678C218yesmaximal, complemented
2#50676C214yesmaximal, complemented
3#50675C214yesmaximal, complemented
4#45434C212yesmaximal, complemented
5#45430C212yesmaximal, complemented
6#45393C214yesmaximal, complemented
7#45350C212yesmaximal, complemented
8#45211C212yesmaximal, complemented
9#45147C214yesmaximal, complemented
10#39418C214yesmaximal, complemented
11#39417C214yesmaximal, complemented
12#39387C212yesmaximal, complemented
13#39385C212yesmaximal, complemented
14#37384C214yesmaximal, complemented
15#36598C212yesmaximal, complemented
16#36591C212yesmaximal, complemented
17#35318C214yesmaximal, complemented
18#35317C211yesmaximal, characteristic, complemented
19#35279C211yesmaximal, characteristic, complemented
20#35190C211yesmaximal, characteristic
21#34625C211yesmaximal, characteristic, complemented
22#34393C211yesmaximal, characteristic, complemented
23#34371C211yesmaximal, characteristic, complemented
24#34125C211yesmaximal, characteristic, complemented
25C2×#542C2214yes—
26C2×#541C2214yes—
27C2×#536C2214yes—
28C2×#532C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C2×C4×#41C2211yescharacteristic
31#2868C2212yes—
32#2862C2214yes—
33#2861C2214yes—
34#2858C2212yes—
35#2857C2214yes—
36#2850C2214yes—
37#2777C2218yes—
38#2773C2218yes—
39#2768C2218yes—
40#2748C2218yes—
41#2743C2218yes—
42#2741C2218yes—
43#2740C2218yes—
44#2738C2218yes—
45#2730C2218yes—
46#2721C2218yes—
47#2721C2218yes—
48#2707C2218yes—
49#2706C2218yes—
50#2705C2218yes—
51#2705C2218yes—
52#2704C2218yes—
53#2702C2218yes—
54#2700C2218yes—
55#2698C2218yes—
56#2687C2218yes—
57#2667C2212yes—
58#2666C2214yes—
59#2665C2212yes—
60#2660C2212yes—
61#2658C2212yes—
62#2658C2212yes—
63#2647C2212yes—
64#2635C2214yes—
65#2629C2212yes—
66#2628C2212yes—
67#2628C2214yes—
68#2621C2214yes—
69#2620C2214yes—
70#2598C2214yes—
71#2595C2218yes—
72#2582C2214yes—
73#2571C2214yes—
74#2570C2218yes—
75#2568C2211yescharacteristic
76#2568C2212yes—
77#2567C2212yes—
78#2563C2212yes—
79#2560C2218yes—
80#2558C2218yes—
81#2557C2218yes—
82#2556C2218yes—
83#2556C2218yes—
84#2556C2218yes—
85#2554C2218yes—
86#2553C2218yes—
87#2553C2218yes—
88#2553C2218yes—
89#2552C2214yes—
90#2552C2214yes—
91#2549C2218yes—
92#2548C2214yes—
93#2548C2211yescharacteristic
94#2542C2212yes—
95#2542C2211yescharacteristic
96#2542C2212yes—
97#2542C2212yes—
98#2542C2214yes—
99#2541C2211yescharacteristic
100#2538C2214yes—
101#2521C2218yes—
102#2521C2218yes—
103#2519C2218yes—
104#2519C2218yes—
105#2516C2218yes—
106#2513C2214yes—
107#2512C2214yes—
108#2512C2214yes—
109#2512C2214yes—
110#2511C2218yes—
111#2501C2214yes—
112#2501C2212yes—
113#2501C2212yes—
114#2500C2212yes—
115#2488C2218yes—
116#2487C2214yes—
117#2448C2214yes—
118#2448C2214yes—
119#2447C2214yes—
120#2446C2214yes—
121#2446C2214yes—
122#2445C2214yes—
123#2431C2212yes—
124#2429C2214yes—
125#2429C2214yes—
126#2427C2214yes—
127#2426C2214yes—
128#2409C2212yes—
129#2409C2212yes—
130#2407C2214yes—
131#2402C2212yes—
132#2399C2212yes—
133#2396C2214yes—
134#2381C2214yes—
135#2377C2214yes—
136#2367C2214yes—
137#2366C2212yes—
138#2365C2212yes—
139#2365C2212yes—
140#2365C2212yes—
141#2357C2212yes—
142#2357C2211yescharacteristic
143#2357C2211yescharacteristic
144#2357C2212yes—
145#2357C2212yes—
146#2357C2214yes—
147#2355C2214yes—
148#2355C2214yes—
149#2351C2211yescharacteristic
150#2351C2211yescharacteristic
151#2349C2212yes—
152#2347C2212yes—
153#2347C2214yes—
154#2345C2214yes—
155#2341C2212yes—
156#2341C2212yes—
157Q8×C22⋊C4C2214yes—
158#2339C2212yes—
159#2331C2212yes—
160#2331C2212yes—
161#2328C2212yes—
162#2327C2214yes—
163#2326C2214yes—
164#2326C2212yes—
165#2324C2214yes—
166#2318C2214yes—
167#2317C2212yes—
168#2313C2214yes—
169#2311C2212yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2214yes—
172C4×#125C2212yes—
173C4×#124C2214yes—
174#2293C2212yes—
175#2293C2214yes—
176#2285C2211yescharacteristic
177#2283C2212yes—
178#2283C2211yescharacteristic
179#2283C2211yescharacteristic
180C42×Q8C2212yes—
181C4×#117C2211yescharacteristic
182C4×#117C2212yes—
183C22×#41C2311yescharacteristic
184C22×#41C2312yes—
185C23×Q8C2312yes—
186#542—416no—
187#541—416no—
188#536—416no—
189#532—28no—
190C2×C4⋊Q8—28no—
191C2×C4⋊Q8C2312yes—
192C2×C4⋊Q8C2314yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2311yescharacteristic
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2314yes—
199C2×#127C2311yescharacteristic
200C2×#127C2312yes—
201C2×#126C2318yes—
202C2×#126C2318yes—
203C2×#126C2318yes—
204C2×#125C2312yes—
205C2×#125C2318yes—
206C2×#125C2318yes—
207C2×#124C2312yes—
208C2×#124C2312yes—
209C2×#124C2314yes—
210C2×#124C2314yes—
211C2×#124C2318yes—
212C2×#123C2318yes—
213C2×#123C2318yes—
214C2×#123C2318yes—
215C2×C22⋊Q8C2318yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2318yes—
220C2×C22⋊Q8C2318yes—
221C2×#121C2312yes—
222C2×#121C2312yes—
223C2×#121C2314yes—
224C4×#41—28no—
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2314yes—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2312yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2314yes—
240C2×C4×D4C2314yes—
241C2×#117C2311yescharacteristic
242C2×#117C2312yes—
243C2×#117C2314yes—
244C2×#117C2312yes—
245C2×#117C2312yes—
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2312yes—
248C22×C42C2312yes—
249C22×C42C2311yescharacteristic
250#400C2314yes—
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2314yes—
255#400C2314yes—
256#400C2314yes—
257#399C2314yes—
258#399C2314yes—
259#399C2318yes—
260#399C2318yes—
261#399C2314yes—
262#399C2314yes—
263#399C2314yes—
264#399C2318yes—
265#399C2314yes—
266#399C2318yes—
267#398C2314yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2314yes—
273#398C2314yes—
274#398C2314yes—
275#398C2314yes—
276#398C2314yes—
277#398C2318yes—
278#398C2318yes—
279#397C2318yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#396C2318yes—
286#396C2318yes—
287#396C2314yes—
288#396C2314yes—
289#396C2318yes—
290#396C2318yes—
291#396C2318yes—
292#395C2314yes—
293#395C2314yes—
294#395C2314yes—
295#395C2314yes—
296#395C2314yes—
297#394C2318yes—
298#394C2314yes—
299#394C2318yes—
300#394C2318yes—
301#394C2318yes—
302#394C2318yes—
303#393C2314yes—
304#393C2314yes—
305#393C2314yes—
306#392C2314yes—
307#392C2318yes—
308#391C2318yes—
309#391C2314yes—
310#391C2314yes—
311#391C2314yes—
312#391C2314yes—
313#391C2312yes—
314#391C2314yes—
315#391C2314yes—
316#391C2318yes—
317#391C2314yes—
318#391C2314yes—
319#391C2318yes—
320#391C2318yes—
321#390C2318yes—
322#390C2314yes—
323#390C2318yes—
324#390C2314yes—
325#390C2314yes—
326#390C2312yes—
327#390C2312yes—
328#390C2312yes—
329#390C2314yes—
330#390C2314yes—
331#390C2312yes—
332#390C2314yes—
333#390C2314yes—
334#390C2312yes—
335#390C2314yes—
336#390C2314yes—
337#390C2314yes—
338#389C2312yes—
339#389C2312yes—
340#389C2314yes—
341#389C2318yes—
342#389C2318yes—
343#389C2312yes—
344#389C2312yes—
345#389C2318yes—
346#389C2314yes—
347#389C2314yes—
348#389C2318yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2312yes—
353#389C2312yes—
354#389C2318yes—
355#389C2318yes—
356#388C2314yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2314yes—
368#388C2314yes—
369#388C2314yes—
370#388C2314yes—
371#388C2314yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#387C2318yes—
378#387C2314yes—
379#387C2314yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#386C2318yes—
391#386C2314yes—
392#386C2314yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#385C2314yes—
399#385C2314yes—
400#385C2318yes—
401#385C2318yes—
402#385C2318yes—
403#385C2318yes—
404#384C2312yes—
405#384C2314yes—
406#384C2314yes—
407#384C2314yes—
408#384C2312yes—
409#384C2312yes—
410#384C2314yes—
411#384C2314yes—
412#383C2312yes—
413#383C2312yes—
414#383C2314yes—
415#382C2312yes—
416#382C2314yes—
417#382C2312yes—
418#382C2318yes—
419#382C2318yes—
420#382C2312yes—
421#382C2312yes—
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#382C2312yes—
425#382C2312yes—
426#381C2312yes—
427#381C2312yes—
428#381C2314yes—
429#381C2312yes—
430#381C2312yes—
431#381C2318yes—
432#380C2318yes—
433#380C2318yes—
434#380C2318yes—
435#380C2314yes—
436#380C2312yes—
437#380C2311yescharacteristic
438#380C2312yes—
439#380C2311yescharacteristic
440#380C2314yes—
441#380C2312yes—
442#380C2318yes—
443C4×C4⋊C4C2318yes—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2318yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2314yes—
467C4×C22⋊C4C2314yes—
468C4×C22⋊C4C2318yes—
469C4×C22⋊C4C2312yes—
470C4×C22⋊C4C2318yes—
471C4×C22⋊C4C2312yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2312yes—
474C4×C22⋊C4C2311yescharacteristic
475C4×C22⋊C4C2311yescharacteristic
476C4×C22⋊C4C2312yes—
477C4×C22⋊C4C2312yes—
478C4×C22⋊C4C2318yes—
479C4×C22⋊C4C2314yes—
480#376C2312yes—
481#376C2312yes—
482#376C2311yescharacteristic
483#376C2311yescharacteristic
484C2×#95C2314yes—
485C43C2312yes—
486C43C2314yes—
487C2×#41—24no—
488C2×#41—24no—
489C2×#41—28no—
490C2×#41—42no—
491C2×#41—48no—
492C22×Q8—28no—
493C22×Q8—48no—
494C22×Q8C2414yes—
495C22×Q8C2412yes—
496C22×Q8C2411yescharacteristic
497C22×Q8C2414yes—
498C22×Q8C2414yes—
499C22×D4C2412yes—
500C22×D4C2412yes—
501C22×D4C2411yescharacteristic
502C22×D4C2412yes—
503C22×D4C2412yes—
504C22×D4C2414yes—
505C22×D4C2418yes—
506C23×C4C2412yes—
507C23×C4C2412yes—
508C23×C4C2411yescharacteristic
509C23×C4C2411yescharacteristic
510C23×C4C2414yes—
511C23×C4C2414yes—
512C23×C4C2412yes—
513C23×C4C2418yes—
514C23×C4C2411yescharacteristic
515C4⋊Q8—28no—
516C4⋊Q8—28no—
517C4⋊Q8—28no—
518C4⋊Q8—28no—
519C4⋊Q8—24no—
520C4⋊Q8—216no—
521C4⋊Q8—28no—
522C4⋊Q8—48no—
523#127—24no—
524#127—44no—
525#126—416no—
526#126—416no—
527#126—416no—
528#125—28no—
529#125—416no—
530#125—416no—
531#124—28no—
532#124—28no—
533#124—216no—
534#124—48no—
535#124—416no—
536#123—416no—
537#123—416no—
538#123—416no—
539C22⋊Q8—416no—
540C22⋊Q8—416no—
541C22⋊Q8—416no—
542C22⋊Q8—48no—
543C22⋊Q8—48no—
544C22⋊Q8—48no—
545#121—28no—
546#121—28no—
547#121—48no—
548C4×Q8—28no—
549C4×Q8—24no—
550C4×Q8—24no—
551C4×Q8—48no—
552C4×Q8—44no—
553C4×Q8—48no—
554C4×Q8—48no—
555C4×Q8—48no—
556C4×D4—28no—
557C4×D4—28no—
558C4×D4—24no—
559C4×D4—24no—
560C4×D4—28no—
561C4×D4—28no—
562C4×D4—48no—
563C4×D4—48no—
564#117—24no—
565#117—28no—
566#117—28no—
567#117—216no—
568#117—44no—
569C2×C4⋊C4—28no—
570C2×C4⋊C4—28no—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C22⋊C4C2412yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2412yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2412yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2412yes—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C42—28no—
643C2×C42#4118yes—
644C2×C42C2412yes—
645C2×C42C2414yes—
646C2×C42C2414yes—
647C2×C42C2412yes—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2412yes—
651C2×C42C2412yes—
652C2×C42C2412yes—
653C2×C42C2414yes—
654C2×C42C2412yes—
655C2×C42C2418yes—
656C2×C42C2418yes—
657C2×C42C2418yes—
658C2×C42C2414yes—
659C2×C42C2414yes—
660C2×C42C2414yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2412yes—
668#95C2412yes—
669#95C2412yes—
670#95C2418yes—
671#95C2411yescharacteristic
672#95C2412yes—
673#95C2411yescharacteristic
674#95C2414yes—
675#95C2412yes—
676#95C2412yes—
677#95C2412yes—
678#95C2411yescharacteristic
679#95C2411yescharacteristic
680#95C2414yes—
681#95C2414yes—
682#95C2412yes—
683#95C2412yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2418yes—
688#95C2418yes—
689#95C2418yes—
690#95C2414yes—
691#95C2414yes—
692#95C2418yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2418yes—
697#95C2418yes—
698#95C2414yes—
699#95C2418yes—
700#95C2418yes—
701#95C2414yes—
702#95C2418yes—
703#95C2412yes—
704#95C2412yes—
705#95C2418yes—
706#95C2418yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710C24C2512yes—
711C24C2514yes—
712C24C2511yescharacteristic
713#41—416no—
714#41—816no—
715C2×Q8—22no—
716C2×Q8—24no—
717C2×Q8—28no—
718C2×Q8—28no—
719C2×Q8—28no—
720C2×Q8—28no—
721C2×Q8—28no—
722C2×Q8—28no—
723C2×Q8—22no—
724C2×Q8—44no—
725C2×Q8—48no—
726C2×Q8—44no—
727C2×Q8—816no—
728C2×Q82−1+414yes—
729C2×D4—24no—
730C2×D4—28no—
731C2×D4—22no—
732C2×D4—24no—
733C2×D4—24no—
734C2×D4—24no—
735C2×D4—28no—
736C2×D4—24no—
737C2×D4—24no—
738C2×D4—22no—
739C2×D4—24no—
740C2×D4—22no—
741C2×D4—42no—
742C2×D4—48no—
743C2×D4—44no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—48no—
747C22×C4—24no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—28no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—28no—
754C22×C4—24no—
755C22×C4—24no—
756C22×C4—28no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—48no—
760C22×C4—48no—
761C22×C4—44no—
762C22×C4—48no—
763C22×C4—48no—
764C22×C4—48no—
765C22×C4C2×#4114yes—
766C22×C4C2×#4114yes—
767C22×C4C2×#4114yes—
768C22×C4C2512yes—
769C22×C4C2514yes—
770C22×C4C2514yes—
771C22×C4C2514yes—
772C22×C4C2514yes—
773C22×C4C2512yes—
774C22×C4C2514yes—
775C22×C4C2512yes—
776C22×C4C2514yes—
777C22×C4C2518yes—
778C22×C4C2514yes—
779C22×C4C2512yes—
780C22×C4C2511yescharacteristic
781C22×C4C2511yescharacteristic
782C22×C4C2511yescharacteristic
783C22×C4C2511yescharacteristic
784C22×C4C2512yes—
785C22×C4C2512yes—
786C22×C4C2512yes—
787C22×C4C2511yescharacteristic
788C22×C4C2511yescharacteristic
789C4⋊C4—28no—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—28no—
793C4⋊C4—24no—
794C4⋊C4—24no—
795C4⋊C4—22no—
796C4⋊C4—22no—
797C4⋊C4—24no—
798C4⋊C4—24no—
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—28no—
802C4⋊C4—28no—
803C4⋊C4—24no—
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—216no—
808C4⋊C4—216no—
809C4⋊C4—28no—
810C4⋊C4—28no—
811C4⋊C4—28no—
812C4⋊C4—28no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—44no—
816C4⋊C4—44no—
817C4⋊C4—44no—
818C4⋊C4—44no—
819C4⋊C4—44no—
820C4⋊C4—44no—
821C4⋊C4—44no—
822C4⋊C4—44no—
823C4⋊C4—44no—
824C4⋊C4—48no—
825C4⋊C4—48no—
826C4⋊C4—48no—
827C4⋊C4—48no—
828C4⋊C4—48no—
829C4⋊C4—48no—
830C4⋊C4—48no—
831C4⋊C4—48no—
832C22⋊C4—24no—
833C22⋊C4—24no—
834C22⋊C4—24no—
835C22⋊C4—28no—
836C22⋊C4—28no—
837C22⋊C4—24no—
838C22⋊C4—24no—
839C22⋊C4—28no—
840C22⋊C4—28no—
841C22⋊C4—216no—
842C22⋊C4—216no—
843C22⋊C4—216no—
844C22⋊C4—48no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—48no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—42no—
851C22⋊C4—42no—
852C22⋊C4—48no—
853C22⋊C4—48no—
854C22⋊C4—48no—
855C22⋊C4—48no—
856C22⋊C4—48no—
857C22⋊C4—48no—
858C22⋊C4—48no—
859C22⋊C4—48no—
860C42—24no—
861C42—24no—
862C42—24no—
863C42—28no—
864C42—24no—
865C42—28no—
866C42—24no—
867C42—24no—
868C42—28no—
869C42—24no—
870C42—24no—
871C42—42no—
872C42—44no—
873C42—42no—
874C42—44no—
875C42—44no—
876C42—48no—
877C42—48no—
878C42—48no—
879C42C2×#4114yes—
880C42C2×#4114yes—
881C42C2×#4114yes—
882C42C2×#4114yes—
883C42H(5,𝔽2)18yes—
884C23—22no—
885C23—21no—
886C23—21no—
887C23—22no—
888C23—22no—
889C23—24no—
890C23—24no—
891C23—28no—
892C23—24no—
893C23—22no—
894C23—24no—
895C23—22no—
896C23—24no—
897C23—28no—
898C23C22×#4112yes—
899C23C2611yescharacteristic
900Q8—28no—
901Q8—416no—
902Q8—48no—
903Q8—88no—
904Q8—88no—
905D4—48no—
906D4—48no—
907D4—44no—
908D4—48no—
909D4—84no—
910D4—88no—
911D4—168no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—28no—
924C2×C4—28no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—24no—
928C2×C4—28no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—28no—
937C2×C4—28no—
938C2×C4—28no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—22no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—44no—
959C2×C4—48no—
960C2×C4—48no—
961C2×C4—84no—
962C2×C4—88no—
963C2×C4—88no—
964C2×C4—168no—
965C2×C4C22×#4112yes—
966C2×C4C22×#4112yes—
967C2×C4C22×#4112yes—
968C2×C4C22×#4112yes—
969C2×C4C22×#4112yes—
970C2×C4C22×#4112yes—
971C2×C4C2×H(5,𝔽2)14yes—
972C2×C4C2×H(5,𝔽2)14yes—
973C2×C4C2×H(5,𝔽2)14yes—
974C2×C4C2×2−1+414yes—
975C2×C4C2×2−1+412yes—
976C2×C4#58512yes—
977C22—22no—
978C22—22no—
979C22—22no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—44no—
984C22—42no—
985C22—44no—
986C22—42no—
987C22—44no—
988C22—48no—
989C22—44no—
990C22—44no—
991C22—48no—
992C22C23×#4111yescharacteristic
993C22C22×H(5,𝔽2)12yes—
994C22C22×2−1+411yescharacteristic
995C22C2×#58511yescharacteristic
996C222−1+612yes—
997C4—22no—
998C4—22no—
999C4—24no—
1000C4—22no—
1001C4—22no—
1002C4—24no—
1003C4—24no—
1004C4—42no—
1005C4—44no—
1006C4—48no—
1007C4—42no—
1008C4—42no—
1009C4—44no—
1010C4—44no—
1011C4—44no—
1012C4—44no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4#349514yes—
1017C4#350814yes—
1018C2—42no—
1019C2—82no—
1020C2—84no—
1021C2C2×#350811yescharacteristic
1022C2C2×#349511yescharacteristic
1023C2#6286011yescharacteristic
1024C2#6293112yes—
1025C2#6294612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35190C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #50678C2semidirect
2. #50676C2semidirect
3. #50675C2semidirect
4. #45434C2semidirect
5. #45430C2semidirect
6. #45393C2semidirect
7. #45350C2semidirect
8. #45211C2semidirect
9. #45147C2semidirect
10. #39418C2semidirect
11. #39417C2semidirect
12. #39387C2semidirect
13. #39385C2semidirect
14. #37384C2semidirect
15. #36598C2semidirect
16. #36591C2semidirect
17. #35318C2semidirect
18. #35317C2semidirect
19. #35279C2semidirect
21. #34625C2semidirect
22. #34393C2semidirect
23. #34371C2semidirect
24. #34125C2semidirect

Maximal subgroups

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

subgroupindex
#506782
#506762
#506752
#454342
#454302
#453932
#453502
#452112
#451472
#394182
#394172
#393872
#393852
#373842
#365982
#365912
#353182
#353172
#352792
#351902
#346252
#343932
#343712
#341252