Finite Group Databasebeta

← #7746763

Subgroups — #7746763

Order 512.

5270 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45379C214yesmaximal, complemented
2#45299C212yesmaximal, complemented
3#45141C212yesmaximal, complemented
4#45094C214yesmaximal, complemented
5#45074C214yesmaximal, complemented
6#45048C214yesmaximal, complemented
7#45020C214yesmaximal, complemented
8#42903C214yesmaximal, complemented
9#42607C214yesmaximal, complemented
10#42584C214yesmaximal, complemented
11#36595C211yesmaximal, characteristic, complemented
12#36574C211yesmaximal, characteristic, complemented
13#36211C212yesmaximal, complemented
14#36209C211yesmaximal, characteristic, complemented
15#36128C211yesmaximal, characteristic, complemented
16#36122C212yesmaximal, complemented
17#36041C212yesmaximal, complemented
18#36018C212yesmaximal, complemented
19#35897C214yesmaximal, complemented
20#35882C214yesmaximal, complemented
21#35288C212yesmaximal, complemented
22#35278C211yesmaximal, characteristic, complemented
23#34551C211yesmaximal, characteristic, complemented
24#34226C212yesmaximal, complemented
25#34209C211yesmaximal, characteristic, complemented
26C2×#559C2212yes—
27C2×#550C2212yes—
28C2×#548C2214yes—
29C2×#540C2212yes—
30C2×#532C2212yes—
31C22×C4⋊Q8C2211yescharacteristic
32C2×#519C2212yes—
33#2867C2211yescharacteristic
34#2859C2211yescharacteristic
35#2859C2212yes—
36#2858C2212yes—
37#2857C2212yes—
38#2856C2212yes—
39#2856C2212yes—
40#2829C2218yes—
41#2803C2218yes—
42#2797C2218yes—
43#2781C2218yes—
44#2761C2218yes—
45#2757C2218yes—
46#2750C2218yes—
47#2710C2218yes—
48#2709C2218yes—
49#2699C2218yes—
50#2688C2218yes—
51#2687C2218yes—
52#2686C2218yes—
53#2649C2218yes—
54#2648C2218yes—
55#2644C2214yes—
56#2641C2212yes—
57#2632C2214yes—
58#2624C2214yes—
59#2619C2214yes—
60#2619C2212yes—
61#2610C2214yes—
62#2598C2214yes—
63#2597C2218yes—
64#2584C2214yes—
65#2581C2212yes—
66#2576C2218yes—
67#2557C2218yes—
68#2548C2212yes—
69#2548C2214yes—
70#2548C2212yes—
71#2548C2214yes—
72#2545C2214yes—
73#2544C2214yes—
74#2541C2214yes—
75#2536C2214yes—
76#2536C2212yes—
77#2535C2214yes—
78#2526C2218yes—
79#2513C2214yes—
80#2513C2214yes—
81#2513C2214yes—
82#2509C2214yes—
83#2508C2214yes—
84#2508C2214yes—
85#2495C2214yes—
86#2491C2214yes—
87#2491C2214yes—
88#2490C2214yes—
89#2490C2214yes—
90#2490C2214yes—
91#2489C2214yes—
92#2488C2218yes—
93#2485C2214yes—
94#2471C2218yes—
95#2458C2218yes—
96#2454C2214yes—
97#2453C2214yes—
98#2452C2214yes—
99#2452C2214yes—
100#2448C2214yes—
101#2447C2214yes—
102#2445C2214yes—
103#2445C2214yes—
104#2445C2214yes—
105#2445C2214yes—
106#2444C2218yes—
107#2444C2218yes—
108#2436C2214yes—
109#2432C2214yes—
110#2431C2214yes—
111#2428C2214yes—
112#2428C2214yes—
113#2428C2214yes—
114#2428C2214yes—
115#2427C2214yes—
116#2426C2218yes—
117#2426C2214yes—
118#2420C2214yes—
119#2420C2218yes—
120#2420C2214yes—
121#2420C2214yes—
122#2419C2218yes—
123#2416C2214yes—
124#2416C2214yes—
125#2414C2218yes—
126#2414C2214yes—
127#2414C2214yes—
128#2402C2212yes—
129#2402C2211yescharacteristic
130#2401C2212yes—
131#2401C2212yes—
132#2401C2212yes—
133#2398C2214yes—
134#2398C2211yescharacteristic
135#2398C2212yes—
136#2396C2212yes—
137#2396C2211yescharacteristic
138#2395C2212yes—
139#2395C2212yes—
140#2395C2212yes—
141#2392C2214yes—
142#2392C2212yes—
143#2392C2211yescharacteristic
144#2370C2214yes—
145#2367C2214yes—
146#2367C2214yes—
147#2366C2214yes—
148#2366C2214yes—
149#2365C2214yes—
150#2365C2214yes—
151#2363C2214yes—
152#2363C2214yes—
153#2363C2214yes—
154#2363C2214yes—
155#2361C2214yes—
156#2361C2214yes—
157#2357C2214yes—
158#2357C2214yes—
159#2356C2212yes—
160#2351C2212yes—
161#2349C2214yes—
162#2346C2214yes—
163#2344C2214yes—
164#2344C2214yes—
165#2341C2214yes—
166#2339C2214yes—
167#2328C2212yes—
168#2327C2212yes—
169#2327C2212yes—
170#2324C2214yes—
171#2324C2214yes—
172#2324C2214yes—
173#2319C2214yes—
174#2319C2214yes—
175#2310C2212yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2211yescharacteristic
178C4×C4⋊Q8C2211yescharacteristic
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×#127C2212yes—
182C4×#127C2212yes—
183#2285C2212yes—
184#2285C2211yescharacteristic
185#2275C2214yes—
186C42×Q8C2211yescharacteristic
187C42×D4C2212yes—
188C42×D4C2211yescharacteristic
189C4×#117C2211yescharacteristic
190C4×#117C2212yes—
191C22×#41C2314yes—
192C23×Q8C2312yes—
193#559—48no—
194#550—48no—
195#548—416no—
196#540—48no—
197#532—216no—
198C2×C4⋊Q8—28no—
199C2×C4⋊Q8C2311yescharacteristic
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2314yes—
202C2×C4⋊Q8C2311yescharacteristic
203C2×#127C2312yes—
204C2×#127C2312yes—
205C2×#127C2314yes—
206C2×#127C2314yes—
207C2×#127C2312yes—
208C2×#127C2314yes—
209C2×#125C2314yes—
210C2×#125C2312yes—
211C2×#124C2314yes—
212C2×#124C2314yes—
213C2×#124C2314yes—
214C2×#124C2314yes—
215C2×#124C2318yes—
216C2×#123C2318yes—
217C2×#123C2318yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2318yes—
220C2×#121C2314yes—
221C2×#121C2314yes—
222C2×#121C2314yes—
223C2×#121C2314yes—
224C2×#121C2314yes—
225C2×#121C2314yes—
226C2×#121C2314yes—
227C2×#121C2314yes—
228C2×#121C2318yes—
229C2×#121C2318yes—
230C2×#121C2318yes—
231#519—48no—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2318yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2312yes—
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2312yes—
260C2×#117C2312yes—
261C2×#117C2312yes—
262C2×#117C2314yes—
263C2×#117C2314yes—
264C2×#117C2314yes—
265C22×C4⋊C4C2314yes—
266C22×C42C2311yescharacteristic
267C22×C42C2312yes—
268#401C2312yes—
269#400C2314yes—
270#400C2312yes—
271#400C2318yes—
272#400C2312yes—
273#400C2318yes—
274#400C2312yes—
275#400C2312yes—
276#400C2311yescharacteristic
277#400C2312yes—
278#400C2312yes—
279#400C2312yes—
280#399C2318yes—
281#399C2311yescharacteristic
282#399C2312yes—
283#398C2318yes—
284#398C2312yes—
285#398C2311yescharacteristic
286#398C2314yes—
287#398C2312yes—
288#398C2312yes—
289#398C2312yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2311yescharacteristic
298#397C2312yes—
299#397C2318yes—
300#397C2312yes—
301#397C2312yes—
302#397C2312yes—
303#397C2312yes—
304#397C2312yes—
305#397C2312yes—
306#396C2312yes—
307#396C2318yes—
308#396C2318yes—
309#396C2312yes—
310#396C2312yes—
311#396C2318yes—
312#395C2314yes—
313#395C2311yescharacteristic
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2314yes—
320#394C2314yes—
321#394C2314yes—
322#394C2314yes—
323#394C2314yes—
324#394C2314yes—
325#394C2314yes—
326#394C2318yes—
327#394C2318yes—
328#394C2312yes—
329#394C2311yescharacteristic
330#394C2312yes—
331#394C2312yes—
332#394C2312yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#393C2311yescharacteristic
337#393C2318yes—
338#393C2312yes—
339#393C2318yes—
340#392C2318yes—
341#392C2314yes—
342#392C2311yescharacteristic
343#392C2314yes—
344#392C2318yes—
345#392C2318yes—
346#391C2312yes—
347#391C2312yes—
348#391C2312yes—
349#391C2312yes—
350#391C2314yes—
351#391C2318yes—
352#391C2314yes—
353#390C2314yes—
354#390C2314yes—
355#390C2314yes—
356#390C2314yes—
357#390C2314yes—
358#390C2314yes—
359#390C2318yes—
360#390C2314yes—
361#390C2314yes—
362#390C2318yes—
363#390C2314yes—
364#390C2318yes—
365#390C2314yes—
366#390C2318yes—
367#390C2314yes—
368#390C2314yes—
369#390C2314yes—
370#390C2314yes—
371#390C2314yes—
372#390C2314yes—
373#390C2318yes—
374#390C2318yes—
375#390C2318yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2318yes—
388#389C2318yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#386C2318yes—
415#386C2318yes—
416#386C2318yes—
417#386C2318yes—
418#386C2318yes—
419#386C2318yes—
420#386C2318yes—
421#386C2318yes—
422#386C2318yes—
423#386C2318yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#384C2311yescharacteristic
433#384C2312yes—
434#384C2311yescharacteristic
435#383C2314yes—
436#382C2318yes—
437#382C2312yes—
438#382C2312yes—
439#382C2314yes—
440#382C2314yes—
441#382C2314yes—
442#381C2318yes—
443#381C2318yes—
444#381C2318yes—
445#381C2318yes—
446#380C2318yes—
447#380C2318yes—
448#380C2314yes—
449#380C2314yes—
450#380C2314yes—
451#380C2314yes—
452#380C2314yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C22⋊C4C2318yes—
480C4×C22⋊C4C2318yes—
481C4×C22⋊C4C2312yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2318yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2312yes—
486C4×C22⋊C4C2312yes—
487C4×C22⋊C4C2318yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497C4×C22⋊C4C2312yes—
498#376C2312yes—
499#376C2311yescharacteristic
500#376C2311yescharacteristic
501#376C2314yes—
502#376C2312yes—
503C2×#95C2318yes—
504C43C2311yescharacteristic
505C43C2312yes—
506C43C2311yescharacteristic
507C2×#41—216no—
508C2×#41—48no—
509C2×#41—48no—
510C22×Q8—28no—
511C22×Q8—28no—
512C22×Q8—44no—
513C22×Q8C2412yes—
514C22×Q8C2414yes—
515C22×Q8C2412yes—
516C22×Q8C2411yescharacteristic
517C22×D4C2414yes—
518C22×D4C2414yes—
519C22×D4C2414yes—
520C22×D4C2412yes—
521C22×D4C2411yescharacteristic
522C22×D4C2418yes—
523C22×D4C2414yes—
524C22×D4C2414yes—
525C22×D4C2418yes—
526C22×D4C2418yes—
527C22×D4C2418yes—
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2412yes—
531C23×C4C2412yes—
532C23×C4C2414yes—
533C23×C4C2411yescharacteristic
534C23×C4C2418yes—
535C23×C4C2418yes—
536C23×C4C2418yes—
537C4⋊Q8—28no—
538C4⋊Q8—216no—
539C4⋊Q8—24no—
540C4⋊Q8#4118yes—
541#127—28no—
542#127—28no—
543#127—48no—
544#127—48no—
545#127—44no—
546#127—48no—
547#125—48no—
548#125—44no—
549#124—216no—
550#124—48no—
551#124—48no—
552#124—48no—
553#124—416no—
554#123—416no—
555#123—416no—
556C22⋊Q8—416no—
557C22⋊Q8—48no—
558#121—216no—
559#121—216no—
560#121—216no—
561#121—416no—
562#121—416no—
563#121—48no—
564#121—48no—
565#121—48no—
566#121—48no—
567#121—48no—
568#121—416no—
569C4×Q8—28no—
570C4×Q8—28no—
571C4×Q8—24no—
572C4×Q8—44no—
573C4×Q8—48no—
574C4×Q8—48no—
575C4×Q8—44no—
576C4×Q8—44no—
577C4×Q8—48no—
578C4×D4—28no—
579C4×D4—216no—
580C4×D4—216no—
581C4×D4—24no—
582C4×D4—48no—
583C4×D4—48no—
584C4×D4—48no—
585C4×D4—48no—
586C4×D4—48no—
587C4×D4—48no—
588C4×D4—48no—
589C4×D4—48no—
590C4×D4—44no—
591C4×D4—44no—
592C4×D4—44no—
593C4×D4—416no—
594#117—24no—
595#117—24no—
596#117—44no—
597#117—44no—
598#117—48no—
599#117—48no—
600#117—48no—
601#117—44no—
602C2×C4⋊C4—216no—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C22⋊C4C2411yescharacteristic
640C2×C22⋊C4C2411yescharacteristic
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2412yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2412yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2418yes—
676C2×C42—24no—
677C2×C42—28no—
678C2×C42C2411yescharacteristic
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2414yes—
683C2×C42C2414yes—
684C2×C42C2412yes—
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2412yes—
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2411yescharacteristic
697C2×C42C2412yes—
698C2×C42C2414yes—
699C2×C42C2414yes—
700C2×C42C2414yes—
701C2×C42C2418yes—
702C2×C42C2418yes—
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705#95C2412yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2411yescharacteristic
710#95C2412yes—
711#95C2412yes—
712#95C2412yes—
713#95C2412yes—
714#95C2412yes—
715#95C2412yes—
716#95C2412yes—
717#95C2412yes—
718#95C2412yes—
719#95C2412yes—
720#95C2412yes—
721#95C2418yes—
722#95C2414yes—
723#95C2412yes—
724#95C2412yes—
725#95C2412yes—
726#95C2411yescharacteristic
727#95C2412yes—
728#95C2412yes—
729#95C2412yes—
730#95C2412yes—
731#95C2412yes—
732#95C2418yes—
733#95C2411yescharacteristic
734#95C2411yescharacteristic
735#95C2412yes—
736#95C2412yes—
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2414yes—
744#95C2418yes—
745#95C2418yes—
746C24C2518yes—
747C24C2512yes—
748C24C2511yescharacteristic
749#41—832no—
750C2×Q8—28no—
751C2×Q8—24no—
752C2×Q8—24no—
753C2×Q8—24no—
754C2×Q8—24no—
755C2×Q8—22no—
756C2×Q8—28no—
757C2×Q8—24no—
758C2×Q8—44no—
759C2×Q8—42no—
760C2×Q8—432no—
761C2×Q8C2×#4118yes—
762C2×D4—24no—
763C2×D4—216no—
764C2×D4—28no—
765C2×D4—28no—
766C2×D4—28no—
767C2×D4—216no—
768C2×D4—22no—
769C2×D4—28no—
770C2×D4—28no—
771C2×D4—28no—
772C2×D4—28no—
773C2×D4—28no—
774C2×D4—28no—
775C2×D4—28no—
776C2×D4—28no—
777C2×D4—42no—
778C2×D4—42no—
779C2×D4—42no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—48no—
786C2×D4—48no—
787C2×D4—48no—
788C2×D4—48no—
789C2×D4—48no—
790C2×D4—48no—
791C2×D4—48no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—28no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—28no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—216no—
809C22×C4—44no—
810C22×C4—48no—
811C22×C4—48no—
812C22×C4—48no—
813C22×C4—48no—
814C22×C4—48no—
815C22×C4—48no—
816C22×C4—48no—
817C22×C4—48no—
818C22×C4H(5,𝔽2)14yes—
819C22×C4C2512yes—
820C22×C4C2512yes—
821C22×C4C2512yes—
822C22×C4C2512yes—
823C22×C4C2512yes—
824C22×C4C2512yes—
825C22×C4C2512yes—
826C22×C4C2514yes—
827C22×C4C2514yes—
828C22×C4C2518yes—
829C22×C4C2512yes—
830C22×C4C2512yes—
831C22×C4C2514yes—
832C22×C4C2512yes—
833C22×C4C2511yescharacteristic
834C22×C4C2511yescharacteristic
835C22×C4C2514yes—
836C22×C4C2511yescharacteristic
837C22×C4C2511yescharacteristic
838C22×C4C2511yescharacteristic
839C22×C4C2511yescharacteristic
840C22×C4C2512yes—
841C4⋊C4—216no—
842C4⋊C4—28no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—28no—
848C4⋊C4—24no—
849C4⋊C4—28no—
850C4⋊C4—22no—
851C4⋊C4—24no—
852C4⋊C4—22no—
853C4⋊C4—28no—
854C4⋊C4—24no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—28no—
859C4⋊C4—42no—
860C4⋊C4—42no—
861C4⋊C4—42no—
862C4⋊C4—42no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—42no—
866C4⋊C4—42no—
867C4⋊C4—42no—
868C4⋊C4—48no—
869C4⋊C4—42no—
870C4⋊C4—42no—
871C4⋊C4—42no—
872C4⋊C4—48no—
873C4⋊C4—48no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4C2×#41116yes—
877C22⋊C4—24no—
878C22⋊C4—24no—
879C22⋊C4—216no—
880C22⋊C4—216no—
881C22⋊C4—22no—
882C22⋊C4—22no—
883C22⋊C4—24no—
884C22⋊C4—24no—
885C22⋊C4—216no—
886C22⋊C4—42no—
887C22⋊C4—42no—
888C22⋊C4—42no—
889C22⋊C4—42no—
890C22⋊C4—48no—
891C22⋊C4—44no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—42no—
897C22⋊C4—42no—
898C22⋊C4—42no—
899C22⋊C4—42no—
900C22⋊C4—42no—
901C22⋊C4—42no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C42—24no—
915C42—24no—
916C42—24no—
917C42—24no—
918C42—22no—
919C42—22no—
920C42—22no—
921C42—22no—
922C42—28no—
923C42—28no—
924C42—24no—
925C42—24no—
926C42—24no—
927C42—24no—
928C42—24no—
929C42—24no—
930C42—24no—
931C42—24no—
932C42—24no—
933C42—24no—
934C42—48no—
935C42—44no—
936C42—44no—
937C42—44no—
938C42—48no—
939C42C2×#4114yes—
940C42H(5,𝔽2)14yes—
941C23—21no—
942C23—21no—
943C23—22no—
944C23—22no—
945C23—28no—
946C23—22no—
947C23—22no—
948C23—28no—
949C23—22no—
950C23—28no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—28no—
955C23—28no—
956C23—28no—
957C23—28no—
958C23—22no—
959C23C2×H(5,𝔽2)12yes—
960C23C2611yescharacteristic
961Q8—216no—
962Q8—416no—
963Q8—44no—
964Q8—48no—
965D4—44no—
966D4—48no—
967D4—416no—
968D4—416no—
969D4—416no—
970D4—88no—
971D4—88no—
972D4—816no—
973D4—816no—
974D4—168no—
975D4—168no—
976C2×C4—21no—
977C2×C4—24no—
978C2×C4—21no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—28no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—24no—
988C2×C4—22no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—28no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—28no—
1019C2×C4—28no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—28no—
1025C2×C4—28no—
1026C2×C4—22no—
1027C2×C4—416no—
1028C2×C4—48no—
1029C2×C4—48no—
1030C2×C4—48no—
1031C2×C4—48no—
1032C2×C4—816no—
1033C2×C4—168no—
1034C2×C4—168no—
1035C2×C4C22×#4118yes—
1036C2×C4C22×#4112yes—
1037C2×C4C22×#4114yes—
1038C2×C4C2×H(5,𝔽2)12yes—
1039C2×C4C2×H(5,𝔽2)12yes—
1040C2×C4C2×H(5,𝔽2)12yes—
1041C2×C4C2×H(5,𝔽2)12yes—
1042C2×C4C2×H(5,𝔽2)12yes—
1043C2×C4#58514yes—
1044C2×C4#58514yes—
1045C22—22no—
1046C22—24no—
1047C22—42no—
1048C22—41no—
1049C22—41no—
1050C22—42no—
1051C22—48no—
1052C22—42no—
1053C22—42no—
1054C22—48no—
1055C22—48no—
1056C22—48no—
1057C22—48no—
1058C22—42no—
1059C22—42no—
1060C22—48no—
1061C22—48no—
1062C22—42no—
1063C22—42no—
1064C22C23×#4111yescharacteristic
1065C22C22×H(5,𝔽2)11yescharacteristic
1066C22C22×H(5,𝔽2)11yescharacteristic
1067C22C2×#58512yes—
1068C22C2×#58512yes—
1069C4—22no—
1070C4—28no—
1071C4—22no—
1072C4—22no—
1073C4—42no—
1074C4—44no—
1075C4—42no—
1076C4—42no—
1077C4—42no—
1078C4—41no—
1079C4—41no—
1080C4—42no—
1081C4—44no—
1082C4—42no—
1083C4—42no—
1084C4—48no—
1085C4—42no—
1086C4—44no—
1087C4—42no—
1088C4—42no—
1089C4#351914yes—
1090C4#352418yes—
1091C2—42no—
1092C2—82no—
1093C2—88no—
1094C2C2×#351911yescharacteristic
1095C2C2×#352412yes—
1096C2#6283611yescharacteristic
1097C2#6283611yescharacteristic
1098C2#6283612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45379C2semidirect
2. #45299C2semidirect
3. #45141C2semidirect
4. #45094C2semidirect
5. #45074C2semidirect
6. #45048C2semidirect
7. #45020C2semidirect
8. #42903C2semidirect
9. #42607C2semidirect
10. #42584C2semidirect
11. #36595C2semidirect
12. #36574C2semidirect
13. #36211C2semidirect
14. #36209C2semidirect
15. #36128C2semidirect
16. #36122C2semidirect
17. #36041C2semidirect
18. #36018C2semidirect
19. #35897C2semidirect
20. #35882C2semidirect
21. #35288C2semidirect
22. #35278C2semidirect
23. #34551C2semidirect
24. #34226C2semidirect
25. #34209C2semidirect

Maximal subgroups

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

subgroupindex
#453792
#452992
#451412
#450942
#450742
#450482
#450202
#429032
#426072
#425842
#365952
#365742
#362112
#362092
#361282
#361222
#360412
#360182
#358972
#358822
#352882
#352782
#345512
#342262
#342092