Finite Group Databasebeta

← #7712520

Subgroups — #7712520

Order 512.

4730 conjugacy classes of subgroups.

The subgroup lattice has 1058 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59710C214yesmaximal, complemented
2#59497C214yesmaximal, complemented
3#45514C214yesmaximal, complemented
4#45513C214yesmaximal, complemented
5#39781C214yesmaximal, complemented
6#39780C214yesmaximal, complemented
7#39758C212yesmaximal, complemented
8#39530C214yesmaximal, complemented
9#39529C214yesmaximal, complemented
10#39374C212yesmaximal, complemented
11#37711C214yesmaximal, complemented
12#37553C212yesmaximal, complemented
13#37435C214yesmaximal, complemented
14#36645C211yesmaximal, characteristic, complemented
15#36631C211yesmaximal, characteristic, complemented
16#36574C211yesmaximal, characteristic, complemented
17#36573C211yesmaximal, characteristic, complemented
18#36211C211yesmaximal, characteristic, complemented
19#36211C212yesmaximal, complemented
20#36210C212yesmaximal, complemented
21#36209C211yesmaximal, characteristic, complemented
22#35294C212yesmaximal, complemented
23#35277C212yesmaximal, complemented
24#34392C212yesmaximal, complemented
25C4×#529C211yesmaximal, characteristic, complemented
26C2×#542C2214yes—
27C2×#533C2212yes—
28C2×#529C2212yes—
29C2×#529C2211yescharacteristic
30#2868C2212yes—
31#2862C2212yes—
32#2861C2212yes—
33#2860C2214yes—
34#2859C2211yescharacteristic
35#2859C2212yes—
36#2859C2211yescharacteristic
37#2859C2211yescharacteristic
38#2859C2212yes—
39#2859C2212yes—
40#2858C2211yescharacteristic
41#2857C2211yescharacteristic
42#2857C2214yes—
43#2857C2214yes—
44#2857C2212yes—
45#2856C2211yescharacteristic
46#2856C2212yes—
47#2854C2214yes—
48#2850C2212yes—
49#2814C2214yes—
50#2813C2214yes—
51#2801C2218yes—
52#2800C2218yes—
53#2798C2218yes—
54#2779C2218yes—
55#2777C2218yes—
56#2772C2218yes—
57#2765C2218yes—
58#2759C2218yes—
59#2757C2218yes—
60#2739C2218yes—
61#2730C2218yes—
62#2728C2218yes—
63#2723C2218yes—
64#2710C2218yes—
65#2696C2218yes—
66#2689C2218yes—
67#2664C2214yes—
68#2662C2214yes—
69#2640C2214yes—
70#2630C2218yes—
71#2629C2214yes—
72#2628C2214yes—
73#2620C2214yes—
74#2601C2218yes—
75#2584C2214yes—
76#2581C2212yes—
77#2580C2212yes—
78#2580C2214yes—
79#2570C2214yes—
80#2570C2214yes—
81#2562C2214yes—
82#2550C2214yes—
83#2550C2214yes—
84#2536C2212yes—
85#2535C2214yes—
86#2535C2212yes—
87#2527C2218yes—
88#2523C2218yes—
89#2521C2218yes—
90#2514C2214yes—
91#2513C2214yes—
92#2513C2214yes—
93#2513C2214yes—
94#2512C2214yes—
95#2512C2214yes—
96#2509C2214yes—
97#2509C2214yes—
98#2508C2214yes—
99#2508C2214yes—
100#2495C2214yes—
101#2495C2214yes—
102#2494C2214yes—
103#2494C2214yes—
104#2491C2214yes—
105#2491C2214yes—
106#2490C2214yes—
107#2490C2214yes—
108#2490C2214yes—
109#2489C2214yes—
110#2488C2218yes—
111#2485C2214yes—
112#2485C2214yes—
113#2469C2218yes—
114#2458C2218yes—
115#2454C2214yes—
116#2454C2214yes—
117#2454C2214yes—
118#2453C2214yes—
119#2452C2214yes—
120#2452C2214yes—
121#2448C2218yes—
122#2441C2214yes—
123#2441C2214yes—
124#2439C2214yes—
125#2439C2214yes—
126#2422C2214yes—
127#2422C2214yes—
128#2421C2214yes—
129#2421C2218yes—
130#2420C2214yes—
131#2420C2214yes—
132#2420C2214yes—
133#2415C2214yes—
134#2414C2214yes—
135#2414C2214yes—
136#2414C2214yes—
137#2376C2218yes—
138#2370C2214yes—
139#2370C2214yes—
140#2363C2214yes—
141#2363C2214yes—
142#2363C2214yes—
143#2362C2214yes—
144#2357C2212yes—
145#2357C2214yes—
146#2356C2212yes—
147#2351C2212yes—
148#2349C2212yes—
149#2349C2214yes—
150#2347C2214yes—
151#2347C2214yes—
152#2346C2214yes—
153#2343C2214yes—
154#2334C2218yes—
155#2331C2214yes—
156#2330C2214yes—
157#2326C2214yes—
158#2319C2214yes—
159#2318C2214yes—
160C4×C4⋊Q8C2211yescharacteristic
161C4×C4⋊Q8C2214yes—
162C4×C4⋊Q8C2214yes—
163C4×C4⋊Q8C2212yes—
164C4×#127C2211yescharacteristic
165C4×#127C2212yes—
166C4×#125C2212yes—
167C4×#126C2212yes—
168C4×#126C2212yes—
169C4×#124C2212yes—
170C4×#124C2212yes—
171C4×C22⋊Q8C2212yes—
172C4×#123C2212yes—
173C4×#123C2212yes—
174C4×#121C2214yes—
175C4×#121C2212yes—
176#2298C2212yes—
177#2295C2211yescharacteristic
178#2293C2214yes—
179#2293C2211yescharacteristic
180#2290C2212yes—
181#2285C2212yes—
182#2285C2212yes—
183#2285C2212yes—
184#2285C2212yes—
185#2283C2211yescharacteristic
186C42×Q8C2211yescharacteristic
187C42×D4C2211yescharacteristic
188C42×D4C2212yes—
189C4×#117C2212yes—
190C2×C43C2211yescharacteristic
191#542—416no—
192#533—48no—
193C2×C4⋊Q8C2311yescharacteristic
194C2×C4⋊Q8C2314yes—
195C2×C4⋊Q8C2314yes—
196C2×C4⋊Q8C2314yes—
197C2×#127C2311yescharacteristic
198#529—216no—
199#529—28no—
200C2×#126C2312yes—
201C2×#126C2314yes—
202C2×#126C2318yes—
203C2×#125C2311yescharacteristic
204C2×#125C2312yes—
205C2×#125C2314yes—
206C2×#125C2314yes—
207C2×#125C2312yes—
208C2×#125C2312yes—
209C2×#124C2312yes—
210C2×#124C2312yes—
211C2×#124C2311yescharacteristic
212C2×#124C2318yes—
213C2×#123C2314yes—
214C2×#123C2312yes—
215C2×#123C2318yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2318yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2318yes—
221C2×#121C2312yes—
222C2×#121C2311yescharacteristic
223C2×#121C2314yes—
224C2×#121C2314yes—
225C2×#121C2314yes—
226C2×#121C2314yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2318yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2312yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2312yes—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2312yes—
243C2×#117C2314yes—
244C2×#117C2312yes—
245C2×#117C2312yes—
246C2×#117C2314yes—
247C2×#117C2314yes—
248C2×#117C2314yes—
249C22×C42C2311yescharacteristic
250C22×C42C2311yescharacteristic
251C22×C42C2312yes—
252C22×C42C2312yes—
253C22×C42C2312yes—
254C22×C42C2311yescharacteristic
255#401C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2314yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#399C2314yes—
263#399C2318yes—
264#399C2318yes—
265#398C2318yes—
266#398C2318yes—
267#398C2318yes—
268#398C2314yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C2314yes—
273#397C2318yes—
274#397C2318yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#396C2318yes—
280#396C2318yes—
281#396C2318yes—
282#396C2318yes—
283#396C2318yes—
284#395C2314yes—
285#395C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2318yes—
290#394C2314yes—
291#394C2318yes—
292#394C2318yes—
293#393C2314yes—
294#393C2318yes—
295#393C2318yes—
296#393C2318yes—
297#392C2318yes—
298#392C2314yes—
299#391C2314yes—
300#391C2312yes—
301#391C2318yes—
302#391C2318yes—
303#391C2314yes—
304#391C2318yes—
305#391C2318yes—
306#391C2312yes—
307#391C2312yes—
308#390C2314yes—
309#390C2314yes—
310#390C2314yes—
311#390C2312yes—
312#390C2314yes—
313#390C2318yes—
314#390C2314yes—
315#390C2314yes—
316#390C2314yes—
317#390C2312yes—
318#390C2314yes—
319#390C2314yes—
320#390C2318yes—
321#390C2314yes—
322#390C2318yes—
323#390C2312yes—
324#389C2312yes—
325#389C2312yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2318yes—
333#389C2318yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2318yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2318yes—
344#389C2318yes—
345#389C2318yes—
346#389C2314yes—
347#389C2314yes—
348#389C2318yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#388C2312yes—
354#388C2312yes—
355#388C2312yes—
356#388C2312yes—
357#388C2312yes—
358#388C2312yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2312yes—
378#388C2312yes—
379#387C2312yes—
380#387C2312yes—
381#387C2312yes—
382#387C2312yes—
383#387C2312yes—
384#387C2312yes—
385#387C2312yes—
386#387C2312yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#386C2312yes—
402#386C2312yes—
403#385C2318yes—
404#385C2318yes—
405#385C2318yes—
406#385C2318yes—
407#385C2318yes—
408#385C2312yes—
409#385C2312yes—
410#384C2311yescharacteristic
411#384C2312yes—
412#384C2314yes—
413#384C2314yes—
414#384C2311yescharacteristic
415#384C2312yes—
416#384C2314yes—
417#383C2311yescharacteristic
418#383C2311yescharacteristic
419#383C2314yes—
420#383C2318yes—
421#382C2312yes—
422#382C2314yes—
423#382C2314yes—
424#382C2314yes—
425#382C2314yes—
426#382C2314yes—
427#382C2312yes—
428#382C2312yes—
429#382C2312yes—
430#382C2318yes—
431#382C2314yes—
432#381C2311yescharacteristic
433#381C2311yescharacteristic
434#381C2314yes—
435#381C2318yes—
436#380C2314yes—
437#380C2314yes—
438#380C2314yes—
439#380C2314yes—
440#380C2314yes—
441#380C2314yes—
442#380C2314yes—
443#380C2314yes—
444#380C2314yes—
445#380C2318yes—
446#380C2314yes—
447#380C2314yes—
448#380C2312yes—
449#380C2314yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C22⋊C4C2312yes—
478C4×C22⋊C4C2312yes—
479C4×C22⋊C4C2312yes—
480C4×C22⋊C4C2312yes—
481C4×C22⋊C4C2312yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2318yes—
485C4×C22⋊C4C2312yes—
486C4×C22⋊C4C2312yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2318yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493#376C2314yes—
494#376C2312yes—
495#376C2312yes—
496C2×#95C2314yes—
497C43C2312yes—
498C43C2312yes—
499C43C2311yescharacteristic
500C43C2312yes—
501C43C2311yescharacteristic
502C43C2311yescharacteristic
503C43C2311yescharacteristic
504C22×Q8C2412yes—
505C22×Q8C2411yescharacteristic
506C22×Q8C2418yes—
507C22×D4C2412yes—
508C22×D4C2414yes—
509C22×D4C2412yes—
510C22×D4C2411yescharacteristic
511C22×D4C2414yes—
512C22×D4C2418yes—
513C23×C4C2412yes—
514C23×C4C2412yes—
515C23×C4C2412yes—
516C23×C4C2412yes—
517C23×C4C2411yescharacteristic
518C23×C4C2414yes—
519C23×C4C2412yes—
520C23×C4C2418yes—
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C4⋊Q8—216no—
524C4⋊Q8—24no—
525C4⋊Q8—48no—
526C4⋊Q8—48no—
527#127—24no—
528#126—28no—
529#126—216no—
530#126—416no—
531#125—28no—
532#125—24no—
533#125—48no—
534#125—48no—
535#125—44no—
536#125—44no—
537#124—28no—
538#124—24no—
539#124—28no—
540#124—416no—
541#123—28no—
542#123—216no—
543#123—416no—
544C22⋊Q8—28no—
545C22⋊Q8—24no—
546C22⋊Q8—416no—
547C22⋊Q8—416no—
548C22⋊Q8—48no—
549#121—28no—
550#121—24no—
551#121—48no—
552#121—48no—
553#121—48no—
554#121—48no—
555C4×Q8—28no—
556C4×Q8—24no—
557C4×Q8—44no—
558C4×Q8—416no—
559C4×Q8—48no—
560C4×D4—28no—
561C4×D4—216no—
562C4×D4—24no—
563C4×D4—28no—
564C4×D4—48no—
565C4×D4—48no—
566C4×D4—48no—
567C4×D4—48no—
568C4×D4—44no—
569C4×D4—44no—
570C4×D4—44no—
571#117—216no—
572#117—28no—
573#117—28no—
574#117—48no—
575#117—48no—
576#117—48no—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2412yes—
619C2×C22⋊C4C2412yes—
620C2×C22⋊C4C2412yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2412yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2412yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C42—24no—
649C2×C42—24no—
650C2×C42—28no—
651C2×C42—44no—
652C2×C42—44no—
653C2×C42#4118yes—
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2414yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2411yescharacteristic
665C2×C42C2412yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2411yescharacteristic
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2418yes—
673C2×C42C2418yes—
674C2×C42C2418yes—
675C2×C42C2418yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686#95C2411yescharacteristic
687#95C2414yes—
688#95C2418yes—
689#95C2411yescharacteristic
690#95C2412yes—
691#95C2412yes—
692#95C2412yes—
693#95C2412yes—
694#95C2412yes—
695#95C2412yes—
696#95C2412yes—
697#95C2412yes—
698#95C2418yes—
699#95C2411yescharacteristic
700#95C2412yes—
701#95C2412yes—
702#95C2412yes—
703#95C2412yes—
704#95C2412yes—
705#95C2412yes—
706#95C2412yes—
707#95C2412yes—
708#95C2414yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712#95C2411yescharacteristic
713#95C2412yes—
714#95C2412yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2414yes—
721#95C2418yes—
722#95C2414yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729C24C2512yes—
730C24C2514yes—
731C24C2511yescharacteristic
732C2×Q8—22no—
733C2×Q8—24no—
734C2×Q8—24no—
735C2×Q8—216no—
736C2×Q8—24no—
737C2×Q8—42no—
738C2×Q8—48no—
739C2×Q8—48no—
740C2×D4—24no—
741C2×D4—28no—
742C2×D4—22no—
743C2×D4—24no—
744C2×D4—24no—
745C2×D4—24no—
746C2×D4—28no—
747C2×D4—28no—
748C2×D4—28no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—28no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—48no—
777C22×C4—48no—
778C22×C4—48no—
779C22×C4—48no—
780C22×C4C2×#4114yes—
781C22×C4C2×#4114yes—
782C22×C4C2×#4114yes—
783C22×C4C2512yes—
784C22×C4C2512yes—
785C22×C4C2512yes—
786C22×C4C2512yes—
787C22×C4C2514yes—
788C22×C4C2512yes—
789C22×C4C2512yes—
790C22×C4C2514yes—
791C22×C4C2512yes—
792C22×C4C2514yes—
793C22×C4C2518yes—
794C22×C4C2518yes—
795C22×C4C2512yes—
796C22×C4C2512yes—
797C22×C4C2511yescharacteristic
798C22×C4C2511yescharacteristic
799C22×C4C2511yescharacteristic
800C22×C4C2511yescharacteristic
801C22×C4C2511yescharacteristic
802C22×C4C2512yes—
803C22×C4C2511yescharacteristic
804C22×C4C2512yes—
805C4⋊C4—28no—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—28no—
809C4⋊C4—22no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—28no—
813C4⋊C4—22no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—28no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—28no—
820C4⋊C4—28no—
821C4⋊C4—216no—
822C4⋊C4—28no—
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—28no—
826C4⋊C4—28no—
827C4⋊C4—28no—
828C4⋊C4—28no—
829C4⋊C4—42no—
830C4⋊C4—42no—
831C4⋊C4—42no—
832C4⋊C4—42no—
833C4⋊C4—42no—
834C4⋊C4—42no—
835C4⋊C4—48no—
836C4⋊C4—48no—
837C4⋊C4—48no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C4⋊C4—48no—
841C4⋊C4—48no—
842C4⋊C4—48no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C22⋊C4—24no—
846C22⋊C4—28no—
847C22⋊C4—28no—
848C22⋊C4—24no—
849C22⋊C4—24no—
850C22⋊C4—28no—
851C22⋊C4—24no—
852C22⋊C4—28no—
853C22⋊C4—24no—
854C22⋊C4—28no—
855C22⋊C4—24no—
856C22⋊C4—24no—
857C22⋊C4—216no—
858C22⋊C4—48no—
859C22⋊C4—48no—
860C22⋊C4—48no—
861C22⋊C4—48no—
862C22⋊C4—42no—
863C22⋊C4—42no—
864C22⋊C4—48no—
865C22⋊C4—48no—
866C22⋊C4—42no—
867C22⋊C4—42no—
868C22⋊C4—42no—
869C22⋊C4—42no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C42—28no—
877C42—24no—
878C42—24no—
879C42—22no—
880C42—24no—
881C42—24no—
882C42—22no—
883C42—24no—
884C42—24no—
885C42—24no—
886C42—24no—
887C42—24no—
888C42—24no—
889C42—24no—
890C42—24no—
891C42—24no—
892C42—24no—
893C42—24no—
894C42—42no—
895C42—42no—
896C42—42no—
897C42—42no—
898C42—48no—
899C42—48no—
900C42—48no—
901C42—48no—
902C42C2×#4114yes—
903C42C2×#4114yes—
904C42C2×#4114yes—
905C42C2×#4114yes—
906C42H(5,𝔽2)14yes—
907C422−1+414yes—
908C23—21no—
909C23—21no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—24no—
914C23—22no—
915C23—24no—
916C23—22no—
917C23—24no—
918C23—22no—
919C23—22no—
920C23—28no—
921C23—28no—
922C23—22no—
923C23—22no—
924C23C22×#4112yes—
925C23C2611yescharacteristic
926Q8—44no—
927Q8—48no—
928Q8—816no—
929D4—44no—
930D4—48no—
931D4—48no—
932D4—416no—
933D4—88no—
934D4—168no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—28no—
944C2×C4—24no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—22no—
949C2×C4—24no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—24no—
954C2×C4—28no—
955C2×C4—28no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—28no—
977C2×C4—28no—
978C2×C4—28no—
979C2×C4—28no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—28no—
983C2×C4—28no—
984C2×C4—44no—
985C2×C4—44no—
986C2×C4—48no—
987C2×C4—48no—
988C2×C4—48no—
989C2×C4—48no—
990C2×C4—48no—
991C2×C4—88no—
992C2×C4—168no—
993C2×C4C22×#4112yes—
994C2×C4C22×#4112yes—
995C2×C4C22×#4112yes—
996C2×C4C22×#4112yes—
997C2×C4C22×#4112yes—
998C2×C4C22×#4112yes—
999C2×C4C2×H(5,𝔽2)14yes—
1000C2×C4C2×H(5,𝔽2)12yes—
1001C2×C4C2×2−1+412yes—
1002C2×C4C2×2−1+414yes—
1003C2×C4#58514yes—
1004C2×C4#58514yes—
1005C22—22no—
1006C22—22no—
1007C22—22no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—42no—
1012C22—48no—
1013C22—42no—
1014C22—44no—
1015C22—44no—
1016C22—42no—
1017C22—42no—
1018C22—44no—
1019C22—48no—
1020C22—42no—
1021C22—42no—
1022C22C23×#4111yescharacteristic
1023C22C22×H(5,𝔽2)11yescharacteristic
1024C22C22×2−1+411yescharacteristic
1025C22C2×#58512yes—
1026C22C2×#58512yes—
1027C4—22no—
1028C4—22no—
1029C4—22no—
1030C4—22no—
1031C4—22no—
1032C4—24no—
1033C4—42no—
1034C4—42no—
1035C4—42no—
1036C4—42no—
1037C4—44no—
1038C4—44no—
1039C4—42no—
1040C4—44no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—48no—
1046C4—48no—
1047C4#351114yes—
1048C4#356518yes—
1049C2—42no—
1050C2—82no—
1051C2—84no—
1052C2C2×#356512yes—
1053C2C2×#351111yescharacteristic
1054C2#6281511yescharacteristic
1055C2#6281511yescharacteristic
1056C2#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. #59710C2semidirect
2. #59497C2semidirect
3. #45514C2semidirect
4. #45513C2semidirect
5. #39781C2semidirect
6. #39780C2semidirect
7. #39758C2semidirect
8. #39530C2semidirect
9. #39529C2semidirect
10. #39374C2semidirect
11. #37711C2semidirect
12. #37553C2semidirect
13. #37435C2semidirect
14. #36645C2semidirect
15. #36631C2semidirect
16. #36574C2semidirect
17. #36573C2semidirect
18. #36211C2semidirect
19. #36211C2semidirect
20. #36210C2semidirect
21. #36209C2semidirect
22. #35294C2semidirect
23. #35277C2semidirect
24. #34392C2semidirect
25. C4×#529C2semidirect

Maximal subgroups

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

subgroupindex
#597102
#594972
#455142
#455132
#397812
#397802
#397582
#395302
#395292
#393742
#377112
#375532
#374352
#366452
#366312
#365742
#365732
#362112
#362102
#362092
#352942
#352772
#343922
C4×#5292