Finite Group Databasebeta

← #7712519

Subgroups — #7712519

Order 512.

5278 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59691C214yesmaximal, complemented
2#59474C214yesmaximal, complemented
3#45518C214yesmaximal, complemented
4#45516C214yesmaximal, complemented
5#39786C214yesmaximal, complemented
6#39785C214yesmaximal, complemented
7#39766C212yesmaximal, complemented
8#39525C214yesmaximal, complemented
9#39524C214yesmaximal, complemented
10#39382C212yesmaximal, complemented
11#37701C212yesmaximal, complemented
12#37700C212yesmaximal, complemented
13#37559C212yesmaximal, complemented
14#37432C212yesmaximal, complemented
15#37432C212yesmaximal, complemented
16#36644C211yesmaximal, characteristic, complemented
17#36635C211yesmaximal, characteristic, complemented
18#36609C212yesmaximal, complemented
19#36150C212yesmaximal, complemented
20#36150C212yesmaximal, complemented
21#36149C212yesmaximal, complemented
22#35322C211yesmaximal, characteristic, complemented
23#35319C211yesmaximal, characteristic, complemented
24#35293C211yesmaximal, characteristic, complemented
25#35278C211yesmaximal, characteristic, complemented
26#34402C212yesmaximal, complemented
27C4×#529C211yesmaximal, characteristic, complemented
28C2×#541C2212yes—
29C2×#540C2212yes—
30C2×#533C2212yes—
31C2×#532C2212yes—
32C2×#532C2212yes—
33C2×#532C2212yes—
34C2×#532C2212yes—
35C2×#529C2211yescharacteristic
36#2868C2211yescharacteristic
37#2867C2211yescharacteristic
38#2864C2212yes—
39#2863C2214yes—
40#2862C2212yes—
41#2862C2211yescharacteristic
42#2859C2211yescharacteristic
43#2858C2212yes—
44#2858C2212yes—
45#2858C2212yes—
46#2858C2212yes—
47#2857C2212yes—
48#2857C2212yes—
49#2856C2214yes—
50#2856C2214yes—
51#2856C2212yes—
52#2855C2214yes—
53#2851C2212yes—
54#2816C2214yes—
55#2815C2214yes—
56#2797C2218yes—
57#2797C2218yes—
58#2796C2218yes—
59#2786C2218yes—
60#2786C2218yes—
61#2752C2218yes—
62#2752C2218yes—
63#2751C2218yes—
64#2740C2218yes—
65#2740C2218yes—
66#2714C2218yes—
67#2714C2218yes—
68#2711C2218yes—
69#2708C2218yes—
70#2694C2218yes—
71#2688C2218yes—
72#2661C2214yes—
73#2661C2214yes—
74#2642C2212yes—
75#2641C2212yes—
76#2633C2214yes—
77#2631C2214yes—
78#2621C2212yes—
79#2621C2212yes—
80#2621C2212yes—
81#2619C2212yes—
82#2619C2212yes—
83#2619C2212yes—
84#2603C2214yes—
85#2603C2214yes—
86#2595C2218yes—
87#2592C2214yes—
88#2592C2214yes—
89#2580C2214yes—
90#2565C2214yes—
91#2565C2214yes—
92#2554C2218yes—
93#2544C2214yes—
94#2544C2214yes—
95#2540C2214yes—
96#2540C2214yes—
97#2535C2214yes—
98#2516C2218yes—
99#2513C2214yes—
100#2513C2214yes—
101#2506C2214yes—
102#2506C2214yes—
103#2499C2214yes—
104#2499C2214yes—
105#2496C2214yes—
106#2496C2214yes—
107#2490C2218yes—
108#2490C2214yes—
109#2490C2214yes—
110#2467C2218yes—
111#2460C2218yes—
112#2454C2214yes—
113#2454C2214yes—
114#2448C2214yes—
115#2448C2214yes—
116#2448C2214yes—
117#2448C2214yes—
118#2447C2214yes—
119#2447C2214yes—
120#2447C2214yes—
121#2447C2214yes—
122#2445C2214yes—
123#2445C2214yes—
124#2444C2218yes—
125#2431C2214yes—
126#2431C2214yes—
127#2428C2214yes—
128#2428C2214yes—
129#2427C2214yes—
130#2427C2214yes—
131#2427C2214yes—
132#2427C2214yes—
133#2426C2214yes—
134#2426C2214yes—
135#2426C2214yes—
136#2426C2214yes—
137#2420C2214yes—
138#2420C2214yes—
139#2419C2218yes—
140#2414C2214yes—
141#2414C2214yes—
142#2407C2214yes—
143#2407C2214yes—
144#2407C2214yes—
145#2407C2214yes—
146#2377C2218yes—
147#2367C2214yes—
148#2367C2214yes—
149#2367C2214yes—
150#2367C2214yes—
151#2363C2214yes—
152#2363C2214yes—
153#2357C2214yes—
154#2353C2218yes—
155#2349C2214yes—
156#2341C2214yes—
157#2341C2214yes—
158#2339C2214yes—
159#2339C2214yes—
160#2333C2218yes—
161#2328C2212yes—
162#2328C2212yes—
163#2328C2212yes—
164#2327C2212yes—
165#2327C2212yes—
166#2327C2212yes—
167#2318C2218yes—
168C4×C4⋊Q8C2212yes—
169C4×C4⋊Q8C2212yes—
170C4×#127C2212yes—
171C4×#127C2214yes—
172C4×#127C2214yes—
173C4×#125C2212yes—
174C4×#125C2212yes—
175C4×#126C2212yes—
176C4×#126C2212yes—
177C4×#124C2212yes—
178C4×C22⋊Q8C2214yes—
179C4×C22⋊Q8C2212yes—
180C4×#123C2212yes—
181C4×#123C2212yes—
182C4×#121C2212yes—
183#2298C2211yescharacteristic
184#2298C2211yescharacteristic
185#2295C2214yes—
186#2295C2211yescharacteristic
187#2293C2211yescharacteristic
188#2290C2211yescharacteristic
189#2290C2211yescharacteristic
190#2283C2212yes—
191#2283C2211yescharacteristic
192C42×Q8C2211yescharacteristic
193C42×D4C2211yescharacteristic
194C42×D4C2211yescharacteristic
195C42×D4C2211yescharacteristic
196C4×#117C2211yescharacteristic
197C4×#117C2211yescharacteristic
198C2×C43C2211yescharacteristic
199C22×#41C2314yes—
200C22×#41C2314yes—
201#541—48no—
202#540—48no—
203#533—48no—
204#532—216no—
205#532—48no—
206#532—48no—
207#532—48no—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×#127C2312yes—
213C2×#127C2312yes—
214C2×#127C2312yes—
215C2×#127C2314yes—
216C2×#127C2314yes—
217#529—28no—
218C2×#126C2311yescharacteristic
219C2×#126C2311yescharacteristic
220C2×#126C2318yes—
221C2×#125C2311yescharacteristic
222C2×#125C2312yes—
223C2×#125C2314yes—
224C2×#125C2318yes—
225C2×#124C2314yes—
226C2×#124C2311yescharacteristic
227C2×#124C2314yes—
228C2×#124C2314yes—
229C2×#124C2314yes—
230C2×#124C2314yes—
231C2×#124C2314yes—
232C2×#123C2311yescharacteristic
233C2×#123C2311yescharacteristic
234C2×#123C2318yes—
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2314yes—
240C2×#121C2314yes—
241C2×#121C2314yes—
242C2×#121C2311yescharacteristic
243C2×#121C2314yes—
244C2×#121C2314yes—
245C2×#121C2318yes—
246C2×#121C2314yes—
247C2×#121C2314yes—
248C2×#121C2314yes—
249C2×#121C2314yes—
250C2×#121C2314yes—
251C2×#121C2318yes—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2314yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2318yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2312yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×#117C2311yescharacteristic
275C2×#117C2311yescharacteristic
276C2×#117C2311yescharacteristic
277C2×#117C2311yescharacteristic
278C2×#117C2314yes—
279C22×C42C2311yescharacteristic
280C22×C42C2311yescharacteristic
281C22×C42C2311yescharacteristic
282C22×C42C2311yescharacteristic
283C22×C42C2312yes—
284C22×C42C2312yes—
285C22×C42C2311yescharacteristic
286#400C2318yes—
287#400C2318yes—
288#399C2318yes—
289#399C2318yes—
290#399C2318yes—
291#398C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2318yes—
295#398C2314yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2314yes—
301#397C2314yes—
302#397C2314yes—
303#397C2314yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#396C2318yes—
311#396C2318yes—
312#394C2314yes—
313#394C2314yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2314yes—
318#394C2314yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#393C2318yes—
326#392C2314yes—
327#392C2314yes—
328#392C2314yes—
329#392C2314yes—
330#392C2318yes—
331#392C2318yes—
332#392C2318yes—
333#392C2318yes—
334#391C2314yes—
335#391C2314yes—
336#391C2314yes—
337#391C2314yes—
338#391C2314yes—
339#391C2314yes—
340#391C2314yes—
341#391C2314yes—
342#391C2314yes—
343#391C2314yes—
344#391C2312yes—
345#390C2314yes—
346#390C2314yes—
347#390C2314yes—
348#390C2314yes—
349#390C2318yes—
350#390C2314yes—
351#390C2314yes—
352#390C2318yes—
353#390C2318yes—
354#390C2318yes—
355#390C2314yes—
356#390C2314yes—
357#390C2314yes—
358#390C2314yes—
359#390C2314yes—
360#390C2318yes—
361#390C2318yes—
362#390C2314yes—
363#390C2318yes—
364#390C2318yes—
365#390C2314yes—
366#390C2314yes—
367#390C2318yes—
368#390C2318yes—
369#390C2312yes—
370#389C2314yes—
371#389C2312yes—
372#389C2312yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#388C2312yes—
383#388C2312yes—
384#388C2312yes—
385#388C2312yes—
386#388C2312yes—
387#388C2312yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2312yes—
401#388C2312yes—
402#387C2312yes—
403#387C2312yes—
404#387C2312yes—
405#387C2312yes—
406#387C2312yes—
407#387C2312yes—
408#387C2318yes—
409#387C2312yes—
410#387C2312yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#386C2318yes—
421#386C2318yes—
422#386C2318yes—
423#386C2318yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2312yes—
433#386C2312yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2318yes—
438#385C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2312yes—
442#385C2312yes—
443#384C2312yes—
444#384C2314yes—
445#384C2314yes—
446#383C2312yes—
447#383C2314yes—
448#382C2312yes—
449#382C2312yes—
450#382C2314yes—
451#382C2314yes—
452#382C2312yes—
453#382C2312yes—
454#381C2314yes—
455#381C2318yes—
456#381C2312yes—
457#381C2318yes—
458#381C2318yes—
459#380C2318yes—
460#380C2314yes—
461#380C2314yes—
462#380C2314yes—
463#380C2318yes—
464#380C2314yes—
465#380C2318yes—
466#380C2312yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2318yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2318yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2318yes—
497C4×C22⋊C4C2318yes—
498C4×C22⋊C4C2311yescharacteristic
499C4×C22⋊C4C2311yescharacteristic
500C4×C22⋊C4C2312yes—
501C4×C22⋊C4C2311yescharacteristic
502C4×C22⋊C4C2311yescharacteristic
503C4×C22⋊C4C2312yes—
504C4×C22⋊C4C2311yescharacteristic
505C4×C22⋊C4C2311yescharacteristic
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2312yes—
508#376C2311yescharacteristic
509#376C2311yescharacteristic
510#376C2311yescharacteristic
511#376C2311yescharacteristic
512#376C2314yes—
513C2×#95C2318yes—
514C43C2312yes—
515C43C2311yescharacteristic
516C43C2312yes—
517C43C2311yescharacteristic
518C43C2311yescharacteristic
519C43C2311yescharacteristic
520C43C2311yescharacteristic
521C43C2311yescharacteristic
522C2×#41—216no—
523C2×#41—48no—
524C2×#41—48no—
525C2×#41—48no—
526C2×#41—48no—
527C2×#41—48no—
528C22×Q8C2414yes—
529C22×Q8C2414yes—
530C22×Q8C2411yescharacteristic
531C22×D4C2414yes—
532C22×D4C2414yes—
533C22×D4C2414yes—
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C22×D4C2411yescharacteristic
537C22×D4C2418yes—
538C22×D4C2414yes—
539C22×D4C2414yes—
540C22×D4C2418yes—
541C22×D4C2418yes—
542C22×D4C2418yes—
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2411yescharacteristic
549C23×C4C2418yes—
550C23×C4C2412yes—
551C23×C4C2418yes—
552C23×C4C2418yes—
553C23×C4C2411yescharacteristic
554C23×C4C2411yescharacteristic
555C4⋊Q8—28no—
556C4⋊Q8—28no—
557C4⋊Q8—28no—
558C4⋊Q8—28no—
559#127—28no—
560#127—28no—
561#127—28no—
562#127—48no—
563#127—48no—
564#126—24no—
565#126—24no—
566#126—416no—
567#125—24no—
568#125—28no—
569#125—48no—
570#125—416no—
571#124—24no—
572#124—216no—
573#124—48no—
574#124—48no—
575#124—48no—
576#124—48no—
577#124—48no—
578#123—24no—
579#123—24no—
580#123—416no—
581C22⋊Q8—24no—
582C22⋊Q8—48no—
583C22⋊Q8—48no—
584C22⋊Q8—48no—
585C22⋊Q8—48no—
586#121—24no—
587#121—216no—
588#121—216no—
589#121—416no—
590#121—48no—
591#121—48no—
592#121—48no—
593#121—48no—
594#121—48no—
595#121—48no—
596#121—416no—
597#121—48no—
598C4×Q8—24no—
599C4×Q8—44no—
600C4×Q8—48no—
601C4×Q8—48no—
602C4×Q8—48no—
603C4×Q8—48no—
604C4×D4—24no—
605C4×D4—24no—
606C4×D4—24no—
607C4×D4—216no—
608C4×D4—216no—
609C4×D4—48no—
610C4×D4—48no—
611C4×D4—48no—
612C4×D4—48no—
613C4×D4—48no—
614C4×D4—416no—
615C4×D4—48no—
616C4×D4—48no—
617C4×D4—44no—
618C4×D4—44no—
619C4×D4—44no—
620#117—24no—
621#117—24no—
622#117—24no—
623#117—24no—
624#117—48no—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2411yescharacteristic
662C2×C22⋊C4C2411yescharacteristic
663C2×C22⋊C4C2411yescharacteristic
664C2×C22⋊C4C2411yescharacteristic
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2411yescharacteristic
669C2×C22⋊C4C2411yescharacteristic
670C2×C22⋊C4C2411yescharacteristic
671C2×C22⋊C4C2411yescharacteristic
672C2×C22⋊C4C2411yescharacteristic
673C2×C22⋊C4C2411yescharacteristic
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C42—24no—
700C2×C42—24no—
701C2×C42—24no—
702C2×C42—24no—
703C2×C42—44no—
704C2×C42—44no—
705C2×C42#4118yescomplemented
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2411yescharacteristic
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2411yescharacteristic
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2418yes—
727C2×C42C2418yes—
728C2×C42C2418yes—
729C2×C42C2412yes—
730C2×C42C2412yes—
731C2×C42C2412yes—
732C2×C42C2412yes—
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739#95C2412yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2412yes—
744#95C2412yes—
745#95C2412yes—
746#95C2412yes—
747#95C2412yes—
748#95C2412yes—
749#95C2412yes—
750#95C2412yes—
751#95C2414yes—
752#95C2414yes—
753#95C2412yes—
754#95C2412yes—
755#95C2412yes—
756#95C2412yes—
757#95C2412yes—
758#95C2412yes—
759#95C2412yes—
760#95C2412yes—
761#95C2412yes—
762#95C2418yes—
763#95C2418yes—
764#95C2414yes—
765#95C2414yes—
766#95C2412yes—
767#95C2412yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773#95C2418yes—
774#95C2418yes—
775#95C2418yes—
776C24C2511yescharacteristic
777C24C2511yescharacteristic
778C24C2518yes—
779C24C2511yescharacteristic
780#41—832no—
781#41—832no—
782C2×Q8—22no—
783C2×Q8—28no—
784C2×Q8—28no—
785C2×Q8—28no—
786C2×Q8—28no—
787C2×Q8—28no—
788C2×Q8—28no—
789C2×Q8—42no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—216no—
793C2×D4—22no—
794C2×D4—28no—
795C2×D4—28no—
796C2×D4—28no—
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—216no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4—28no—
806C2×D4—42no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—48no—
810C2×D4—48no—
811C2×D4—48no—
812C2×D4—48no—
813C2×D4—48no—
814C2×D4—48no—
815C2×D4—48no—
816C2×D4—48no—
817C2×D4—48no—
818C2×D4—48no—
819C2×D4—48no—
820C2×D4—48no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—22no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—216no—
840C22×C4—42no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4C2×#4114yes—
853C22×C4C2×#4114yes—
854C22×C4C2×#4114yes—
855C22×C4C2512yes—
856C22×C4C2512yes—
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C22×C4C2518yes—
862C22×C4C2518yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2512yes—
866C22×C4C2518yes—
867C22×C4C2512yes—
868C22×C4C2511yescharacteristic
869C22×C4C2511yescharacteristic
870C22×C4C2511yescharacteristic
871C22×C4C2511yescharacteristic
872C22×C4C2511yescharacteristic
873C22×C4C2511yescharacteristic
874C22×C4C2511yescharacteristic
875C22×C4C2512yes—
876C22×C4C2511yescharacteristic
877C22×C4C2512yes—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—22no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—22no—
890C4⋊C4—24no—
891C4⋊C4—24no—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—28no—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—216no—
898C4⋊C4—216no—
899C4⋊C4—28no—
900C4⋊C4—28no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—48no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C22⋊C4—22no—
914C22⋊C4—22no—
915C22⋊C4—22no—
916C22⋊C4—22no—
917C22⋊C4—22no—
918C22⋊C4—22no—
919C22⋊C4—216no—
920C22⋊C4—216no—
921C22⋊C4—22no—
922C22⋊C4—22no—
923C22⋊C4—22no—
924C22⋊C4—22no—
925C22⋊C4—24no—
926C22⋊C4—24no—
927C22⋊C4—48no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—42no—
935C22⋊C4—42no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C42—22no—
953C42—22no—
954C42—24no—
955C42—24no—
956C42—22no—
957C42—24no—
958C42—22no—
959C42—24no—
960C42—22no—
961C42—22no—
962C42—22no—
963C42—22no—
964C42—24no—
965C42—24no—
966C42—24no—
967C42—24no—
968C42—24no—
969C42—24no—
970C42—24no—
971C42—24no—
972C42—42no—
973C42—42no—
974C42—42no—
975C42—42no—
976C42—48no—
977C42—48no—
978C42—48no—
979C42C2×#4114yes—
980C42C2×#4114yes—
981C42C2×#4114yes—
982C42C2×#4114yes—
983C42H(5,𝔽2)14yes—
984C42H(5,𝔽2)14yes—
985C23—21no—
986C23—21no—
987C23—22no—
988C23—22no—
989C23—21no—
990C23—21no—
991C23—28no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—28no—
996C23—28no—
997C23—21no—
998C23—28no—
999C23—28no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—28no—
1005C23—28no—
1006C23C22×#4112yes—
1007C23C2611yescharacteristic
1008Q8—44no—
1009Q8—416no—
1010Q8—416no—
1011D4—44no—
1012D4—44no—
1013D4—44no—
1014D4—416no—
1015D4—416no—
1016D4—416no—
1017D4—88no—
1018D4—88no—
1019D4—816no—
1020D4—816no—
1021D4—816no—
1022D4—168no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—28no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—28no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—28no—
1048C2×C4—28no—
1049C2×C4—28no—
1050C2×C4—28no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—28no—
1066C2×C4—28no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—28no—
1070C2×C4—28no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—44no—
1074C2×C4—44no—
1075C2×C4—48no—
1076C2×C4—44no—
1077C2×C4—44no—
1078C2×C4—48no—
1079C2×C4—48no—
1080C2×C4—48no—
1081C2×C4—816no—
1082C2×C4—816no—
1083C2×C4—168no—
1084C2×C4C22×#4112yes—
1085C2×C4C22×#4112yes—
1086C2×C4C22×#4112yes—
1087C2×C4C22×#4112yes—
1088C2×C4C22×#4112yes—
1089C2×C4C22×#4112yes—
1090C2×C4C2×H(5,𝔽2)14yes—
1091C2×C4C2×H(5,𝔽2)12yes—
1092C2×C4C2×H(5,𝔽2)12yes—
1093C2×C4C2×H(5,𝔽2)14yes—
1094C2×C4#58514yes—
1095C2×C4#58514yes—
1096C22—22no—
1097C22—22no—
1098C22—22no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—48no—
1104C22—48no—
1105C22—41no—
1106C22—41no—
1107C22—48no—
1108C22—41no—
1109C22—41no—
1110C22—41no—
1111C22—41no—
1112C22—48no—
1113C22—48no—
1114C22—48no—
1115C22—48no—
1116C22—42no—
1117C22—42no—
1118C22C23×#4111yescharacteristic
1119C22C22×H(5,𝔽2)11yescharacteristic
1120C22C22×H(5,𝔽2)11yescharacteristic
1121C22C2×#58512yes—
1122C22C2×#58512yes—
1123C4—22no—
1124C4—22no—
1125C4—22no—
1126C4—22no—
1127C4—22no—
1128C4—24no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—48no—
1133C4—41no—
1134C4—41no—
1135C4—48no—
1136C4—41no—
1137C4—41no—
1138C4—41no—
1139C4—41no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—48no—
1144C4#350814yes—
1145C4#356218yes—
1146C2—42no—
1147C2—81no—
1148C2—81no—
1149C2—88no—
1150C2C2×#356212yes—
1151C2C2×#350811yescharacteristic
1152C2#6281511yescharacteristic
1153C2#6281511yescharacteristic
1154C2#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. #59691C2semidirect
2. #59474C2semidirect
3. #45518C2semidirect
4. #45516C2semidirect
5. #39786C2semidirect
6. #39785C2semidirect
7. #39766C2semidirect
8. #39525C2semidirect
9. #39524C2semidirect
10. #39382C2semidirect
11. #37701C2semidirect
12. #37700C2semidirect
13. #37559C2semidirect
14. #37432C2semidirect
15. #37432C2semidirect
16. #36644C2semidirect
17. #36635C2semidirect
18. #36609C2semidirect
19. #36150C2semidirect
20. #36150C2semidirect
21. #36149C2semidirect
22. #35322C2semidirect
23. #35319C2semidirect
24. #35293C2semidirect
25. #35278C2semidirect
26. #34402C2semidirect
27. C4×#529C2semidirect
705. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#596912
#594742
#455182
#455162
#397862
#397852
#397662
#395252
#395242
#393822
#377012
#377002
#375592
#374322
#366442
#366352
#366092
#361502
#361492
#353222
#353192
#352932
#352782
#344022
C4×#5292