Finite Group Databasebeta

← #7646605

Subgroups — #7646605

Order 512.

5308 conjugacy classes of subgroups.

The subgroup lattice has 1262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42690C214yesmaximal, complemented
2#42688C214yesmaximal, complemented
3#42664C214yesmaximal, complemented
4#42658C214yesmaximal, complemented
5#39763C212yesmaximal, complemented
6#39735C212yesmaximal, complemented
7#39507C212yesmaximal, complemented
8#39481C212yesmaximal, complemented
9#39191C212yesmaximal, complemented
10#39156C212yesmaximal, complemented
11#38975C212yesmaximal, complemented
12#38942C212yesmaximal, complemented
13#37493C214yesmaximal, complemented
14#36987C218yesmaximal, complemented
15#35518C212yesmaximal, complemented
16#35516C212yesmaximal, complemented
17#35286C211yesmaximal, characteristic, complemented
18#35273C211yesmaximal, characteristic, complemented
19#35229C214yesmaximal, complemented
20#35157C212yesmaximal, complemented
21#35150C212yesmaximal, complemented
22#34936C211yesmaximal, characteristic, complemented
23#34935C211yesmaximal, characteristic, complemented
24#34206C211yesmaximal, characteristic, complemented
25C2×#2354C211yesmaximal, characteristic, complemented
26#34060C211yesmaximal, characteristic, complemented
27C2×#537C2212yes—
28C2×#532C2211yescharacteristic
29C2×#525C2212yes—
30C2×#525C2212yes—
31C2×#525C2212yes—
32C2×#520C2212yes—
33C2×C4×#41C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C22×#117C2212yes—
36#2859C2212yescomplemented
37#2859C2212yescomplemented
38#2857C2212yescomplemented
39#2856C2212yescomplemented
40#2854C2218yes—
41#2853C2218yes—
42#2829C2218yes—
43#2828C2218yes—
44#2803C2218yescomplemented
45#2803C2218yescomplemented
46#2800C2218yescomplemented
47#2800C2218yescomplemented
48#2777C2218yescomplemented
49#2773C2218yescomplemented
50#2761C2218yescomplemented
51#2756C2218yescomplemented
52#2753C2218yescomplemented
53#2753C2218yescomplemented
54#2741C2218yescomplemented
55#2740C2218yescomplemented
56#2711C2218yescomplemented
57#2707C2218yescomplemented
58#2703C2218yescomplemented
59#2699C2218yescomplemented
60#2661C2218yes—
61#2654C2218yescomplemented
62#2651C2218yescomplemented
63#2648C2218yes—
64#2647C2214yescomplemented
65#2644C2214yes—
66#2641C2214yes—
67#2624C2214yes—
68#2622C2218yes—
69#2620C2214yescomplemented
70#2619C2214yes—
71#2617C2218yes—
72#2571C2212yescomplemented
73#2571C2212yescomplemented
74#2552C2212yescomplemented
75#2552C2212yescomplemented
76#2542C2211yescharacteristic
77#2542C2211yescharacteristic
78#2541C2211yescharacteristic
79#2541C2211yescharacteristic
80#2540C2212yes—
81#2540C2212yes—
82#2539C2214yes—
83#2538C2211yescharacteristic
84#2538C2211yescharacteristic
85#2538C2212yescomplemented
86#2538C2214yescomplemented
87#2538C2212yescomplemented
88#2537C2211yescharacteristic
89#2537C2211yescharacteristic
90#2537C2212yescomplemented
91#2537C2214yescomplemented
92#2537C2212yescomplemented
93#2536C2212yes—
94#2536C2214yescomplemented
95#2535C2212yes—
96#2535C2214yescomplemented
97#2534C2214yes—
98#2522C2218yescomplemented
99#2516C2218yescomplemented
100#2513C2214yes—
101#2513C2214yescomplemented
102#2507C2214yescomplemented
103#2501C2212yes—
104#2500C2214yescomplemented
105#2500C2214yescomplemented
106#2499C2214yescomplemented
107#2499C2214yescomplemented
108#2497C2214yescomplemented
109#2490C2214yes—
110#2490C2214yescomplemented
111#2487C2214yescomplemented
112#2486C2212yes—
113#2486C2214yescomplemented
114#2485C2214yescomplemented
115#2485C2214yescomplemented
116#2485C2214yescomplemented
117#2485C2214yescomplemented
118#2485C2214yescomplemented
119#2485C2214yescomplemented
120#2445C2214yes—
121#2442C2214yes—
122#2442C2214yes—
123#2433C2212yes—
124#2428C2214yes—
125#2425C2218yes—
126#2424C2218yes—
127#2423C2214yescomplemented
128#2422C2214yescomplemented
129#2421C2214yescomplemented
130#2420C2214yescomplemented
131#2419C2218yes—
132#2418C2218yes—
133#2417C2214yescomplemented
134#2416C2214yes—
135#2416C2214yes—
136#2416C2214yescomplemented
137#2415C2214yescomplemented
138#2415C2214yescomplemented
139#2415C2214yescomplemented
140#2415C2214yescomplemented
141#2415C2214yescomplemented
142#2414C2214yescomplemented
143#2414C2214yescomplemented
144#2414C2214yescomplemented
145#2414C2214yescomplemented
146#2414C2214yescomplemented
147#2408C2212yes—
148#2397C2214yes—
149#2392C2214yes—
150#2367C2214yescomplemented
151#2366C2212yescomplemented
152#2365C2212yescomplemented
153#2354C2212yes—
154#2354C2212yes—
155#2354C2212yes—
156#2354C2212yes—
157#2354C2214yes—
158#2354C2214yes—
159#2354C2212yescomplemented
160#2352C2214yescomplemented
161D4×C4⋊C4C2212yescomplemented
162#2330C2214yescomplemented
163#2325C2214yes—
164#2324C2214yescomplemented
165#2320C2212yescomplemented
166#2319C2212yescomplemented
167#2319C2214yescomplemented
168#2318C2214yes—
169#2317C2211yescharacteristic
170#2317C2211yescharacteristic
171#2317C2212yes—
172#2316C2212yes—
173#2314C2212yescomplemented
174#2314C2212yescomplemented
175#2314C2214yescomplemented
176#2311C2211yescharacteristic
177#2311C2211yescharacteristic
178#2311C2212yes—
179#2311C2212yes—
180C4×#127C2212yes—
181C4×#127C2212yes—
182C4×#121C2212yes—
183C4×#121C2212yes—
184C4×#121C2214yes—
185#2295C2212yescomplemented
186#2293C2212yescomplemented
187C2×#390C2212yes—
188#2290C2214yes—
189C2×#388C2214yes—
190#2285C2211yescharacteristic
191#2285C2212yescomplemented
192C2×#384C2211yescharacteristic
193#2283C2212yescomplemented
194#2280C2212yes—
195C2×#380C2212yes—
196C4×#117C2211yescharacteristic
197C2×C4×C4⋊C4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2311yescharacteristic
200C22×#41C2312yes—
201C23×D4C2311yescharacteristic
202C24×C4C2312yes—
203#537—48no—
204#532—28no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×#127C2311yescharacteristic
207C2×#127C2312yes—
208C2×#127C2312yes—
209C2×#125C2314yes—
210C2×#125C2314yes—
211C2×#124C2312yes—
212#525—48no—
213#525—48no—
214#525—48no—
215C2×#123C2314yes—
216C2×#123C2314yes—
217C2×#123C2314yes—
218C2×#123C2318yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2314yes—
227C2×#121C2312yes—
228C2×#121C2312yes—
229C2×#121C2314yes—
230C2×#121C2318yes—
231C2×#121C2314yes—
232C2×#121C2312yes—
233C2×#121C2312yes—
234C2×#121C2312yes—
235C2×#121C2312yes—
236C2×#121C2312yes—
237C2×#121C2312yes—
238C2×#121C2312yes—
239C2×#121C2312yes—
240C2×#121C2314yes—
241C2×#121C2314yes—
242C2×#121C2318yes—
243C2×#120C2314yes—
244C2×#120C2314yes—
245C2×#120C2314yes—
246#520—48no—
247C4×#41—28no—
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2314yes—
251C2×C4×D4—28no—
252C2×C4×D4C2312yes—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2312yes—
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2312yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2312yes—
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2318yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×#117—48no—
274C2×#117C2311yescharacteristic
275C2×#117C2311yescharacteristic
276C2×#117C2312yes—
277C2×#117C2311yescharacteristic
278C2×#117C2312yes—
279C2×#117C2314yes—
280C2×#117C2314yes—
281C2×#117C2314yes—
282C2×#117C2314yes—
283C2×#117C2314yes—
284C2×#117C2314yes—
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2314yes—
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2312yes—
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2314yes—
294C22×C22⋊C4C2314yes—
295C22×C42C2312yes—
296C22×C42C2314yes—
297C22×C42C2312yes—
298C22×C42C2311yescharacteristic
299#400C2318yes—
300#400C2318yes—
301#400C2318yes—
302#399C2318yes—
303#399C2314yes—
304#399C2314yes—
305#399C2314yes—
306#399C2314yes—
307#398C2318yes—
308#398C2318yes—
309#398C2314yes—
310#398C2318yes—
311#398C2318yes—
312#397C2318yes—
313#397C2318yes—
314#397C2318yes—
315#397C2318yes—
316#397C2318yes—
317#397C2318yes—
318#397C2318yes—
319#397C2314yes—
320#397C2318yes—
321#397C2318yes—
322#397C2318yes—
323#396C2318yes—
324#396C2318yes—
325#396C2318yes—
326#396C2314yes—
327#396C2314yes—
328#396C2318yes—
329#394C2318yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#394C2318yes—
334#394C2314yes—
335#394C2318yes—
336#394C2318yes—
337#394C2318yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2314yes—
345#394C2314yes—
346#394C2318yes—
347#392C2314yes—
348#392C2314yes—
349#392C2318yes—
350#392C2318yes—
351#392C2314yes—
352#392C2318yes—
353#392C2314yes—
354#392C2314yes—
355#391C2312yes—
356#391C2312yes—
357#391C2314yes—
358#391C2314yes—
359#390C2312yes—
360#390C2312yes—
361#390C2312yes—
362#390C2312yes—
363#390C2314yes—
364#390C2314yes—
365#390C2314yes—
366#390C2314yes—
367#390C2312yes—
368#390C2312yes—
369#390C2314yes—
370#390C2314yes—
371#390C2318yes—
372#390C2314yes—
373#390C2318yes—
374#390C2318yes—
375#390C2314yes—
376#390C2314yes—
377#390C2314yes—
378#390C2314yes—
379#390C2312yes—
380#390C2312yes—
381#390C2318yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2312yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2314yes—
393#389C2314yes—
394#389C2312yes—
395#389C2314yes—
396#389C2312yes—
397#389C2318yes—
398#389C2314yes—
399#389C2318yes—
400#389C2318yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
425#388C2318yes—
426#388C2314yes—
427#388C2314yes—
428#387C2314yes—
429#387C2314yes—
430#387C2314yes—
431#387C2314yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#386C2314yes—
440#386C2314yes—
441#386C2318yes—
442#386C2318yes—
443#386C2318yes—
444#386C2318yes—
445#386C2318yes—
446#386C2318yes—
447#386C2314yes—
448#386C2314yes—
449#385C2314yes—
450#385C2314yes—
451#385C2318yes—
452#385C2318yes—
453#385C2318yes—
454#384C2312yes—
455#384C2312yes—
456#384C2312yes—
457#384C2312yes—
458#384C2312yes—
459#384C2312yes—
460#384C2314yes—
461#384C2311yescharacteristic
462#384C2312yes—
463#384C2311yescharacteristic
464#384C2312yes—
465#383C2314yes—
466#382C2314yes—
467#382C2312yes—
468#382C2312yes—
469#382C2314yes—
470#382C2314yes—
471#382C2314yes—
472#382C2312yes—
473#381C2314yes—
474#381C2318yes—
475#381C2314yes—
476#380C2312yes—
477#380C2312yes—
478#380C2312yes—
479#380C2312yes—
480#380C2314yes—
481#380C2314yes—
482#380C2314yes—
483#380C2314yes—
484#380C2312yes—
485#380C2314yes—
486#380C2318yes—
487#380C2314yes—
488#380C2318yes—
489#380C2312yes—
490#380C2312yes—
491#380C2314yes—
492#380C2314yes—
493#380C2314yes—
494#380C2314yes—
495#380C2314yes—
496#380C2312yes—
497#380C2312yes—
498#380C2312yes—
499#380C2312yes—
500#380C2312yes—
501#379C2314yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2314yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2318yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2311yescharacteristic
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2318yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2312yes—
523#376C2312yes—
524#376C2314yes—
525C2×#95C2312yes—
526C2×#95C2314yes—
527C43C2312yes—
528C25C2412yes—
529C2×#41—24no—
530C2×#41—28no—
531C2×#41—28no—
532C2×#41—24no—
533C2×#41—28no—
534C2×#41—24no—
535C22×Q8C2411yescharacteristic
536C22×Q8C2412yes—
537C22×D4—24no—
538C22×D4—42no—
539C22×D4—42no—
540C22×D4C2412yes—
541C22×D4C2412yes—
542C22×D4C2414yes—
543C22×D4C2411yescharacteristic
544C22×D4C2412yes—
545C22×D4C2411yescharacteristic
546C22×D4C2411yescharacteristic
547C22×D4C2412yes—
548C22×D4C2412yes—
549C22×D4C2414yes—
550C22×D4C2414yes—
551C22×D4C2414yes—
552C22×D4C2414yes—
553C22×D4C2414yes—
554C22×D4C2414yes—
555C22×D4C2418yes—
556C23×C4—28no—
557C23×C4—28no—
558C23×C4—28no—
559C23×C4C2412yes—
560C23×C4C2414yes—
561C23×C4C2412yes—
562C23×C4C2412yes—
563C23×C4C2412yes—
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2412yes—
567C23×C4C2411yescharacteristic
568C23×C4C2414yes—
569C23×C4C2412yes—
570C23×C4C2412yes—
571C23×C4C2412yes—
572C23×C4C2418yes—
573C23×C4C2411yescharacteristic
574C23×C4C2411yescharacteristic
575C4⋊Q8—24no—
576#127—24no—
577#127—44no—
578#127—44no—
579#125—48no—
580#125—84no—
581#124—28no—
582#123—48no—
583#123—48no—
584#123—48no—
585#123—88no—
586C22⋊Q8—44no—
587C22⋊Q8—44no—
588C22⋊Q8—44no—
589C22⋊Q8—44no—
590C22⋊Q8—44no—
591C22⋊Q8—44no—
592C22⋊Q8—48no—
593C22⋊Q8—48no—
594#121—28no—
595#121—28no—
596#121—48no—
597#121—44no—
598#121—44no—
599#121—44no—
600#121—44no—
601#121—44no—
602#121—44no—
603#121—44no—
604#121—44no—
605#121—48no—
606#121—48no—
607#121—416no—
608#121—88no—
609#121—84no—
610#120—48no—
611#120—48no—
612#120—48no—
613C4×Q8—24no—
614C4×Q8—24no—
615C4×Q8—48no—
616C4×D4—28no—
617C4×D4—28no—
618C4×D4—24no—
619C4×D4—24no—
620C4×D4—28no—
621C4×D4—24no—
622C4×D4—24no—
623C4×D4—28no—
624C4×D4—24no—
625C4×D4—24no—
626C4×D4—28no—
627C4×D4—28no—
628C4×D4—48no—
629C4×D4—48no—
630C4×D4—48no—
631C4×D4—48no—
632C4×D4—48no—
633C4×D4—48no—
634C4×D4—48no—
635C4×D4—48no—
636C4×D4—416no—
637#117—24no—
638#117—28no—
639#117—24no—
640#117—24no—
641#117—28no—
642#117—48no—
643#117—48no—
644#117—48no—
645#117—48no—
646#117—48no—
647#117—48no—
648C2×C4⋊C4—24no—
649C2×C4⋊C4—24no—
650C2×C4⋊C4—28no—
651C2×C4⋊C4—24no—
652C2×C4⋊C4—44no—
653C2×C4⋊C4—48no—
654C2×C4⋊C4—82no—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2418yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2418yes—
692C2×C4⋊C4C2418yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2418yes—
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2418yes—
697C2×C4⋊C4C2418yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2412yes—
700C2×C22⋊C4—28no—
701C2×C22⋊C4—48no—
702C2×C22⋊C4—84no—
703C2×C22⋊C4C2412yes—
704C2×C22⋊C4C2412yes—
705C2×C22⋊C4C2412yes—
706C2×C22⋊C4C2412yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2412yes—
709C2×C22⋊C4C2412yes—
710C2×C22⋊C4C2412yes—
711C2×C22⋊C4C2412yes—
712C2×C22⋊C4C2412yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2418yes—
716C2×C22⋊C4C2418yes—
717C2×C22⋊C4C2418yes—
718C2×C22⋊C4C2418yes—
719C2×C22⋊C4C2418yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2418yes—
735C2×C22⋊C4C2418yes—
736C2×C22⋊C4C2418yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2418yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2418yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2418yes—
746C2×C42—28no—
747C2×C42—44no—
748C2×C42—48no—
749C2×C42#4118yes—
750C2×C42C2412yes—
751C2×C42C2412yes—
752C2×C42C2412yes—
753C2×C42C2412yes—
754C2×C42C2414yes—
755C2×C42C2414yes—
756C2×C42C2412yes—
757C2×C42C2412yes—
758C2×C42C2412yes—
759C2×C42C2418yes—
760C2×C42C2418yes—
761C2×C42C2418yes—
762C2×C42C2412yes—
763C2×C42C2412yes—
764C2×C42C2414yes—
765C2×C42C2411yescharacteristic
766C2×C42C2411yescharacteristic
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769#95C2418yes—
770#95C2418yes—
771#95C2414yes—
772#95C2414yes—
773#95C2412yes—
774#95C2412yes—
775#95C2412yes—
776#95C2412yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2418yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2418yes—
793#95C2418yes—
794#95C2418yes—
795#95C2418yes—
796#95C2418yes—
797#95C2418yes—
798#95C2418yes—
799C24—24no—
800C24—24no—
801C24—24no—
802C24—42no—
803C24—42no—
804C24—42no—
805C24—42no—
806C24C2512yes—
807C24C2512yes—
808C24C2512yes—
809C24C2514yes—
810C24C2511yescharacteristic
811#41—416no—
812#41—432no—
813C2×Q8—22no—
814C2×Q8—24no—
815C2×Q8—24no—
816C2×Q8—22no—
817C2×Q8—22no—
818C2×Q8—24no—
819C2×D4—24no—
820C2×D4—28no—
821C2×D4—28no—
822C2×D4—24no—
823C2×D4—28no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—22no—
829C2×D4—24no—
830C2×D4—24no—
831C2×D4—24no—
832C2×D4—24no—
833C2×D4—22no—
834C2×D4—22no—
835C2×D4—24no—
836C2×D4—24no—
837C2×D4—24no—
838C2×D4—22no—
839C2×D4—22no—
840C2×D4—22no—
841C2×D4—22no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—416no—
845C2×D4—44no—
846C2×D4—44no—
847C2×D4—44no—
848C2×D4—44no—
849C2×D4—44no—
850C2×D4—44no—
851C2×D4—44no—
852C2×D4—44no—
853C2×D4—42no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—42no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—48no—
866C2×D4—48no—
867C2×D4—48no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—28no—
875C22×C4—24no—
876C22×C4—24no—
877C22×C4—24no—
878C22×C4—24no—
879C22×C4—24no—
880C22×C4—24no—
881C22×C4—24no—
882C22×C4—28no—
883C22×C4—28no—
884C22×C4—24no—
885C22×C4—24no—
886C22×C4—24no—
887C22×C4—24no—
888C22×C4—24no—
889C22×C4—24no—
890C22×C4—24no—
891C22×C4—24no—
892C22×C4—24no—
893C22×C4—28no—
894C22×C4—24no—
895C22×C4—24no—
896C22×C4—24no—
897C22×C4—24no—
898C22×C4—42no—
899C22×C4—41no—
900C22×C4—41no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—44no—
905C22×C4—44no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—48no—
909C22×C4—48no—
910C22×C4—48no—
911C22×C4—432no—
912C22×C4C2×#4114yes—
913C22×C4C2×#4114yes—
914C22×C4C2×#4114yes—
915C22×C4H(5,𝔽2)14yes—
916C22×C4H(5,𝔽2)14yes—
917C22×C4C2512yes—
918C22×C4C2512yes—
919C22×C4C2512yes—
920C22×C4C2512yes—
921C22×C4C2514yes—
922C22×C4C2514yes—
923C22×C4C2514yes—
924C22×C4C2514yes—
925C22×C4C2512yes—
926C22×C4C2512yes—
927C22×C4C2512yes—
928C22×C4C2512yes—
929C22×C4C2518yes—
930C22×C4C2512yes—
931C22×C4C2514yes—
932C22×C4C2511yescharacteristic
933C22×C4C2511yescharacteristic
934C22×C4C2511yescharacteristic
935C22×C4C2511yescharacteristic
936C22×C4C2511yescharacteristic
937C22×C4C2511yescharacteristic
938C4⋊C4—24no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—24no—
944C4⋊C4—24no—
945C4⋊C4—24no—
946C4⋊C4—24no—
947C4⋊C4—24no—
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—28no—
951C4⋊C4—28no—
952C4⋊C4—24no—
953C4⋊C4—24no—
954C4⋊C4—24no—
955C4⋊C4—22no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—28no—
960C4⋊C4—24no—
961C4⋊C4—24no—
962C4⋊C4—44no—
963C4⋊C4—48no—
964C4⋊C4—44no—
965C4⋊C4—44no—
966C4⋊C4—42no—
967C4⋊C4—44no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4—44no—
976C4⋊C4—48no—
977C4⋊C4—48no—
978C4⋊C4—44no—
979C4⋊C4—48no—
980C4⋊C4—48no—
981C4⋊C4—48no—
982C4⋊C4—42no—
983C22⋊C4—24no—
984C22⋊C4—28no—
985C22⋊C4—24no—
986C22⋊C4—24no—
987C22⋊C4—24no—
988C22⋊C4—24no—
989C22⋊C4—24no—
990C22⋊C4—24no—
991C22⋊C4—24no—
992C22⋊C4—24no—
993C22⋊C4—28no—
994C22⋊C4—28no—
995C22⋊C4—48no—
996C22⋊C4—48no—
997C22⋊C4—48no—
998C22⋊C4—48no—
999C22⋊C4—44no—
1000C22⋊C4—48no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—48no—
1005C22⋊C4—48no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—48no—
1020C22⋊C4—44no—
1021C22⋊C4—48no—
1022C22⋊C4—48no—
1023C22⋊C4—44no—
1024C22⋊C4—48no—
1025C22⋊C4—44no—
1026C42—24no—
1027C42—24no—
1028C42—24no—
1029C42—24no—
1030C42—24no—
1031C42—28no—
1032C42—28no—
1033C42—24no—
1034C42—24no—
1035C42—44no—
1036C42—48no—
1037C42—48no—
1038C42—42no—
1039C42—48no—
1040C42—42no—
1041C42C2×#4114yes—
1042C42C2×#4114yes—
1043C42C2×#4114yes—
1044C42C2×#4114yes—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—24no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—24no—
1058C23—24no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—24no—
1063C23—24no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—24no—
1072C23—22no—
1073C23—22no—
1074C23—24no—
1075C23—22no—
1076C23—22no—
1077C23—48no—
1078C23—48no—
1079C23—48no—
1080C23—84no—
1081C23—84no—
1082C23—84no—
1083C23—84no—
1084C23C22×#4112yes—
1085C23C2×H(5,𝔽2)12yes—
1086C23C2×H(5,𝔽2)12yes—
1087C23C2611yescharacteristic
1088Q8—44no—
1089Q8—48no—
1090D4—48no—
1091D4—48no—
1092D4—416no—
1093D4—44no—
1094D4—48no—
1095D4—48no—
1096D4—44no—
1097D4—44no—
1098D4—84no—
1099D4—88no—
1100D4—88no—
1101D4—88no—
1102D4—88no—
1103D4—88no—
1104D4—88no—
1105D4—168no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—28no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—28no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—24no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—22no—
1145C2×C4—24no—
1146C2×C4—28no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—28no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—44no—
1159C2×C4—48no—
1160C2×C4—48no—
1161C2×C4—48no—
1162C2×C4—48no—
1163C2×C4—48no—
1164C2×C4—48no—
1165C2×C4—416no—
1166C2×C4—48no—
1167C2×C4—48no—
1168C2×C4—84no—
1169C2×C4—84no—
1170C2×C4—88no—
1171C2×C4—168no—
1172C2×C4#540116yes—
1173C2×C4C22×#4112yes—
1174C2×C4C22×#4112yes—
1175C2×C4C22×#4112yes—
1176C2×C4C22×#4112yes—
1177C2×C4C22×#4112yes—
1178C2×C4C22×#4112yes—
1179C2×C4C2×H(5,𝔽2)12yes—
1180C2×C4C2×H(5,𝔽2)12yes—
1181C2×C4C2×H(5,𝔽2)12yes—
1182C2×C4C2×H(5,𝔽2)12yes—
1183C2×C4#58512yes—
1184C2×C4#58512yes—
1185C22—22no—
1186C22—22no—
1187C22—22no—
1188C22—22no—
1189C22—22no—
1190C22—22no—
1191C22—42no—
1192C22—42no—
1193C22—42no—
1194C22—44no—
1195C22—42no—
1196C22—44no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—44no—
1201C22—42no—
1202C22—42no—
1203C22—44no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—44no—
1211C22—42no—
1212C22—44no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—44no—
1219C22—816no—
1220C22C2×#54014yes—
1221C22C23×#4111yescharacteristic
1222C22C22×H(5,𝔽2)11yescharacteristic
1223C22C22×H(5,𝔽2)11yescharacteristic
1224C22C2×#58511yescharacteristic
1225C22C2×#58511yescharacteristic
1226C22H(7,𝔽2)11yescharacteristic
1227C222−1+611yescharacteristic
1228C4—22no—
1229C4—22no—
1230C4—22no—
1231C4—42no—
1232C4—42no—
1233C4—44no—
1234C4—42no—
1235C4—44no—
1236C4—44no—
1237C4—42no—
1238C4—42no—
1239C4—42no—
1240C4—42no—
1241C4—44no—
1242C4—48no—
1243C4—42no—
1244C4—44no—
1245C4—42no—
1246C4C2×#54014yes—
1247C4C2×#54014yes—
1248C4#349314yes—
1249C2—24no—
1250C2—82no—
1251C2—84no—
1252C2—82no—
1253C2—82no—
1254C2C22×#54011yescharacteristic
1255C2C2×#349311yescharacteristic
1256C2#6285611yescharacteristic
1257C2#6292511yescharacteristic
1258C2#6293011yescharacteristic
1259C2#6295511yescharacteristic
1260C2#6296011yescharacteristic
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. #42690C2semidirect
2. #42688C2semidirect
3. #42664C2semidirect
4. #42658C2semidirect
5. #39763C2semidirect
6. #39735C2semidirect
7. #39507C2semidirect
8. #39481C2semidirect
9. #39191C2semidirect
10. #39156C2semidirect
11. #38975C2semidirect
12. #38942C2semidirect
13. #37493C2semidirect
14. #36987C2semidirect
15. #35518C2semidirect
16. #35516C2semidirect
17. #35286C2semidirect
18. #35273C2semidirect
19. #35229C2semidirect
20. #35157C2semidirect
21. #35150C2semidirect
22. #34936C2semidirect
23. #34935C2semidirect
24. #34206C2semidirect
25. C2×#2354C2semidirect
26. #34060C2semidirect
36. #2859C22semidirect
37. #2859C22semidirect
38. #2857C22semidirect
39. #2856C22semidirect
44. #2803C22semidirect
45. #2803C22semidirect
46. #2800C22semidirect
47. #2800C22semidirect
48. #2777C22semidirect
49. #2773C22semidirect
50. #2761C22semidirect
51. #2756C22semidirect
52. #2753C22semidirect
53. #2753C22semidirect
54. #2741C22semidirect
55. #2740C22semidirect
56. #2711C22semidirect
57. #2707C22semidirect
58. #2703C22semidirect
59. #2699C22semidirect
61. #2654C22semidirect
62. #2651C22semidirect
64. #2647C22semidirect
69. #2620C22semidirect
72. #2571C22semidirect
73. #2571C22semidirect
74. #2552C22semidirect
75. #2552C22semidirect
85. #2538C22semidirect
86. #2538C22semidirect
87. #2538C22semidirect
90. #2537C22semidirect
91. #2537C22semidirect
92. #2537C22semidirect
94. #2536C22semidirect
96. #2535C22semidirect
98. #2522C22semidirect
99. #2516C22semidirect
101. #2513C22semidirect
102. #2507C22semidirect
104. #2500C22semidirect
105. #2500C22semidirect
106. #2499C22semidirect
107. #2499C22semidirect
108. #2497C22semidirect
110. #2490C22semidirect
111. #2487C22semidirect
113. #2486C22semidirect
114. #2485C22semidirect
115. #2485C22semidirect
116. #2485C22semidirect
117. #2485C22semidirect
118. #2485C22semidirect
119. #2485C22semidirect
127. #2423C22semidirect
128. #2422C22semidirect
129. #2421C22semidirect
130. #2420C22semidirect
133. #2417C22semidirect
136. #2416C22semidirect
137. #2415C22semidirect
138. #2415C22semidirect
139. #2415C22semidirect
140. #2415C22semidirect
141. #2415C22semidirect
142. #2414C22semidirect
143. #2414C22semidirect
144. #2414C22semidirect
145. #2414C22semidirect
146. #2414C22semidirect
150. #2367C22semidirect
151. #2366C22semidirect
152. #2365C22semidirect
159. #2354C22semidirect
160. #2352C22semidirect
161. D4×C4⋊C4C22semidirect
162. #2330C22semidirect
164. #2324C22semidirect
165. #2320C22semidirect
166. #2319C22semidirect
167. #2319C22semidirect
173. #2314C22semidirect
174. #2314C22semidirect
175. #2314C22semidirect
185. #2295C22semidirect
186. #2293C22semidirect
191. #2285C22semidirect
193. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#426902
#426882
#426642
#426582
#397632
#397352
#395072
#394812
#391912
#391562
#389752
#389422
#374932
#369872
#355182
#355162
#352862
#352732
#352292
#351572
#351502
#349362
#349352
#342062
C2×#23542
#340602