Finite Group Databasebeta

← #7652676

Subgroups — #7652676

Order 512.

5496 conjugacy classes of subgroups.

The subgroup lattice has 1191 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42705C214yesmaximal, complemented
2#42629C214yesmaximal, complemented
3#42533C214yesmaximal, complemented
4#42529C214yesmaximal, complemented
5#40758C218yesmaximal, complemented
6#40054C214yesmaximal, complemented
7#40026C214yesmaximal, complemented
8#39785C214yesmaximal, complemented
9#39202C214yesmaximal, complemented
10#38534C218yesmaximal, complemented
11#35679C211yesmaximal, characteristic, complemented
12#35677C211yesmaximal, characteristic, complemented
13#35619C211yesmaximal, characteristic, complemented
14#35617C211yesmaximal, characteristic, complemented
15#35533C211yesmaximal, characteristic, complemented
16#35528C211yesmaximal, characteristic, complemented
17#35329C211yesmaximal, characteristic, complemented
18#35272C211yesmaximal, characteristic, complemented
19#35152C211yesmaximal, characteristic, complemented
20C2×#2544C211yesmaximal, characteristic, complemented
21#34815C211yesmaximal, characteristic, complemented
22#34744C211yesmaximal, characteristic, complemented
23#34268C211yesmaximal, characteristic, complemented
24#34265C211yesmaximal, characteristic, complemented
25#34255C211yesmaximal, characteristic, complemented
26C2×#536C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#535C2211yescharacteristic
31C2×#535C2211yescharacteristic
32C2×#532C2211yescharacteristic
33C22×#127C2211yescharacteristic
34C22×#124C2211yescharacteristic
35C22×#124C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C2×#518C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C22×C4×D4C2211yescharacteristic
41#2858C2212yescomplemented
42#2858C2212yescomplemented
43#2856C2212yes—
44#2856C2212yes—
45#2849C2214yes—
46#2837C2218yescomplemented
47#2828C2218yescomplemented
48#2803C2218yescomplemented
49#2797C2218yescomplemented
50#2797C2218yescomplemented
51#2753C2218yescomplemented
52#2752C2218yescomplemented
53#2752C2218yescomplemented
54#2748C2218yescomplemented
55#2743C2218yescomplemented
56#2741C2218yescomplemented
57#2740C2218yescomplemented
58#2711C2218yescomplemented
59#2703C2218yescomplemented
60#2701C2218yescomplemented
61#2699C2218yescomplemented
62#2688C2218yescomplemented
63#2671C2218yescomplemented
64#2661C2218yescomplemented
65#2658C2212yescomplemented
66#2657C2212yescomplemented
67#2651C2218yescomplemented
68#2649C2218yescomplemented
69#2648C2218yescomplemented
70#2635C2218yescomplemented
71#2624C2218yescomplemented
72#2622C2214yes—
73#2619C2212yes—
74#2619C2212yes—
75#2548C2214yes—
76#2548C2214yescomplemented
77#2548C2212yescomplemented
78#2547C2214yescomplemented
79#2545C2214yescomplemented
80#2545C2212yescomplemented
81#2544C2214yes—
82#2544C2214yes—
83#2544C2214yes—
84#2544C2214yes—
85#2544C2214yes—
86#2544C2214yescomplemented
87#2544C2212yescomplemented
88#2541C2214yes—
89#2541C2214yes—
90#2541C2212yescomplemented
91#2540C2214yescomplemented
92#2540C2214yescomplemented
93#2539C2218yes—
94#2516C2218yescomplemented
95#2509C2212yescomplemented
96#2508C2212yescomplemented
97#2507C2212yescomplemented
98#2506C2212yescomplemented
99#2505C2214yes—
100#2503C2212yescomplemented
101#2502C2212yescomplemented
102#2499C2212yescomplemented
103#2499C2212yescomplemented
104#2490C2218yescomplemented
105#2482C2218yes—
106#2476C2218yescomplemented
107#2473C2214yes—
108#2471C2218yescomplemented
109#2464C2218yescomplemented
110#2448C2214yescomplemented
111#2448C2212yescomplemented
112#2448C2214yescomplemented
113#2448C2214yescomplemented
114#2448C2214yescomplemented
115#2447C2214yescomplemented
116#2447C2214yescomplemented
117#2447C2212yescomplemented
118#2446C2214yescomplemented
119#2446C2212yescomplemented
120#2445C2212yescomplemented
121#2445C2214yescomplemented
122#2444C2214yes—
123#2443C2214yes—
124#2428C2214yes—
125#2428C2214yes—
126#2427C2214yescomplemented
127#2427C2214yescomplemented
128#2426C2214yescomplemented
129#2426C2214yescomplemented
130#2424C2218yes—
131#2422C2214yescomplemented
132#2420C2218yescomplemented
133#2420C2214yescomplemented
134#2419C2218yes—
135#2416C2214yescomplemented
136#2414C2214yescomplemented
137#2412C2214yes—
138#2412C2214yes—
139#2411C2214yes—
140#2411C2214yes—
141#2410C2218yes—
142#2408C2218yes—
143#2402C2214yescomplemented
144#2395C2214yescomplemented
145C2×#394C2214yes—
146#2367C2214yescomplemented
147#2367C2214yescomplemented
148#2366C2214yescomplemented
149#2365C2214yescomplemented
150#2363C2214yescomplemented
151#2361C2214yescomplemented
152#2359C2218yes—
153#2357C2214yescomplemented
154#2354C2214yescomplemented
155#2342C2218yes—
156#2333C2218yescomplemented
157#2324C2218yescomplemented
158#2323C2214yescomplemented
159#2321C2214yes—
160#2319C2214yescomplemented
161#2317C2211yescharacteristic
162#2311C2211yescharacteristic
163#2310C2211yescharacteristic
164#2309C2211yescharacteristic
165#2309C2211yescharacteristic
166#2309C2211yescharacteristic
167C4×#125C2214yescomplemented
168C4×C22⋊Q8C2214yescomplemented
169C4×#123C2214yescomplemented
170C4×#120C2214yes—
171#2297C2211yescharacteristic
172#2297C2211yescharacteristic
173#2297C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176#2296C2211yescharacteristic
177#2296C2211yescharacteristic
178#2296C2211yescharacteristic
179C2×#391C2211yescharacteristic
180#2293C2214yescomplemented
181C2×#390C2211yescharacteristic
182C2×#386C2214yes—
183#2285C2211yescharacteristic
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C23×D4C2311yescharacteristic
191C23×D4C2311yescharacteristic
192C23×D4C2314yes—
193C24×C4C2312yes—
194#536—28no—
195#536—44no—
196#535—28no—
197#535—44no—
198#535—44no—
199#535—44no—
200#532—44no—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2311yescharacteristic
204C2×#127—44no—
205C2×#127C2312yes—
206C2×#127C2312yes—
207C2×#127C2312yes—
208C2×#127C2312yes—
209C2×#127C2311yescharacteristic
210C2×#127C2314yes—
211C2×#127C2312yes—
212C2×#127C2312yes—
213C2×#125C2314yes—
214C2×#124—44no—
215C2×#124—44no—
216C2×#124C2312yes—
217C2×#124C2312yes—
218C2×#124C2312yes—
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#124C2312yes—
222C2×#124C2312yes—
223C2×#124C2312yes—
224C2×#124C2314yes—
225C2×#124C2314yes—
226C2×#124C2314yes—
227C2×#124C2312yes—
228C2×#124C2312yes—
229C2×#123C2314yes—
230C2×#123C2314yes—
231C2×#123C2314yes—
232C2×#123C2318yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2312yes—
236C2×#121C2314yes—
237C2×#121C2318yes—
238C2×#121C2318yes—
239C2×#121C2312yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×#121C2314yes—
244C2×#121C2314yes—
245C2×#121C2318yes—
246C2×#121C2318yes—
247C2×#121C2318yes—
248C2×#120C2314yes—
249C2×#120C2314yes—
250C2×#120C2314yes—
251C2×#120C2314yes—
252#520—44no—
253#519—44no—
254#518—28no—
255C4×#41—44no—
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2314yes—
259C2×C4×Q8C2312yes—
260C2×C4×D4—44no—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2318yes—
271C2×#117C2311yescharacteristic
272C2×#117C2311yescharacteristic
273C2×#117C2311yescharacteristic
274C2×#117C2311yescharacteristic
275C2×#117C2311yescharacteristic
276C2×#117C2312yes—
277C2×#117C2314yes—
278C2×#117C2312yes—
279C2×#117C2318yes—
280C2×#117C2311yescharacteristic
281C22×C4⋊C4C2311yescharacteristic
282C22×C4⋊C4C2312yes—
283C22×C4⋊C4C2312yes—
284C22×C22⋊C4C2314yes—
285C22×C22⋊C4C2312yes—
286C22×C22⋊C4C2312yes—
287C22×C22⋊C4C2314yes—
288C22×C22⋊C4C2312yes—
289C22×C22⋊C4C2314yes—
290C22×C42C2311yescharacteristic
291C22×C42C2311yescharacteristic
292C22×C42C2311yescharacteristic
293C22×C42C2312yes—
294#400C2314yes—
295#400C2318yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#399C2318yes—
301#399C2318yes—
302#399C2314yes—
303#399C2318yes—
304#399C2318yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2318yes—
309#398C2314yes—
310#398C2314yes—
311#397C2318yes—
312#397C2318yes—
313#397C2318yes—
314#397C2318yes—
315#397C2318yes—
316#397C2314yes—
317#397C2318yes—
318#397C2318yes—
319#397C2314yes—
320#397C2314yes—
321#397C2318yes—
322#396C2318yes—
323#396C2318yes—
324#396C2318yes—
325#394C2314yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#394C2318yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#394C2314yes—
337#394C2318yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#392C2318yes—
344#392C2318yes—
345#392C2318yes—
346#392C2318yes—
347#392C2318yes—
348#392C2318yes—
349#392C2318yes—
350#391C2312yes—
351#391C2312yes—
352#391C2314yes—
353#391C2312yes—
354#391C2312yes—
355#391C2314yes—
356#391C2312yes—
357#391C2312yes—
358#391C2312yes—
359#391C2312yes—
360#390C2314yes—
361#390C2312yes—
362#390C2312yes—
363#390C2312yes—
364#390C2312yes—
365#390C2314yes—
366#390C2314yes—
367#390C2314yes—
368#390C2312yes—
369#390C2318yes—
370#390C2312yes—
371#390C2318yes—
372#390C2318yes—
373#390C2318yes—
374#390C2318yes—
375#390C2318yes—
376#390C2318yes—
377#390C2318yes—
378#390C2318yes—
379#390C2314yes—
380#390C2312yes—
381#390C2318yes—
382#390C2312yes—
383#390C2312yes—
384#390C2312yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2312yes—
389#389C2312yes—
390#389C2318yes—
391#389C2312yes—
392#389C2312yes—
393#389C2312yes—
394#389C2312yes—
395#389C2312yes—
396#389C2312yes—
397#389C2312yes—
398#389C2312yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2314yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2314yes—
425#387C2314yes—
426#386C2314yes—
427#386C2312yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2318yes—
433#386C2318yes—
434#386C2312yes—
435#386C2318yes—
436#386C2312yes—
437#386C2318yes—
438#386C2318yes—
439#386C2318yes—
440#386C2314yes—
441#386C2312yes—
442#386C2318yes—
443#386C2314yes—
444#386C2318yes—
445#385C2314yes—
446#385C2312yes—
447#385C2318yes—
448#385C2318yes—
449#385C2312yes—
450#385C2314yes—
451#385C2314yes—
452#385C2318yes—
453#385C2318yes—
454#385C2312yes—
455#385C2312yes—
456#385C2314yes—
457#385C2314yes—
458#384C2312yes—
459#384C2311yescharacteristic
460#384C2311yescharacteristic
461#382C2314yes—
462#382C2312yes—
463#382C2311yescharacteristic
464#382C2311yescharacteristic
465#381C2314yes—
466#381C2318yes—
467#381C2314yes—
468#381C2318yes—
469#381C2318yes—
470#380C2314yes—
471#380C2318yes—
472#380C2318yes—
473#380C2318yes—
474#380C2314yes—
475#379C2314yes—
476#379C2314yes—
477#379C2314yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2318yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2318yes—
496C4×C22⋊C4C2318yes—
497C4×C22⋊C4C2318yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2314yes—
500C4×C22⋊C4C2312yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2312yes—
503#376C2312yes—
504C2×#95C2314yes—
505C2×#95C2312yes—
506C43C2312yes—
507C25C2412yes—
508C25C2412yes—
509C2×#41—24no—
510C2×#41—24no—
511C2×#41—24no—
512C2×#41—24no—
513C2×#41—24no—
514C2×#41—24no—
515C22×Q8—24no—
516C22×Q8—24no—
517C22×Q8—24no—
518C22×Q8C2412yes—
519C22×Q8C2412yes—
520C22×Q8C2411yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×D4—24no—
523C22×D4—24no—
524C22×D4—24no—
525C22×D4—24no—
526C22×D4—24no—
527C22×D4—24no—
528C22×D4—48no—
529C22×D4—48no—
530C22×D4—84no—
531C22×D4C2412yes—
532C22×D4C2412yes—
533C22×D4C2412yes—
534C22×D4C2412yes—
535C22×D4C2412yes—
536C22×D4C2412yes—
537C22×D4C2411yescharacteristic
538C22×D4C2411yescharacteristic
539C22×D4C2418yes—
540C22×D4C2418yes—
541C22×D4C2414yes—
542C22×D4C2414yes—
543C22×D4C2418yes—
544C22×D4C2414yes—
545C22×D4C2414yes—
546C22×D4C2414yes—
547C22×D4C2418yes—
548C23×C4—44no—
549C23×C4—84no—
550C23×C4C2412yes—
551C23×C4C2412yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2411yescharacteristic
555C23×C4C2412yes—
556C23×C4C2412yes—
557C23×C4C2411yescharacteristic
558C23×C4C2418yes—
559C23×C4C2414yes—
560C23×C4C2414yes—
561C23×C4C2418yes—
562C23×C4C2411yescharacteristic
563C4⋊Q8—28no—
564C4⋊Q8—42no—
565C4⋊Q8—44no—
566#127—28no—
567#127—44no—
568#127—44no—
569#127—48no—
570#127—42no—
571#127—44no—
572#127—44no—
573#127—44no—
574#125—48no—
575#124—28no—
576#124—28no—
577#124—48no—
578#124—48no—
579#124—48no—
580#124—44no—
581#124—44no—
582#124—42no—
583#124—42no—
584#124—44no—
585#124—44no—
586#124—44no—
587#124—44no—
588#123—216no—
589#123—48no—
590#123—48no—
591#123—88no—
592C22⋊Q8—216no—
593C22⋊Q8—44no—
594C22⋊Q8—44no—
595#121—216no—
596#121—416no—
597#121—416no—
598#121—44no—
599#121—44no—
600#121—48no—
601#121—44no—
602#121—44no—
603#121—48no—
604#121—88no—
605#121—88no—
606#121—88no—
607#120—216no—
608#120—48no—
609#120—48no—
610#120—48no—
611C4×Q8—44no—
612C4×Q8—48no—
613C4×Q8—48no—
614C4×Q8—44no—
615C4×D4—216no—
616C4×D4—216no—
617C4×D4—48no—
618C4×D4—48no—
619C4×D4—44no—
620C4×D4—44no—
621C4×D4—48no—
622C4×D4—48no—
623C4×D4—48no—
624C4×D4—88no—
625#117—24no—
626#117—24no—
627#117—24no—
628#117—24no—
629#117—24no—
630#117—44no—
631#117—48no—
632#117—44no—
633#117—88no—
634#117#4118yes—
635C2×C4⋊C4—24no—
636C2×C4⋊C4—44no—
637C2×C4⋊C4—44no—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2412yes—
672C2×C22⋊C4—216no—
673C2×C22⋊C4—44no—
674C2×C22⋊C4—44no—
675C2×C22⋊C4—44no—
676C2×C22⋊C4—48no—
677C2×C22⋊C4—84no—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2412yes—
718C2×C42—24no—
719C2×C42—24no—
720C2×C42—24no—
721C2×C42—44no—
722C2×C42C2412yes—
723C2×C42C2411yescharacteristic
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2412yes—
729C2×C42C2412yes—
730C2×C42C2412yes—
731C2×C42C2412yes—
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2414yes—
736C2×C42C2414yes—
737C2×C42C2418yes—
738C2×C42C2418yes—
739C2×C42C2414yes—
740C2×C42C2414yes—
741C2×C42C2412yes—
742#95C2418yes—
743#95C2412yes—
744#95C2412yes—
745#95C2412yes—
746#95C2412yes—
747#95C2418yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2418yes—
755#95C2414yes—
756#95C2414yes—
757#95C2418yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2418yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2418yes—
772#95C2418yes—
773C24—24no—
774C24—24no—
775C24—24no—
776C24—24no—
777C24—24no—
778C24—24no—
779C24—44no—
780C24—44no—
781C24—44no—
782C24—44no—
783C24C2514yes—
784C24C2514yes—
785C24C2512yes—
786C24C2512yes—
787C24C2511yescharacteristic
788#41—416no—
789#41—416no—
790C2×Q8—24no—
791C2×Q8—22no—
792C2×Q8—24no—
793C2×Q8—22no—
794C2×Q8—24no—
795C2×Q8—24no—
796C2×Q8—22no—
797C2×Q8—22no—
798C2×Q8—24no—
799C2×Q8—22no—
800C2×Q8—24no—
801C2×Q8—22no—
802C2×Q8—416no—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—22no—
813C2×D4—24no—
814C2×D4—22no—
815C2×D4—216no—
816C2×D4—24no—
817C2×D4—22no—
818C2×D4—24no—
819C2×D4—22no—
820C2×D4—24no—
821C2×D4—24no—
822C2×D4—24no—
823C2×D4—24no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—216no—
829C2×D4—44no—
830C2×D4—48no—
831C2×D4—48no—
832C2×D4—44no—
833C2×D4—48no—
834C2×D4—48no—
835C2×D4—44no—
836C2×D4—48no—
837C2×D4—48no—
838C2×D4—48no—
839C2×D4—44no—
840C2×D4—48no—
841C2×D4—44no—
842C2×D4—44no—
843C2×D4—44no—
844C2×D4—48no—
845C2×D4—48no—
846C2×D4—48no—
847C2×D4—48no—
848C2×D4—48no—
849C2×D4—48no—
850C2×D4—416no—
851C2×D4—416no—
852C2×D4—832no—
853C22×C4—24no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—24no—
868C22×C4—216no—
869C22×C4—28no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—44no—
874C22×C4—42no—
875C22×C4—44no—
876C22×C4—42no—
877C22×C4—48no—
878C22×C4—48no—
879C22×C4—48no—
880C22×C4—48no—
881C22×C4—44no—
882C22×C4—48no—
883C22×C4—44no—
884C22×C4—48no—
885C22×C4—816no—
886C22×C4C2×#4114yes—
887C22×C4H(5,𝔽2)14yes—
888C22×C4H(5,𝔽2)14yes—
889C22×C4C2512yes—
890C22×C4C2512yes—
891C22×C4C2514yes—
892C22×C4C2512yes—
893C22×C4C2512yes—
894C22×C4C2514yes—
895C22×C4C2512yes—
896C22×C4C2512yes—
897C22×C4C2514yes—
898C22×C4C2512yes—
899C22×C4C2514yes—
900C22×C4C2512yes—
901C22×C4C2512yes—
902C22×C4C2512yes—
903C22×C4C2514yes—
904C22×C4C2512yes—
905C22×C4C2514yes—
906C22×C4C2512yes—
907C22×C4C2511yescharacteristic
908C22×C4C2511yescharacteristic
909C4⋊C4—24no—
910C4⋊C4—216no—
911C4⋊C4—24no—
912C4⋊C4—24no—
913C4⋊C4—22no—
914C4⋊C4—22no—
915C4⋊C4—24no—
916C4⋊C4—24no—
917C4⋊C4—22no—
918C4⋊C4—22no—
919C4⋊C4—24no—
920C4⋊C4—24no—
921C4⋊C4—28no—
922C4⋊C4—28no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—48no—
928C4⋊C4—44no—
929C4⋊C4—48no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4C2×#4118yes—
943C22⋊C4—24no—
944C22⋊C4—24no—
945C22⋊C4—24no—
946C22⋊C4—24no—
947C22⋊C4—24no—
948C22⋊C4—216no—
949C22⋊C4—216no—
950C22⋊C4—216no—
951C22⋊C4—28no—
952C22⋊C4—48no—
953C22⋊C4—48no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—48no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—48no—
966C22⋊C4—44no—
967C22⋊C4—48no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—48no—
972C22⋊C4—48no—
973C22⋊C4—48no—
974C22⋊C4—44no—
975C22⋊C4—48no—
976C22⋊C4—48no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4C2×#4118yes—
983C42—24no—
984C42—22no—
985C42—22no—
986C42—24no—
987C42—24no—
988C42—24no—
989C42—24no—
990C42—22no—
991C42—22no—
992C42—24no—
993C42—24no—
994C42—24no—
995C42—24no—
996C42—44no—
997C42—44no—
998C42—48no—
999C42—44no—
1000C42—48no—
1001C42—44no—
1002C42C2×#4118yes—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—24no—
1007C23—24no—
1008C23—22no—
1009C23—22no—
1010C23—24no—
1011C23—22no—
1012C23—24no—
1013C23—24no—
1014C23—22no—
1015C23—24no—
1016C23—22no—
1017C23—24no—
1018C23—28no—
1019C23—24no—
1020C23—28no—
1021C23—24no—
1022C23—28no—
1023C23—24no—
1024C23—28no—
1025C23—416no—
1026C23—48no—
1027C23—48no—
1028C23—84no—
1029C23—88no—
1030C23—84no—
1031C23—88no—
1032C23—88no—
1033C23—84no—
1034C23—84no—
1035C23C22×#4112yes—
1036C23C2×H(5,𝔽2)12yes—
1037C23C2×H(5,𝔽2)12yes—
1038C23C2611yescharacteristic
1039Q8—48no—
1040Q8—48no—
1041Q8—44no—
1042Q8—44no—
1043D4—48no—
1044D4—48no—
1045D4—48no—
1046D4—48no—
1047D4—48no—
1048D4—48no—
1049D4—44no—
1050D4—44no—
1051D4—816no—
1052D4—816no—
1053D4—88no—
1054D4—816no—
1055D4—164no—
1056D4—164no—
1057D4—164no—
1058D4—164no—
1059D4—168no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—24no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—24no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—22no—
1098C2×C4—28no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—48no—
1108C2×C4—44no—
1109C2×C4—44no—
1110C2×C4—48no—
1111C2×C4—48no—
1112C2×C4—48no—
1113C2×C4—816no—
1114C2×C4—88no—
1115C2×C4—84no—
1116C2×C4—84no—
1117C2×C4—816no—
1118C2×C4—164no—
1119C2×C4#540116yes—
1120C2×C4C22×#4118yes—
1121C2×C4C22×#4112yes—
1122C2×C4C22×#4112yes—
1123C2×C4C2×H(5,𝔽2)12yes—
1124C2×C4C2×H(5,𝔽2)12yes—
1125C2×C4C2×H(5,𝔽2)12yes—
1126C2×C4C2×H(5,𝔽2)12yes—
1127C2×C4#58514yes—
1128C22—24no—
1129C22—22no—
1130C22—22no—
1131C22—24no—
1132C22—48no—
1133C22—44no—
1134C22—48no—
1135C22—44no—
1136C22—42no—
1137C22—44no—
1138C22—44no—
1139C22—42no—
1140C22—44no—
1141C22—42no—
1142C22—42no—
1143C22—44no—
1144C22—44no—
1145C22—48no—
1146C22—48no—
1147C22—44no—
1148C22—42no—
1149C22—42no—
1150C22—44no—
1151C22—44no—
1152C22—816no—
1153C22—168no—
1154C22C2×#54014yes—
1155C22C23×#4111yescharacteristic
1156C22C22×H(5,𝔽2)11yescharacteristic
1157C22C22×H(5,𝔽2)11yescharacteristic
1158C22C2×#58512yes—
1159C22H(7,𝔽2)12yes—
1160C4—28no—
1161C4—24no—
1162C4—44no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—42no—
1167C4—44no—
1168C4—42no—
1169C4—42no—
1170C4—42no—
1171C4—42no—
1172C4—44no—
1173C4—42no—
1174C4—44no—
1175C4—42no—
1176C4—42no—
1177C4—44no—
1178C4C2×#54014yes—
1179C4C2×#54014yes—
1180C2—24no—
1181C2—82no—
1182C2—82no—
1183C2—84no—
1184C2—84no—
1185C2C22×#54011yescharacteristic
1186C2#6283611yescharacteristic
1187C2#6287611yescharacteristic
1188C2#6292412yes—
1189C2#6301012yes—
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. #42705C2semidirect
2. #42629C2semidirect
3. #42533C2semidirect
4. #42529C2semidirect
5. #40758C2semidirect
6. #40054C2semidirect
7. #40026C2semidirect
8. #39785C2semidirect
9. #39202C2semidirect
10. #38534C2semidirect
11. #35679C2semidirect
12. #35677C2semidirect
13. #35619C2semidirect
14. #35617C2semidirect
15. #35533C2semidirect
16. #35528C2semidirect
17. #35329C2semidirect
18. #35272C2semidirect
19. #35152C2semidirect
20. C2×#2544C2semidirect
21. #34815C2semidirect
22. #34744C2semidirect
23. #34268C2semidirect
24. #34265C2semidirect
25. #34255C2semidirect
41. #2858C22semidirect
42. #2858C22semidirect
46. #2837C22semidirect
47. #2828C22semidirect
48. #2803C22semidirect
49. #2797C22semidirect
50. #2797C22semidirect
51. #2753C22semidirect
52. #2752C22semidirect
53. #2752C22semidirect
54. #2748C22semidirect
55. #2743C22semidirect
56. #2741C22semidirect
57. #2740C22semidirect
58. #2711C22semidirect
59. #2703C22semidirect
60. #2701C22semidirect
61. #2699C22semidirect
62. #2688C22semidirect
63. #2671C22semidirect
64. #2661C22semidirect
65. #2658C22semidirect
66. #2657C22semidirect
67. #2651C22semidirect
68. #2649C22semidirect
69. #2648C22semidirect
70. #2635C22semidirect
71. #2624C22semidirect
76. #2548C22semidirect
77. #2548C22semidirect
78. #2547C22semidirect
79. #2545C22semidirect
80. #2545C22semidirect
86. #2544C22semidirect
87. #2544C22semidirect
90. #2541C22semidirect
91. #2540C22semidirect
92. #2540C22semidirect
94. #2516C22semidirect
95. #2509C22semidirect
96. #2508C22semidirect
97. #2507C22semidirect
98. #2506C22semidirect
100. #2503C22semidirect
101. #2502C22semidirect
102. #2499C22semidirect
103. #2499C22semidirect
104. #2490C22semidirect
106. #2476C22semidirect
108. #2471C22semidirect
109. #2464C22semidirect
110. #2448C22semidirect
111. #2448C22semidirect
112. #2448C22semidirect
113. #2448C22semidirect
114. #2448C22semidirect
115. #2447C22semidirect
116. #2447C22semidirect
117. #2447C22semidirect
118. #2446C22semidirect
119. #2446C22semidirect
120. #2445C22semidirect
121. #2445C22semidirect
126. #2427C22semidirect
127. #2427C22semidirect
128. #2426C22semidirect
129. #2426C22semidirect
131. #2422C22semidirect
132. #2420C22semidirect
133. #2420C22semidirect
135. #2416C22semidirect
136. #2414C22semidirect
143. #2402C22semidirect
144. #2395C22semidirect
146. #2367C22semidirect
147. #2367C22semidirect
148. #2366C22semidirect
149. #2365C22semidirect
150. #2363C22semidirect
151. #2361C22semidirect
153. #2357C22semidirect
154. #2354C22semidirect
156. #2333C22semidirect
157. #2324C22semidirect
158. #2323C22semidirect
160. #2319C22semidirect
167. C4×#125C22semidirect
168. C4×C22⋊Q8C22semidirect
169. C4×#123C22semidirect
180. #2293C22semidirect

Maximal subgroups

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

subgroupindex
#427052
#426292
#425332
#425292
#407582
#400542
#400262
#397852
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C2×#25442
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