Finite Group Databasebeta

← #8093533

Subgroups — #8093533

Order 512.

5614 conjugacy classes of subgroups.

The subgroup lattice has 1253 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53151C214yesmaximal, complemented
2#53096C214yesmaximal, complemented
3#53066C214yesmaximal, complemented
4#53063C214yesmaximal, complemented
5#53059C214yesmaximal, complemented
6#53022C214yesmaximal, complemented
7#52962C214yesmaximal, complemented
8#52960C214yesmaximal, complemented
9#52375C218yesmaximal, complemented
10#52372C218yesmaximal, complemented
11#35676C211yesmaximal, characteristic, complemented
12#35660C211yesmaximal, characteristic, complemented
13#35659C211yesmaximal, characteristic, complemented
14#35633C211yesmaximal, characteristic, complemented
15#35630C211yesmaximal, characteristic, complemented
16#35617C211yesmaximal, characteristic, complemented
17#35565C211yesmaximal, characteristic, complemented
18#35557C211yesmaximal, characteristic, complemented
19#35541C211yesmaximal, characteristic, complemented
20#35533C211yesmaximal, characteristic, complemented
21#35530C211yesmaximal, characteristic, complemented
22#35514C211yesmaximal, characteristic, complemented
23#34635C211yesmaximal, characteristic, complemented
24#34633C211yesmaximal, characteristic, complemented
25C2×#2620C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#535C2211yescharacteristic
31C2×#535C2211yescharacteristic
32C2×#532C2211yescharacteristic
33C22×#124C2211yescharacteristic
34C2×#525C2211yescharacteristic
35C2×#525C2211yescharacteristic
36C2×#525C2211yescharacteristic
37C22×C22⋊Q8C2211yescharacteristic
38C22×#121C2211yescharacteristic
39C2×#520C2211yescharacteristic
40C2×#518C2211yescharacteristic
41C22×#117C2211yescharacteristic
42#2841C2218yescomplemented
43#2838C2218yescomplemented
44#2830C2218yescomplemented
45#2830C2218yescomplemented
46#2829C2218yescomplemented
47#2828C2218yescomplemented
48#2827C2218yescomplemented
49#2826C2218yescomplemented
50#2826C2218yescomplemented
51#2825C2218yescomplemented
52#2825C2218yescomplemented
53#2824C2218yescomplemented
54#2824C2218yescomplemented
55#2818C2218yescomplemented
56#2813C2218yescomplemented
57#2813C2218yescomplemented
58#2797C2218yescomplemented
59#2784C2218yescomplemented
60#2780C2218yescomplemented
61#2778C2218yescomplemented
62#2757C2218yescomplemented
63#2749C2218yescomplemented
64#2748C2218yescomplemented
65#2737C2218yescomplemented
66#2709C2218yescomplemented
67#2709C2218yescomplemented
68#2705C2218yescomplemented
69#2693C2218yescomplemented
70#2691C2218yescomplemented
71#2691C2218yescomplemented
72#2688C2218yescomplemented
73#2673C2218yescomplemented
74#2625C2212yescomplemented
75#2625C2212yescomplemented
76#2624C2212yescomplemented
77#2624C2212yescomplemented
78#2623C2214yes—
79#2622C2214yes—
80#2621C2212yescomplemented
81#2620C2214yes—
82#2620C2214yes—
83#2620C2214yes—
84#2620C2214yes—
85#2620C2212yescomplemented
86#2620C2212yescomplemented
87#2619C2212yescomplemented
88#2618C2214yes—
89#2617C2214yes—
90#2548C2212yescomplemented
91#2547C2214yescomplemented
92#2545C2212yescomplemented
93#2544C2214yescomplemented
94#2544C2212yescomplemented
95#2541C2214yes—
96#2541C2214yes—
97#2541C2212yescomplemented
98#2540C2214yes—
99#2540C2214yes—
100#2539C2214yes—
101#2537C2214yes—
102#2535C2214yes—
103#2534C2214yes—
104#2514C2214yescomplemented
105#2514C2214yescomplemented
106#2512C2214yescomplemented
107#2511C2214yescomplemented
108#2511C2214yescomplemented
109#2511C2214yescomplemented
110#2502C2212yescomplemented
111#2501C2212yescomplemented
112#2500C2212yescomplemented
113#2499C2212yescomplemented
114#2497C2214yescomplemented
115#2496C2214yescomplemented
116#2493C2218yes—
117#2486C2214yes—
118#2481C2218yes—
119#2447C2214yescomplemented
120#2445C2214yescomplemented
121#2443C2218yes—
122#2436C2214yescomplemented
123#2436C2212yescomplemented
124#2436C2212yescomplemented
125#2436C2212yescomplemented
126#2434C2212yescomplemented
127#2433C2214yes—
128#2432C2212yescomplemented
129#2431C2212yescomplemented
130#2431C2214yescomplemented
131#2431C2212yescomplemented
132#2431C2212yescomplemented
133#2430C2218yes—
134#2429C2214yescomplemented
135#2428C2214yes—
136#2427C2214yes—
137#2427C2214yescomplemented
138#2427C2214yescomplemented
139#2427C2214yescomplemented
140#2424C2218yes—
141#2423C2214yescomplemented
142#2422C2214yescomplemented
143#2422C2214yescomplemented
144#2420C2214yescomplemented
145#2417C2214yescomplemented
146#2416C2214yescomplemented
147#2415C2214yescomplemented
148#2414C2214yescomplemented
149#2412C2218yes—
150#2412C2218yes—
151#2412C2214yes—
152#2410C2214yes—
153#2409C2214yescomplemented
154#2409C2214yescomplemented
155#2409C2214yescomplemented
156#2407C2214yescomplemented
157#2407C2214yescomplemented
158#2407C2214yescomplemented
159#2406C2214yes—
160#2404C2214yes—
161#2404C2218yes—
162#2395C2214yescomplemented
163#2395C2214yescomplemented
164#2392C2214yescomplemented
165#2392C2214yescomplemented
166C2×#396C2214yes—
167C2×#394C2214yes—
168#2317C2211yescharacteristic
169#2316C2211yescharacteristic
170#2311C2211yescharacteristic
171#2311C2211yescharacteristic
172#2311C2211yescharacteristic
173#2310C2211yescharacteristic
174#2310C2211yescharacteristic
175#2297C2211yescharacteristic
176#2297C2211yescharacteristic
177#2297C2211yescharacteristic
178#2297C2211yescharacteristic
179#2296C2211yescharacteristic
180#2296C2211yescharacteristic
181C2×#391C2211yescharacteristic
182C2×#390C2211yescharacteristic
183#2285C2211yescharacteristic
184C2×#384C2211yescharacteristic
185#2280C2211yescharacteristic
186#2274C2211yescharacteristic
187C2×2−1+4—44no—
188C2×2−1+4—44no—
189C2×2−1+4—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2311yescharacteristic
193C22×#41C2314yes—
194C22×#41C2312yes—
195C22×#41C2312yes—
196C23×Q8C2311yescharacteristic
197C23×Q8C2312yes—
198C23×Q8C2312yes—
199C23×D4C2311yescharacteristic
200C23×D4C2312yes—
201C24×C4C2311yescharacteristic
202#537—44no—
203#536—44no—
204#535—44no—
205#535—44no—
206#535—44no—
207#532—44no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×#127C2311yescharacteristic
211C2×#127C2312yes—
212C2×#127C2312yes—
213C2×#127C2312yes—
214C2×#127C2318yes—
215C2×#126C2318yes—
216C2×#124—44no—
217C2×#124C2312yes—
218C2×#124C2312yes—
219C2×#124C2314yes—
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#124C2312yes—
223C2×#124C2312yes—
224C2×#124C2312yes—
225C2×#124C2312yes—
226#525—44no—
227#525—44no—
228#525—44no—
229C2×#123C2312yes—
230C2×#123C2312yes—
231C2×#123C2312yes—
232C2×#123C2314yes—
233C2×#123C2318yes—
234C2×#123C2318yes—
235C2×C22⋊Q8—44no—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2312yes—
244C2×#121—44no—
245C2×#121C2314yes—
246C2×#121C2312yes—
247C2×#121C2312yes—
248C2×#121C2314yes—
249C2×#121C2314yes—
250C2×#121C2312yes—
251C2×#121C2312yes—
252C2×#121C2312yes—
253C2×#121C2314yes—
254C2×#121C2312yes—
255C2×#121C2314yes—
256C2×#121C2312yes—
257C2×#121C2314yes—
258C2×#121C2318yes—
259C2×#121C2318yes—
260C2×#120C2312yes—
261C2×#120C2312yes—
262C2×#120C2312yes—
263C2×#120C2314yes—
264C2×#120C2314yes—
265C2×#120C2314yes—
266#520—44no—
267#518—44no—
268C2×C4×Q8C2312yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2314yes—
277C2×#117—44no—
278C2×#117C2311yescharacteristic
279C2×#117C2311yescharacteristic
280C2×#117C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C2×#117C2312yes—
284C2×#117C2312yes—
285C2×#117C2312yes—
286C2×#117C2312yes—
287C2×#117C2312yes—
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2312yes—
293C22×C4⋊C4C2314yes—
294C22×C22⋊C4C2312yes—
295C22×C22⋊C4C2312yes—
296C22×C22⋊C4C2314yes—
297C22×C22⋊C4C2312yes—
298C22×C22⋊C4C2314yes—
299C22×C22⋊C4C2314yes—
300C22×C42C2311yescharacteristic
301C22×C42C2311yescharacteristic
302#401C2318yes—
303#400C2318yes—
304#400C2318yes—
305#400C2318yes—
306#400C2318yes—
307#400C2318yes—
308#400C2314yes—
309#400C2314yes—
310#399C2314yes—
311#399C2318yes—
312#399C2318yes—
313#399C2314yes—
314#398C2318yes—
315#398C2318yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#397C2314yes—
321#397C2314yes—
322#397C2318yes—
323#397C2318yes—
324#397C2314yes—
325#397C2314yes—
326#397C2318yes—
327#397C2318yes—
328#397C2318yes—
329#397C2314yes—
330#397C2318yes—
331#397C2318yes—
332#397C2318yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#396C2318yes—
337#396C2318yes—
338#396C2314yes—
339#396C2318yes—
340#396C2318yes—
341#396C2318yes—
342#396C2314yes—
343#396C2314yes—
344#396C2318yes—
345#396C2314yes—
346#396C2318yes—
347#395C2318yes—
348#395C2318yes—
349#394C2314yes—
350#394C2318yes—
351#394C2318yes—
352#394C2318yes—
353#394C2318yes—
354#394C2318yes—
355#394C2314yes—
356#394C2314yes—
357#394C2318yes—
358#394C2318yes—
359#394C2318yes—
360#394C2318yes—
361#394C2314yes—
362#394C2318yes—
363#394C2318yes—
364#394C2318yes—
365#394C2314yes—
366#394C2318yes—
367#394C2318yes—
368#394C2318yes—
369#394C2314yes—
370#394C2314yes—
371#394C2318yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#393C2318yes—
376#393C2318yes—
377#393C2318yes—
378#393C2318yes—
379#392C2314yes—
380#392C2318yes—
381#392C2318yes—
382#392C2318yes—
383#392C2318yes—
384#392C2318yes—
385#392C2318yes—
386#392C2314yes—
387#392C2318yes—
388#392C2318yes—
389#392C2318yes—
390#391C2314yes—
391#391C2314yes—
392#391C2312yes—
393#391C2312yes—
394#391C2314yes—
395#391C2312yes—
396#391C2312yes—
397#391C2312yes—
398#391C2314yes—
399#391C2312yes—
400#391C2312yes—
401#391C2312yes—
402#391C2312yes—
403#391C2312yes—
404#391C2311yescharacteristic
405#391C2311yescharacteristic
406#390C2312yes—
407#390C2312yes—
408#390C2312yes—
409#390C2318yes—
410#390C2318yes—
411#390C2318yes—
412#390C2318yes—
413#390C2312yes—
414#390C2312yes—
415#390C2314yes—
416#390C2312yes—
417#390C2312yes—
418#390C2312yes—
419#390C2311yescharacteristic
420#390C2311yescharacteristic
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2318yes—
425#389C2312yes—
426#389C2312yes—
427#389C2312yes—
428#389C2312yes—
429#388C2318yes—
430#388C2318yes—
431#388C2318yes—
432#388C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#386C2314yes—
440#386C2314yes—
441#386C2314yes—
442#386C2318yes—
443#386C2318yes—
444#386C2318yes—
445#386C2318yes—
446#386C2318yes—
447#386C2318yes—
448#386C2318yes—
449#386C2318yes—
450#386C2318yes—
451#386C2318yes—
452#386C2318yes—
453#386C2318yes—
454#386C2318yes—
455#386C2318yes—
456#386C2318yes—
457#386C2314yes—
458#386C2314yes—
459#386C2314yes—
460#386C2314yes—
461#385C2318yes—
462#385C2318yes—
463#385C2318yes—
464#385C2318yes—
465#385C2318yes—
466#385C2318yes—
467#385C2314yes—
468#385C2314yes—
469#385C2314yes—
470#384C2312yes—
471#384C2314yes—
472#384C2312yes—
473#384C2312yes—
474#384C2312yes—
475#383C2318yes—
476#382C2312yes—
477#382C2312yes—
478#381C2314yes—
479#381C2314yes—
480#381C2318yes—
481#381C2312yes—
482#380C2314yes—
483#380C2314yes—
484#380C2314yes—
485#380C2314yes—
486#380C2318yes—
487#380C2318yes—
488#380C2314yes—
489#380C2312yes—
490#380C2312yes—
491#380C2318yes—
492#380C2318yes—
493#379C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C22⋊C4C2312yes—
501C4×C22⋊C4C2312yes—
502C4×C22⋊C4C2312yes—
503C4×C22⋊C4C2312yes—
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2312yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2314yes—
509C2×#95C2314yes—
510C25C2412yes—
511C25C2411yescharacteristic
5122−1+4—464no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C2×#41—24no—
518C2×#41—24no—
519C2×#41—24no—
520C2×#41—24no—
521C2×#41—24no—
522C2×#41—48no—
523C2×#41—48no—
524C2×#41—48no—
525C2×#41—44no—
526C2×#41—44no—
527C2×#41—44no—
528C2×#41—44no—
529C2×#41—44no—
530C2×#41—44no—
531C22×Q8—24no—
532C22×Q8—24no—
533C22×Q8—24no—
534C22×Q8—44no—
535C22×Q8—44no—
536C22×Q8—44no—
537C22×Q8—44no—
538C22×Q8—44no—
539C22×Q8—44no—
540C22×Q8C2411yescharacteristic
541C22×Q8C2412yes—
542C22×Q8C2411yescharacteristic
543C22×Q8C2412yes—
544C22×Q8C2411yescharacteristic
545C22×Q8C2414yes—
546C22×D4—24no—
547C22×D4—24no—
548C22×D4—24no—
549C22×D4—44no—
550C22×D4—84no—
551C22×D4C2412yes—
552C22×D4C2412yes—
553C22×D4C2412yes—
554C22×D4C2411yescharacteristic
555C22×D4C2412yes—
556C22×D4C2412yes—
557C22×D4C2411yescharacteristic
558C22×D4C2411yescharacteristic
559C22×D4C2414yes—
560C22×D4C2414yes—
561C22×D4C2414yes—
562C22×D4C2414yes—
563C22×D4C2414yes—
564C22×D4C2418yes—
565C22×D4C2418yes—
566C22×D4C2414yes—
567C22×D4C2414yes—
568C22×D4C2418yes—
569C22×D4C2414yes—
570C23×C4—24no—
571C23×C4—24no—
572C23×C4—24no—
573C23×C4C2412yes—
574C23×C4C2411yescharacteristic
575C23×C4C2412yes—
576C23×C4C2412yes—
577C23×C4C2412yes—
578C23×C4C2412yes—
579C23×C4C2412yes—
580C23×C4C2412yes—
581C23×C4C2412yes—
582C23×C4C2412yes—
583C23×C4C2412yes—
584C23×C4C2418yes—
585C23×C4C2414yes—
586C23×C4C2414yes—
587C23×C4C2414yes—
588C23×C4C2411yescharacteristic
589C4⋊Q8—42no—
590C4⋊Q8—44no—
591#127—42no—
592#127—44no—
593#127—44no—
594#127—44no—
595#127—88no—
596#126—88no—
597#124—44no—
598#124—44no—
599#124—48no—
600#124—42no—
601#124—42no—
602#124—44no—
603#124—44no—
604#124—44no—
605#124—44no—
606#123—44no—
607#123—44no—
608#123—44no—
609#123—48no—
610#123—88no—
611#123—88no—
612C22⋊Q8—48no—
613C22⋊Q8—48no—
614C22⋊Q8—44no—
615C22⋊Q8—44no—
616C22⋊Q8—44no—
617C22⋊Q8—48no—
618C22⋊Q8—44no—
619C22⋊Q8—44no—
620#121—48no—
621#121—48no—
622#121—44no—
623#121—44no—
624#121—44no—
625#121—44no—
626#121—44no—
627#121—48no—
628#121—48no—
629#121—44no—
630#121—44no—
631#121—48no—
632#121—48no—
633#121—88no—
634#121—88no—
635#120—44no—
636#120—44no—
637#120—44no—
638#120—48no—
639#120—48no—
640#120—48no—
641C4×Q8—44no—
642C4×D4—48no—
643C4×D4—48no—
644C4×D4—44no—
645C4×D4—48no—
646C4×D4—48no—
647C4×D4—48no—
648C4×D4—48no—
649C4×D4—48no—
650#117—24no—
651#117—24no—
652#117—24no—
653#117—24no—
654#117—24no—
655#117—44no—
656#117—44no—
657#117—44no—
658#117—44no—
659#117—44no—
660C2×C4⋊C4—24no—
661C2×C4⋊C4—24no—
662C2×C4⋊C4—44no—
663C2×C4⋊C4—44no—
664C2×C4⋊C4—44no—
665C2×C4⋊C4—84no—
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2418yes—
682C2×C4⋊C4C2418yes—
683C2×C4⋊C4C2418yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2418yes—
691C2×C4⋊C4C2418yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2418yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C22⋊C4—48no—
699C2×C22⋊C4—44no—
700C2×C22⋊C4—44no—
701C2×C22⋊C4—44no—
702C2×C22⋊C4—48no—
703C2×C22⋊C4—84no—
704C2×C22⋊C4C2412yes—
705C2×C22⋊C4C2412yes—
706C2×C22⋊C4C2412yes—
707C2×C22⋊C4C2412yes—
708C2×C22⋊C4C2412yes—
709C2×C22⋊C4C2412yes—
710C2×C22⋊C4C2412yes—
711C2×C22⋊C4C2412yes—
712C2×C22⋊C4C2412yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2418yes—
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⋊C4C2418yes—
731C2×C22⋊C4C2418yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2418yes—
737C2×C22⋊C4C2418yes—
738C2×C22⋊C4C2418yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2418yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C42—24no—
750C2×C42—24no—
751C2×C42C2412yes—
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2412yes—
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2412yes—
758C2×C42C2412yes—
759C2×C42C2412yes—
760C2×C42C2412yes—
761C2×C42C2412yes—
762C2×C42C2414yes—
763C2×C42C2418yes—
764#95C2418yes—
765#95C2418yes—
766#95C2418yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2418yes—
784#95C2418yes—
785#95C2418yes—
786#95C2418yes—
787#95C2418yes—
788#95C2418yes—
789#95C2418yes—
790#95C2418yes—
791#95C2418yes—
792C24—22no—
793C24—22no—
794C24—24no—
795C24—24no—
796C24—24no—
797C24—22no—
798C24—42no—
799C24—42no—
800C24—44no—
801C24—44no—
802C24C2512yes—
803C24C2514yes—
804C24C2512yes—
805C24C2512yes—
806C24C2512yes—
807C24C2511yescharacteristic
808#41—464no—
809#41—432no—
810#41—432no—
811#41—416no—
812#41—416no—
813#41—416no—
814C2×Q8—22no—
815C2×Q8—22no—
816C2×Q8—24no—
817C2×Q8—24no—
818C2×Q8—24no—
819C2×Q8—22no—
820C2×Q8—22no—
821C2×Q8—22no—
822C2×Q8—22no—
823C2×Q8—24no—
824C2×Q8—24no—
825C2×Q8—22no—
826C2×Q8—22no—
827C2×Q8—24no—
828C2×Q8—22no—
829C2×Q8—44no—
830C2×Q8—44no—
831C2×Q8—44no—
832C2×Q8—432no—
833C2×Q8—432no—
834C2×Q8—416no—
835C2×D4—24no—
836C2×D4—24no—
837C2×D4—24no—
838C2×D4—24no—
839C2×D4—24no—
840C2×D4—24no—
841C2×D4—24no—
842C2×D4—24no—
843C2×D4—24no—
844C2×D4—24no—
845C2×D4—22no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—22no—
850C2×D4—24no—
851C2×D4—22no—
852C2×D4—22no—
853C2×D4—22no—
854C2×D4—24no—
855C2×D4—22no—
856C2×D4—22no—
857C2×D4—22no—
858C2×D4—22no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—48no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—48no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—48no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—48no—
879C2×D4—48no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—48no—
883C2×D4—48no—
884C2×D4—48no—
885C2×D4—48no—
886C2×D4—48no—
887C2×D4—48no—
888C2×D4—48no—
889C2×D4—416no—
890C2×D4—816no—
891C22×C4—24no—
892C22×C4—22no—
893C22×C4—24no—
894C22×C4—24no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—24no—
898C22×C4—24no—
899C22×C4—24no—
900C22×C4—24no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—24no—
905C22×C4—24no—
906C22×C4—24no—
907C22×C4—24no—
908C22×C4—24no—
909C22×C4—24no—
910C22×C4—24no—
911C22×C4—24no—
912C22×C4—24no—
913C22×C4—24no—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—44no—
919C22×C4—44no—
920C22×C4—44no—
921C22×C4—44no—
922C22×C4—44no—
923C22×C4—44no—
924C22×C4—42no—
925C22×C4—44no—
926C22×C4—44no—
927C22×C4—42no—
928C22×C4—48no—
929C22×C4—44no—
930C22×C4—48no—
931C22×C4—48no—
932C22×C4—48no—
933C22×C4—416no—
934C22×C4H(5,𝔽2)14yes—
935C22×C4H(5,𝔽2)14yes—
936C22×C4H(5,𝔽2)14yes—
937C22×C4C2512yes—
938C22×C4C2514yes—
939C22×C4C2514yes—
940C22×C4C2512yes—
941C22×C4C2514yes—
942C22×C4C2512yes—
943C22×C4C2512yes—
944C22×C4C2514yes—
945C22×C4C2514yes—
946C22×C4C2514yes—
947C22×C4C2512yes—
948C22×C4C2512yes—
949C22×C4C2512yes—
950C22×C4C2512yes—
951C22×C4C2514yes—
952C22×C4C2512yes—
953C22×C4C2512yes—
954C22×C4C2511yescharacteristic
955C22×C4C2511yescharacteristic
956C4⋊C4—24no—
957C4⋊C4—24no—
958C4⋊C4—24no—
959C4⋊C4—24no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—24no—
963C4⋊C4—24no—
964C4⋊C4—24no—
965C4⋊C4—24no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—44no—
971C4⋊C4—48no—
972C4⋊C4—48no—
973C4⋊C4—48no—
974C4⋊C4—44no—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C4⋊C4—44no—
978C4⋊C4—44no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—48no—
984C4⋊C4—48no—
985C4⋊C4—44no—
986C4⋊C4—48no—
987C4⋊C4—44no—
988C22⋊C4—24no—
989C22⋊C4—24no—
990C22⋊C4—24no—
991C22⋊C4—24no—
992C22⋊C4—24no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—48no—
998C22⋊C4—48no—
999C22⋊C4—48no—
1000C22⋊C4—48no—
1001C22⋊C4—48no—
1002C22⋊C4—48no—
1003C22⋊C4—48no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
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—48no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C22⋊C4—48no—
1026C22⋊C4—48no—
1027C22⋊C4—48no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—48no—
1032C22⋊C4—44no—
1033C42—24no—
1034C42—24no—
1035C42—22no—
1036C42—22no—
1037C42—22no—
1038C42—22no—
1039C42—24no—
1040C42—24no—
1041C42—24no—
1042C42—24no—
1043C42—24no—
1044C42—44no—
1045C42—48no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—24no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—24no—
1055C23—24no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—24no—
1064C23—24no—
1065C23—28no—
1066C23—22no—
1067C23—24no—
1068C23—22no—
1069C23—24no—
1070C23—22no—
1071C23—24no—
1072C23—24no—
1073C23—28no—
1074C23—22no—
1075C23—44no—
1076C23—44no—
1077C23—44no—
1078C23—48no—
1079C23—84no—
1080C23—84no—
1081C23—84no—
1082C23—88no—
1083C23—88no—
1084C23—84no—
1085C23C2×H(5,𝔽2)12yes—
1086C23C2×H(5,𝔽2)12yes—
1087C23C2×H(5,𝔽2)12yes—
1088C23C2611yescharacteristic
1089Q8—416no—
1090Q8—48no—
1091Q8—44no—
1092Q8—48no—
1093Q8—44no—
1094Q8—44no—
1095D4—416no—
1096D4—48no—
1097D4—48no—
1098D4—48no—
1099D4—48no—
1100D4—48no—
1101D4—44no—
1102D4—44no—
1103D4—44no—
1104D4—88no—
1105D4—88no—
1106D4—88no—
1107D4—88no—
1108D4—816no—
1109D4—168no—
1110D4—164no—
1111D4—164no—
1112D4—168no—
1113D4—164no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—24no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—24no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—28no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—28no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—24no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—48no—
1162C2×C4—416no—
1163C2×C4—416no—
1164C2×C4—44no—
1165C2×C4—48no—
1166C2×C4—48no—
1167C2×C4—48no—
1168C2×C4—48no—
1169C2×C4—48no—
1170C2×C4—48no—
1171C2×C4—84no—
1172C2×C4—84no—
1173C2×C4—84no—
1174C2×C4—164no—
1175C2×C4—168no—
1176C2×C4#560116yes—
1177C2×C4C2×H(5,𝔽2)12yes—
1178C2×C4C2×H(5,𝔽2)12yes—
1179C2×C4C2×H(5,𝔽2)12yes—
1180C2×C4C2×H(5,𝔽2)12yes—
1181C2×C4C2×H(5,𝔽2)12yes—
1182C2×C4C2×H(5,𝔽2)12yes—
1183C22—24no—
1184C22—22no—
1185C22—24no—
1186C22—22no—
1187C22—42no—
1188C22—44no—
1189C22—44no—
1190C22—44no—
1191C22—48no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—44no—
1196C22—42no—
1197C22—42no—
1198C22—48no—
1199C22—42no—
1200C22—42no—
1201C22—44no—
1202C22—44no—
1203C22—44no—
1204C22—42no—
1205C22—44no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—44no—
1214C22—88no—
1215C22—168no—
1216C22C2×#56014yes—
1217C22C22×H(5,𝔽2)11yescharacteristic
1218C22C22×H(5,𝔽2)11yescharacteristic
1219C22C22×H(5,𝔽2)11yescharacteristic
1220C22H(7,𝔽2)12yes—
1221C222−1+612yes—
1222C4—42no—
1223C4—42no—
1224C4—42no—
1225C4—42no—
1226C4—44no—
1227C4—44no—
1228C4—44no—
1229C4—42no—
1230C4—44no—
1231C4—44no—
1232C4—44no—
1233C4—42no—
1234C4—42no—
1235C4—42no—
1236C4—42no—
1237C4—44no—
1238C4—42no—
1239C4C2×#56014yes—
1240C4C2×#56014yes—
1241C2—24no—
1242C2—82no—
1243C2—82no—
1244C2—82no—
1245C2—82no—
1246C2—84no—
1247C2C22×#56011yescharacteristic
1248C2#6287512yes—
1249C2#6287611yescharacteristic
1250C2#6287812yes—
1251C2#6288711yescharacteristic
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. #53151C2semidirect
2. #53096C2semidirect
3. #53066C2semidirect
4. #53063C2semidirect
5. #53059C2semidirect
6. #53022C2semidirect
7. #52962C2semidirect
8. #52960C2semidirect
9. #52375C2semidirect
10. #52372C2semidirect
11. #35676C2semidirect
12. #35660C2semidirect
13. #35659C2semidirect
14. #35633C2semidirect
15. #35630C2semidirect
16. #35617C2semidirect
17. #35565C2semidirect
18. #35557C2semidirect
19. #35541C2semidirect
20. #35533C2semidirect
21. #35530C2semidirect
22. #35514C2semidirect
23. #34635C2semidirect
24. #34633C2semidirect
25. C2×#2620C2semidirect
42. #2841C22semidirect
43. #2838C22semidirect
44. #2830C22semidirect
45. #2830C22semidirect
46. #2829C22semidirect
47. #2828C22semidirect
48. #2827C22semidirect
49. #2826C22semidirect
50. #2826C22semidirect
51. #2825C22semidirect
52. #2825C22semidirect
53. #2824C22semidirect
54. #2824C22semidirect
55. #2818C22semidirect
56. #2813C22semidirect
57. #2813C22semidirect
58. #2797C22semidirect
59. #2784C22semidirect
60. #2780C22semidirect
61. #2778C22semidirect
62. #2757C22semidirect
63. #2749C22semidirect
64. #2748C22semidirect
65. #2737C22semidirect
66. #2709C22semidirect
67. #2709C22semidirect
68. #2705C22semidirect
69. #2693C22semidirect
70. #2691C22semidirect
71. #2691C22semidirect
72. #2688C22semidirect
73. #2673C22semidirect
74. #2625C22semidirect
75. #2625C22semidirect
76. #2624C22semidirect
77. #2624C22semidirect
80. #2621C22semidirect
85. #2620C22semidirect
86. #2620C22semidirect
87. #2619C22semidirect
90. #2548C22semidirect
91. #2547C22semidirect
92. #2545C22semidirect
93. #2544C22semidirect
94. #2544C22semidirect
97. #2541C22semidirect
104. #2514C22semidirect
105. #2514C22semidirect
106. #2512C22semidirect
107. #2511C22semidirect
108. #2511C22semidirect
109. #2511C22semidirect
110. #2502C22semidirect
111. #2501C22semidirect
112. #2500C22semidirect
113. #2499C22semidirect
114. #2497C22semidirect
115. #2496C22semidirect
119. #2447C22semidirect
120. #2445C22semidirect
122. #2436C22semidirect
123. #2436C22semidirect
124. #2436C22semidirect
125. #2436C22semidirect
126. #2434C22semidirect
128. #2432C22semidirect
129. #2431C22semidirect
130. #2431C22semidirect
131. #2431C22semidirect
132. #2431C22semidirect
134. #2429C22semidirect
137. #2427C22semidirect
138. #2427C22semidirect
139. #2427C22semidirect
141. #2423C22semidirect
142. #2422C22semidirect
143. #2422C22semidirect
144. #2420C22semidirect
145. #2417C22semidirect
146. #2416C22semidirect
147. #2415C22semidirect
148. #2414C22semidirect
153. #2409C22semidirect
154. #2409C22semidirect
155. #2409C22semidirect
156. #2407C22semidirect
157. #2407C22semidirect
158. #2407C22semidirect
162. #2395C22semidirect
163. #2395C22semidirect
164. #2392C22semidirect
165. #2392C22semidirect

Maximal subgroups

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

subgroupindex
#531512
#530962
#530662
#530632
#530592
#530222
#529622
#529602
#523752
#523722
#356762
#356602
#356592
#356332
#356302
#356172
#355652
#355572
#355412
#355332
#355302
#355142
#346352
#346332
C2×#26202