Finite Group Databasebeta

← #8095650

Subgroups — #8095650

Order 512.

5510 conjugacy classes of subgroups.

The subgroup lattice has 1249 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53151C214yesmaximal, complemented
2#53136C214yesmaximal, complemented
3#53060C214yesmaximal, complemented
4#53051C214yesmaximal, complemented
5#52369C218yesmaximal, complemented
6#45721C214yesmaximal, complemented
7#45677C214yesmaximal, complemented
8#45663C214yesmaximal, complemented
9#45550C218yesmaximal, complemented
10#45518C214yesmaximal, complemented
11#35660C211yesmaximal, characteristic, complemented
12#35660C211yesmaximal, characteristic, complemented
13#35659C211yesmaximal, characteristic, complemented
14#35634C211yesmaximal, characteristic, complemented
15#35629C211yesmaximal, characteristic, complemented
16#35557C211yesmaximal, characteristic, complemented
17#35328C211yesmaximal, characteristic, complemented
18#35307C211yesmaximal, characteristic, complemented
19#35307C211yesmaximal, characteristic, complemented
20#35273C211yesmaximal, characteristic, complemented
21#35150C211yesmaximal, characteristic, complemented
22#35150C211yesmaximal, characteristic, complemented
23C2×#2499C211yesmaximal, characteristic, complemented
24#34743C211yesmaximal, characteristic, complemented
25#34743C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#537C2211yescharacteristic
29C2×#537C2211yescharacteristic
30C2×#536C2211yescharacteristic
31C2×#536C2211yescharacteristic
32C2×#532C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C2×#525C2211yescharacteristic
35C2×#525C2211yescharacteristic
36C2×#525C2211yescharacteristic
37C2×#525C2211yescharacteristic
38C22×C22⋊Q8C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C22×#117C2211yescharacteristic
42#2857C2212yescomplemented
43#2856C2212yescomplemented
44#2855C2214yescomplemented
45#2855C2214yescomplemented
46#2854C2214yes—
47#2854C2214yes—
48#2850C2212yescomplemented
49#2850C2212yescomplemented
50#2838C2218yes—
51#2838C2218yescomplemented
52#2830C2218yes—
53#2829C2218yes—
54#2829C2218yescomplemented
55#2828C2218yes—
56#2827C2218yes—
57#2825C2218yes—
58#2824C2218yes—
59#2815C2218yes—
60#2797C2218yes—
61#2797C2218yes—
62#2797C2218yescomplemented
63#2796C2218yes—
64#2796C2218yescomplemented
65#2796C2218yescomplemented
66#2795C2218yescomplemented
67#2792C2218yescomplemented
68#2790C2218yescomplemented
69#2780C2218yescomplemented
70#2752C2218yescomplemented
71#2749C2218yes—
72#2746C2218yescomplemented
73#2742C2218yescomplemented
74#2737C2218yes—
75#2737C2218yescomplemented
76#2714C2218yes—
77#2714C2218yescomplemented
78#2691C2218yes—
79#2688C2218yes—
80#2625C2214yescomplemented
81#2625C2214yescomplemented
82#2621C2212yescomplemented
83#2620C2212yescomplemented
84#2620C2212yescomplemented
85#2619C2212yescomplemented
86#2617C2214yes—
87#2617C2214yes—
88#2543C2218yes—
89#2542C2214yes—
90#2542C2214yes—
91#2540C2214yes—
92#2540C2214yes—
93#2539C2214yes—
94#2538C2214yescomplemented
95#2537C2214yescomplemented
96#2536C2214yescomplemented
97#2535C2214yescomplemented
98#2514C2214yescomplemented
99#2513C2214yescomplemented
100#2512C2214yescomplemented
101#2511C2214yescomplemented
102#2510C2218yes—
103#2501C2214yes—
104#2499C2214yes—
105#2499C2214yes—
106#2499C2214yes—
107#2499C2214yes—
108#2497C2214yescomplemented
109#2496C2214yescomplemented
110#2495C2214yescomplemented
111#2494C2214yescomplemented
112#2481C2218yes—
113#2447C2214yescomplemented
114#2447C2214yescomplemented
115#2446C2214yescomplemented
116#2446C2214yescomplemented
117#2436C2212yescomplemented
118#2436C2212yescomplemented
119#2434C2212yescomplemented
120#2434C2212yescomplemented
121#2432C2212yescomplemented
122#2432C2212yescomplemented
123#2431C2212yescomplemented
124#2431C2212yescomplemented
125#2430C2218yes—
126#2430C2218yes—
127#2429C2212yes—
128#2429C2212yes—
129#2428C2212yes—
130#2428C2212yes—
131#2427C2212yes—
132#2427C2212yes—
133#2426C2212yes—
134#2426C2212yes—
135#2425C2214yes—
136#2425C2214yes—
137#2424C2214yes—
138#2424C2214yes—
139#2419C2218yes—
140#2419C2218yes—
141#2416C2218yes—
142#2415C2214yes—
143#2415C2214yes—
144#2415C2214yes—
145#2415C2214yes—
146#2414C2214yes—
147#2414C2214yes—
148#2414C2214yes—
149#2414C2214yes—
150#2409C2214yes—
151#2409C2214yes—
152#2409C2214yescomplemented
153#2409C2214yescomplemented
154#2407C2214yes—
155#2407C2214yes—
156#2407C2214yescomplemented
157#2407C2214yescomplemented
158#2406C2214yes—
159#2404C2214yes—
160#2392C2214yes—
161#2392C2214yes—
162C2×#397C2214yes—
163#2383C2218yescomplemented
164#2377C2218yescomplemented
165#2316C2211yescharacteristic
166#2316C2211yescharacteristic
167#2311C2211yescharacteristic
168#2311C2211yescharacteristic
169#2311C2211yescharacteristic
170#2311C2211yescharacteristic
171#2311C2211yescharacteristic
172#2311C2211yescharacteristic
173#2310C2211yescharacteristic
174C4×#121C2214yes—
175C4×#121C2214yes—
176#2297C2211yescharacteristic
177#2297C2211yescharacteristic
178#2296C2211yescharacteristic
179#2296C2211yescharacteristic
180C2×#391C2211yescharacteristic
181C2×#391C2211yescharacteristic
182C2×#387C2214yes—
183C2×#384C2211yescharacteristic
184C2×#382C2211yescharacteristic
185#2274C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C2×2−1+4—44no—
188C2×2−1+4—44no—
189C2×2−1+4—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2311yescharacteristic
193C22×#41C2311yescharacteristic
194C22×#41C2314yes—
195C22×#41C2312yes—
196C22×#41C2312yes—
197C23×Q8C2311yescharacteristic
198C23×Q8C2312yes—
199C23×Q8C2312yes—
200C24×C4C2311yescharacteristic
201#537—44no—
202#537—44no—
203#537—44no—
204#536—44no—
205#536—44no—
206#532—44no—
207#532—44no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×#127C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#126C2318yes—
215C2×#124C2311yescharacteristic
216C2×#124C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2312yes—
220C2×#124C2312yes—
221#525—44no—
222#525—44no—
223#525—44no—
224#525—44no—
225C2×#123C2312yes—
226C2×#123C2312yes—
227C2×#123C2312yes—
228C2×#123C2312yes—
229C2×#123C2314yes—
230C2×#123C2314yes—
231C2×C22⋊Q8—44no—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2312yes—
246C2×#121C2312yes—
247C2×#121C2312yes—
248C2×#121C2314yes—
249C2×#121C2314yes—
250C2×#121C2312yes—
251C2×#121C2312yes—
252C2×#121C2318yes—
253C2×#121C2312yes—
254C2×#121C2312yes—
255C2×#121C2312yes—
256C2×#121C2312yes—
257C2×#121C2312yes—
258C2×#121C2312yes—
259C2×#121C2314yes—
260C2×#121C2314yes—
261C2×#121C2314yes—
262C2×#121C2314yes—
263C2×#121C2314yes—
264C2×#120C2312yes—
265C2×#120C2312yes—
266C2×#120C2312yes—
267C2×#120C2312yes—
268C4×#41—44no—
269C4×#41—44no—
270C2×C4×Q8C2312yes—
271C2×C4×Q8C2312yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2312yes—
282C2×#117—44no—
283C2×#117C2311yescharacteristic
284C2×#117C2311yescharacteristic
285C2×#117C2311yescharacteristic
286C2×#117C2311yescharacteristic
287C2×#117C2312yes—
288C2×#117C2312yes—
289C2×#117C2314yes—
290C2×#117C2314yes—
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2311yescharacteristic
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2314yes—
295C22×C4⋊C4C2312yes—
296C22×C22⋊C4C2312yes—
297C22×C22⋊C4C2312yes—
298C22×C22⋊C4C2312yes—
299C22×C42C2311yescharacteristic
300C22×C42C2311yescharacteristic
301C22×C42C2312yes—
302C22×C42C2312yes—
303C22×C42C2312yes—
304#401C2318yes—
305#400C2318yes—
306#400C2318yes—
307#400C2318yes—
308#400C2318yes—
309#400C2318yes—
310#399C2318yes—
311#399C2318yes—
312#399C2318yes—
313#398C2318yes—
314#398C2318yes—
315#398C2318yes—
316#398C2314yes—
317#398C2314yes—
318#397C2318yes—
319#397C2318yes—
320#397C2318yes—
321#397C2318yes—
322#397C2318yes—
323#397C2318yes—
324#397C2318yes—
325#397C2318yes—
326#397C2318yes—
327#397C2318yes—
328#397C2318yes—
329#397C2318yes—
330#397C2314yes—
331#397C2318yes—
332#397C2314yes—
333#397C2318yes—
334#396C2318yes—
335#396C2314yes—
336#396C2318yes—
337#396C2314yes—
338#396C2318yes—
339#396C2314yes—
340#396C2314yes—
341#395C2318yes—
342#395C2318yes—
343#395C2318yes—
344#394C2314yes—
345#394C2318yes—
346#394C2318yes—
347#394C2318yes—
348#394C2314yes—
349#394C2314yes—
350#394C2318yes—
351#394C2318yes—
352#394C2318yes—
353#394C2318yes—
354#394C2318yes—
355#394C2314yes—
356#394C2318yes—
357#394C2314yes—
358#394C2318yes—
359#394C2314yes—
360#393C2318yes—
361#393C2318yes—
362#393C2318yes—
363#392C2318yes—
364#392C2314yes—
365#392C2318yes—
366#392C2318yes—
367#392C2318yes—
368#392C2318yes—
369#392C2318yes—
370#392C2314yes—
371#392C2318yes—
372#391C2314yes—
373#391C2314yes—
374#391C2312yes—
375#391C2312yes—
376#391C2312yes—
377#391C2312yes—
378#391C2312yes—
379#391C2312yes—
380#391C2312yes—
381#391C2312yes—
382#391C2312yes—
383#391C2312yes—
384#391C2314yes—
385#391C2314yes—
386#391C2312yes—
387#391C2312yes—
388#390C2312yes—
389#390C2312yes—
390#390C2312yes—
391#390C2312yes—
392#390C2312yes—
393#390C2312yes—
394#390C2318yes—
395#390C2314yes—
396#390C2318yes—
397#390C2318yes—
398#390C2318yes—
399#390C2318yes—
400#390C2318yes—
401#390C2312yes—
402#390C2312yes—
403#390C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2318yes—
409#389C2318yes—
410#389C2318yes—
411#389C2312yes—
412#389C2312yes—
413#389C2312yes—
414#389C2312yes—
415#389C2314yes—
416#389C2314yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2314yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#387C2318yes—
431#387C2318yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#386C2314yes—
442#386C2314yes—
443#386C2314yes—
444#386C2314yes—
445#386C2314yes—
446#386C2314yes—
447#386C2314yes—
448#386C2318yes—
449#386C2318yes—
450#386C2318yes—
451#386C2318yes—
452#386C2318yes—
453#386C2318yes—
454#386C2314yes—
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#385C2318yes—
468#385C2318yes—
469#385C2314yes—
470#385C2314yes—
471#384C2312yes—
472#384C2312yes—
473#384C2318yes—
474#384C2314yes—
475#383C2318yes—
476#382C2312yes—
477#382C2312yes—
478#382C2314yes—
479#381C2314yes—
480#381C2318yes—
481#381C2318yes—
482#380C2314yes—
483#380C2314yes—
484#380C2314yes—
485#380C2314yes—
486#380C2314yes—
487#380C2314yes—
488#380C2314yes—
489#380C2314yes—
490#380C2318yes—
491#380C2314yes—
492#380C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C22⋊C4C2312yes—
498C4×C22⋊C4C2312yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2312yes—
501C4×C22⋊C4C2312yes—
502C4×C22⋊C4C2312yes—
503C4×C22⋊C4C2312yes—
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2314yes—
506C2×#95C2314yes—
507C2×#95C2314yes—
508C2×#95C2314yes—
509C2×#95C2312yes—
510C25C2411yescharacteristic
5112−1+4—464no—
512C2×#41—24no—
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—24no—
523C2×#41—24no—
524C2×#41—48no—
525C2×#41—48no—
526C2×#41—48no—
527C2×#41—44no—
528C2×#41—44no—
529C2×#41—44no—
530C2×#41—44no—
531C2×#41—44no—
532C2×#41—44no—
533C22×Q8—24no—
534C22×Q8—24no—
535C22×Q8—24no—
536C22×Q8—44no—
537C22×Q8—44no—
538C22×Q8—44no—
539C22×Q8—44no—
540C22×Q8—44no—
541C22×Q8—44no—
542C22×Q8C2411yescharacteristic
543C22×Q8C2411yescharacteristic
544C22×Q8C2412yes—
545C22×Q8C2412yes—
546C22×Q8C2411yescharacteristic
547C22×Q8C2411yescharacteristic
548C22×Q8C2414yes—
549C22×D4C2412yes—
550C22×D4C2412yes—
551C22×D4C2411yescharacteristic
552C22×D4C2411yescharacteristic
553C22×D4C2412yes—
554C22×D4C2412yes—
555C22×D4C2411yescharacteristic
556C22×D4C2411yescharacteristic
557C22×D4C2414yes—
558C22×D4C2414yes—
559C22×D4C2414yes—
560C22×D4C2414yes—
561C22×D4C2414yes—
562C22×D4C2414yes—
563C22×D4C2414yes—
564C22×D4C2414yes—
565C22×D4C2414yes—
566C22×D4C2414yes—
567C23×C4—24no—
568C23×C4—24no—
569C23×C4—24no—
570C23×C4C2412yes—
571C23×C4C2411yescharacteristic
572C23×C4C2412yes—
573C23×C4C2412yes—
574C23×C4C2412yes—
575C23×C4C2412yes—
576C23×C4C2412yes—
577C23×C4C2412yes—
578C23×C4C2412yes—
579C23×C4C2412yes—
580C23×C4C2412yes—
581C23×C4C2412yes—
582C23×C4C2412yes—
583C23×C4C2414yes—
584C23×C4C2414yes—
585C23×C4C2414yes—
586C23×C4C2414yes—
587C23×C4C2411yescharacteristic
588C4⋊Q8—42no—
589C4⋊Q8—42no—
590C4⋊Q8—44no—
591C4⋊Q8—44no—
592#127—42no—
593#127—42no—
594#126—416no—
595#124—42no—
596#124—42no—
597#124—42no—
598#124—42no—
599#124—44no—
600#124—44no—
601#123—44no—
602#123—44no—
603#123—44no—
604#123—44no—
605#123—48no—
606#123—48no—
607C22⋊Q8—48no—
608C22⋊Q8—48no—
609C22⋊Q8—44no—
610C22⋊Q8—44no—
611C22⋊Q8—44no—
612C22⋊Q8—44no—
613C22⋊Q8—48no—
614C22⋊Q8—48no—
615C22⋊Q8—44no—
616C22⋊Q8—44no—
617C22⋊Q8—44no—
618C22⋊Q8—44no—
619C22⋊Q8—44no—
620C22⋊Q8—44no—
621#121—48no—
622#121—48no—
623#121—416no—
624#121—44no—
625#121—44no—
626#121—44no—
627#121—44no—
628#121—44no—
629#121—44no—
630#121—44no—
631#121—44no—
632#121—44no—
633#121—44no—
634#121—48no—
635#121—48no—
636#121—48no—
637#121—48no—
638#121—48no—
639#120—44no—
640#120—44no—
641#120—44no—
642#120—44no—
643C4×Q8—44no—
644C4×Q8—44no—
645C4×D4—44no—
646C4×D4—44no—
647C4×D4—48no—
648C4×D4—48no—
649C4×D4—48no—
650C4×D4—48no—
651C4×D4—48no—
652C4×D4—48no—
653C4×D4—48no—
654C4×D4—48no—
655#117—24no—
656#117—24no—
657#117—24no—
658#117—24no—
659#117—44no—
660#117—44no—
661#117—48no—
662#117—48no—
663C2×C4⋊C4—24no—
664C2×C4⋊C4—24no—
665C2×C4⋊C4—24no—
666C2×C4⋊C4—48no—
667C2×C4⋊C4—44no—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2418yes—
681C2×C4⋊C4C2418yes—
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⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2418yes—
695C2×C4⋊C4C2418yes—
696C2×C4⋊C4C2418yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2418yes—
700C2×C22⋊C4—44no—
701C2×C22⋊C4—44no—
702C2×C22⋊C4—44no—
703C2×C22⋊C4C2412yes—
704C2×C22⋊C4C2412yes—
705C2×C22⋊C4C2412yes—
706C2×C22⋊C4C2412yes—
707C2×C22⋊C4C2412yes—
708C2×C22⋊C4C2412yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2412yes—
713C2×C22⋊C4C2412yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
735C2×C22⋊C4C2418yes—
736C2×C22⋊C4C2418yes—
737C2×C22⋊C4C2418yes—
738C2×C22⋊C4C2418yes—
739C2×C22⋊C4C2418yes—
740C2×C22⋊C4C2418yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2418yes—
744C2×C22⋊C4C2418yes—
745C2×C42—24no—
746C2×C42—24no—
747C2×C42—44no—
748C2×C42—44no—
749C2×C42—44no—
750C2×C42C2412yes—
751C2×C42C2412yes—
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2412yes—
755C2×C42C2412yes—
756C2×C42C2412yes—
757C2×C42C2412yes—
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2418yes—
761C2×C42C2414yes—
762C2×C42C2414yes—
763C2×C42C2418yes—
764#95C2412yes—
765#95C2412yes—
766#95C2412yes—
767#95C2412yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773#95C2418yes—
774#95C2418yes—
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—
792#95C2418yes—
793C24—22no—
794C24—22no—
795C24—22no—
796C24—42no—
797C24—42no—
798C24C2512yes—
799C24C2512yes—
800C24C2512yes—
801C24C2512yes—
802C24C2512yes—
803C24C2511yescharacteristic
804#41—464no—
805#41—432no—
806#41—432no—
807#41—416no—
808#41—416no—
809#41—416no—
810#41—416no—
811C2×Q8—22no—
812C2×Q8—22no—
813C2×Q8—22no—
814C2×Q8—22no—
815C2×Q8—22no—
816C2×Q8—22no—
817C2×Q8—24no—
818C2×Q8—24no—
819C2×Q8—24no—
820C2×Q8—24no—
821C2×Q8—22no—
822C2×Q8—22no—
823C2×Q8—22no—
824C2×Q8—22no—
825C2×Q8—24no—
826C2×Q8—24no—
827C2×Q8—22no—
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—24no—
846C2×D4—24no—
847C2×D4—22no—
848C2×D4—22no—
849C2×D4—22no—
850C2×D4—22no—
851C2×D4—22no—
852C2×D4—22no—
853C2×D4—22no—
854C2×D4—22no—
855C2×D4—22no—
856C2×D4—22no—
857C2×D4—22no—
858C2×D4—22no—
859C2×D4—28no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—48no—
884C2×D4—48no—
885C2×D4—48no—
886C22×C4—24no—
887C22×C4—22no—
888C22×C4—24no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—24no—
892C22×C4—24no—
893C22×C4—24no—
894C22×C4—24no—
895C22×C4—24no—
896C22×C4—24no—
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—28no—
917C22×C4—42no—
918C22×C4—44no—
919C22×C4—44no—
920C22×C4—44no—
921C22×C4—44no—
922C22×C4—44no—
923C22×C4—44no—
924C22×C4—44no—
925C22×C4—44no—
926C22×C4—42no—
927C22×C4—44no—
928C22×C4—44no—
929C22×C4—44no—
930C22×C4—44no—
931C22×C4—44no—
932C22×C4—44no—
933C22×C4—42no—
934C22×C4—416no—
935C22×C4H(5,𝔽2)14yes—
936C22×C4H(5,𝔽2)14yes—
937C22×C4H(5,𝔽2)14yes—
938C22×C4C2512yes—
939C22×C4C2514yes—
940C22×C4C2512yes—
941C22×C4C2514yes—
942C22×C4C2514yes—
943C22×C4C2512yes—
944C22×C4C2512yes—
945C22×C4C2514yes—
946C22×C4C2514yes—
947C22×C4C2514yes—
948C22×C4C2512yes—
949C22×C4C2514yes—
950C22×C4C2514yes—
951C22×C4C2512yes—
952C22×C4C2512yes—
953C22×C4C2512yes—
954C22×C4C2512yes—
955C22×C4C2511yescharacteristic
956C22×C4C2511yescharacteristic
957C4⋊C4—24no—
958C4⋊C4—24no—
959C4⋊C4—24no—
960C4⋊C4—24no—
961C4⋊C4—24no—
962C4⋊C4—24no—
963C4⋊C4—24no—
964C4⋊C4—24no—
965C4⋊C4—24no—
966C4⋊C4—24no—
967C4⋊C4—216no—
968C4⋊C4—28no—
969C4⋊C4—48no—
970C4⋊C4—48no—
971C4⋊C4—44no—
972C4⋊C4—44no—
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—44no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—48no—
987C4⋊C4—48no—
988C4⋊C4—48no—
989C22⋊C4—24no—
990C22⋊C4—24no—
991C22⋊C4—24no—
992C22⋊C4—24no—
993C22⋊C4—24no—
994C22⋊C4—24no—
995C22⋊C4—28no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—48no—
999C22⋊C4—48no—
1000C22⋊C4—44no—
1001C22⋊C4—48no—
1002C22⋊C4—48no—
1003C22⋊C4—44no—
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—44no—
1026C22⋊C4—44no—
1027C22⋊C4—48no—
1028C22⋊C4—48no—
1029C22⋊C4—48no—
1030C22⋊C4—48no—
1031C42—22no—
1032C42—22no—
1033C42—22no—
1034C42—22no—
1035C42—24no—
1036C42—24no—
1037C42—24no—
1038C42—24no—
1039C42—24no—
1040C42—24no—
1041C42—48no—
1042C42—44no—
1043C42—44no—
1044C42—48no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—24no—
1063C23—22no—
1064C23—22no—
1065C23—24no—
1066C23—24no—
1067C23—24no—
1068C23—24no—
1069C23—24no—
1070C23—24no—
1071C23—24no—
1072C23—22no—
1073C23—22no—
1074C23—44no—
1075C23—44no—
1076C23—44no—
1077C23—84no—
1078C23—84no—
1079C23C2×H(5,𝔽2)12yes—
1080C23C2×H(5,𝔽2)12yes—
1081C23C2×H(5,𝔽2)12yes—
1082C23C2611yescharacteristic
1083Q8—416no—
1084Q8—48no—
1085Q8—48no—
1086Q8—44no—
1087Q8—44no—
1088Q8—44no—
1089Q8—44no—
1090D4—416no—
1091D4—48no—
1092D4—48no—
1093D4—48no—
1094D4—48no—
1095D4—44no—
1096D4—44no—
1097D4—44no—
1098D4—44no—
1099D4—88no—
1100D4—88no—
1101D4—88no—
1102D4—88no—
1103D4—88no—
1104D4—88no—
1105D4—164no—
1106D4—164no—
1107D4—164no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—24no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—28no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—28no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—28no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—22no—
1155C2×C4—48no—
1156C2×C4—416no—
1157C2×C4—416no—
1158C2×C4—44no—
1159C2×C4—48no—
1160C2×C4—48no—
1161C2×C4—48no—
1162C2×C4—48no—
1163C2×C4—48no—
1164C2×C4—48no—
1165C2×C4—48no—
1166C2×C4—88no—
1167C2×C4—84no—
1168C2×C4—84no—
1169C2×C4—84no—
1170C2×C4—84no—
1171C2×C4—88no—
1172C2×C4#560116yes—
1173C2×C4C2×H(5,𝔽2)12yes—
1174C2×C4C2×H(5,𝔽2)12yes—
1175C2×C4C2×H(5,𝔽2)12yes—
1176C2×C4C2×H(5,𝔽2)12yes—
1177C2×C4C2×H(5,𝔽2)12yes—
1178C2×C4C2×H(5,𝔽2)12yes—
1179C2×C4#58514yes—
1180C22—22no—
1181C22—22no—
1182C22—24no—
1183C22—24no—
1184C22—42no—
1185C22—42no—
1186C22—42no—
1187C22—42no—
1188C22—42no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—42no—
1193C22—42no—
1194C22—44no—
1195C22—44no—
1196C22—42no—
1197C22—42no—
1198C22—44no—
1199C22—44no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—44no—
1206C22—44no—
1207C22—42no—
1208C22—42no—
1209C22—44no—
1210C22—44no—
1211C22—88no—
1212C22C2×#56014yes—
1213C22C22×H(5,𝔽2)11yescharacteristic
1214C22C22×H(5,𝔽2)11yescharacteristic
1215C22C22×H(5,𝔽2)11yescharacteristic
1216C22C2×#58512yes—
1217C222−1+612yes—
1218C4—24no—
1219C4—44no—
1220C4—44no—
1221C4—44no—
1222C4—42no—
1223C4—44no—
1224C4—44no—
1225C4—42no—
1226C4—42no—
1227C4—42no—
1228C4—44no—
1229C4—42no—
1230C4—42no—
1231C4—42no—
1232C4—44no—
1233C4—42no—
1234C4—44no—
1235C4C2×#56014yes—
1236C4C2×#56014yes—
1237C2—24no—
1238C2—82no—
1239C2—82no—
1240C2—82no—
1241C2—82no—
1242C2—82no—
1243C2C22×#56011yescharacteristic
1244C2#6283611yescharacteristic
1245C2#6288711yescharacteristic
1246C2#6292712yes—
1247C2#6296012yes—
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. #53136C2semidirect
3. #53060C2semidirect
4. #53051C2semidirect
5. #52369C2semidirect
6. #45721C2semidirect
7. #45677C2semidirect
8. #45663C2semidirect
9. #45550C2semidirect
10. #45518C2semidirect
11. #35660C2semidirect
12. #35660C2semidirect
13. #35659C2semidirect
14. #35634C2semidirect
15. #35629C2semidirect
16. #35557C2semidirect
17. #35328C2semidirect
18. #35307C2semidirect
19. #35307C2semidirect
20. #35273C2semidirect
21. #35150C2semidirect
22. #35150C2semidirect
23. C2×#2499C2semidirect
24. #34743C2semidirect
25. #34743C2semidirect
42. #2857C22semidirect
43. #2856C22semidirect
44. #2855C22semidirect
45. #2855C22semidirect
48. #2850C22semidirect
49. #2850C22semidirect
51. #2838C22semidirect
54. #2829C22semidirect
62. #2797C22semidirect
64. #2796C22semidirect
65. #2796C22semidirect
66. #2795C22semidirect
67. #2792C22semidirect
68. #2790C22semidirect
69. #2780C22semidirect
70. #2752C22semidirect
72. #2746C22semidirect
73. #2742C22semidirect
75. #2737C22semidirect
77. #2714C22semidirect
80. #2625C22semidirect
81. #2625C22semidirect
82. #2621C22semidirect
83. #2620C22semidirect
84. #2620C22semidirect
85. #2619C22semidirect
94. #2538C22semidirect
95. #2537C22semidirect
96. #2536C22semidirect
97. #2535C22semidirect
98. #2514C22semidirect
99. #2513C22semidirect
100. #2512C22semidirect
101. #2511C22semidirect
108. #2497C22semidirect
109. #2496C22semidirect
110. #2495C22semidirect
111. #2494C22semidirect
113. #2447C22semidirect
114. #2447C22semidirect
115. #2446C22semidirect
116. #2446C22semidirect
117. #2436C22semidirect
118. #2436C22semidirect
119. #2434C22semidirect
120. #2434C22semidirect
121. #2432C22semidirect
122. #2432C22semidirect
123. #2431C22semidirect
124. #2431C22semidirect
152. #2409C22semidirect
153. #2409C22semidirect
156. #2407C22semidirect
157. #2407C22semidirect
163. #2383C22semidirect
164. #2377C22semidirect

Maximal subgroups

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

subgroupindex
#531512
#531362
#530602
#530512
#523692
#457212
#456772
#456632
#455502
#455182
#356602
#356592
#356342
#356292
#355572
#353282
#353072
#352732
#351502
C2×#24992
#347432