Finite Group Databasebeta

← #8095313

Subgroups — #8095313

Order 512.

5384 conjugacy classes of subgroups.

The subgroup lattice has 1181 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53136C214yesmaximal, complemented
2#53041C214yesmaximal, complemented
3#53041C214yesmaximal, complemented
4#53011C214yesmaximal, complemented
5#52913C218yesmaximal, complemented
6#46048C214yesmaximal, complemented
7#46002C214yesmaximal, complemented
8#45677C214yesmaximal, complemented
9#45538C218yesmaximal, complemented
10#45497C214yesmaximal, complemented
11#35674C211yesmaximal, characteristic, complemented
12#35667C211yesmaximal, characteristic, complemented
13#35661C211yesmaximal, characteristic, complemented
14#35633C211yesmaximal, characteristic, complemented
15#35621C211yesmaximal, characteristic, complemented
16#35619C211yesmaximal, characteristic, complemented
17#35317C211yesmaximal, characteristic, complemented
18#35316C211yesmaximal, characteristic, complemented
19#35313C211yesmaximal, characteristic, complemented
20#35307C211yesmaximal, characteristic, complemented
21#35242C211yesmaximal, characteristic, complemented
22#35242C211yesmaximal, characteristic, complemented
23#34814C211yesmaximal, characteristic, complemented
24#34743C211yesmaximal, characteristic
25C2×#2434C211yesmaximal, characteristic, complemented
26C24×Q8C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#536C2211yescharacteristic
31C2×#536C2211yescharacteristic
32C2×#536C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C22×C4⋊Q8C2211yescharacteristic
35C22×C4⋊Q8C2211yescharacteristic
36C2×#525C2211yescharacteristic
37C2×#525C2211yescharacteristic
38C22×C22⋊Q8C2211yescharacteristic
39C2×#520C2211yescharacteristic
40C2×#519C2211yescharacteristic
41C2×C4×#41C2211yescharacteristic
42#2868C2212yescomplemented
43#2863C2214yescomplemented
44#2858C2212yescomplemented
45#2857C2212yescomplemented
46#2857C2212yescomplemented
47#2855C2214yescomplemented
48#2849C2214yes—
49#2849C2214yes—
50#2843C2218yescomplemented
51#2841C2218yescomplemented
52#2841C2218yescomplemented
53#2838C2218yescomplemented
54#2838C2218yescomplemented
55#2838C2218yescomplemented
56#2838C2218yescomplemented
57#2830C2218yescomplemented
58#2827C2218yes—
59#2827C2218yes—
60#2797C2218yes—
61#2796C2218yes—
62#2796C2218yes—
63#2792C2218yescomplemented
64#2792C2218yescomplemented
65#2792C2218yescomplemented
66#2790C2218yes—
67#2790C2218yes—
68#2790C2218yes—
69#2784C2218yescomplemented
70#2780C2218yes—
71#2780C2218yes—
72#2749C2218yes—
73#2746C2218yes—
74#2746C2218yes—
75#2742C2218yescomplemented
76#2742C2218yescomplemented
77#2737C2218yescomplemented
78#2737C2218yescomplemented
79#2691C2218yes—
80#2658C2212yescomplemented
81#2658C2212yescomplemented
82#2645C2214yescomplemented
83#2625C2214yescomplemented
84#2621C2212yescomplemented
85#2621C2212yescomplemented
86#2614C2214yes—
87#2614C2214yes—
88#2547C2212yescomplemented
89#2547C2214yescomplemented
90#2546C2212yescomplemented
91#2546C2214yescomplemented
92#2546C2214yescomplemented
93#2545C2212yescomplemented
94#2545C2214yescomplemented
95#2544C2212yescomplemented
96#2542C2214yescomplemented
97#2542C2214yescomplemented
98#2538C2214yes—
99#2536C2214yes—
100#2534C2214yes—
101#2514C2214yescomplemented
102#2511C2214yescomplemented
103#2503C2212yescomplemented
104#2502C2212yescomplemented
105#2501C2218yes—
106#2499C2212yescomplemented
107#2499C2212yescomplemented
108#2497C2212yes—
109#2496C2212yes—
110#2495C2212yes—
111#2494C2212yes—
112#2493C2214yes—
113#2493C2218yes—
114#2486C2214yes—
115#2486C2218yes—
116#2484C2218yes—
117#2480C2214yes—
118#2447C2214yescomplemented
119#2447C2214yescomplemented
120#2446C2214yescomplemented
121#2446C2214yescomplemented
122#2446C2214yescomplemented
123#2446C2214yescomplemented
124#2446C2214yescomplemented
125#2446C2214yescomplemented
126#2436C2214yes—
127#2436C2214yes—
128#2434C2214yes—
129#2434C2214yes—
130#2434C2214yes—
131#2434C2214yes—
132#2434C2214yes—
133#2434C2214yes—
134#2429C2214yes—
135#2429C2214yes—
136#2429C2212yes—
137#2429C2214yescomplemented
138#2429C2214yescomplemented
139#2428C2212yes—
140#2427C2214yes—
141#2427C2212yes—
142#2426C2212yes—
143#2426C2214yes—
144#2425C2218yes—
145#2425C2214yes—
146#2424C2214yes—
147#2419C2218yes—
148#2419C2218yes—
149#2417C2214yes—
150#2417C2214yescomplemented
151#2415C2214yes—
152#2415C2214yescomplemented
153#2413C2214yes—
154#2413C2218yes—
155#2411C2214yes—
156#2409C2214yes—
157#2409C2214yes—
158#2409C2214yes—
159#2409C2214yes—
160#2401C2214yes—
161#2392C2214yes—
162C2×#395C2214yes—
163#2383C2218yes—
164#2377C2218yes—
165#2317C2211yescharacteristic
166#2316C2211yescharacteristic
167#2311C2211yescharacteristic
168#2310C2211yescharacteristic
169#2310C2211yescharacteristic
170#2310C2211yescharacteristic
171#2310C2211yescharacteristic
172#2310C2211yescharacteristic
173C4×#126C2214yes—
174C4×#121C2214yes—
175#2297C2211yescharacteristic
176#2296C2211yescharacteristic
177#2296C2211yescharacteristic
178#2296C2211yescharacteristic
179C2×#391C2211yescharacteristic
180C2×#391C2211yescharacteristic
181C2×#385C2214yes—
182#2285C2211yescharacteristic
183#2280C2211yescharacteristic
184#2280C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8—44no—
190C23×Q8—44no—
191C23×Q8—44no—
192C23×Q8C2311yescharacteristic
193C23×Q8C2311yescharacteristic
194C23×Q8C2311yescharacteristic
195C23×Q8C2312yes—
196C23×Q8C2314yes—
197C23×Q8C2314yes—
198C24×C4C2311yescharacteristic
199C24×C4C2312yes—
200#536—44no—
201#536—44no—
202#536—44no—
203#536—44no—
204#536—44no—
205#536—44no—
206#532—44no—
207C2×C4⋊Q8—44no—
208C2×C4⋊Q8—44no—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2314yes—
219C2×C4⋊Q8C2314yes—
220C2×C4⋊Q8C2312yes—
221C2×C4⋊Q8C2312yes—
222C2×#127C2311yescharacteristic
223C2×#126C2314yes—
224C2×#124C2312yes—
225C2×#124C2312yes—
226C2×#124C2312yes—
227C2×#124C2312yes—
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#124C2312yes—
231C2×#124C2312yes—
232#525—44no—
233#525—44no—
234C2×#123C2314yes—
235C2×#123C2314yes—
236C2×#123C2314yes—
237C2×#123C2314yes—
238C2×#123C2312yes—
239C2×#123C2312yes—
240C2×#123C2314yes—
241C2×#123C2314yes—
242C2×C22⋊Q8—44no—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2312yes—
247C2×C22⋊Q8C2312yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2312yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2314yes—
256C2×#121C2314yes—
257C2×#121C2312yes—
258C2×#121C2312yes—
259C2×#121C2314yes—
260C2×#120C2312yes—
261C2×#120C2312yes—
262#520—44no—
263#519—44no—
264C4×#41—44no—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2314yes—
267C2×C4×Q8C2314yes—
268C2×C4×Q8C2312yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2312yes—
276C2×#117C2311yescharacteristic
277C2×#117C2311yescharacteristic
278C2×#117C2311yescharacteristic
279C2×#117C2311yescharacteristic
280C2×#117C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C2×#117C2312yes—
283C2×#117C2314yes—
284C2×#117C2312yes—
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2314yes—
288C22×C4⋊C4C2314yes—
289C22×C4⋊C4C2312yes—
290C22×C22⋊C4C2312yes—
291C22×C22⋊C4C2312yes—
292C22×C42C2311yescharacteristic
293C22×C42C2311yescharacteristic
294C22×C42C2312yes—
295#401C2314yes—
296#401C2318yes—
297#400C2318yes—
298#400C2318yes—
299#400C2318yes—
300#400C2318yes—
301#400C2314yes—
302#400C2314yes—
303#400C2318yes—
304#400C2318yes—
305#400C2314yes—
306#400C2318yes—
307#399C2318yes—
308#399C2318yes—
309#399C2318yes—
310#399C2318yes—
311#398C2318yes—
312#398C2318yes—
313#398C2318yes—
314#398C2318yes—
315#398C2318yes—
316#398C2318yes—
317#398C2318yes—
318#398C2318yes—
319#398C2318yes—
320#398C2318yes—
321#398C2314yes—
322#398C2318yes—
323#397C2314yes—
324#397C2314yes—
325#397C2318yes—
326#397C2318yes—
327#397C2318yes—
328#397C2318yes—
329#397C2318yes—
330#397C2318yes—
331#397C2318yes—
332#397C2314yes—
333#397C2318yes—
334#397C2314yes—
335#396C2318yes—
336#396C2318yes—
337#396C2318yes—
338#396C2318yes—
339#396C2318yes—
340#396C2314yes—
341#396C2318yes—
342#396C2314yes—
343#396C2314yes—
344#395C2318yes—
345#395C2318yes—
346#395C2318yes—
347#395C2318yes—
348#395C2318yes—
349#395C2318yes—
350#395C2318yes—
351#395C2318yes—
352#394C2314yes—
353#394C2314yes—
354#394C2318yes—
355#394C2318yes—
356#394C2314yes—
357#394C2318yes—
358#393C2318yes—
359#393C2318yes—
360#393C2318yes—
361#393C2318yes—
362#392C2314yes—
363#391C2314yes—
364#391C2312yes—
365#391C2312yes—
366#391C2312yes—
367#391C2312yes—
368#391C2314yes—
369#391C2314yes—
370#391C2314yes—
371#391C2312yes—
372#391C2312yes—
373#391C2314yes—
374#391C2314yes—
375#391C2314yes—
376#391C2312yes—
377#391C2312yes—
378#391C2312yes—
379#391C2312yes—
380#391C2312yes—
381#391C2314yes—
382#391C2312yes—
383#391C2314yes—
384#390C2312yes—
385#390C2318yes—
386#390C2318yes—
387#390C2318yes—
388#390C2314yes—
389#390C2312yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2318yes—
394#389C2318yes—
395#389C2318yes—
396#389C2318yes—
397#389C2312yes—
398#389C2318yes—
399#389C2312yes—
400#389C2312yes—
401#389C2318yes—
402#389C2318yes—
403#389C2312yes—
404#389C2312yes—
405#389C2312yes—
406#389C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2314yes—
416#388C2318yes—
417#388C2318yes—
418#387C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#387C2318yes—
432#386C2314yes—
433#386C2318yes—
434#386C2318yes—
435#386C2318yes—
436#386C2318yes—
437#386C2318yes—
438#386C2318yes—
439#386C2314yes—
440#386C2314yes—
441#386C2314yes—
442#385C2318yes—
443#385C2318yes—
444#385C2318yes—
445#385C2314yes—
446#385C2318yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#385C2318yes—
451#385C2314yes—
452#385C2314yes—
453#385C2314yes—
454#385C2318yes—
455#385C2318yes—
456#384C2312yes—
457#384C2318yes—
458#384C2311yescharacteristic
459#384C2311yescharacteristic
460#384C2318yes—
461#383C2314yes—
462#383C2318yes—
463#382C2312yes—
464#382C2311yescharacteristic
465#382C2311yescharacteristic
466#381C2314yes—
467#381C2314yes—
468#381C2314yes—
469#381C2314yes—
470#381C2314yes—
471#381C2318yes—
472#381C2318yes—
473#381C2312yes—
474#381C2312yes—
475#380C2314yes—
476#380C2314yes—
477#380C2314yes—
478#380C2318yes—
479#380C2318yes—
480#380C2318yes—
481#380C2318yes—
482#380C2312yes—
483#380C2312yes—
484#380C2312yes—
485#380C2312yes—
486#380C2314yes—
487#379C2312yes—
488#379C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2312yes—
501C4×C22⋊C4C2312yes—
502C4×C22⋊C4C2312yes—
503C4×C22⋊C4C2312yes—
504C4×C22⋊C4C2314yes—
505#376C2312yes—
506C2×#95C2312yes—
507C2×#95C2314yes—
508C2×#95C2314yes—
509C43C2312yes—
510C25C2411yescharacteristic
511C2×#41—24no—
512C2×#41—24no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C22×Q8—24no—
518C22×Q8—24no—
519C22×Q8—24no—
520C22×Q8—24no—
521C22×Q8—24no—
522C22×Q8—24no—
523C22×Q8—24no—
524C22×Q8—24no—
525C22×Q8—24no—
526C22×Q8—44no—
527C22×Q8—44no—
528C22×Q8—44no—
529C22×Q8—48no—
530C22×Q8—48no—
531C22×Q8—48no—
532C22×Q8—48no—
533C22×Q8—48no—
534C22×Q8—48no—
535C22×Q8—464no—
536C22×Q8C2412yes—
537C22×Q8C2412yes—
538C22×Q8C2411yescharacteristic
539C22×Q8C2411yescharacteristic
540C22×Q8C2412yes—
541C22×Q8C2412yes—
542C22×Q8C2412yes—
543C22×Q8C2412yes—
544C22×Q8C2418yes—
545C22×D4C2412yes—
546C22×D4C2412yes—
547C22×D4C2411yescharacteristic
548C22×D4C2411yescharacteristic
549C22×D4C2414yes—
550C22×D4C2414yes—
551C22×D4C2414yes—
552C23×C4—24no—
553C23×C4—24no—
554C23×C4—24no—
555C23×C4—44no—
556C23×C4—44no—
557C23×C4—44no—
558C23×C4C2412yes—
559C23×C4C2411yescharacteristic
560C23×C4C2412yes—
561C23×C4C2412yes—
562C23×C4C2412yes—
563C23×C4C2412yes—
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2412yes—
567C23×C4C2412yes—
568C23×C4C2412yes—
569C23×C4C2414yes—
570C23×C4C2414yes—
571C23×C4C2418yes—
572C23×C4C2411yescharacteristic
573C4⋊Q8—44no—
574C4⋊Q8—44no—
575C4⋊Q8—48no—
576C4⋊Q8—48no—
577C4⋊Q8—44no—
578C4⋊Q8—44no—
579C4⋊Q8—42no—
580C4⋊Q8—44no—
581C4⋊Q8—44no—
582C4⋊Q8—44no—
583C4⋊Q8—44no—
584C4⋊Q8—44no—
585C4⋊Q8—44no—
586#127—42no—
587#126—216no—
588#124—42no—
589#124—42no—
590#124—44no—
591#124—44no—
592#124—44no—
593#124—44no—
594#124—44no—
595#124—44no—
596#123—44no—
597#123—44no—
598#123—48no—
599#123—48no—
600#123—48no—
601#123—48no—
602#123—48no—
603#123—48no—
604C22⋊Q8—48no—
605C22⋊Q8—48no—
606C22⋊Q8—44no—
607C22⋊Q8—44no—
608C22⋊Q8—44no—
609C22⋊Q8—44no—
610C22⋊Q8—48no—
611C22⋊Q8—48no—
612C22⋊Q8—44no—
613C22⋊Q8—44no—
614C22⋊Q8—48no—
615C22⋊Q8—44no—
616C22⋊Q8—44no—
617#121—216no—
618#121—44no—
619#121—44no—
620#121—48no—
621#120—44no—
622#120—44no—
623C4×Q8—44no—
624C4×Q8—48no—
625C4×Q8—48no—
626C4×Q8—44no—
627C4×D4—44no—
628C4×D4—44no—
629C4×D4—48no—
630C4×D4—48no—
631C4×D4—48no—
632C4×D4—48no—
633C4×D4—48no—
634#117—24no—
635#117—24no—
636#117—24no—
637#117—24no—
638#117—24no—
639#117—24no—
640#117—44no—
641#117—48no—
642#117—44no—
643C2×C4⋊C4—24no—
644C2×C4⋊C4—44no—
645C2×C4⋊C4—44no—
646C2×C4⋊C4—48no—
647C2×C4⋊C4—48no—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2418yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2418yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2418yes—
687C2×C4⋊C4C2418yes—
688C2×C22⋊C4—28no—
689C2×C22⋊C4—44no—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2412yes—
692C2×C22⋊C4C2412yes—
693C2×C22⋊C4C2412yes—
694C2×C22⋊C4C2412yes—
695C2×C22⋊C4C2412yes—
696C2×C22⋊C4C2412yes—
697C2×C22⋊C4C2412yes—
698C2×C22⋊C4C2412yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2418yes—
716C2×C22⋊C4C2418yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2418yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2418yes—
724C2×C22⋊C4C2412yes—
725C2×C42—24no—
726C2×C42—24no—
727C2×C42—44no—
728C2×C42C2412yes—
729C2×C42C2411yescharacteristic
730C2×C42C2412yes—
731C2×C42C2412yes—
732C2×C42C2412yes—
733C2×C42C2412yes—
734C2×C42C2412yes—
735C2×C42C2412yes—
736C2×C42C2412yes—
737C2×C42C2411yescharacteristic
738C2×C42C2414yes—
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2414yes—
742C2×C42C2418yes—
743C2×C42C2414yes—
744C2×C42C2414yes—
745#95C2412yes—
746#95C2412yes—
747#95C2412yes—
748#95C2412yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773#95C2418yes—
774#95C2418yes—
775#95C2418yes—
776#95C2418yes—
777#95C2418yes—
778#95C2418yes—
779#95C2418yes—
780#95C2418yes—
781#95C2418yes—
782C24—22no—
783C24—24no—
784C24—22no—
785C24—22no—
786C24—42no—
787C24C2512yes—
788C24C2512yes—
789C24C2512yes—
790C24C2511yescharacteristic
791#41—416no—
792#41—416no—
793C2×Q8—24no—
794C2×Q8—24no—
795C2×Q8—22no—
796C2×Q8—22no—
797C2×Q8—24no—
798C2×Q8—24no—
799C2×Q8—22no—
800C2×Q8—24no—
801C2×Q8—22no—
802C2×Q8—24no—
803C2×Q8—24no—
804C2×Q8—24no—
805C2×Q8—24no—
806C2×Q8—24no—
807C2×Q8—22no—
808C2×Q8—24no—
809C2×Q8—24no—
810C2×Q8—24no—
811C2×Q8—24no—
812C2×Q8—22no—
813C2×Q8—24no—
814C2×Q8—24no—
815C2×Q8—24no—
816C2×Q8—24no—
817C2×Q8—48no—
818C2×Q8—48no—
819C2×Q8—48no—
820C2×Q8—464no—
821C2×Q8—464no—
822C2×Q8—432no—
823C2×Q8—416no—
824C2×Q8—416no—
825C2×Q8—416no—
826C2×D4—24no—
827C2×D4—24no—
828C2×D4—24no—
829C2×D4—24no—
830C2×D4—24no—
831C2×D4—24no—
832C2×D4—28no—
833C2×D4—28no—
834C2×D4—22no—
835C2×D4—22no—
836C2×D4—22no—
837C2×D4—22no—
838C2×D4—22no—
839C2×D4—22no—
840C2×D4—28no—
841C2×D4—44no—
842C2×D4—44no—
843C2×D4—44no—
844C2×D4—44no—
845C2×D4—44no—
846C2×D4—44no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—22no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—22no—
856C22×C4—22no—
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—24no—
869C22×C4—24no—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—24no—
875C22×C4—24no—
876C22×C4—28no—
877C22×C4—48no—
878C22×C4—48no—
879C22×C4—48no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—48no—
887C22×C4—432no—
888C22×C4—416no—
889C22×C4H(5,𝔽2)14yes—
890C22×C4H(5,𝔽2)14yes—
891C22×C4H(5,𝔽2)14yes—
892C22×C4C2514yes—
893C22×C4C2512yes—
894C22×C4C2512yes—
895C22×C4C2514yes—
896C22×C4C2512yes—
897C22×C4C2512yes—
898C22×C4C2512yes—
899C22×C4C2514yes—
900C22×C4C2514yes—
901C22×C4C2514yes—
902C22×C4C2512yes—
903C22×C4C2514yes—
904C22×C4C2514yes—
905C22×C4C2512yes—
906C22×C4C2514yes—
907C22×C4C2512yes—
908C22×C4C2512yes—
909C22×C4C2512yes—
910C22×C4C2512yes—
911C22×C4C2511yescharacteristic
912C22×C4C2511yescharacteristic
913C4⋊C4—24no—
914C4⋊C4—24no—
915C4⋊C4—22no—
916C4⋊C4—22no—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—24no—
920C4⋊C4—24no—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—28no—
924C4⋊C4—28no—
925C4⋊C4—28no—
926C4⋊C4—28no—
927C4⋊C4—44no—
928C4⋊C4—48no—
929C4⋊C4—48no—
930C4⋊C4—48no—
931C4⋊C4—48no—
932C4⋊C4—48no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4—48no—
936C4⋊C4—48no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—48no—
941C4⋊C4—44no—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—48no—
946C4⋊C4—44no—
947C4⋊C4—48no—
948C4⋊C4—44no—
949C4⋊C4—44no—
950C4⋊C4—44no—
951C4⋊C4—48no—
952C4⋊C4—44no—
953C22⋊C4—24no—
954C22⋊C4—24no—
955C22⋊C4—24no—
956C22⋊C4—24no—
957C22⋊C4—24no—
958C22⋊C4—24no—
959C22⋊C4—24no—
960C22⋊C4—28no—
961C22⋊C4—28no—
962C22⋊C4—24no—
963C22⋊C4—24no—
964C22⋊C4—28no—
965C22⋊C4—48no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—48no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—48no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—48no—
983C22⋊C4—44no—
984C22⋊C4—48no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C42−1+418yes—
988C42—22no—
989C42—22no—
990C42—24no—
991C42—24no—
992C42—22no—
993C42—22no—
994C42—24no—
995C42—24no—
996C42—24no—
997C42—24no—
998C42—24no—
999C42—24no—
1000C42—28no—
1001C42—44no—
1002C42—44no—
1003C42—44no—
1004C42—48no—
1005C23—22no—
1006C23—22no—
1007C23—28no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—24no—
1021C23—24no—
1022C23—24no—
1023C23—24no—
1024C23—48no—
1025C23—48no—
1026C23—44no—
1027C23—44no—
1028C23C2×H(5,𝔽2)12yes—
1029C23C2×H(5,𝔽2)12yes—
1030C23C2×H(5,𝔽2)12yes—
1031C23C2×2−1+414yes—
1032C23C2611yescharacteristic
1033Q8—432no—
1034Q8—48no—
1035Q8—48no—
1036Q8—48no—
1037Q8—48no—
1038Q8—48no—
1039Q8—48no—
1040Q8—44no—
1041Q8—44no—
1042D4—48no—
1043D4—48no—
1044D4—44no—
1045D4—44no—
1046D4—88no—
1047D4—88no—
1048D4—88no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—28no—
1096C2×C4—24no—
1097C2×C4—22no—
1098C2×C4—24no—
1099C2×C4—48no—
1100C2×C4—48no—
1101C2×C4—432no—
1102C2×C4—44no—
1103C2×C4—48no—
1104C2×C4—48no—
1105C2×C4—48no—
1106C2×C4—48no—
1107C2×C4—48no—
1108C2×C4—48no—
1109C2×C4—48no—
1110C2×C4—88no—
1111C2×C4—84no—
1112C2×C4—164no—
1113C2×C4#560116yes—
1114C2×C4C2×H(5,𝔽2)12yes—
1115C2×C4C2×H(5,𝔽2)12yes—
1116C2×C4C2×H(5,𝔽2)12yes—
1117C2×C4C2×H(5,𝔽2)12yes—
1118C2×C4C2×H(5,𝔽2)12yes—
1119C2×C4C2×H(5,𝔽2)12yes—
1120C2×C4C2×2−1+414yes—
1121C2×C4C2×2−1+414yes—
1122C22—22no—
1123C22—22no—
1124C22—24no—
1125C22—24no—
1126C22—24no—
1127C22—24no—
1128C22—24no—
1129C22—416no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—44no—
1139C22—44no—
1140C22—44no—
1141C22—44no—
1142C22—42no—
1143C22—42no—
1144C22C2×#56014yes—
1145C22C22×H(5,𝔽2)11yescharacteristic
1146C22C22×H(5,𝔽2)11yescharacteristic
1147C22C22×H(5,𝔽2)11yescharacteristic
1148C22C22×2−1+412yes—
1149C222−1+612yes—
1150C4—24no—
1151C4—24no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—44no—
1156C4—42no—
1157C4—44no—
1158C4—44no—
1159C4—42no—
1160C4—42no—
1161C4—44no—
1162C4—44no—
1163C4—42no—
1164C4—44no—
1165C4—44no—
1166C4—42no—
1167C4—42no—
1168C4—44no—
1169C4C2×#56014yes—
1170C4C2×#56014yes—
1171C2—24no—
1172C2—44no—
1173C2—82no—
1174C2—82no—
1175C2C22×#56011yescharacteristic
1176C2#6283311yescharacteristic
1177C2#6288711yescharacteristic
1178C2#6294212yes—
1179C2#6294212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34743C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #53136C2semidirect
2. #53041C2semidirect
3. #53041C2semidirect
4. #53011C2semidirect
5. #52913C2semidirect
6. #46048C2semidirect
7. #46002C2semidirect
8. #45677C2semidirect
9. #45538C2semidirect
10. #45497C2semidirect
11. #35674C2semidirect
12. #35667C2semidirect
13. #35661C2semidirect
14. #35633C2semidirect
15. #35621C2semidirect
16. #35619C2semidirect
17. #35317C2semidirect
18. #35316C2semidirect
19. #35313C2semidirect
20. #35307C2semidirect
21. #35242C2semidirect
22. #35242C2semidirect
23. #34814C2semidirect
25. C2×#2434C2semidirect
42. #2868C22semidirect
43. #2863C22semidirect
44. #2858C22semidirect
45. #2857C22semidirect
46. #2857C22semidirect
47. #2855C22semidirect
50. #2843C22semidirect
51. #2841C22semidirect
52. #2841C22semidirect
53. #2838C22semidirect
54. #2838C22semidirect
55. #2838C22semidirect
56. #2838C22semidirect
57. #2830C22semidirect
63. #2792C22semidirect
64. #2792C22semidirect
65. #2792C22semidirect
69. #2784C22semidirect
75. #2742C22semidirect
76. #2742C22semidirect
77. #2737C22semidirect
78. #2737C22semidirect
80. #2658C22semidirect
81. #2658C22semidirect
82. #2645C22semidirect
83. #2625C22semidirect
84. #2621C22semidirect
85. #2621C22semidirect
88. #2547C22semidirect
89. #2547C22semidirect
90. #2546C22semidirect
91. #2546C22semidirect
92. #2546C22semidirect
93. #2545C22semidirect
94. #2545C22semidirect
95. #2544C22semidirect
96. #2542C22semidirect
97. #2542C22semidirect
101. #2514C22semidirect
102. #2511C22semidirect
103. #2503C22semidirect
104. #2502C22semidirect
106. #2499C22semidirect
107. #2499C22semidirect
118. #2447C22semidirect
119. #2447C22semidirect
120. #2446C22semidirect
121. #2446C22semidirect
122. #2446C22semidirect
123. #2446C22semidirect
124. #2446C22semidirect
125. #2446C22semidirect
137. #2429C22semidirect
138. #2429C22semidirect
150. #2417C22semidirect
152. #2415C22semidirect

Maximal subgroups

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

subgroupindex
#531362
#530412
#530112
#529132
#460482
#460022
#456772
#455382
#454972
#356742
#356672
#356612
#356332
#356212
#356192
#353172
#353162
#353132
#353072
#352422
#348142
#347432
C2×#24342