Finite Group Databasebeta

← #8095625

Subgroups — #8095625

Order 512.

5526 conjugacy classes of subgroups.

The subgroup lattice has 1211 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53073C214yesmaximal, complemented
2#53066C214yesmaximal, complemented
3#53047C214yesmaximal, complemented
4#53047C214yesmaximal, complemented
5#52340C218yesmaximal, complemented
6#45708C214yesmaximal, complemented
7#45628C214yesmaximal, complemented
8#45628C214yesmaximal, complemented
9#45538C218yesmaximal, complemented
10#45522C214yesmaximal, complemented
11#35677C211yesmaximal, characteristic, complemented
12#35672C211yesmaximal, characteristic, complemented
13#35667C211yesmaximal, characteristic, complemented
14#35634C211yesmaximal, characteristic, complemented
15#35630C211yesmaximal, characteristic, complemented
16#35558C211yesmaximal, characteristic, complemented
17#35327C211yesmaximal, characteristic, complemented
18#35316C211yesmaximal, characteristic, complemented
19#35308C211yesmaximal, characteristic, complemented
20#35256C211yesmaximal, characteristic, complemented
21#35149C211yesmaximal, characteristic, complemented
22#35149C211yesmaximal, characteristic, complemented
23#34742C211yesmaximal, characteristic, complemented
24#34742C211yesmaximal, characteristic, complemented
25C2×#2432C211yesmaximal, characteristic, complemented
26C23×#41C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#536C2211yescharacteristic
31C2×#536C2211yescharacteristic
32C2×#535C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C22×C4⋊Q8C2211yescharacteristic
35C22×#124C2211yescharacteristic
36C2×#525C2211yescharacteristic
37C2×#525C2211yescharacteristic
38C22×C22⋊Q8C2211yescharacteristic
39C2×#519C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C2×C4×#41C2211yescharacteristic
42#2857C2212yescomplemented
43#2857C2214yescomplemented
44#2856C2212yescomplemented
45#2850C2212yescomplemented
46#2850C2214yescomplemented
47#2850C2212yescomplemented
48#2849C2214yes—
49#2849C2214yes—
50#2837C2218yescomplemented
51#2837C2218yescomplemented
52#2837C2218yescomplemented
53#2829C2218yescomplemented
54#2829C2218yescomplemented
55#2828C2218yescomplemented
56#2827C2218yescomplemented
57#2827C2218yescomplemented
58#2825C2218yescomplemented
59#2813C2218yescomplemented
60#2803C2218yescomplemented
61#2803C2218yescomplemented
62#2801C2218yescomplemented
63#2797C2218yescomplemented
64#2796C2218yescomplemented
65#2796C2218yescomplemented
66#2790C2218yescomplemented
67#2790C2218yescomplemented
68#2790C2218yescomplemented
69#2780C2218yescomplemented
70#2780C2218yescomplemented
71#2756C2218yescomplemented
72#2756C2218yescomplemented
73#2749C2218yescomplemented
74#2746C2218yescomplemented
75#2746C2218yescomplemented
76#2705C2218yescomplemented
77#2705C2218yescomplemented
78#2703C2218yescomplemented
79#2691C2218yescomplemented
80#2621C2212yescomplemented
81#2621C2214yescomplemented
82#2620C2212yescomplemented
83#2620C2214yescomplemented
84#2620C2212yescomplemented
85#2619C2212yescomplemented
86#2613C2214yes—
87#2613C2214yes—
88#2548C2212yescomplemented
89#2548C2212yescomplemented
90#2547C2214yescomplemented
91#2546C2212yescomplemented
92#2546C2214yescomplemented
93#2546C2212yescomplemented
94#2545C2212yescomplemented
95#2545C2214yescomplemented
96#2545C2212yescomplemented
97#2545C2212yescomplemented
98#2545C2212yescomplemented
99#2544C2214yescomplemented
100#2542C2214yescomplemented
101#2542C2214yescomplemented
102#2540C2214yescomplemented
103#2540C2214yescomplemented
104#2539C2214yes—
105#2534C2218yes—
106#2514C2214yescomplemented
107#2514C2214yescomplemented
108#2513C2214yescomplemented
109#2513C2214yescomplemented
110#2512C2214yescomplemented
111#2512C2214yescomplemented
112#2511C2214yescomplemented
113#2511C2214yescomplemented
114#2501C2214yes—
115#2493C2218yes—
116#2486C2218yes—
117#2484C2214yes—
118#2482C2214yes—
119#2480C2218yes—
120#2432C2214yes—
121#2432C2214yes—
122#2432C2214yes—
123#2432C2214yes—
124#2432C2214yes—
125#2432C2214yes—
126#2431C2214yes—
127#2431C2214yes—
128#2429C2214yescomplemented
129#2429C2214yescomplemented
130#2429C2214yescomplemented
131#2428C2214yescomplemented
132#2427C2214yescomplemented
133#2426C2214yescomplemented
134#2426C2214yescomplemented
135#2426C2214yescomplemented
136#2425C2218yes—
137#2424C2218yes—
138#2423C2212yescomplemented
139#2423C2214yescomplemented
140#2423C2212yescomplemented
141#2423C2214yescomplemented
142#2422C2212yescomplemented
143#2422C2212yescomplemented
144#2421C2212yescomplemented
145#2421C2214yescomplemented
146#2421C2212yescomplemented
147#2421C2214yescomplemented
148#2420C2212yescomplemented
149#2420C2212yescomplemented
150#2419C2214yes—
151#2419C2214yes—
152#2418C2214yes—
153#2418C2214yes—
154#2413C2218yes—
155#2411C2218yes—
156#2407C2214yes—
157#2407C2214yes—
158#2407C2214yes—
159#2407C2214yes—
160#2395C2214yescomplemented
161#2395C2214yescomplemented
162C2×#394C2214yes—
163#2383C2218yescomplemented
164#2377C2218yescomplemented
165#2317C2211yescharacteristic
166#2317C2211yescharacteristic
167#2310C2211yescharacteristic
168#2310C2211yescharacteristic
169#2310C2211yescharacteristic
170#2309C2211yescharacteristic
171#2309C2211yescharacteristic
172C4×#123C2214yescomplemented
173C4×#123C2214yescomplemented
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2296C2211yescharacteristic
177#2296C2211yescharacteristic
178C2×#391C2211yescharacteristic
179C2×#390C2211yescharacteristic
180C2×#385C2214yes—
181#2285C2211yescharacteristic
182#2285C2211yescharacteristic
183#2280C2211yescharacteristic
184#2280C2211yescharacteristic
185#2274C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41—44no—
188C22×#41—44no—
189C22×#41—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2314yes—
193C22×#41C2314yes—
194C23×Q8C2311yescharacteristic
195C23×Q8C2311yescharacteristic
196C23×D4C2311yescharacteristic
197C23×D4C2312yes—
198C24×C4C2311yescharacteristic
199C24×C4C2312yes—
200#537—44no—
201#536—44no—
202#536—44no—
203#536—44no—
204#536—44no—
205#535—44no—
206#535—44no—
207C2×C4⋊Q8—44no—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×#127C2312yes—
216C2×#127C2312yes—
217C2×#126C2318yes—
218C2×#124—44no—
219C2×#124C2312yes—
220C2×#124C2312yes—
221C2×#124C2312yes—
222C2×#124C2312yes—
223C2×#124C2314yes—
224C2×#124C2312yes—
225C2×#124C2312yes—
226C2×#124C2312yes—
227C2×#124C2312yes—
228#525—44no—
229#525—44no—
230C2×#123C2312yes—
231C2×#123C2312yes—
232C2×#123C2314yes—
233C2×#123C2314yes—
234C2×#123C2314yes—
235C2×#123C2314yes—
236C2×#123C2314yes—
237C2×#123C2314yes—
238C2×C22⋊Q8—44no—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2312yes—
249C2×C22⋊Q8C2312yes—
250C2×#121C2312yes—
251C2×#121C2314yes—
252C2×#121C2312yes—
253C2×#121C2312yes—
254C2×#121C2312yes—
255C2×#121C2318yes—
256C2×#121C2312yes—
257C2×#121C2312yes—
258C2×#121C2314yes—
259C2×#120C2314yes—
260C2×#120C2314yes—
261C2×#120C2312yes—
262C2×#120C2312yes—
263#519—44no—
264C4×#41—44no—
265C4×#41—44no—
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2312yes—
271C2×C4×Q8C2312yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2312yes—
278C2×#117C2311yescharacteristic
279C2×#117C2311yescharacteristic
280C2×#117C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C2×#117C2311yescharacteristic
284C2×#117C2312yes—
285C2×#117C2312yes—
286C2×#117C2314yes—
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2314yes—
289C22×C4⋊C4C2312yes—
290C22×C22⋊C4C2312yes—
291C22×C22⋊C4C2312yes—
292C22×C22⋊C4C2314yes—
293C22×C22⋊C4C2314yes—
294C22×C42C2311yescharacteristic
295C22×C42C2311yescharacteristic
296C22×C42C2312yes—
297C22×C42C2312yes—
298#401C2318yes—
299#400C2314yes—
300#400C2318yes—
301#400C2318yes—
302#400C2318yes—
303#400C2318yes—
304#400C2314yes—
305#399C2318yes—
306#399C2318yes—
307#399C2314yes—
308#399C2318yes—
309#399C2318yes—
310#399C2314yes—
311#398C2314yes—
312#398C2318yes—
313#398C2318yes—
314#398C2318yes—
315#398C2318yes—
316#398C2318yes—
317#398C2318yes—
318#398C2314yes—
319#397C2318yes—
320#397C2318yes—
321#397C2318yes—
322#397C2314yes—
323#397C2314yes—
324#397C2318yes—
325#397C2318yes—
326#397C2318yes—
327#397C2314yes—
328#397C2314yes—
329#397C2318yes—
330#397C2314yes—
331#397C2314yes—
332#396C2318yes—
333#396C2318yes—
334#396C2318yes—
335#396C2318yes—
336#396C2318yes—
337#396C2318yes—
338#396C2318yes—
339#396C2318yes—
340#396C2318yes—
341#394C2314yes—
342#394C2318yes—
343#394C2318yes—
344#394C2318yes—
345#394C2318yes—
346#394C2318yes—
347#394C2318yes—
348#394C2314yes—
349#394C2314yes—
350#394C2318yes—
351#394C2318yes—
352#394C2318yes—
353#394C2318yes—
354#394C2318yes—
355#394C2318yes—
356#394C2318yes—
357#394C2318yes—
358#394C2318yes—
359#394C2314yes—
360#392C2318yes—
361#392C2318yes—
362#392C2318yes—
363#392C2318yes—
364#392C2318yes—
365#392C2318yes—
366#391C2314yes—
367#391C2314yes—
368#391C2314yes—
369#391C2312yes—
370#391C2314yes—
371#391C2312yes—
372#391C2314yes—
373#391C2311yescharacteristic
374#391C2312yes—
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2312yes—
378#391C2311yescharacteristic
379#391C2314yes—
380#390C2314yes—
381#390C2312yes—
382#390C2314yes—
383#390C2312yes—
384#390C2314yes—
385#390C2318yes—
386#390C2318yes—
387#390C2318yes—
388#390C2311yescharacteristic
389#390C2312yes—
390#390C2311yescharacteristic
391#390C2318yes—
392#390C2311yescharacteristic
393#390C2312yes—
394#390C2311yescharacteristic
395#390C2318yes—
396#390C2318yes—
397#390C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2318yes—
401#389C2318yes—
402#389C2318yes—
403#389C2318yes—
404#389C2318yes—
405#389C2312yes—
406#389C2312yes—
407#389C2312yes—
408#389C2312yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2314yes—
414#388C2314yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2318yes—
424#388C2314yes—
425#388C2314yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2314yes—
431#387C2314yes—
432#387C2318yes—
433#387C2314yes—
434#387C2314yes—
435#386C2314yes—
436#386C2318yes—
437#386C2318yes—
438#386C2318yes—
439#386C2318yes—
440#386C2318yes—
441#386C2318yes—
442#386C2318yes—
443#386C2318yes—
444#386C2314yes—
445#386C2314yes—
446#386C2314yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#385C2314yes—
451#385C2314yes—
452#385C2318yes—
453#385C2318yes—
454#385C2314yes—
455#385C2318yes—
456#385C2314yes—
457#385C2314yes—
458#385C2314yes—
459#385C2318yes—
460#385C2318yes—
461#384C2312yes—
462#384C2312yes—
463#384C2312yes—
464#384C2312yes—
465#384C2318yes—
466#383C2318yes—
467#382C2312yes—
468#382C2312yes—
469#382C2312yes—
470#382C2312yes—
471#381C2314yes—
472#381C2314yes—
473#381C2314yes—
474#381C2312yes—
475#381C2312yes—
476#381C2314yes—
477#381C2314yes—
478#380C2318yes—
479#380C2318yes—
480#380C2318yes—
481#380C2312yes—
482#380C2312yes—
483#380C2312yes—
484#380C2312yes—
485#380C2314yes—
486#380C2314yes—
487#379C2314yes—
488#379C2314yes—
489#379C2312yes—
490#379C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2312yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2314yes—
503C4×C22⋊C4C2314yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2312yes—
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2314yes—
508C2×#95C2314yes—
509C2×#95C2312yes—
510C25C2411yescharacteristic
511C25C2412yes—
512C2×#41—24no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C2×#41—24no—
518C2×#41—48no—
519C2×#41—48no—
520C2×#41—48no—
521C2×#41—48no—
522C2×#41—48no—
523C2×#41—48no—
524C2×#41—464no—
525C22×Q8—24no—
526C22×Q8—24no—
527C22×Q8—24no—
528C22×Q8—24no—
529C22×Q8—24no—
530C22×Q8—24no—
531C22×Q8C2412yes—
532C22×Q8C2412yes—
533C22×Q8C2411yescharacteristic
534C22×Q8C2411yescharacteristic
535C22×Q8C2412yes—
536C22×Q8C2412yes—
537C22×D4—24no—
538C22×D4—24no—
539C22×D4—24no—
540C22×D4—44no—
541C22×D4—44no—
542C22×D4—44no—
543C22×D4C2412yes—
544C22×D4C2412yes—
545C22×D4C2411yescharacteristic
546C22×D4C2411yescharacteristic
547C22×D4C2412yes—
548C22×D4C2412yes—
549C22×D4C2414yes—
550C22×D4C2414yes—
551C22×D4C2414yes—
552C22×D4C2418yes—
553C22×D4C2414yes—
554C22×D4C2414yes—
555C22×D4C2418yes—
556C23×C4—24no—
557C23×C4—24no—
558C23×C4—24no—
559C23×C4—44no—
560C23×C4—44no—
561C23×C4—44no—
562C23×C4C2412yes—
563C23×C4C2411yescharacteristic
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2412yes—
567C23×C4C2412yes—
568C23×C4C2412yes—
569C23×C4C2412yes—
570C23×C4C2412yes—
571C23×C4C2412yes—
572C23×C4C2414yes—
573C23×C4C2414yes—
574C23×C4C2418yes—
575C23×C4C2411yescharacteristic
576C4⋊Q8—44no—
577C4⋊Q8—44no—
578C4⋊Q8—48no—
579C4⋊Q8—44no—
580C4⋊Q8—44no—
581C4⋊Q8—44no—
582C4⋊Q8—44no—
583#127—44no—
584#127—44no—
585#126—416no—
586#124—44no—
587#124—44no—
588#124—48no—
589#124—44no—
590#124—44no—
591#124—44no—
592#124—44no—
593#124—44no—
594#124—44no—
595#123—48no—
596#123—48no—
597#123—44no—
598#123—44no—
599#123—48no—
600#123—48no—
601#123—48no—
602#123—48no—
603C22⋊Q8—48no—
604C22⋊Q8—48no—
605C22⋊Q8—44no—
606C22⋊Q8—44no—
607C22⋊Q8—48no—
608C22⋊Q8—44no—
609C22⋊Q8—44no—
610C22⋊Q8—48no—
611C22⋊Q8—48no—
612C22⋊Q8—44no—
613C22⋊Q8—44no—
614#121—416no—
615#121—44no—
616#121—44no—
617#121—48no—
618#121—44no—
619#121—44no—
620#121—44no—
621#121—44no—
622#121—48no—
623#120—44no—
624#120—44no—
625#120—48no—
626#120—48no—
627C4×Q8—44no—
628C4×Q8—44no—
629C4×Q8—44no—
630C4×Q8—44no—
631C4×Q8—44no—
632C4×Q8—44no—
633C4×D4—44no—
634C4×D4—44no—
635C4×D4—48no—
636C4×D4—48no—
637C4×D4—48no—
638C4×D4—48no—
639#117—24no—
640#117—24no—
641#117—24no—
642#117—24no—
643#117—24no—
644#117—24no—
645#117—44no—
646#117—44no—
647#117—48no—
648C2×C4⋊C4—24no—
649C2×C4⋊C4—44no—
650C2×C4⋊C4—48no—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2418yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2418yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C22⋊C4—48no—
687C2×C22⋊C4—44no—
688C2×C22⋊C4—44no—
689C2×C22⋊C4—48no—
690C2×C22⋊C4C2418yes—
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⋊C4C2418yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2412yes—
704C2×C22⋊C4C2412yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2418yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2418yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2418yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2418yes—
726C2×C22⋊C4C2418yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2418yes—
732C2×C22⋊C4C2418yes—
733C2×C42—24no—
734C2×C42—24no—
735C2×C42—44no—
736C2×C42—44no—
737C2×C42C2411yescharacteristic
738C2×C42C2412yes—
739C2×C42C2412yes—
740C2×C42C2411yescharacteristic
741C2×C42C2412yes—
742C2×C42C2412yes—
743C2×C42C2412yes—
744C2×C42C2412yes—
745C2×C42C2412yes—
746C2×C42C2412yes—
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2414yes—
750C2×C42C2414yes—
751C2×C42C2414yes—
752C2×C42C2414yes—
753C2×C42C2418yes—
754#95C2412yes—
755#95C2412yes—
756#95C2412yes—
757#95C2412yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2418yes—
778#95C2418yes—
779#95C2418yes—
780#95C2418yes—
781#95C2418yes—
782#95C2418yes—
783#95C2418yes—
784#95C2418yes—
785C24—22no—
786C24—24no—
787C24—22no—
788C24—22no—
789C24—24no—
790C24—24no—
791C24—44no—
792C24—42no—
793C24—42no—
794C24—44no—
795C24C2512yes—
796C24C2514yes—
797C24C2512yes—
798C24C2512yes—
799C24C2511yescharacteristic
800#41—464no—
801#41—464no—
802#41—416no—
803#41—416no—
804C2×Q8—24no—
805C2×Q8—24no—
806C2×Q8—22no—
807C2×Q8—22no—
808C2×Q8—24no—
809C2×Q8—22no—
810C2×Q8—24no—
811C2×Q8—22no—
812C2×Q8—24no—
813C2×Q8—24no—
814C2×Q8—24no—
815C2×Q8—22no—
816C2×Q8—24no—
817C2×Q8—24no—
818C2×Q8—24no—
819C2×Q8—22no—
820C2×Q8—24no—
821C2×Q8—24no—
822C2×Q8—416no—
823C2×Q8—416no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—24no—
827C2×D4—24no—
828C2×D4—24no—
829C2×D4—24no—
830C2×D4—22no—
831C2×D4—22no—
832C2×D4—22no—
833C2×D4—22no—
834C2×D4—24no—
835C2×D4—24no—
836C2×D4—22no—
837C2×D4—22no—
838C2×D4—24no—
839C2×D4—24no—
840C2×D4—24no—
841C2×D4—24no—
842C2×D4—48no—
843C2×D4—48no—
844C2×D4—48no—
845C2×D4—44no—
846C2×D4—44no—
847C2×D4—44no—
848C2×D4—44no—
849C2×D4—44no—
850C2×D4—44no—
851C2×D4—44no—
852C2×D4—44no—
853C2×D4—48no—
854C2×D4—44no—
855C2×D4—48no—
856C2×D4—48no—
857C2×D4—48no—
858C2×D4—48no—
859C2×D4—48no—
860C2×D4—432no—
861C2×D4—416no—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—22no—
867C22×C4—24no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—24no—
875C22×C4—24no—
876C22×C4—24no—
877C22×C4—24no—
878C22×C4—24no—
879C22×C4—24no—
880C22×C4—24no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—24no—
886C22×C4—24no—
887C22×C4—28no—
888C22×C4—48no—
889C22×C4—48no—
890C22×C4—48no—
891C22×C4—42no—
892C22×C4—44no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—42no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—42no—
900C22×C4—432no—
901C22×C4—416no—
902C22×C4H(5,𝔽2)14yes—
903C22×C4H(5,𝔽2)14yes—
904C22×C4H(5,𝔽2)14yes—
905C22×C4C2512yes—
906C22×C4C2512yes—
907C22×C4C2514yes—
908C22×C4C2512yes—
909C22×C4C2514yes—
910C22×C4C2512yes—
911C22×C4C2514yes—
912C22×C4C2514yes—
913C22×C4C2512yes—
914C22×C4C2512yes—
915C22×C4C2512yes—
916C22×C4C2514yes—
917C22×C4C2514yes—
918C22×C4C2512yes—
919C22×C4C2514yes—
920C22×C4C2512yes—
921C22×C4C2512yes—
922C22×C4C2512yes—
923C22×C4C2511yescharacteristic
924C22×C4C2511yescharacteristic
925C4⋊C4—24no—
926C4⋊C4—24no—
927C4⋊C4—24no—
928C4⋊C4—24no—
929C4⋊C4—22no—
930C4⋊C4—22no—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—24no—
934C4⋊C4—24no—
935C4⋊C4—28no—
936C4⋊C4—28no—
937C4⋊C4—48no—
938C4⋊C4—48no—
939C4⋊C4—48no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C4⋊C4—44no—
948C4⋊C4—44no—
949C4⋊C4—44no—
950C4⋊C4—48no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—44no—
954C4⋊C4—48no—
955C4⋊C4—48no—
956C4⋊C4—48no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—48no—
960C22⋊C4—24no—
961C22⋊C4—24no—
962C22⋊C4—24no—
963C22⋊C4—24no—
964C22⋊C4—24no—
965C22⋊C4—24no—
966C22⋊C4—216no—
967C22⋊C4—24no—
968C22⋊C4—24no—
969C22⋊C4—28no—
970C22⋊C4—48no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—48no—
974C22⋊C4—48no—
975C22⋊C4—48no—
976C22⋊C4—48no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—48no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—48no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—48no—
996C22⋊C4—48no—
997C22⋊C4—48no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—48no—
1002C22⋊C4—48no—
1003C42—22no—
1004C42—22no—
1005C42—22no—
1006C42—22no—
1007C42—24no—
1008C42—24no—
1009C42—24no—
1010C42—24no—
1011C42—24no—
1012C42—24no—
1013C42—24no—
1014C42—24no—
1015C42—44no—
1016C42—44no—
1017C42—44no—
1018C42—44no—
1019C42—48no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—24no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—24no—
1033C23—24no—
1034C23—28no—
1035C23—22no—
1036C23—22no—
1037C23—24no—
1038C23—24no—
1039C23—22no—
1040C23—28no—
1041C23—24no—
1042C23—24no—
1043C23—22no—
1044C23—44no—
1045C23—44no—
1046C23—416no—
1047C23—48no—
1048C23—44no—
1049C23—84no—
1050C23—84no—
1051C23—84no—
1052C23—84no—
1053C23—88no—
1054C23C2×H(5,𝔽2)12yes—
1055C23C2×H(5,𝔽2)12yes—
1056C23C2×H(5,𝔽2)12yes—
1057C23C2611yescharacteristic
1058Q8—48no—
1059Q8—48no—
1060Q8—48no—
1061Q8—48no—
1062Q8—44no—
1063Q8—44no—
1064D4—432no—
1065D4—48no—
1066D4—48no—
1067D4—48no—
1068D4—48no—
1069D4—44no—
1070D4—44no—
1071D4—88no—
1072D4—88no—
1073D4—164no—
1074D4—164no—
1075D4—164no—
1076D4—168no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—24no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—28no—
1109C2×C4—22no—
1110C2×C4—24no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—22no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—22no—
1123C2×C4—24no—
1124C2×C4—22no—
1125C2×C4—48no—
1126C2×C4—432no—
1127C2×C4—44no—
1128C2×C4—48no—
1129C2×C4—48no—
1130C2×C4—48no—
1131C2×C4—48no—
1132C2×C4—48no—
1133C2×C4—48no—
1134C2×C4—88no—
1135C2×C4—84no—
1136C2×C4—84no—
1137C2×C4—88no—
1138C2×C4#560116yes—
1139C2×C4C2×H(5,𝔽2)12yes—
1140C2×C4C2×H(5,𝔽2)12yes—
1141C2×C4C2×H(5,𝔽2)12yes—
1142C2×C4C2×H(5,𝔽2)12yes—
1143C2×C4C2×H(5,𝔽2)12yes—
1144C2×C4C2×H(5,𝔽2)12yes—
1145C2×C4#58514yes—
1146C22—22no—
1147C22—22no—
1148C22—24no—
1149C22—24no—
1150C22—42no—
1151C22—42no—
1152C22—44no—
1153C22—42no—
1154C22—42no—
1155C22—44no—
1156C22—42no—
1157C22—42no—
1158C22—44no—
1159C22—42no—
1160C22—44no—
1161C22—48no—
1162C22—42no—
1163C22—44no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22—44no—
1168C22—42no—
1169C22—44no—
1170C22—48no—
1171C22—42no—
1172C22—816no—
1173C22—88no—
1174C22C2×#56014yes—
1175C22C22×H(5,𝔽2)11yescharacteristic
1176C22C22×H(5,𝔽2)11yescharacteristic
1177C22C22×H(5,𝔽2)11yescharacteristic
1178C22C2×#58512yes—
1179C222−1+612yes—
1180C4—24no—
1181C4—42no—
1182C4—44no—
1183C4—42no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—44no—
1188C4—42no—
1189C4—44no—
1190C4—42no—
1191C4—44no—
1192C4—42no—
1193C4—42no—
1194C4—44no—
1195C4—42no—
1196C4—44no—
1197C4—44no—
1198C4C2×#56014yes—
1199C4C2×#56014yes—
1200C2—24no—
1201C2—82no—
1202C2—82no—
1203C2—84no—
1204C2—82no—
1205C2C22×#56011yescharacteristic
1206C2#6283611yescharacteristic
1207C2#6288711yescharacteristic
1208C2#6292512yes—
1209C2#6295412yes—
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. #53073C2semidirect
2. #53066C2semidirect
3. #53047C2semidirect
4. #53047C2semidirect
5. #52340C2semidirect
6. #45708C2semidirect
7. #45628C2semidirect
8. #45628C2semidirect
9. #45538C2semidirect
10. #45522C2semidirect
11. #35677C2semidirect
12. #35672C2semidirect
13. #35667C2semidirect
14. #35634C2semidirect
15. #35630C2semidirect
16. #35558C2semidirect
17. #35327C2semidirect
18. #35316C2semidirect
19. #35308C2semidirect
20. #35256C2semidirect
21. #35149C2semidirect
22. #35149C2semidirect
23. #34742C2semidirect
24. #34742C2semidirect
25. C2×#2432C2semidirect
42. #2857C22semidirect
43. #2857C22semidirect
44. #2856C22semidirect
45. #2850C22semidirect
46. #2850C22semidirect
47. #2850C22semidirect
50. #2837C22semidirect
51. #2837C22semidirect
52. #2837C22semidirect
53. #2829C22semidirect
54. #2829C22semidirect
55. #2828C22semidirect
56. #2827C22semidirect
57. #2827C22semidirect
58. #2825C22semidirect
59. #2813C22semidirect
60. #2803C22semidirect
61. #2803C22semidirect
62. #2801C22semidirect
63. #2797C22semidirect
64. #2796C22semidirect
65. #2796C22semidirect
66. #2790C22semidirect
67. #2790C22semidirect
68. #2790C22semidirect
69. #2780C22semidirect
70. #2780C22semidirect
71. #2756C22semidirect
72. #2756C22semidirect
73. #2749C22semidirect
74. #2746C22semidirect
75. #2746C22semidirect
76. #2705C22semidirect
77. #2705C22semidirect
78. #2703C22semidirect
79. #2691C22semidirect
80. #2621C22semidirect
81. #2621C22semidirect
82. #2620C22semidirect
83. #2620C22semidirect
84. #2620C22semidirect
85. #2619C22semidirect
88. #2548C22semidirect
89. #2548C22semidirect
90. #2547C22semidirect
91. #2546C22semidirect
92. #2546C22semidirect
93. #2546C22semidirect
94. #2545C22semidirect
95. #2545C22semidirect
96. #2545C22semidirect
97. #2545C22semidirect
98. #2545C22semidirect
99. #2544C22semidirect
100. #2542C22semidirect
101. #2542C22semidirect
102. #2540C22semidirect
103. #2540C22semidirect
106. #2514C22semidirect
107. #2514C22semidirect
108. #2513C22semidirect
109. #2513C22semidirect
110. #2512C22semidirect
111. #2512C22semidirect
112. #2511C22semidirect
113. #2511C22semidirect
128. #2429C22semidirect
129. #2429C22semidirect
130. #2429C22semidirect
131. #2428C22semidirect
132. #2427C22semidirect
133. #2426C22semidirect
134. #2426C22semidirect
135. #2426C22semidirect
138. #2423C22semidirect
139. #2423C22semidirect
140. #2423C22semidirect
141. #2423C22semidirect
142. #2422C22semidirect
143. #2422C22semidirect
144. #2421C22semidirect
145. #2421C22semidirect
146. #2421C22semidirect
147. #2421C22semidirect
148. #2420C22semidirect
149. #2420C22semidirect
160. #2395C22semidirect
161. #2395C22semidirect
163. #2383C22semidirect
164. #2377C22semidirect
172. C4×#123C22semidirect
173. C4×#123C22semidirect

Maximal subgroups

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

subgroupindex
#530732
#530662
#530472
#523402
#457082
#456282
#455382
#455222
#356772
#356722
#356672
#356342
#356302
#355582
#353272
#353162
#353082
#352562
#351492
#347422
C2×#24322