Finite Group Databasebeta

← #8095614

Subgroups — #8095614

Order 512.

5902 conjugacy classes of subgroups.

The subgroup lattice has 1257 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53073C214yesmaximal, complemented
2#53066C214yesmaximal, complemented
3#53059C214yesmaximal, complemented
4#53059C214yesmaximal, complemented
5#52308C218yesmaximal, complemented
6#45708C214yesmaximal, complemented
7#45604C214yesmaximal, complemented
8#45604C214yesmaximal, complemented
9#45536C218yesmaximal, complemented
10#45522C214yesmaximal, complemented
11#35630C211yesmaximal, characteristic, complemented
12#35617C211yesmaximal, characteristic, complemented
13#35565C211yesmaximal, characteristic, complemented
14#35558C211yesmaximal, characteristic, complemented
15#35540C211yesmaximal, characteristic, complemented
16#35528C211yesmaximal, characteristic, complemented
17#35327C211yesmaximal, characteristic, complemented
18#35308C211yesmaximal, characteristic, complemented
19#35272C211yesmaximal, characteristic, complemented
20#35256C211yesmaximal, characteristic, complemented
21#35149C211yesmaximal, characteristic, complemented
22#35149C211yesmaximal, characteristic, complemented
23#34742C211yesmaximal, characteristic, complemented
24#34742C211yesmaximal, characteristic, complemented
25C2×#2431C211yesmaximal, characteristic, complemented
26C23×#41C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#535C2211yescharacteristic
31C2×#535C2211yescharacteristic
32C2×#535C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C22×#127C2211yescharacteristic
35C22×#124C2211yescharacteristic
36C2×#525C2211yescharacteristic
37C2×#525C2211yescharacteristic
38C22×#121C2211yescharacteristic
39C2×#518C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C2×C4×#41C2211yescharacteristic
42#2857C2212yescomplemented
43#2856C2212yescomplemented
44#2856C2214yescomplemented
45#2850C2212yescomplemented
46#2850C2214yescomplemented
47#2850C2212yescomplemented
48#2849C2214yes—
49#2849C2214yes—
50#2829C2218yescomplemented
51#2828C2218yescomplemented
52#2828C2218yescomplemented
53#2827C2218yescomplemented
54#2825C2218yescomplemented
55#2825C2218yescomplemented
56#2825C2218yescomplemented
57#2818C2218yescomplemented
58#2813C2218yescomplemented
59#2813C2218yescomplemented
60#2803C2218yescomplemented
61#2797C2218yescomplemented
62#2797C2218yescomplemented
63#2796C2218yescomplemented
64#2780C2218yescomplemented
65#2756C2218yescomplemented
66#2749C2218yescomplemented
67#2749C2218yescomplemented
68#2746C2218yescomplemented
69#2705C2218yescomplemented
70#2703C2218yescomplemented
71#2703C2218yescomplemented
72#2691C2218yescomplemented
73#2691C2218yescomplemented
74#2688C2218yescomplemented
75#2688C2218yescomplemented
76#2688C2218yescomplemented
77#2673C2218yescomplemented
78#2673C2218yescomplemented
79#2673C2218yescomplemented
80#2621C2212yescomplemented
81#2620C2212yescomplemented
82#2620C2214yescomplemented
83#2620C2212yescomplemented
84#2619C2212yescomplemented
85#2619C2214yescomplemented
86#2613C2214yes—
87#2613C2214yes—
88#2548C2214yescomplemented
89#2547C2212yescomplemented
90#2547C2212yescomplemented
91#2545C2214yescomplemented
92#2544C2212yescomplemented
93#2544C2212yescomplemented
94#2544C2214yescomplemented
95#2544C2212yescomplemented
96#2544C2212yescomplemented
97#2541C2212yescomplemented
98#2541C2214yescomplemented
99#2541C2214yescomplemented
100#2541C2214yescomplemented
101#2541C2212yescomplemented
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#2493C2218yes—
115#2483C2214yes—
116#2480C2218yes—
117#2433C2214yes—
118#2432C2214yescomplemented
119#2432C2214yescomplemented
120#2431C2214yes—
121#2431C2214yes—
122#2431C2214yes—
123#2431C2214yes—
124#2431C2214yescomplemented
125#2431C2214yescomplemented
126#2429C2214yescomplemented
127#2428C2214yescomplemented
128#2428C2214yescomplemented
129#2428C2214yescomplemented
130#2427C2214yescomplemented
131#2427C2214yescomplemented
132#2427C2214yescomplemented
133#2426C2214yescomplemented
134#2425C2218yes—
135#2424C2218yes—
136#2423C2212yescomplemented
137#2423C2212yescomplemented
138#2422C2212yescomplemented
139#2422C2214yescomplemented
140#2422C2212yescomplemented
141#2422C2214yescomplemented
142#2421C2212yescomplemented
143#2421C2212yescomplemented
144#2420C2212yescomplemented
145#2420C2214yescomplemented
146#2420C2212yescomplemented
147#2420C2214yescomplemented
148#2419C2214yes—
149#2419C2214yes—
150#2418C2214yes—
151#2418C2214yes—
152#2412C2218yes—
153#2410C2218yes—
154#2408C2218yes—
155#2407C2214yescomplemented
156#2407C2214yescomplemented
157#2407C2214yescomplemented
158#2407C2214yescomplemented
159#2405C2214yes—
160#2395C2214yescomplemented
161#2395C2214yescomplemented
162C2×#392C2214yes—
163#2377C2218yescomplemented
164#2377C2218yescomplemented
165#2317C2211yescharacteristic
166#2317C2211yescharacteristic
167#2310C2211yescharacteristic
168#2310C2211yescharacteristic
169#2309C2211yescharacteristic
170#2309C2211yescharacteristic
171#2309C2211yescharacteristic
172C4×#123C2214yescomplemented
173C4×#123C2214yescomplemented
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2296C2211yescharacteristic
177#2296C2211yescharacteristic
178C2×#391C2211yescharacteristic
179C2×#390C2211yescharacteristic
180C2×#386C2214yes—
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×D4C2311yescharacteristic
196C23×D4C2311yescharacteristic
197C23×D4C2312yes—
198C23×D4C2314yes—
199C23×D4C2312yes—
200C24×C4C2311yescharacteristic
201C24×C4C2312yes—
202#537—44no—
203#536—44no—
204#536—44no—
205#535—44no—
206#535—44no—
207#535—44no—
208#535—44no—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×#127—44no—
212C2×#127C2312yes—
213C2×#127C2312yes—
214C2×#127C2312yes—
215C2×#127C2314yes—
216C2×#127C2312yes—
217C2×#127C2312yes—
218C2×#127C2312yes—
219C2×#127C2318yes—
220C2×#126C2318yes—
221C2×#124—44no—
222C2×#124C2312yes—
223C2×#124C2312yes—
224C2×#124C2312yes—
225C2×#124C2312yes—
226C2×#124C2314yes—
227C2×#124C2312yes—
228C2×#124C2312yes—
229C2×#124C2312yes—
230C2×#124C2312yes—
231#525—44no—
232#525—44no—
233C2×#123C2312yes—
234C2×#123C2312yes—
235C2×#123C2314yes—
236C2×#123C2314yes—
237C2×#123C2314yes—
238C2×#123C2314yes—
239C2×#123C2318yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2312yes—
247C2×#121—44no—
248C2×#121C2312yes—
249C2×#121C2314yes—
250C2×#121C2312yes—
251C2×#121C2314yes—
252C2×#121C2314yes—
253C2×#121C2312yes—
254C2×#121C2312yes—
255C2×#121C2318yes—
256C2×#121C2318yes—
257C2×#121C2314yes—
258C2×#121C2314yes—
259C2×#121C2312yes—
260C2×#121C2312yes—
261C2×#121C2314yes—
262C2×#121C2318yes—
263C2×#121C2318yes—
264C2×#121C2318yes—
265C2×#120C2314yes—
266C2×#120C2314yes—
267C2×#120C2312yes—
268C2×#120C2312yes—
269C2×#120C2314yes—
270C2×#120C2314yes—
271#518—44no—
272C4×#41—44no—
273C4×#41—44no—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2312yes—
286C2×#117C2311yescharacteristic
287C2×#117C2311yescharacteristic
288C2×#117C2311yescharacteristic
289C2×#117C2311yescharacteristic
290C2×#117C2311yescharacteristic
291C2×#117C2311yescharacteristic
292C2×#117C2312yes—
293C2×#117C2312yes—
294C22×C4⋊C4C2311yescharacteristic
295C22×C22⋊C4C2312yes—
296C22×C22⋊C4C2314yes—
297C22×C22⋊C4C2314yes—
298C22×C22⋊C4C2312yes—
299C22×C22⋊C4C2314yes—
300C22×C42C2311yescharacteristic
301C22×C42C2311yescharacteristic
302C22×C42C2312yes—
303C22×C42C2312yes—
304#401C2318yes—
305#400C2314yes—
306#400C2318yes—
307#400C2318yes—
308#400C2314yes—
309#400C2318yes—
310#399C2318yes—
311#399C2314yes—
312#399C2314yes—
313#398C2314yes—
314#398C2318yes—
315#398C2314yes—
316#397C2314yes—
317#397C2314yes—
318#397C2314yes—
319#397C2314yes—
320#397C2318yes—
321#397C2318yes—
322#397C2318yes—
323#397C2318yes—
324#397C2318yes—
325#397C2318yes—
326#397C2318yes—
327#397C2318yes—
328#397C2314yes—
329#397C2314yes—
330#396C2318yes—
331#396C2318yes—
332#396C2318yes—
333#396C2318yes—
334#396C2318yes—
335#394C2314yes—
336#394C2314yes—
337#394C2318yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2318yes—
345#394C2318yes—
346#394C2318yes—
347#394C2318yes—
348#394C2318yes—
349#394C2314yes—
350#394C2314yes—
351#394C2318yes—
352#394C2318yes—
353#394C2318yes—
354#394C2318yes—
355#394C2318yes—
356#392C2318yes—
357#392C2318yes—
358#392C2318yes—
359#392C2318yes—
360#392C2318yes—
361#392C2318yes—
362#392C2318yes—
363#392C2318yes—
364#392C2318yes—
365#392C2318yes—
366#392C2318yes—
367#392C2318yes—
368#392C2318yes—
369#392C2318yes—
370#392C2318yes—
371#392C2318yes—
372#391C2314yes—
373#391C2312yes—
374#391C2314yes—
375#391C2312yes—
376#391C2314yes—
377#391C2311yescharacteristic
378#391C2312yes—
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2312yes—
382#391C2311yescharacteristic
383#391C2314yes—
384#390C2314yes—
385#390C2314yes—
386#390C2314yes—
387#390C2312yes—
388#390C2314yes—
389#390C2312yes—
390#390C2314yes—
391#390C2318yes—
392#390C2318yes—
393#390C2318yes—
394#390C2311yescharacteristic
395#390C2312yes—
396#390C2311yescharacteristic
397#390C2318yes—
398#390C2311yescharacteristic
399#390C2312yes—
400#390C2311yescharacteristic
401#390C2318yes—
402#390C2318yes—
403#390C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2318yes—
407#389C2312yes—
408#389C2312yes—
409#389C2312yes—
410#389C2312yes—
411#388C2314yes—
412#388C2314yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2314yes—
421#388C2314yes—
422#387C2318yes—
423#387C2314yes—
424#387C2314yes—
425#387C2318yes—
426#387C2318yes—
427#387C2314yes—
428#387C2314yes—
429#386C2314yes—
430#386C2318yes—
431#386C2318yes—
432#386C2318yes—
433#386C2318yes—
434#386C2318yes—
435#386C2318yes—
436#386C2318yes—
437#386C2318yes—
438#386C2318yes—
439#386C2318yes—
440#386C2318yes—
441#386C2318yes—
442#386C2318yes—
443#386C2318yes—
444#386C2318yes—
445#386C2314yes—
446#386C2314yes—
447#386C2314yes—
448#386C2318yes—
449#386C2318yes—
450#385C2318yes—
451#385C2318yes—
452#385C2314yes—
453#385C2314yes—
454#385C2318yes—
455#385C2318yes—
456#385C2314yes—
457#385C2318yes—
458#385C2314yes—
459#385C2314yes—
460#385C2314yes—
461#384C2312yes—
462#384C2312yes—
463#384C2312yes—
464#384C2312yes—
465#383C2318yes—
466#382C2312yes—
467#382C2312yes—
468#382C2312yes—
469#382C2312yes—
470#381C2314yes—
471#381C2314yes—
472#381C2312yes—
473#381C2312yes—
474#381C2314yes—
475#381C2318yes—
476#381C2314yes—
477#380C2318yes—
478#380C2318yes—
479#380C2312yes—
480#380C2312yes—
481#380C2312yes—
482#380C2312yes—
483#380C2314yes—
484#380C2318yes—
485#380C2314yes—
486#379C2314yes—
487#379C2314yes—
488#379C2314yes—
489#379C2312yes—
490#379C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
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—
510C25C2412yes—
511C25C2411yescharacteristic
512C25C2412yes—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C2×#41—24no—
518C2×#41—24no—
519C2×#41—48no—
520C2×#41—48no—
521C2×#41—48no—
522C2×#41—48no—
523C2×#41—48no—
524C2×#41—48no—
525C2×#41—464no—
526C22×Q8—24no—
527C22×Q8—24no—
528C22×Q8—24no—
529C22×Q8C2411yescharacteristic
530C22×Q8C2411yescharacteristic
531C22×Q8C2412yes—
532C22×Q8C2412yes—
533C22×D4—24no—
534C22×D4—24no—
535C22×D4—24no—
536C22×D4—24no—
537C22×D4—24no—
538C22×D4—24no—
539C22×D4—48no—
540C22×D4—44no—
541C22×D4—44no—
542C22×D4—44no—
543C22×D4—44no—
544C22×D4—48no—
545C22×D4—84no—
546C22×D4—84no—
547C22×D4C2412yes—
548C22×D4C2412yes—
549C22×D4C2412yes—
550C22×D4C2412yes—
551C22×D4C2411yescharacteristic
552C22×D4C2411yescharacteristic
553C22×D4C2412yes—
554C22×D4C2412yes—
555C22×D4C2418yes—
556C22×D4C2414yes—
557C22×D4C2414yes—
558C22×D4C2414yes—
559C22×D4C2418yes—
560C22×D4C2418yes—
561C22×D4C2418yes—
562C22×D4C2414yes—
563C22×D4C2414yes—
564C22×D4C2418yes—
565C22×D4C2418yes—
566C22×D4C2418yes—
567C23×C4—24no—
568C23×C4—24no—
569C23×C4—24no—
570C23×C4—44no—
571C23×C4—44no—
572C23×C4—44no—
573C23×C4C2411yescharacteristic
574C23×C4C2412yes—
575C23×C4C2412yes—
576C23×C4C2412yes—
577C23×C4C2412yes—
578C23×C4C2412yes—
579C23×C4C2412yes—
580C23×C4C2412yes—
581C23×C4C2412yes—
582C23×C4C2414yes—
583C23×C4C2414yes—
584C23×C4C2414yes—
585C23×C4C2414yes—
586C23×C4C2418yes—
587C23×C4C2411yescharacteristic
588C4⋊Q8—44no—
589C4⋊Q8—44no—
590#127—44no—
591#127—44no—
592#127—48no—
593#127—44no—
594#127—44no—
595#127—44no—
596#127—44no—
597#127—88no—
598#126—88no—
599#124—44no—
600#124—44no—
601#124—48no—
602#124—44no—
603#124—44no—
604#124—44no—
605#124—44no—
606#124—44no—
607#124—44no—
608#123—48no—
609#123—48no—
610#123—44no—
611#123—44no—
612#123—48no—
613#123—48no—
614#123—88no—
615C22⋊Q8—44no—
616C22⋊Q8—44no—
617C22⋊Q8—44no—
618C22⋊Q8—44no—
619C22⋊Q8—48no—
620C22⋊Q8—44no—
621C22⋊Q8—44no—
622#121—416no—
623#121—48no—
624#121—48no—
625#121—416no—
626#121—44no—
627#121—44no—
628#121—44no—
629#121—44no—
630#121—48no—
631#121—48no—
632#121—48no—
633#121—44no—
634#121—44no—
635#121—48no—
636#121—88no—
637#121—88no—
638#121—88no—
639#120—44no—
640#120—44no—
641#120—48no—
642#120—48no—
643#120—48no—
644#120—48no—
645C4×Q8—44no—
646C4×Q8—44no—
647C4×D4—44no—
648C4×D4—44no—
649C4×D4—44no—
650C4×D4—44no—
651C4×D4—44no—
652C4×D4—44no—
653C4×D4—48no—
654C4×D4—48no—
655C4×D4—48no—
656C4×D4—48no—
657#117—24no—
658#117—24no—
659#117—24no—
660#117—24no—
661#117—24no—
662#117—24no—
663#117—44no—
664#117—44no—
665C2×C4⋊C4—24no—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2418yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2418yes—
689C2×C4⋊C4C2418yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C22⋊C4—44no—
695C2×C22⋊C4—48no—
696C2×C22⋊C4—44no—
697C2×C22⋊C4—48no—
698C2×C22⋊C4—84no—
699C2×C22⋊C4C2412yes—
700C2×C22⋊C4C2412yes—
701C2×C22⋊C4C2412yes—
702C2×C22⋊C4C2412yes—
703C2×C22⋊C4C2412yes—
704C2×C22⋊C4C2412yes—
705C2×C22⋊C4C2412yes—
706C2×C22⋊C4C2412yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2418yes—
715C2×C22⋊C4C2412yes—
716C2×C22⋊C4C2412yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2418yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2418yes—
727C2×C22⋊C4C2418yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2418yes—
733C2×C22⋊C4C2418yes—
734C2×C22⋊C4C2418yes—
735C2×C22⋊C4C2418yes—
736C2×C22⋊C4C2418yes—
737C2×C22⋊C4C2418yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2418yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C42—24no—
747C2×C42—24no—
748C2×C42—44no—
749C2×C42—44no—
750C2×C42C2411yescharacteristic
751C2×C42C2412yes—
752C2×C42C2412yes—
753C2×C42C2411yescharacteristic
754C2×C42C2412yes—
755C2×C42C2412yes—
756C2×C42C2412yes—
757C2×C42C2412yes—
758C2×C42C2412yes—
759C2×C42C2412yes—
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762C2×C42C2414yes—
763C2×C42C2414yes—
764C2×C42C2418yes—
765#95C2412yes—
766#95C2412yes—
767#95C2412yes—
768#95C2412yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2418yes—
789#95C2418yes—
790#95C2418yes—
791#95C2418yes—
792#95C2418yes—
793#95C2418yes—
794C24—22no—
795C24—24no—
796C24—24no—
797C24—24no—
798C24—22no—
799C24—22no—
800C24—24no—
801C24—24no—
802C24—24no—
803C24—42no—
804C24—44no—
805C24—44no—
806C24—42no—
807C24—44no—
808C24—44no—
809C24C2514yes—
810C24C2512yes—
811C24C2514yes—
812C24C2512yes—
813C24C2512yes—
814C24C2511yescharacteristic
815#41—464no—
816#41—464no—
817#41—416no—
818#41—416no—
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—24no—
829C2×Q8—24no—
830C2×Q8—24no—
831C2×Q8—416no—
832C2×D4—24no—
833C2×D4—24no—
834C2×D4—24no—
835C2×D4—24no—
836C2×D4—24no—
837C2×D4—24no—
838C2×D4—24no—
839C2×D4—24no—
840C2×D4—22no—
841C2×D4—22no—
842C2×D4—24no—
843C2×D4—22no—
844C2×D4—24no—
845C2×D4—22no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—22no—
850C2×D4—24no—
851C2×D4—24no—
852C2×D4—24no—
853C2×D4—22no—
854C2×D4—24no—
855C2×D4—24no—
856C2×D4—216no—
857C2×D4—48no—
858C2×D4—48no—
859C2×D4—48no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—48no—
863C2×D4—48no—
864C2×D4—48no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—48no—
868C2×D4—48no—
869C2×D4—48no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—48no—
873C2×D4—48no—
874C2×D4—48no—
875C2×D4—48no—
876C2×D4—48no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—48no—
881C2×D4—48no—
882C2×D4—48no—
883C2×D4—48no—
884C2×D4—48no—
885C2×D4—48no—
886C2×D4—48no—
887C2×D4—48no—
888C2×D4—48no—
889C2×D4—432no—
890C2×D4—416no—
891C2×D4—416no—
892C2×D4—832no—
893C2×D4—816no—
894C22×C4—24no—
895C22×C4—22no—
896C22×C4—24no—
897C22×C4—22no—
898C22×C4—22no—
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—48no—
918C22×C4—48no—
919C22×C4—48no—
920C22×C4—42no—
921C22×C4—44no—
922C22×C4—44no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—44no—
926C22×C4—44no—
927C22×C4—44no—
928C22×C4—44no—
929C22×C4—44no—
930C22×C4—44no—
931C22×C4—48no—
932C22×C4—48no—
933C22×C4—432no—
934C22×C4—416no—
935C22×C4H(5,𝔽2)14yes—
936C22×C4H(5,𝔽2)14yes—
937C22×C4H(5,𝔽2)14yes—
938C22×C4C2512yes—
939C22×C4C2512yes—
940C22×C4C2512yes—
941C22×C4C2514yes—
942C22×C4C2512yes—
943C22×C4C2514yes—
944C22×C4C2514yes—
945C22×C4C2514yes—
946C22×C4C2514yes—
947C22×C4C2512yes—
948C22×C4C2512yes—
949C22×C4C2512yes—
950C22×C4C2514yes—
951C22×C4C2512yes—
952C22×C4C2512yes—
953C22×C4C2512yes—
954C22×C4C2512yes—
955C22×C4C2511yescharacteristic
956C22×C4C2511yescharacteristic
957C4⋊C4—24no—
958C4⋊C4—24no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—24no—
964C4⋊C4—24no—
965C4⋊C4—24no—
966C4⋊C4—24no—
967C4⋊C4—28no—
968C4⋊C4—28no—
969C4⋊C4—44no—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4—44no—
976C4⋊C4—48no—
977C4⋊C4—48no—
978C4⋊C4—44no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—48no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C22⋊C4—24no—
986C22⋊C4—24no—
987C22⋊C4—24no—
988C22⋊C4—24no—
989C22⋊C4—24no—
990C22⋊C4—24no—
991C22⋊C4—24no—
992C22⋊C4—24no—
993C22⋊C4—28no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—48no—
999C22⋊C4—48no—
1000C22⋊C4—48no—
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—48no—
1010C22⋊C4—48no—
1011C22⋊C4—48no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—48no—
1015C22⋊C4—48no—
1016C22⋊C4—48no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—48no—
1022C22⋊C4—48no—
1023C22⋊C4—48no—
1024C22⋊C4—48no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C42—22no—
1033C42—22no—
1034C42—22no—
1035C42—22no—
1036C42—24no—
1037C42—24no—
1038C42—24no—
1039C42—24no—
1040C42—24no—
1041C42—24no—
1042C42—24no—
1043C42—24no—
1044C42—44no—
1045C42—44no—
1046C42—48no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—24no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—24no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—24no—
1059C23—24no—
1060C23—24no—
1061C23—22no—
1062C23—22no—
1063C23—24no—
1064C23—22no—
1065C23—22no—
1066C23—24no—
1067C23—28no—
1068C23—24no—
1069C23—28no—
1070C23—22no—
1071C23—28no—
1072C23—24no—
1073C23—24no—
1074C23—28no—
1075C23—22no—
1076C23—44no—
1077C23—416no—
1078C23—44no—
1079C23—48no—
1080C23—44no—
1081C23—48no—
1082C23—84no—
1083C23—84no—
1084C23—84no—
1085C23—84no—
1086C23—88no—
1087C23—84no—
1088C23—88no—
1089C23—84no—
1090C23—88no—
1091C23C2×H(5,𝔽2)12yes—
1092C23C2×H(5,𝔽2)12yes—
1093C23C2×H(5,𝔽2)12yes—
1094C23C2611yescharacteristic
1095Q8—48no—
1096Q8—48no—
1097Q8—44no—
1098Q8—44no—
1099D4—432no—
1100D4—48no—
1101D4—48no—
1102D4—48no—
1103D4—48no—
1104D4—48no—
1105D4—48no—
1106D4—44no—
1107D4—44no—
1108D4—816no—
1109D4—88no—
1110D4—88no—
1111D4—816no—
1112D4—816no—
1113D4—164no—
1114D4—164no—
1115D4—164no—
1116D4—168no—
1117D4—168no—
1118D4—168no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—24no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—24no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—28no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—48no—
1165C2×C4—432no—
1166C2×C4—44no—
1167C2×C4—48no—
1168C2×C4—48no—
1169C2×C4—48no—
1170C2×C4—48no—
1171C2×C4—48no—
1172C2×C4—88no—
1173C2×C4—84no—
1174C2×C4—84no—
1175C2×C4—88no—
1176C2×C4—164no—
1177C2×C4—164no—
1178C2×C4#560116yes—
1179C2×C4C2×H(5,𝔽2)12yes—
1180C2×C4C2×H(5,𝔽2)12yes—
1181C2×C4C2×H(5,𝔽2)12yes—
1182C2×C4C2×H(5,𝔽2)12yes—
1183C2×C4C2×H(5,𝔽2)12yes—
1184C2×C4C2×H(5,𝔽2)12yes—
1185C2×C4#58514yes—
1186C22—22no—
1187C22—22no—
1188C22—24no—
1189C22—24no—
1190C22—44no—
1191C22—42no—
1192C22—44no—
1193C22—42no—
1194C22—42no—
1195C22—44no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—44no—
1200C22—44no—
1201C22—48no—
1202C22—48no—
1203C22—42no—
1204C22—44no—
1205C22—42no—
1206C22—44no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—44no—
1211C22—44no—
1212C22—42no—
1213C22—44no—
1214C22—48no—
1215C22—48no—
1216C22—42no—
1217C22—88no—
1218C22—816no—
1219C22—168no—
1220C22C2×#56014yes—
1221C22C22×H(5,𝔽2)11yescharacteristic
1222C22C22×H(5,𝔽2)11yescharacteristic
1223C22C22×H(5,𝔽2)11yescharacteristic
1224C22C2×#58512yes—
1225C22H(7,𝔽2)12yes—
1226C4—24no—
1227C4—42no—
1228C4—42no—
1229C4—44no—
1230C4—42no—
1231C4—42no—
1232C4—42no—
1233C4—44no—
1234C4—44no—
1235C4—42no—
1236C4—44no—
1237C4—42no—
1238C4—42no—
1239C4—42no—
1240C4—42no—
1241C4—44no—
1242C4—44no—
1243C4C2×#56014yes—
1244C4C2×#56014yes—
1245C2—24no—
1246C2—82no—
1247C2—82no—
1248C2—84no—
1249C2—82no—
1250C2—84no—
1251C2C22×#56011yescharacteristic
1252C2#6283611yescharacteristic
1253C2#6287611yescharacteristic
1254C2#6292412yes—
1255C2#6295512yes—
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. #53059C2semidirect
4. #53059C2semidirect
5. #52308C2semidirect
6. #45708C2semidirect
7. #45604C2semidirect
8. #45604C2semidirect
9. #45536C2semidirect
10. #45522C2semidirect
11. #35630C2semidirect
12. #35617C2semidirect
13. #35565C2semidirect
14. #35558C2semidirect
15. #35540C2semidirect
16. #35528C2semidirect
17. #35327C2semidirect
18. #35308C2semidirect
19. #35272C2semidirect
20. #35256C2semidirect
21. #35149C2semidirect
22. #35149C2semidirect
23. #34742C2semidirect
24. #34742C2semidirect
25. C2×#2431C2semidirect
42. #2857C22semidirect
43. #2856C22semidirect
44. #2856C22semidirect
45. #2850C22semidirect
46. #2850C22semidirect
47. #2850C22semidirect
50. #2829C22semidirect
51. #2828C22semidirect
52. #2828C22semidirect
53. #2827C22semidirect
54. #2825C22semidirect
55. #2825C22semidirect
56. #2825C22semidirect
57. #2818C22semidirect
58. #2813C22semidirect
59. #2813C22semidirect
60. #2803C22semidirect
61. #2797C22semidirect
62. #2797C22semidirect
63. #2796C22semidirect
64. #2780C22semidirect
65. #2756C22semidirect
66. #2749C22semidirect
67. #2749C22semidirect
68. #2746C22semidirect
69. #2705C22semidirect
70. #2703C22semidirect
71. #2703C22semidirect
72. #2691C22semidirect
73. #2691C22semidirect
74. #2688C22semidirect
75. #2688C22semidirect
76. #2688C22semidirect
77. #2673C22semidirect
78. #2673C22semidirect
79. #2673C22semidirect
80. #2621C22semidirect
81. #2620C22semidirect
82. #2620C22semidirect
83. #2620C22semidirect
84. #2619C22semidirect
85. #2619C22semidirect
88. #2548C22semidirect
89. #2547C22semidirect
90. #2547C22semidirect
91. #2545C22semidirect
92. #2544C22semidirect
93. #2544C22semidirect
94. #2544C22semidirect
95. #2544C22semidirect
96. #2544C22semidirect
97. #2541C22semidirect
98. #2541C22semidirect
99. #2541C22semidirect
100. #2541C22semidirect
101. #2541C22semidirect
102. #2540C22semidirect
103. #2540C22semidirect
106. #2514C22semidirect
107. #2514C22semidirect
108. #2513C22semidirect
109. #2513C22semidirect
110. #2512C22semidirect
111. #2512C22semidirect
112. #2511C22semidirect
113. #2511C22semidirect
118. #2432C22semidirect
119. #2432C22semidirect
124. #2431C22semidirect
125. #2431C22semidirect
126. #2429C22semidirect
127. #2428C22semidirect
128. #2428C22semidirect
129. #2428C22semidirect
130. #2427C22semidirect
131. #2427C22semidirect
132. #2427C22semidirect
133. #2426C22semidirect
136. #2423C22semidirect
137. #2423C22semidirect
138. #2422C22semidirect
139. #2422C22semidirect
140. #2422C22semidirect
141. #2422C22semidirect
142. #2421C22semidirect
143. #2421C22semidirect
144. #2420C22semidirect
145. #2420C22semidirect
146. #2420C22semidirect
147. #2420C22semidirect
155. #2407C22semidirect
156. #2407C22semidirect
157. #2407C22semidirect
158. #2407C22semidirect
160. #2395C22semidirect
161. #2395C22semidirect
163. #2377C22semidirect
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
#530592
#523082
#457082
#456042
#455362
#455222
#356302
#356172
#355652
#355582
#355402
#355282
#353272
#353082
#352722
#352562
#351492
#347422
C2×#24312