Finite Group Databasebeta

← #8094848

Subgroups — #8094848

Order 512.

5902 conjugacy classes of subgroups.

The subgroup lattice has 1206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53117C214yesmaximal, complemented
2#53106C214yesmaximal, complemented
3#52995C214yesmaximal, complemented
4#52973C214yesmaximal, complemented
5#52316C218yesmaximal, complemented
6#46044C214yesmaximal, complemented
7#45997C214yesmaximal, complemented
8#45610C214yesmaximal, complemented
9#45484C214yesmaximal, complemented
10#45443C218yesmaximal, complemented
11#35554C211yesmaximal, characteristic, complemented
12#35554C211yesmaximal, characteristic, complemented
13#35529C211yesmaximal, characteristic, complemented
14#35528C211yesmaximal, characteristic, complemented
15#35528C211yesmaximal, characteristic, complemented
16#35515C211yesmaximal, characteristic, complemented
17#35285C211yesmaximal, characteristic, complemented
18#35272C211yesmaximal, characteristic, complemented
19#35264C211yesmaximal, characteristic, complemented
20#35254C211yesmaximal, characteristic, complemented
21#35174C211yesmaximal, characteristic, complemented
22#35152C211yesmaximal, characteristic, complemented
23C2×#2541C211yesmaximal, characteristic, complemented
24#34815C211yesmaximal, characteristic, complemented
25#34745C211yesmaximal, characteristic, complemented
26C2×#562C2218yescomplemented
27C2×#544C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#535C2211yescharacteristic
31C2×#533C2211yescharacteristic
32C22×#127C2211yescharacteristic
33C22×#127C2211yescharacteristic
34C22×#127C2211yescharacteristic
35C22×#121C2214yes—
36C2×#518C2211yescharacteristic
37C2×#518C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic
39C22×C4×D4C2211yescharacteristic
40#2861C2212yescomplemented
41#2858C2212yescomplemented
42#2858C2214yescomplemented
43#2856C2212yescomplemented
44#2856C2212yescomplemented
45#2854C2214yescomplemented
46#2849C2214yes—
47#2848C2214yes—
48#2829C2218yescomplemented
49#2829C2218yescomplemented
50#2826C2218yescomplemented
51#2824C2218yescomplemented
52#2819C2218yescomplemented
53#2816C2218yescomplemented
54#2813C2218yescomplemented
55#2813C2218yescomplemented
56#2813C2218yescomplemented
57#2813C2218yescomplemented
58#2730C2218yescomplemented
59#2711C2218yescomplemented
60#2710C2218yescomplemented
61#2708C2218yescomplemented
62#2706C2218yescomplemented
63#2701C2218yescomplemented
64#2696C2218yescomplemented
65#2686C2218yescomplemented
66#2682C2218yescomplemented
67#2682C2218yescomplemented
68#2681C2218yescomplemented
69#2676C2218yescomplemented
70#2676C2218yescomplemented
71#2676C2218yescomplemented
72#2676C2218yescomplemented
73#2672C2218yescomplemented
74#2671C2218yescomplemented
75#2671C2218yescomplemented
76#2671C2218yescomplemented
77#2671C2218yescomplemented
78#2641C2214yescomplemented
79#2641C2212yescomplemented
80#2640C2212yescomplemented
81#2626C2214yes—
82#2624C2214yescomplemented
83#2622C2214yes—
84#2619C2212yescomplemented
85#2619C2212yescomplemented
86#2580C2214yescomplemented
87#2566C2212yescomplemented
88#2566C2212yescomplemented
89#2563C2212yescomplemented
90#2548C2214yescomplemented
91#2548C2214yescomplemented
92#2548C2214yescomplemented
93#2544C2212yescomplemented
94#2544C2214yescomplemented
95#2544C2212yescomplemented
96#2542C2212yescomplemented
97#2541C2214yes—
98#2541C2214yes—
99#2541C2214yes—
100#2541C2214yes—
101#2541C2212yescomplemented
102#2541C2214yescomplemented
103#2541C2214yescomplemented
104#2541C2212yescomplemented
105#2538C2214yescomplemented
106#2509C2212yescomplemented
107#2508C2212yescomplemented
108#2507C2212yescomplemented
109#2506C2212yescomplemented
110#2505C2214yes—
111#2491C2214yescomplemented
112#2490C2214yescomplemented
113#2473C2214yes—
114#2472C2218yes—
115#2454C2214yescomplemented
116#2454C2214yescomplemented
117#2454C2214yescomplemented
118#2454C2212yescomplemented
119#2454C2214yescomplemented
120#2453C2212yescomplemented
121#2452C2214yescomplemented
122#2452C2214yescomplemented
123#2452C2214yescomplemented
124#2452C2212yescomplemented
125#2452C2214yescomplemented
126#2451C2212yescomplemented
127#2450C2214yes—
128#2449C2214yes—
129#2448C2214yescomplemented
130#2447C2214yescomplemented
131#2445C2214yescomplemented
132#2445C2214yescomplemented
133#2445C2214yescomplemented
134#2445C2214yescomplemented
135#2445C2214yescomplemented
136#2445C2214yescomplemented
137#2445C2214yescomplemented
138#2445C2214yescomplemented
139#2445C2214yescomplemented
140#2445C2214yescomplemented
141#2437C2218yes—
142#2437C2218yes—
143#2435C2218yes—
144#2428C2214yescomplemented
145#2428C2214yescomplemented
146#2428C2214yescomplemented
147#2428C2214yescomplemented
148#2422C2214yescomplemented
149#2420C2214yescomplemented
150#2418C2218yes—
151#2410C2214yes—
152#2410C2218yes—
153#2410C2214yes—
154#2408C2218yes—
155#2405C2214yes—
156#2405C2218yes—
157#2405C2214yes—
158#2402C2214yescomplemented
159#2396C2214yescomplemented
160C2×#392C2214yes—
161#2377C2218yescomplemented
162#2317C2211yescharacteristic
163#2316C2211yescharacteristic
164#2311C2211yescharacteristic
165#2309C2211yescharacteristic
166#2309C2211yescharacteristic
167#2309C2211yescharacteristic
168#2309C2211yescharacteristic
169#2309C2211yescharacteristic
170#2309C2211yescharacteristic
171#2309C2211yescharacteristic
172C4×#125C2214yescomplemented
173C4×C22⋊Q8C2214yescomplemented
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2296C2211yescharacteristic
177#2296C2211yescharacteristic
178#2296C2211yescharacteristic
179#2296C2211yescharacteristic
180#2296C2211yescharacteristic
181#2296C2211yescharacteristic
182C2×#390C2211yescharacteristic
183C2×#390C2211yescharacteristic
184#2285C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×D4C2311yescharacteristic
189C23×D4C2311yescharacteristic
190C23×D4C2311yescharacteristic
191C23×D4C2312yes—
192C23×D4C2314yes—
193C23×D4C2314yes—
194C23×D4C2312yes—
195C24×C4C2312yes—
196#562—432no—
197#544—44no—
198#535—44no—
199#535—44no—
200#535—44no—
201#533—44no—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×#127—44no—
206C2×#127—44no—
207C2×#127—44no—
208C2×#127C2312yes—
209C2×#127C2312yes—
210C2×#127C2312yes—
211C2×#127C2312yes—
212C2×#127C2312yes—
213C2×#127C2314yes—
214C2×#127C2314yes—
215C2×#127C2314yes—
216C2×#127C2314yes—
217C2×#127C2312yes—
218C2×#127C2312yes—
219C2×#125C2314yes—
220C2×#125C2312yes—
221C2×#125C2312yes—
222C2×#125C2312yes—
223C2×#124C2318yes—
224C2×#124C2318yes—
225C2×#124C2312yes—
226C2×#124C2312yes—
227C2×#124C2312yes—
228C2×#124C2318yes—
229C2×#123C2318yes—
230C2×#123C2318yes—
231C2×#123C2318yes—
232C2×#123C2318yes—
233C2×#123C2318yes—
234C2×#123C2318yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2318yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2318yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2318yes—
241C2×#121—416no—
242C2×#121C2318yes—
243C2×#121C2318yes—
244C2×#121C2314yes—
245C2×#121C2312yes—
246C2×#121C2312yes—
247C2×#121C2312yes—
248C2×#121C2312yes—
249C2×#121C2318yes—
250C2×#121C2318yes—
251C2×#121C2318yes—
252C2×#121C2318yes—
253C2×#121C2318yes—
254C2×#121C2318yes—
255C2×#121C2318yes—
256C2×#121C2318yes—
257C2×#120C2314yes—
258C2×#120C2314yes—
259C2×#120C2314yes—
260#518—44no—
261#518—44no—
262C4×#41—44no—
263C2×C4×Q8C2314yes—
264C2×C4×Q8C2312yes—
265C2×C4×D4—44no—
266C2×C4×D4C2312yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2312yes—
276C2×#117C2311yescharacteristic
277C2×#117C2311yescharacteristic
278C2×#117C2311yescharacteristic
279C2×#117C2311yescharacteristic
280C2×#117C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C2×#117C2312yes—
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2312yes—
286C22×C22⋊C4C2312yes—
287C22×C22⋊C4C2314yes—
288C22×C22⋊C4C2314yes—
289C22×C22⋊C4C2314yes—
290C22×C22⋊C4C2314yes—
291C22×C42C2311yescharacteristic
292C22×C42C2311yescharacteristic
293C22×C42C2311yescharacteristic
294C22×C42C2312yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#399C2318yes—
301#399C2318yes—
302#399C2318yes—
303#399C2314yes—
304#399C2318yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#397C2318yes—
312#397C2318yes—
313#397C2318yes—
314#397C2318yes—
315#396C2318yes—
316#396C2318yes—
317#396C2318yes—
318#396C2318yes—
319#396C2318yes—
320#396C2318yes—
321#396C2314yes—
322#396C2314yes—
323#395C2314yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#394C2318yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#394C2318yes—
337#394C2318yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2318yes—
345#394C2318yes—
346#394C2318yes—
347#394C2318yes—
348#393C2318yes—
349#393C2318yes—
350#393C2314yes—
351#393C2318yes—
352#393C2318yes—
353#392C2318yes—
354#392C2318yes—
355#392C2318yes—
356#392C2318yes—
357#392C2318yes—
358#392C2318yes—
359#392C2318yes—
360#392C2318yes—
361#392C2318yes—
362#392C2318yes—
363#391C2312yes—
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2312yes—
367#391C2314yes—
368#390C2312yes—
369#390C2312yes—
370#390C2312yes—
371#390C2312yes—
372#390C2314yes—
373#390C2312yes—
374#390C2312yes—
375#390C2312yes—
376#390C2312yes—
377#390C2314yes—
378#390C2314yes—
379#390C2314yes—
380#390C2314yes—
381#390C2312yes—
382#390C2314yes—
383#390C2314yes—
384#390C2314yes—
385#390C2312yes—
386#390C2314yes—
387#390C2312yes—
388#390C2312yes—
389#390C2312yes—
390#390C2318yes—
391#390C2318yes—
392#390C2314yes—
393#390C2318yes—
394#390C2311yescharacteristic
395#390C2312yes—
396#390C2318yes—
397#390C2318yes—
398#390C2312yes—
399#390C2311yescharacteristic
400#390C2312yes—
401#390C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2312yes—
408#389C2312yes—
409#389C2312yes—
410#389C2312yes—
411#389C2312yes—
412#389C2314yes—
413#389C2312yes—
414#389C2312yes—
415#389C2312yes—
416#389C2312yes—
417#389C2312yes—
418#389C2312yes—
419#389C2312yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2318yes—
424#387C2314yes—
425#387C2314yes—
426#387C2314yes—
427#387C2314yes—
428#387C2314yes—
429#387C2314yes—
430#386C2314yes—
431#386C2318yes—
432#386C2318yes—
433#386C2318yes—
434#386C2318yes—
435#386C2312yes—
436#386C2318yes—
437#386C2318yes—
438#386C2312yes—
439#386C2318yes—
440#386C2318yes—
441#386C2318yes—
442#386C2318yes—
443#386C2314yes—
444#385C2318yes—
445#385C2318yes—
446#385C2318yes—
447#385C2314yes—
448#385C2318yes—
449#385C2312yes—
450#385C2312yes—
451#385C2318yes—
452#385C2318yes—
453#385C2312yes—
454#385C2318yes—
455#385C2312yes—
456#385C2312yes—
457#385C2312yes—
458#385C2314yes—
459#385C2314yes—
460#385C2314yes—
461#385C2314yes—
462#385C2314yes—
463#384C2311yescharacteristic
464#384C2312yes—
465#384C2311yescharacteristic
466#382C2314yes—
467#382C2311yescharacteristic
468#382C2312yes—
469#382C2311yescharacteristic
470#381C2318yes—
471#380C2318yes—
472#380C2314yes—
473#380C2314yes—
474#380C2318yes—
475#380C2314yes—
476#380C2314yes—
477#380C2318yes—
478#379C2314yes—
479#379C2314yes—
480#379C2314yes—
481#379C2314yes—
482#379C2314yes—
483#379C2314yes—
484#379C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C22⋊C4C2314yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2314yes—
503#376C2312yes—
504C2×#95C2312yes—
505C43C2312yes—
506C25C2412yes—
507C25C2412yes—
508C25C2412yes—
509C2×#41—24no—
510C2×#41—24no—
511C2×#41—24no—
512C22×Q8C2411yescharacteristic
513C22×Q8C2414yes—
514C22×Q8C2414yes—
515C22×D4—24no—
516C22×D4—24no—
517C22×D4—24no—
518C22×D4—24no—
519C22×D4—24no—
520C22×D4—24no—
521C22×D4—24no—
522C22×D4—24no—
523C22×D4—24no—
524C22×D4—48no—
525C22×D4—48no—
526C22×D4—48no—
527C22×D4—44no—
528C22×D4—44no—
529C22×D4—48no—
530C22×D4—48no—
531C22×D4—84no—
532C22×D4—84no—
533C22×D4—84no—
534C22×D4C2412yes—
535C22×D4C2412yes—
536C22×D4C2412yes—
537C22×D4C2412yes—
538C22×D4C2412yes—
539C22×D4C2412yes—
540C22×D4C2412yes—
541C22×D4C2411yescharacteristic
542C22×D4C2418yes—
543C22×D4C2418yes—
544C22×D4C2418yes—
545C22×D4C2414yes—
546C22×D4C2418yes—
547C22×D4C2414yes—
548C22×D4C2414yes—
549C22×D4C2414yes—
550C22×D4C2418yes—
551C22×D4C2418yes—
552C22×D4C2418yes—
553C23×C4—48no—
554C23×C4—44no—
555C23×C4C2411yescharacteristic
556C23×C4C2412yes—
557C23×C4C2412yes—
558C23×C4C2412yes—
559C23×C4C2412yes—
560C23×C4C2411yescharacteristic
561C23×C4C2414yes—
562C23×C4C2418yes—
563C23×C4C2414yes—
564C23×C4C2418yes—
565C23×C4C2414yes—
566C23×C4C2411yescharacteristic
567C4⋊Q8—44no—
568C4⋊Q8—44no—
569C4⋊Q8—44no—
570#127—44no—
571#127—44no—
572#127—48no—
573#127—48no—
574#127—48no—
575#127—48no—
576#127—44no—
577#127—44no—
578#127—44no—
579#127—44no—
580#127—44no—
581#125—216no—
582#125—44no—
583#125—44no—
584#125—44no—
585#124—416no—
586#124—44no—
587#124—44no—
588#124—44no—
589#124—416no—
590#124—88no—
591#123—416no—
592#123—416no—
593#123—416no—
594#123—416no—
595#123—88no—
596#123—88no—
597C22⋊Q8—216no—
598C22⋊Q8—48no—
599C22⋊Q8—48no—
600C22⋊Q8—416no—
601C22⋊Q8—416no—
602C22⋊Q8—416no—
603#121—232no—
604#121—416no—
605#121—416no—
606#121—416no—
607#121—416no—
608#121—416no—
609#121—48no—
610#121—44no—
611#121—44no—
612#121—44no—
613#121—44no—
614#121—416no—
615#121—88no—
616#121—88no—
617#121—88no—
618#120—48no—
619#120—48no—
620#120—48no—
621C4×Q8—48no—
622C4×Q8—44no—
623C4×D4—48no—
624C4×D4—48no—
625C4×D4—44no—
626C4×D4—48no—
627C4×D4—44no—
628C4×D4—48no—
629C4×D4—44no—
630C4×D4—44no—
631C4×D4—44no—
632C4×D4—48no—
633#117—24no—
634#117—24no—
635#117—24no—
636#117—24no—
637#117—24no—
638#117—24no—
639#117—24no—
640#117—44no—
641C2×C4⋊C4—24no—
642C2×C4⋊C4—28no—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2411yescharacteristic
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⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2412yes—
682C2×C22⋊C4—48no—
683C2×C22⋊C4—48no—
684C2×C22⋊C4—48no—
685C2×C22⋊C4—48no—
686C2×C22⋊C4—44no—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2412yes—
694C2×C22⋊C4C2412yes—
695C2×C22⋊C4C2412yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2418yes—
715C2×C22⋊C4C2418yes—
716C2×C22⋊C4C2418yes—
717C2×C22⋊C4C2418yes—
718C2×C22⋊C4C2418yes—
719C2×C22⋊C4C2418yes—
720C2×C22⋊C4C2418yes—
721C2×C22⋊C4C2418yes—
722C2×C22⋊C4C2418yes—
723C2×C22⋊C4C2418yes—
724C2×C22⋊C4C2418yes—
725C2×C22⋊C4C2418yes—
726C2×C22⋊C4C2418yes—
727C2×C42—24no—
728C2×C42—24no—
729C2×C42—24no—
730C2×C42—44no—
731C2×C42C2412yes—
732C2×C42C2411yescharacteristic
733C2×C42C2412yes—
734C2×C42C2412yes—
735C2×C42C2412yes—
736C2×C42C2412yes—
737C2×C42C2412yes—
738C2×C42C2412yes—
739C2×C42C2412yes—
740C2×C42C2412yes—
741C2×C42C2412yes—
742C2×C42C2412yes—
743C2×C42C2414yes—
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2414yes—
748C2×C42C2414yes—
749#95C2412yes—
750#95C2412yes—
751#95C2412yes—
752#95C2412yes—
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#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2418yes—
774#95C2418yes—
775#95C2418yes—
776C24—24no—
777C24—24no—
778C24—24no—
779C24—24no—
780C24—24no—
781C24—24no—
782C24—24no—
783C24—24no—
784C24—24no—
785C24—44no—
786C24—44no—
787C24—44no—
788C24—44no—
789C24—44no—
790C24—44no—
791C24C2514yes—
792C24C2514yes—
793C24C2514yes—
794C24C2512yes—
795C24C2511yescharacteristic
796#41—416no—
797C2×Q8—22no—
798C2×Q8—22no—
799C2×Q8—28no—
800C2×Q8—22no—
801C2×Q8—44no—
802C2×Q8—44no—
803C2×Q8—48no—
804C2×Q8—44no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—22no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—24no—
821C2×D4—22no—
822C2×D4—216no—
823C2×D4—216no—
824C2×D4—216no—
825C2×D4—24no—
826C2×D4—24no—
827C2×D4—24no—
828C2×D4—24no—
829C2×D4—24no—
830C2×D4—24no—
831C2×D4—22no—
832C2×D4—48no—
833C2×D4—48no—
834C2×D4—48no—
835C2×D4—48no—
836C2×D4—48no—
837C2×D4—48no—
838C2×D4—48no—
839C2×D4—48no—
840C2×D4—48no—
841C2×D4—48no—
842C2×D4—48no—
843C2×D4—48no—
844C2×D4—48no—
845C2×D4—48no—
846C2×D4—48no—
847C2×D4—44no—
848C2×D4—44no—
849C2×D4—48no—
850C2×D4—44no—
851C2×D4—44no—
852C2×D4—48no—
853C2×D4—48no—
854C2×D4—48no—
855C2×D4—48no—
856C2×D4—48no—
857C2×D4—48no—
858C2×D4—416no—
859C2×D4—416no—
860C2×D4—416no—
861C2×D4—816no—
862C2×D4—832no—
863C2×D4—832no—
864C2×D4—816no—
865C22×C4—22no—
866C22×C4—24no—
867C22×C4—22no—
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—216no—
877C22×C4—28no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—48no—
884C22×C4—48no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—48no—
888C22×C4—44no—
889C22×C4—48no—
890C22×C4—48no—
891C22×C4—48no—
892C22×C4—48no—
893C22×C4—816no—
894C22×C4H(5,𝔽2)14yes—
895C22×C4H(5,𝔽2)14yes—
896C22×C42−1+414yes—
897C22×C4C2512yes—
898C22×C4C2512yes—
899C22×C4C2512yes—
900C22×C4C2512yes—
901C22×C4C2512yes—
902C22×C4C2514yes—
903C22×C4C2514yes—
904C22×C4C2512yes—
905C22×C4C2512yes—
906C22×C4C2512yes—
907C22×C4C2514yes—
908C22×C4C2512yes—
909C22×C4C2512yes—
910C22×C4C2514yes—
911C22×C4C2514yes—
912C22×C4C2512yes—
913C22×C4C2512yes—
914C22×C4C2512yes—
915C22×C4C2511yescharacteristic
916C22×C4C2511yescharacteristic
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—24no—
920C4⋊C4—24no—
921C4⋊C4—24no—
922C4⋊C4—24no—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—24no—
927C4⋊C4—22no—
928C4⋊C4—24no—
929C4⋊C4—22no—
930C4⋊C4—22no—
931C4⋊C4—28no—
932C4⋊C4—28no—
933C4⋊C4—28no—
934C4⋊C4—28no—
935C4⋊C4—28no—
936C4⋊C4—28no—
937C4⋊C4—28no—
938C4⋊C4—24no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—44no—
946C4⋊C4—48no—
947C4⋊C4—48no—
948C4⋊C4—44no—
949C4⋊C4—44no—
950C4⋊C4—44no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—44no—
954C4⋊C4—44no—
955C4⋊C4H(5,𝔽2)18yes—
956C22⋊C4—24no—
957C22⋊C4—24no—
958C22⋊C4—24no—
959C22⋊C4—24no—
960C22⋊C4—24no—
961C22⋊C4—24no—
962C22⋊C4—24no—
963C22⋊C4—216no—
964C22⋊C4—216no—
965C22⋊C4—28no—
966C22⋊C4—28no—
967C22⋊C4—48no—
968C22⋊C4—44no—
969C22⋊C4—48no—
970C22⋊C4—44no—
971C22⋊C4—48no—
972C22⋊C4—48no—
973C22⋊C4—44no—
974C22⋊C4—48no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—48no—
980C22⋊C4—48no—
981C22⋊C4—48no—
982C22⋊C4—48no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—48no—
986C22⋊C4—48no—
987C22⋊C4—48no—
988C22⋊C4—48no—
989C22⋊C4—48no—
990C22⋊C4—48no—
991C22⋊C4—48no—
992C22⋊C4—48no—
993C22⋊C4—48no—
994C22⋊C4—48no—
995C22⋊C4—48no—
996C42—22no—
997C42—22no—
998C42—24no—
999C42—24no—
1000C42—24no—
1001C42—24no—
1002C42—22no—
1003C42—22no—
1004C42—24no—
1005C42—24no—
1006C42—24no—
1007C42—24no—
1008C42—24no—
1009C42—24no—
1010C42—28no—
1011C42—24no—
1012C42—44no—
1013C42—44no—
1014C23—22no—
1015C23—22no—
1016C23—24no—
1017C23—28no—
1018C23—28no—
1019C23—24no—
1020C23—28no—
1021C23—22no—
1022C23—24no—
1023C23—24no—
1024C23—24no—
1025C23—24no—
1026C23—22no—
1027C23—24no—
1028C23—22no—
1029C23—24no—
1030C23—24no—
1031C23—24no—
1032C23—28no—
1033C23—24no—
1034C23—28no—
1035C23—28no—
1036C23—416no—
1037C23—48no—
1038C23—48no—
1039C23—48no—
1040C23—84no—
1041C23—84no—
1042C23—88no—
1043C23—84no—
1044C23—84no—
1045C23—84no—
1046C23—84no—
1047C23—88no—
1048C23—88no—
1049C23—88no—
1050C23—88no—
1051C23C2×H(5,𝔽2)12yes—
1052C23C2×H(5,𝔽2)12yes—
1053C23C2×2−1+412yes—
1054C23C2611yescharacteristic
1055Q8—44no—
1056Q8—88no—
1057Q8—164no—
1058D4—48no—
1059D4—48no—
1060D4—48no—
1061D4—48no—
1062D4—48no—
1063D4—48no—
1064D4—48no—
1065D4—44no—
1066D4—816no—
1067D4—816no—
1068D4—816no—
1069D4—816no—
1070D4—816no—
1071D4—816no—
1072D4—164no—
1073D4—164no—
1074D4—164no—
1075D4—164no—
1076D4—168no—
1077C2×C4—28no—
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—22no—
1087C2×C4—24no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—28no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—22no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—48no—
1123C2×C4—48no—
1124C2×C4—44no—
1125C2×C4—48no—
1126C2×C4—88no—
1127C2×C4—816no—
1128C2×C4—84no—
1129C2×C4—164no—
1130C2×C4—164no—
1131C2×C4—168no—
1132C2×C4#562116yescomplemented
1133C2×C4C2×H(5,𝔽2)14yes—
1134C2×C4C2×H(5,𝔽2)14yes—
1135C2×C4C2×H(5,𝔽2)14yes—
1136C2×C4C2×H(5,𝔽2)12yes—
1137C2×C4C2×H(5,𝔽2)12yes—
1138C2×C4C2×H(5,𝔽2)12yes—
1139C2×C4C2×H(5,𝔽2)12yes—
1140C2×C4C2×2−1+412yes—
1141C2×C4C2×2−1+412yes—
1142C22—22no—
1143C22—22no—
1144C22—24no—
1145C22—24no—
1146C22—44no—
1147C22—44no—
1148C22—44no—
1149C22—42no—
1150C22—44no—
1151C22—44no—
1152C22—42no—
1153C22—44no—
1154C22—44no—
1155C22—48no—
1156C22—48no—
1157C22—48no—
1158C22—44no—
1159C22—48no—
1160C22—48no—
1161C22—48no—
1162C22—42no—
1163C22—44no—
1164C22—44no—
1165C22—44no—
1166C22—816no—
1167C22—168no—
1168C22—168no—
1169C22C2×#56214yes—
1170C22C22×H(5,𝔽2)11yescharacteristic
1171C22C22×H(5,𝔽2)12yes—
1172C22C22×H(5,𝔽2)11yescharacteristic
1173C22C22×2−1+411yescharacteristic
1174C22H(7,𝔽2)12yes—
1175C4—24no—
1176C4—24no—
1177C4—24no—
1178C4—44no—
1179C4—42no—
1180C4—42no—
1181C4—42no—
1182C4—42no—
1183C4—42no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—44no—
1189C4—44no—
1190C4—44no—
1191C4—44no—
1192C4—42no—
1193C4C2×#56214yes—
1194C4C2×#56214yes—
1195C2—24no—
1196C2—82no—
1197C2—84no—
1198C2—84no—
1199C2—84no—
1200C2C22×#56211yescharacteristic
1201C2#6283211yescharacteristic
1202C2#6287611yescharacteristic
1203C2#6291212yes—
1204C2#6291712yes—
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. #53117C2semidirect
2. #53106C2semidirect
3. #52995C2semidirect
4. #52973C2semidirect
5. #52316C2semidirect
6. #46044C2semidirect
7. #45997C2semidirect
8. #45610C2semidirect
9. #45484C2semidirect
10. #45443C2semidirect
11. #35554C2semidirect
12. #35554C2semidirect
13. #35529C2semidirect
14. #35528C2semidirect
15. #35528C2semidirect
16. #35515C2semidirect
17. #35285C2semidirect
18. #35272C2semidirect
19. #35264C2semidirect
20. #35254C2semidirect
21. #35174C2semidirect
22. #35152C2semidirect
23. C2×#2541C2semidirect
24. #34815C2semidirect
25. #34745C2semidirect
26. C2×#562C22semidirect
40. #2861C22semidirect
41. #2858C22semidirect
42. #2858C22semidirect
43. #2856C22semidirect
44. #2856C22semidirect
45. #2854C22semidirect
48. #2829C22semidirect
49. #2829C22semidirect
50. #2826C22semidirect
51. #2824C22semidirect
52. #2819C22semidirect
53. #2816C22semidirect
54. #2813C22semidirect
55. #2813C22semidirect
56. #2813C22semidirect
57. #2813C22semidirect
58. #2730C22semidirect
59. #2711C22semidirect
60. #2710C22semidirect
61. #2708C22semidirect
62. #2706C22semidirect
63. #2701C22semidirect
64. #2696C22semidirect
65. #2686C22semidirect
66. #2682C22semidirect
67. #2682C22semidirect
68. #2681C22semidirect
69. #2676C22semidirect
70. #2676C22semidirect
71. #2676C22semidirect
72. #2676C22semidirect
73. #2672C22semidirect
74. #2671C22semidirect
75. #2671C22semidirect
76. #2671C22semidirect
77. #2671C22semidirect
78. #2641C22semidirect
79. #2641C22semidirect
80. #2640C22semidirect
82. #2624C22semidirect
84. #2619C22semidirect
85. #2619C22semidirect
86. #2580C22semidirect
87. #2566C22semidirect
88. #2566C22semidirect
89. #2563C22semidirect
90. #2548C22semidirect
91. #2548C22semidirect
92. #2548C22semidirect
93. #2544C22semidirect
94. #2544C22semidirect
95. #2544C22semidirect
96. #2542C22semidirect
101. #2541C22semidirect
102. #2541C22semidirect
103. #2541C22semidirect
104. #2541C22semidirect
105. #2538C22semidirect
106. #2509C22semidirect
107. #2508C22semidirect
108. #2507C22semidirect
109. #2506C22semidirect
111. #2491C22semidirect
112. #2490C22semidirect
115. #2454C22semidirect
116. #2454C22semidirect
117. #2454C22semidirect
118. #2454C22semidirect
119. #2454C22semidirect
120. #2453C22semidirect
121. #2452C22semidirect
122. #2452C22semidirect
123. #2452C22semidirect
124. #2452C22semidirect
125. #2452C22semidirect
126. #2451C22semidirect
129. #2448C22semidirect
130. #2447C22semidirect
131. #2445C22semidirect
132. #2445C22semidirect
133. #2445C22semidirect
134. #2445C22semidirect
135. #2445C22semidirect
136. #2445C22semidirect
137. #2445C22semidirect
138. #2445C22semidirect
139. #2445C22semidirect
140. #2445C22semidirect
144. #2428C22semidirect
145. #2428C22semidirect
146. #2428C22semidirect
147. #2428C22semidirect
148. #2422C22semidirect
149. #2420C22semidirect
158. #2402C22semidirect
159. #2396C22semidirect
161. #2377C22semidirect
172. C4×#125C22semidirect
173. C4×C22⋊Q8C22semidirect
1132. C2×C4#562semidirect

Maximal subgroups

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

subgroupindex
#531172
#531062
#529952
#529732
#523162
#460442
#459972
#456102
#454842
#454432
#355542
#355292
#355282
#355152
#352852
#352722
#352642
#352542
#351742
#351522
C2×#25412
#348152
#347452