Finite Group Databasebeta

← #8095636

Subgroups — #8095636

Order 512.

5846 conjugacy classes of subgroups.

The subgroup lattice has 1225 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53144C214yesmaximal, complemented
2#53144C214yesmaximal, complemented
3#53080C214yesmaximal, complemented
4#53074C214yesmaximal, complemented
5#52367C218yesmaximal, complemented
6#46084C214yesmaximal, complemented
7#46043C214yesmaximal, complemented
8#46043C214yesmaximal, complemented
9#46016C214yesmaximal, complemented
10#45539C218yesmaximal, complemented
11#35676C211yesmaximal, characteristic, complemented
12#35666C211yesmaximal, characteristic, complemented
13#35659C211yesmaximal, characteristic, complemented
14#35644C211yesmaximal, characteristic, complemented
15#35628C211yesmaximal, characteristic, complemented
16#35556C211yesmaximal, characteristic, complemented
17#35338C211yesmaximal, characteristic, complemented
18#35320C211yesmaximal, characteristic, complemented
19#35312C211yesmaximal, characteristic, complemented
20#35264C211yesmaximal, characteristic, complemented
21#35149C211yesmaximal, characteristic, complemented
22#35149C211yesmaximal, characteristic, complemented
23#34813C211yesmaximal, characteristic, complemented
24#34813C211yesmaximal, characteristic, complemented
25C2×#2432C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C23×#41C2211yescharacteristic
28C2×#544C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#536C2211yescharacteristic
31C2×#535C2211yescharacteristic
32C2×#535C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C22×C4⋊Q8C2211yescharacteristic
36C22×#124C2211yescharacteristic
37C2×#525C2211yescharacteristic
38C2×#525C2211yescharacteristic
39C22×C22⋊Q8C2211yescharacteristic
40#2862C2214yescomplemented
41#2862C2212yescomplemented
42#2861C2212yescomplemented
43#2861C2214yescomplemented
44#2861C2212yescomplemented
45#2858C2212yescomplemented
46#2849C2214yes—
47#2849C2214yes—
48#2835C2218yescomplemented
49#2832C2218yescomplemented
50#2832C2218yescomplemented
51#2832C2218yescomplemented
52#2828C2218yescomplemented
53#2828C2218yescomplemented
54#2824C2218yescomplemented
55#2824C2218yescomplemented
56#2824C2218yescomplemented
57#2819C2218yescomplemented
58#2804C2218yescomplemented
59#2804C2218yescomplemented
60#2785C2218yescomplemented
61#2782C2218yescomplemented
62#2782C2218yescomplemented
63#2782C2218yescomplemented
64#2782C2218yescomplemented
65#2763C2218yescomplemented
66#2763C2218yescomplemented
67#2763C2218yescomplemented
68#2753C2218yescomplemented
69#2753C2218yescomplemented
70#2753C2218yescomplemented
71#2753C2218yescomplemented
72#2753C2218yescomplemented
73#2753C2218yescomplemented
74#2733C2218yescomplemented
75#2712C2218yescomplemented
76#2712C2218yescomplemented
77#2712C2218yescomplemented
78#2642C2214yescomplemented
79#2642C2212yescomplemented
80#2641C2212yescomplemented
81#2640C2214yescomplemented
82#2640C2212yescomplemented
83#2640C2212yescomplemented
84#2613C2214yes—
85#2613C2214yes—
86#2592C2214yescomplemented
87#2592C2214yescomplemented
88#2592C2214yescomplemented
89#2592C2214yescomplemented
90#2568C2214yescomplemented
91#2568C2214yescomplemented
92#2568C2214yescomplemented
93#2561C2218yes—
94#2561C2214yes—
95#2548C2214yescomplemented
96#2503C2214yes—
97#2503C2218yes—
98#2492C2214yescomplemented
99#2492C2214yescomplemented
100#2492C2214yescomplemented
101#2492C2212yescomplemented
102#2492C2214yescomplemented
103#2492C2212yescomplemented
104#2491C2212yescomplemented
105#2491C2214yescomplemented
106#2491C2212yescomplemented
107#2491C2214yescomplemented
108#2490C2212yescomplemented
109#2490C2214yescomplemented
110#2490C2212yescomplemented
111#2490C2214yescomplemented
112#2489C2214yescomplemented
113#2489C2214yescomplemented
114#2489C2214yescomplemented
115#2489C2214yescomplemented
116#2489C2212yescomplemented
117#2489C2212yescomplemented
118#2488C2218yes—
119#2488C2218yes—
120#2488C2214yes—
121#2488C2214yes—
122#2472C2214yes—
123#2472C2214yes—
124#2472C2218yes—
125#2472C2218yes—
126#2436C2212yescomplemented
127#2436C2214yescomplemented
128#2436C2212yescomplemented
129#2434C2212yescomplemented
130#2434C2214yescomplemented
131#2434C2212yescomplemented
132#2432C2214yes—
133#2432C2214yes—
134#2432C2214yes—
135#2432C2214yes—
136#2432C2214yes—
137#2432C2214yes—
138#2432C2214yescomplemented
139#2432C2212yescomplemented
140#2432C2212yescomplemented
141#2431C2214yes—
142#2431C2214yes—
143#2431C2212yescomplemented
144#2431C2214yescomplemented
145#2431C2212yescomplemented
146#2409C2214yescomplemented
147#2409C2214yescomplemented
148#2407C2214yes—
149#2407C2214yes—
150#2407C2214yes—
151#2407C2214yes—
152#2407C2214yescomplemented
153#2407C2214yescomplemented
154#2406C2214yes—
155#2406C2218yes—
156#2404C2214yes—
157#2404C2218yes—
158#2398C2214yescomplemented
159#2398C2214yescomplemented
160C2×#394C2214yes—
161#2379C2218yescomplemented
162#2379C2218yescomplemented
163#2311C2211yescharacteristic
164#2311C2211yescharacteristic
165#2310C2211yescharacteristic
166#2310C2211yescharacteristic
167#2310C2211yescharacteristic
168#2310C2211yescharacteristic
169#2310C2211yescharacteristic
170#2309C2211yescharacteristic
171#2309C2211yescharacteristic
172C4×#124C2214yescomplemented
173C4×#124C2214yescomplemented
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2297C2211yescharacteristic
177#2297C2211yescharacteristic
178C2×#391C2211yescharacteristic
179C2×#390C2211yescharacteristic
180C2×#385C2214yes—
181#2280C2211yescharacteristic
182#2280C2211yescharacteristic
183#2274C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C2×2−1+4—44no—
188C2×2−1+4—44no—
189C2×2−1+4—44no—
190C22×#41—44no—
191C22×#41—44no—
192C22×#41—44no—
193C22×#41C2311yescharacteristic
194C22×#41C2311yescharacteristic
195C22×#41C2314yes—
196C22×#41C2314yes—
197C22×#41C2314yes—
198C22×#41C2312yes—
199C22×#41C2312yes—
200C23×Q8C2311yescharacteristic
201C23×Q8C2311yescharacteristic
202C23×Q8C2312yes—
203C23×Q8C2312yes—
204C23×D4C2311yescharacteristic
205C23×D4C2312yes—
206C24×C4C2311yescharacteristic
207C24×C4C2312yes—
208#544—44no—
209#536—44no—
210#536—44no—
211#535—44no—
212#535—44no—
213#533—44no—
214#533—44no—
215C2×C4⋊Q8—44no—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2312yes—
219C2×C4⋊Q8C2312yes—
220C2×C4⋊Q8C2312yes—
221C2×C4⋊Q8C2312yes—
222C2×C4⋊Q8C2312yes—
223C2×C4⋊Q8C2312yes—
224C2×C4⋊Q8C2312yes—
225C2×#127C2312yes—
226C2×#127C2312yes—
227C2×#125C2312yes—
228C2×#125C2312yes—
229C2×#125C2312yes—
230C2×#125C2312yes—
231C2×#124—44no—
232C2×#124C2314yes—
233C2×#124C2318yes—
234C2×#124C2314yes—
235C2×#124C2312yes—
236C2×#124C2312yes—
237C2×#124C2312yes—
238C2×#124C2312yes—
239C2×#124C2312yes—
240C2×#124C2318yes—
241C2×#124C2312yes—
242C2×#124C2314yes—
243#525—44no—
244#525—44no—
245C2×#123C2312yes—
246C2×#123C2312yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×C22⋊Q8—44no—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2314yes—
260C2×#121C2312yes—
261C2×#121C2314yes—
262C2×#121C2312yes—
263C2×#121C2312yes—
264C2×#121C2312yes—
265C2×#120C2314yes—
266C2×#120C2314yes—
267C2×#120C2312yes—
268C2×#120C2312yes—
269C2×C4×Q8C2314yes—
270C2×C4×Q8C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×#117C2311yescharacteristic
274C2×#117C2311yescharacteristic
275C2×#117C2311yescharacteristic
276C2×#117C2311yescharacteristic
277C2×#117C2311yescharacteristic
278C2×#117C2311yescharacteristic
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2314yes—
281C22×C4⋊C4C2312yes—
282C22×C22⋊C4C2312yes—
283C22×C22⋊C4C2314yes—
284C22×C22⋊C4C2312yes—
285C22×C22⋊C4C2314yes—
286C22×C42C2311yescharacteristic
287C22×C42C2311yescharacteristic
288#400C2318yes—
289#400C2318yes—
290#400C2318yes—
291#400C2318yes—
292#400C2318yes—
293#400C2318yes—
294#400C2318yes—
295#400C2318yes—
296#400C2318yes—
297#400C2314yes—
298#400C2314yes—
299#400C2318yes—
300#400C2314yes—
301#400C2314yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2314yes—
306#397C2314yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2314yes—
311#397C2318yes—
312#397C2314yes—
313#395C2318yes—
314#395C2318yes—
315#395C2318yes—
316#394C2314yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2314yes—
321#394C2314yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#394C2318yes—
330#394C2314yes—
331#394C2318yes—
332#394C2318yes—
333#394C2318yes—
334#394C2318yes—
335#393C2318yes—
336#393C2318yes—
337#393C2318yes—
338#393C2318yes—
339#393C2318yes—
340#393C2314yes—
341#393C2314yes—
342#393C2318yes—
343#393C2318yes—
344#393C2318yes—
345#393C2314yes—
346#393C2318yes—
347#393C2318yes—
348#393C2314yes—
349#392C2318yes—
350#392C2318yes—
351#392C2318yes—
352#392C2318yes—
353#392C2318yes—
354#392C2318yes—
355#392C2318yes—
356#391C2314yes—
357#391C2312yes—
358#391C2312yes—
359#391C2314yes—
360#391C2312yes—
361#391C2312yes—
362#391C2314yes—
363#391C2314yes—
364#391C2312yes—
365#391C2312yes—
366#391C2314yes—
367#391C2314yes—
368#391C2314yes—
369#391C2312yes—
370#391C2312yes—
371#391C2312yes—
372#391C2318yes—
373#391C2318yes—
374#391C2314yes—
375#391C2318yes—
376#391C2318yes—
377#391C2312yes—
378#391C2311yescharacteristic
379#391C2312yes—
380#391C2311yescharacteristic
381#391C2314yes—
382#391C2318yes—
383#391C2311yescharacteristic
384#391C2312yes—
385#391C2311yescharacteristic
386#391C2314yes—
387#390C2312yes—
388#390C2312yes—
389#390C2314yes—
390#390C2314yes—
391#390C2314yes—
392#390C2312yes—
393#390C2312yes—
394#390C2314yes—
395#390C2318yes—
396#390C2312yes—
397#390C2314yes—
398#390C2311yescharacteristic
399#390C2312yes—
400#390C2318yes—
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#390C2312yes—
404#390C2311yescharacteristic
405#390C2312yes—
406#390C2314yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2314yes—
416#388C2314yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#386C2314yes—
430#386C2314yes—
431#386C2318yes—
432#386C2318yes—
433#386C2318yes—
434#386C2318yes—
435#386C2318yes—
436#386C2318yes—
437#386C2318yes—
438#386C2318yes—
439#386C2318yes—
440#386C2318yes—
441#386C2314yes—
442#386C2314yes—
443#386C2314yes—
444#386C2314yes—
445#385C2318yes—
446#385C2318yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#385C2318yes—
451#385C2318yes—
452#385C2318yes—
453#385C2318yes—
454#385C2318yes—
455#385C2318yes—
456#385C2318yes—
457#385C2318yes—
458#385C2318yes—
459#382C2318yes—
460#382C2318yes—
461#382C2318yes—
462#382C2318yes—
463#382C2314yes—
464#382C2318yes—
465#382C2314yes—
466#381C2314yes—
467#381C2314yes—
468#381C2314yes—
469#381C2314yes—
470#381C2314yes—
471#381C2312yes—
472#381C2312yes—
473#380C2314yes—
474#380C2314yes—
475#380C2312yes—
476#380C2312yes—
477#380C2312yes—
478#380C2312yes—
479#379C2314yes—
480#379C2314yes—
481#379C2312yes—
482#379C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2312yes—
501C4×C22⋊C4C2312yes—
502C4×C22⋊C4C2312yes—
503C4×C22⋊C4C2314yes—
504#376C2312yes—
505#376C2312yes—
506C2×#95C2314yes—
507C2×#95C2312yes—
508C43C2312yes—
509C43C2312yes—
510C25C2411yescharacteristic
511C25C2412yes—
5122−1+4—464no—
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—48no—
526C2×#41—48no—
527C2×#41—48no—
528C2×#41—44no—
529C2×#41—44no—
530C2×#41—44no—
531C2×#41—44no—
532C2×#41—44no—
533C2×#41—44no—
534C2×#41—464no—
535C22×Q8—24no—
536C22×Q8—24no—
537C22×Q8—24no—
538C22×Q8—24no—
539C22×Q8—24no—
540C22×Q8—24no—
541C22×Q8—44no—
542C22×Q8—44no—
543C22×Q8—44no—
544C22×Q8—44no—
545C22×Q8—44no—
546C22×Q8—44no—
547C22×Q8C2412yes—
548C22×Q8C2412yes—
549C22×Q8C2411yescharacteristic
550C22×Q8C2411yescharacteristic
551C22×Q8C2412yes—
552C22×Q8C2412yes—
553C22×Q8C2414yes—
554C22×Q8C2414yes—
555C22×Q8C2414yes—
556C22×Q8C2414yes—
557C22×D4—24no—
558C22×D4—24no—
559C22×D4—24no—
560C22×D4—44no—
561C22×D4—44no—
562C22×D4—44no—
563C22×D4C2412yes—
564C22×D4C2412yes—
565C22×D4C2412yes—
566C22×D4C2412yes—
567C22×D4C2411yescharacteristic
568C22×D4C2411yescharacteristic
569C22×D4C2414yes—
570C22×D4C2414yes—
571C22×D4C2414yes—
572C22×D4C2418yes—
573C22×D4C2414yes—
574C22×D4C2418yes—
575C22×D4C2414yes—
576C23×C4—24no—
577C23×C4—24no—
578C23×C4—24no—
579C23×C4—44no—
580C23×C4—44no—
581C23×C4—44no—
582C23×C4C2412yes—
583C23×C4C2411yescharacteristic
584C23×C4C2412yes—
585C23×C4C2412yes—
586C23×C4C2412yes—
587C23×C4C2412yes—
588C23×C4C2412yes—
589C23×C4C2412yes—
590C23×C4C2412yes—
591C23×C4C2412yes—
592C23×C4C2418yes—
593C23×C4C2414yes—
594C23×C4C2414yes—
595C23×C4C2411yescharacteristic
596C4⋊Q8—44no—
597C4⋊Q8—44no—
598C4⋊Q8—44no—
599C4⋊Q8—44no—
600C4⋊Q8—48no—
601C4⋊Q8—44no—
602C4⋊Q8—44no—
603C4⋊Q8—44no—
604C4⋊Q8—44no—
605#127—44no—
606#127—44no—
607#125—44no—
608#125—44no—
609#125—44no—
610#125—44no—
611#124—48no—
612#124—416no—
613#124—48no—
614#124—44no—
615#124—44no—
616#124—44no—
617#124—44no—
618#124—44no—
619#124—44no—
620#124—48no—
621#124—416no—
622#123—44no—
623#123—44no—
624#123—48no—
625#123—48no—
626C22⋊Q8—48no—
627C22⋊Q8—48no—
628C22⋊Q8—48no—
629C22⋊Q8—48no—
630C22⋊Q8—48no—
631C22⋊Q8—44no—
632C22⋊Q8—44no—
633C22⋊Q8—44no—
634C22⋊Q8—48no—
635C22⋊Q8—44no—
636#121—44no—
637#121—44no—
638#121—44no—
639#121—48no—
640#121—44no—
641#120—44no—
642#120—44no—
643#120—48no—
644#120—48no—
645C4×Q8—48no—
646C4×Q8—48no—
647C4×D4—48no—
648C4×D4—48no—
649#117—24no—
650#117—24no—
651#117—24no—
652#117—24no—
653#117—24no—
654#117—24no—
655C2×C4⋊C4—24no—
656C2×C4⋊C4—44no—
657C2×C4⋊C4—48no—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2418yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C22⋊C4—44no—
686C2×C22⋊C4—48no—
687C2×C22⋊C4—44no—
688C2×C22⋊C4—48no—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2412yes—
693C2×C22⋊C4C2412yes—
694C2×C22⋊C4C2412yes—
695C2×C22⋊C4C2412yes—
696C2×C22⋊C4C2412yes—
697C2×C22⋊C4C2412yes—
698C2×C22⋊C4C2414yes—
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⋊C4C2418yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2418yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2418yes—
721C2×C22⋊C4C2418yes—
722C2×C22⋊C4C2418yes—
723C2×C22⋊C4C2418yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2418yes—
731C2×C22⋊C4C2418yes—
732C2×C42—24no—
733C2×C42—24no—
734C2×C42C2412yes—
735C2×C42C2412yes—
736C2×C42C2412yes—
737C2×C42C2412yes—
738C2×C42C2412yes—
739C2×C42C2412yes—
740C2×C42C2412yes—
741C2×C42C2412yes—
742C2×C42C2414yes—
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2414yes—
748C2×C42C2418yes—
749C2×C42C2414yes—
750C2×C42C2414yes—
751#95C2412yes—
752#95C2412yes—
753#95C2412yes—
754#95C2412yes—
755#95C2418yes—
756#95C2418yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2418yes—
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#95C2418yes—
775#95C2418yes—
776#95C2418yes—
777#95C2418yes—
778#95C2418yes—
779#95C2418yes—
780#95C2418yes—
781#95C2418yes—
782#95C2418yes—
783#95C2418yes—
784#95C2418yes—
785#95C2418yes—
786C24—22no—
787C24—24no—
788C24—22no—
789C24—22no—
790C24—24no—
791C24—24no—
792C24—44no—
793C24—42no—
794C24—42no—
795C24—44no—
796C24C2512yes—
797C24C2514yes—
798C24C2512yes—
799C24C2512yes—
800C24C2511yescharacteristic
801#41—464no—
802#41—464no—
803#41—464no—
804#41—432no—
805#41—432no—
806#41—416no—
807#41—416no—
808C2×Q8—24no—
809C2×Q8—24no—
810C2×Q8—24no—
811C2×Q8—24no—
812C2×Q8—22no—
813C2×Q8—22no—
814C2×Q8—24no—
815C2×Q8—24no—
816C2×Q8—22no—
817C2×Q8—22no—
818C2×Q8—24no—
819C2×Q8—24no—
820C2×Q8—24no—
821C2×Q8—24no—
822C2×Q8—24no—
823C2×Q8—24no—
824C2×Q8—22no—
825C2×Q8—22no—
826C2×Q8—28no—
827C2×Q8—44no—
828C2×Q8—44no—
829C2×Q8—44no—
830C2×Q8—44no—
831C2×Q8—44no—
832C2×Q8—44no—
833C2×Q8—44no—
834C2×Q8—44no—
835C2×Q8—44no—
836C2×Q8—48no—
837C2×Q8—432no—
838C2×Q8—432no—
839C2×Q8—416no—
840C2×Q8—416no—
841C2×D4—24no—
842C2×D4—24no—
843C2×D4—24no—
844C2×D4—24no—
845C2×D4—24no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—22no—
850C2×D4—22no—
851C2×D4—24no—
852C2×D4—24no—
853C2×D4—22no—
854C2×D4—22no—
855C2×D4—24no—
856C2×D4—24no—
857C2×D4—22no—
858C2×D4—22no—
859C2×D4—48no—
860C2×D4—48no—
861C2×D4—48no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—48no—
873C2×D4—44no—
874C2×D4—48no—
875C2×D4—48no—
876C2×D4—48no—
877C2×D4—48no—
878C2×D4—432no—
879C2×D4—416no—
880C22×C4—24no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—22no—
884C22×C4—24no—
885C22×C4—24no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—24no—
889C22×C4—24no—
890C22×C4—24no—
891C22×C4—24no—
892C22×C4—24no—
893C22×C4—24no—
894C22×C4—24no—
895C22×C4—24no—
896C22×C4—24no—
897C22×C4—24no—
898C22×C4—24no—
899C22×C4—24no—
900C22×C4—24no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—24no—
905C22×C4—48no—
906C22×C4—48no—
907C22×C4—48no—
908C22×C4—42no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—44no—
915C22×C4—42no—
916C22×C4—44no—
917C22×C4—42no—
918C22×C4—432no—
919C22×C4—416no—
920C22×C4H(5,𝔽2)14yes—
921C22×C4H(5,𝔽2)14yes—
922C22×C4H(5,𝔽2)14yes—
923C22×C4C2512yes—
924C22×C4C2514yes—
925C22×C4C2512yes—
926C22×C4C2512yes—
927C22×C4C2514yes—
928C22×C4C2514yes—
929C22×C4C2512yes—
930C22×C4C2512yes—
931C22×C4C2514yes—
932C22×C4C2512yes—
933C22×C4C2514yes—
934C22×C4C2512yes—
935C22×C4C2512yes—
936C22×C4C2514yes—
937C22×C4C2512yes—
938C22×C4C2512yes—
939C22×C4C2514yes—
940C22×C4C2512yes—
941C22×C4C2511yescharacteristic
942C22×C4C2511yescharacteristic
943C4⋊C4—24no—
944C4⋊C4—24no—
945C4⋊C4—22no—
946C4⋊C4—24no—
947C4⋊C4—22no—
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—22no—
951C4⋊C4—24no—
952C4⋊C4—22no—
953C4⋊C4—48no—
954C4⋊C4—48no—
955C4⋊C4—48no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—44no—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—44no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—48no—
966C4⋊C4—44no—
967C4⋊C4—44no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C22⋊C4—24no—
971C22⋊C4—24no—
972C22⋊C4—24no—
973C22⋊C4—24no—
974C22⋊C4—24no—
975C22⋊C4—24no—
976C22⋊C4—24no—
977C22⋊C4—216no—
978C22⋊C4—24no—
979C22⋊C4—28no—
980C22⋊C4—28no—
981C22⋊C4—42no—
982C22⋊C4—48no—
983C22⋊C4—42no—
984C22⋊C4—48no—
985C22⋊C4—48no—
986C22⋊C4—48no—
987C22⋊C4—44no—
988C22⋊C4—48no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—48no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—48no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—48no—
1004C22⋊C4—44no—
1005C22⋊C4—48no—
1006C22⋊C4—48no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—48no—
1011C22⋊C4—44no—
1012C22⋊C4—48no—
1013C42—24no—
1014C42—24no—
1015C42—22no—
1016C42—22no—
1017C42—22no—
1018C42—22no—
1019C42—24no—
1020C42—24no—
1021C42—24no—
1022C42—24no—
1023C42—24no—
1024C42—24no—
1025C42—28no—
1026C42—44no—
1027C42—44no—
1028C42—44no—
1029C42—48no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—24no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—24no—
1041C23—24no—
1042C23—22no—
1043C23—22no—
1044C23—24no—
1045C23—24no—
1046C23—28no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—24no—
1051C23—24no—
1052C23—28no—
1053C23—22no—
1054C23—44no—
1055C23—44no—
1056C23—416no—
1057C23—48no—
1058C23—44no—
1059C23—84no—
1060C23—84no—
1061C23—84no—
1062C23—84no—
1063C23—88no—
1064C23C2×H(5,𝔽2)12yes—
1065C23C2×H(5,𝔽2)12yes—
1066C23C2×H(5,𝔽2)12yes—
1067C23C2611yescharacteristic
1068Q8—416no—
1069Q8—48no—
1070Q8—48no—
1071Q8—44no—
1072Q8—44no—
1073Q8—48no—
1074Q8—48no—
1075Q8—88no—
1076Q8—88no—
1077Q8—164no—
1078D4—432no—
1079D4—416no—
1080D4—48no—
1081D4—48no—
1082D4—48no—
1083D4—48no—
1084D4—44no—
1085D4—44no—
1086D4—88no—
1087D4—88no—
1088D4—164no—
1089D4—164no—
1090D4—168no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—22no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—28no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—24no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—48no—
1140C2×C4—432no—
1141C2×C4—416no—
1142C2×C4—416no—
1143C2×C4—44no—
1144C2×C4—48no—
1145C2×C4—48no—
1146C2×C4—48no—
1147C2×C4—48no—
1148C2×C4—48no—
1149C2×C4—48no—
1150C2×C4—84no—
1151C2×C4—84no—
1152C2×C4H(3,𝔽4)116yes—
1153C2×C4C2×H(5,𝔽2)12yes—
1154C2×C4C2×H(5,𝔽2)12yes—
1155C2×C4C2×H(5,𝔽2)12yes—
1156C2×C4C2×H(5,𝔽2)12yes—
1157C2×C4C2×H(5,𝔽2)12yes—
1158C2×C4C2×H(5,𝔽2)12yes—
1159C2×C4#58514yes—
1160C22—22no—
1161C22—22no—
1162C22—24no—
1163C22—24no—
1164C22—42no—
1165C22—44no—
1166C22—42no—
1167C22—42no—
1168C22—42no—
1169C22—44no—
1170C22—42no—
1171C22—42no—
1172C22—42no—
1173C22—44no—
1174C22—44no—
1175C22—48no—
1176C22—42no—
1177C22—42no—
1178C22—42no—
1179C22—44no—
1180C22—42no—
1181C22—42no—
1182C22—44no—
1183C22—44no—
1184C22—48no—
1185C22—42no—
1186C22—816no—
1187C22—88no—
1188C22C2×H(3,𝔽4)14yes—
1189C22C22×H(5,𝔽2)11yescharacteristic
1190C22C22×H(5,𝔽2)11yescharacteristic
1191C22C22×H(5,𝔽2)11yescharacteristic
1192C22C2×#58512yes—
1193C222−1+612yes—
1194C4—24no—
1195C4—44no—
1196C4—42no—
1197C4—42no—
1198C4—42no—
1199C4—42no—
1200C4—42no—
1201C4—42no—
1202C4—44no—
1203C4—44no—
1204C4—42no—
1205C4—44no—
1206C4—42no—
1207C4—42no—
1208C4—44no—
1209C4—42no—
1210C4—44no—
1211C4—44no—
1212C4C2×H(3,𝔽4)14yes—
1213C4C2×H(3,𝔽4)14yes—
1214C2—24no—
1215C2—82no—
1216C2—82no—
1217C2—84no—
1218C2—82no—
1219C2C22×H(3,𝔽4)11yescharacteristic
1220C2#6283611yescharacteristic
1221C2#6288711yescharacteristic
1222C2#6292512yes—
1223C2#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. #53144C2semidirect
2. #53144C2semidirect
3. #53080C2semidirect
4. #53074C2semidirect
5. #52367C2semidirect
6. #46084C2semidirect
7. #46043C2semidirect
8. #46043C2semidirect
9. #46016C2semidirect
10. #45539C2semidirect
11. #35676C2semidirect
12. #35666C2semidirect
13. #35659C2semidirect
14. #35644C2semidirect
15. #35628C2semidirect
16. #35556C2semidirect
17. #35338C2semidirect
18. #35320C2semidirect
19. #35312C2semidirect
20. #35264C2semidirect
21. #35149C2semidirect
22. #35149C2semidirect
23. #34813C2semidirect
24. #34813C2semidirect
25. C2×#2432C2semidirect
40. #2862C22semidirect
41. #2862C22semidirect
42. #2861C22semidirect
43. #2861C22semidirect
44. #2861C22semidirect
45. #2858C22semidirect
48. #2835C22semidirect
49. #2832C22semidirect
50. #2832C22semidirect
51. #2832C22semidirect
52. #2828C22semidirect
53. #2828C22semidirect
54. #2824C22semidirect
55. #2824C22semidirect
56. #2824C22semidirect
57. #2819C22semidirect
58. #2804C22semidirect
59. #2804C22semidirect
60. #2785C22semidirect
61. #2782C22semidirect
62. #2782C22semidirect
63. #2782C22semidirect
64. #2782C22semidirect
65. #2763C22semidirect
66. #2763C22semidirect
67. #2763C22semidirect
68. #2753C22semidirect
69. #2753C22semidirect
70. #2753C22semidirect
71. #2753C22semidirect
72. #2753C22semidirect
73. #2753C22semidirect
74. #2733C22semidirect
75. #2712C22semidirect
76. #2712C22semidirect
77. #2712C22semidirect
78. #2642C22semidirect
79. #2642C22semidirect
80. #2641C22semidirect
81. #2640C22semidirect
82. #2640C22semidirect
83. #2640C22semidirect
86. #2592C22semidirect
87. #2592C22semidirect
88. #2592C22semidirect
89. #2592C22semidirect
90. #2568C22semidirect
91. #2568C22semidirect
92. #2568C22semidirect
95. #2548C22semidirect
98. #2492C22semidirect
99. #2492C22semidirect
100. #2492C22semidirect
101. #2492C22semidirect
102. #2492C22semidirect
103. #2492C22semidirect
104. #2491C22semidirect
105. #2491C22semidirect
106. #2491C22semidirect
107. #2491C22semidirect
108. #2490C22semidirect
109. #2490C22semidirect
110. #2490C22semidirect
111. #2490C22semidirect
112. #2489C22semidirect
113. #2489C22semidirect
114. #2489C22semidirect
115. #2489C22semidirect
116. #2489C22semidirect
117. #2489C22semidirect
126. #2436C22semidirect
127. #2436C22semidirect
128. #2436C22semidirect
129. #2434C22semidirect
130. #2434C22semidirect
131. #2434C22semidirect
138. #2432C22semidirect
139. #2432C22semidirect
140. #2432C22semidirect
143. #2431C22semidirect
144. #2431C22semidirect
145. #2431C22semidirect
146. #2409C22semidirect
147. #2409C22semidirect
152. #2407C22semidirect
153. #2407C22semidirect
158. #2398C22semidirect
159. #2398C22semidirect
161. #2379C22semidirect
162. #2379C22semidirect
172. C4×#124C22semidirect
173. C4×#124C22semidirect

Maximal subgroups

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

subgroupindex
#531442
#530802
#530742
#523672
#460842
#460432
#460162
#455392
#356762
#356662
#356592
#356442
#356282
#355562
#353382
#353202
#353122
#352642
#351492
#348132
C2×#24322