Finite Group Databasebeta

← #8095600

Subgroups — #8095600

Order 512.

6238 conjugacy classes of subgroups.

The subgroup lattice has 1272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53116C214yesmaximal, complemented
2#53116C214yesmaximal, complemented
3#53080C214yesmaximal, complemented
4#53074C214yesmaximal, complemented
5#52310C218yesmaximal, complemented
6#46084C214yesmaximal, complemented
7#46054C214yesmaximal, complemented
8#46054C214yesmaximal, complemented
9#46016C214yesmaximal, complemented
10#45568C218yesmaximal, complemented
11#35628C211yesmaximal, characteristic, complemented
12#35616C211yesmaximal, characteristic, complemented
13#35584C211yesmaximal, characteristic, complemented
14#35556C211yesmaximal, characteristic, complemented
15#35527C211yesmaximal, characteristic, complemented
16#35512C211yesmaximal, characteristic, complemented
17#35338C211yesmaximal, characteristic, complemented
18#35312C211yesmaximal, characteristic, complemented
19#35285C211yesmaximal, characteristic, complemented
20#35264C211yesmaximal, characteristic, complemented
21#35149C211yesmaximal, characteristic, complemented
22#35149C211yesmaximal, characteristic, complemented
23#34813C211yesmaximal, characteristic, complemented
24#34813C211yesmaximal, characteristic, complemented
25C2×#2431C211yesmaximal, characteristic, complemented
26C22×H(5,𝔽2)C2211yescharacteristic
27C23×#41C2211yescharacteristic, complemented
28C2×#544C2211yescharacteristic, complemented
29C2×#536C2211yescharacteristic
30C2×#536C2211yescharacteristic
31C2×#535C2211yescharacteristic
32C2×#535C2211yescharacteristic
33C2×#533C2211yescharacteristic, complemented
34C2×#533C2211yescharacteristic, complemented
35C22×#127C2211yescharacteristic
36C22×#124C2211yescharacteristic
37C2×#525C2211yescharacteristic
38C2×#525C2211yescharacteristic
39C22×#121C2211yescharacteristic
40#2862C2212yescomplemented
41#2861C2212yescomplemented
42#2861C2214yescomplemented
43#2861C2212yescomplemented
44#2858C2212yescomplemented
45#2858C2214yescomplemented
46#2849C2214yescomplemented
47#2849C2214yescomplemented
48#2828C2218yescomplemented
49#2828C2218yescomplemented
50#2828C2218yescomplemented
51#2828C2218yescomplemented
52#2824C2218yescomplemented
53#2824C2218yescomplemented
54#2824C2218yescomplemented
55#2819C2218yescomplemented
56#2819C2218yescomplemented
57#2812C2218yescomplemented
58#2804C2218yescomplemented
59#2782C2218yescomplemented
60#2782C2218yescomplemented
61#2753C2218yescomplemented
62#2753C2218yescomplemented
63#2753C2218yescomplemented
64#2753C2218yescomplemented
65#2753C2218yescomplemented
66#2753C2218yescomplemented
67#2733C2218yescomplemented
68#2733C2218yescomplemented
69#2712C2218yescomplemented
70#2712C2218yescomplemented
71#2712C2218yescomplemented
72#2684C2218yescomplemented
73#2684C2218yescomplemented
74#2684C2218yescomplemented
75#2670C2218yescomplemented
76#2670C2218yescomplemented
77#2670C2218yescomplemented
78#2642C2212yescomplemented
79#2641C2214yescomplemented
80#2641C2212yescomplemented
81#2640C2214yescomplemented
82#2640C2212yescomplemented
83#2640C2212yescomplemented
84#2613C2214yescomplemented
85#2613C2214yescomplemented
86#2592C2214yescomplemented
87#2592C2214yescomplemented
88#2592C2214yescomplemented
89#2592C2214yescomplemented
90#2568C2214yescomplemented
91#2561C2214yescomplemented
92#2561C2218yescomplemented
93#2548C2214yescomplemented
94#2548C2214yescomplemented
95#2548C2214yescomplemented
96#2492C2214yescomplemented
97#2492C2212yescomplemented
98#2492C2214yescomplemented
99#2492C2212yescomplemented
100#2491C2214yescomplemented
101#2491C2214yescomplemented
102#2491C2214yescomplemented
103#2491C2212yescomplemented
104#2491C2214yescomplemented
105#2491C2212yescomplemented
106#2490C2214yescomplemented
107#2490C2214yescomplemented
108#2490C2214yescomplemented
109#2490C2214yescomplemented
110#2490C2212yescomplemented
111#2490C2212yescomplemented
112#2489C2212yescomplemented
113#2489C2214yescomplemented
114#2489C2214yescomplemented
115#2489C2212yescomplemented
116#2488C2214yescomplemented
117#2488C2214yescomplemented
118#2488C2218yescomplemented
119#2488C2218yescomplemented
120#2472C2218yescomplemented
121#2472C2218yescomplemented
122#2472C2214yescomplemented
123#2472C2214yescomplemented
124#2435C2214yescomplemented
125#2435C2218yescomplemented
126#2435C2212yescomplemented
127#2435C2214yescomplemented
128#2435C2212yescomplemented
129#2433C2212yescomplemented
130#2433C2214yescomplemented
131#2433C2212yescomplemented
132#2432C2212yescomplemented
133#2432C2214yescomplemented
134#2432C2214yescomplemented
135#2432C2212yescomplemented
136#2432C2214yescomplemented
137#2431C2214yescomplemented
138#2431C2214yescomplemented
139#2431C2214yescomplemented
140#2431C2214yescomplemented
141#2431C2212yescomplemented
142#2431C2214yescomplemented
143#2431C2214yescomplemented
144#2431C2214yescomplemented
145#2431C2212yescomplemented
146#2408C2214yescomplemented
147#2408C2214yescomplemented
148#2407C2214yescomplemented
149#2407C2214yescomplemented
150#2407C2214yescomplemented
151#2407C2214yescomplemented
152#2407C2214yescomplemented
153#2407C2214yescomplemented
154#2405C2214yes—
155#2405C2218yes—
156#2403C2218yes—
157#2403C2214yes—
158#2398C2214yescomplemented
159#2398C2214yescomplemented
160C2×#392C2214yescomplemented
161#2379C2218yescomplemented
162#2375C2218yescomplemented
163#2311C2211yescharacteristic
164#2311C2211yescharacteristic
165#2310C2211yescharacteristic, complemented
166#2310C2211yescharacteristic, complemented
167#2309C2211yescharacteristic
168#2309C2211yescharacteristic
169#2309C2211yescharacteristic
170#2309C2211yescharacteristic, complemented
171#2309C2211yescharacteristic, complemented
172C4×#124C2214yescomplemented
173C4×#124C2214yescomplemented
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2297C2211yescharacteristic
177#2297C2211yescharacteristic
178C2×#391C2211yescharacteristic, complemented
179C2×#390C2211yescharacteristic, complemented
180C2×#386C2214yescomplemented
181#2280C2211yescharacteristic, complemented
182#2280C2211yescharacteristic, complemented
183#2274C2211yescharacteristic, complemented
184C4×#117C2211yescharacteristic, complemented
185C4×#117C2211yescharacteristic, complemented
186C2×C4×C22⋊C4C2211yescharacteristic, complemented
187C2×H(5,𝔽2)—44no—
188C2×H(5,𝔽2)—44no—
189C2×H(5,𝔽2)—44no—
190C22×#41—44no—
191C22×#41—44no—
192C22×#41—44no—
193C22×#41C2311yescharacteristic
194C22×#41C2311yescharacteristic
195C22×#41C2314yes—
196C22×#41C2314yes—
197C22×#41C2312yes—
198C22×#41C2312yes—
199C23×Q8C2311yescharacteristic
200C23×D4C2311yescharacteristic
201C23×D4C2311yescharacteristic
202C23×D4C2312yes—
203C23×D4C2314yes—
204C23×D4C2312yes—
205C23×D4C2312yes—
206C23×D4C2314yes—
207C23×D4C2312yes—
208C24×C4C2311yescharacteristic
209C24×C4C2312yes—
210#544—44no—
211#536—44no—
212#536—44no—
213#535—44no—
214#535—44no—
215#533—44no—
216#533—44no—
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2312yes—
219C2×C4⋊Q8C2312yes—
220C2×C4⋊Q8C2312yes—
221C2×C4⋊Q8C2312yes—
222C2×C4⋊Q8C2312yes—
223C2×#127—44no—
224C2×#127C2312yes—
225C2×#127C2312yes—
226C2×#127C2312yes—
227C2×#127C2314yes—
228C2×#127C2312yes—
229C2×#125C2312yes—
230C2×#125C2312yes—
231C2×#125C2312yes—
232C2×#125C2312yes—
233C2×#124—44no—
234C2×#124C2314yes—
235C2×#124C2318yes—
236C2×#124C2314yes—
237C2×#124C2312yes—
238C2×#124C2312yes—
239C2×#124C2312yes—
240C2×#124C2312yes—
241C2×#124C2312yes—
242C2×#124C2312yes—
243C2×#124C2314yes—
244C2×#124C2318yes—
245C2×#124C2318yes—
246C2×#124C2318yes—
247C2×#124C2318yes—
248#525—44no—
249#525—44no—
250C2×#123C2312yes—
251C2×#123C2312yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2314yes—
262C2×#121—44no—
263C2×#121C2312yes—
264C2×#121C2314yes—
265C2×#121C2312yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×#121C2312yes—
269C2×#121C2312yes—
270C2×#120C2314yes—
271C2×#120C2314yes—
272C2×#120C2312yes—
273C2×#120C2312yes—
274C2×#120C2318yes—
275C2×#120C2318yes—
276C2×#120C2318yes—
277C2×C4×Q8C2314yes—
278C2×C4×Q8C2314yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2314yes—
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C2×#117C2311yescharacteristic
284C2×#117C2311yescharacteristic
285C2×#117C2311yescharacteristic
286C2×#117C2311yescharacteristic
287C22×C4⋊C4C2311yescharacteristic
288C22×C22⋊C4C2314yes—
289C22×C22⋊C4C2312yes—
290C22×C22⋊C4C2312yes—
291C22×C22⋊C4C2314yes—
292C22×C42C2311yescharacteristic
293C22×C42C2311yescharacteristic
294#400C2318yes—
295#400C2318yes—
296#400C2314yes—
297#400C2314yes—
298#400C2318yes—
299#400C2318yes—
300#400C2314yes—
301#400C2314yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2314yes—
306#397C2314yes—
307#397C2318yes—
308#397C2318yes—
309#397C2314yes—
310#397C2318yes—
311#397C2318yes—
312#397C2314yes—
313#394C2314yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#394C2318yes—
330#394C2318yes—
331#394C2314yes—
332#394C2314yes—
333#394C2314yes—
334#394C2318yes—
335#394C2318yes—
336#394C2318yes—
337#393C2318yes—
338#393C2318yes—
339#393C2318yes—
340#393C2314yes—
341#393C2314yes—
342#393C2318yes—
343#393C2318yes—
344#393C2318yes—
345#393C2318yes—
346#393C2314yes—
347#393C2314yes—
348#392C2318yes—
349#392C2318yes—
350#392C2318yes—
351#392C2318yes—
352#392C2318yes—
353#392C2318yes—
354#392C2318yes—
355#392C2318yes—
356#392C2318yes—
357#392C2318yes—
358#392C2318yes—
359#392C2318yes—
360#392C2318yes—
361#392C2318yes—
362#391C2314yes—
363#391C2312yes—
364#391C2312yes—
365#391C2314yes—
366#391C2314yes—
367#391C2312yes—
368#391C2312yes—
369#391C2312yes—
370#391C2314yes—
371#391C2318yes—
372#391C2312yes—
373#391C2311yescharacteristic
374#391C2312yes—
375#391C2311yescharacteristic
376#391C2318yes—
377#391C2314yes—
378#391C2311yescharacteristic
379#391C2312yes—
380#391C2311yescharacteristic
381#391C2314yes—
382#390C2314yes—
383#390C2312yes—
384#390C2312yes—
385#390C2314yes—
386#390C2314yes—
387#390C2314yes—
388#390C2312yes—
389#390C2312yes—
390#390C2314yes—
391#390C2312yes—
392#390C2314yes—
393#390C2312yes—
394#390C2314yes—
395#390C2312yes—
396#390C2312yes—
397#390C2314yes—
398#390C2318yes—
399#390C2318yes—
400#390C2318yes—
401#390C2312yes—
402#390C2314yes—
403#390C2311yescharacteristic
404#390C2312yes—
405#390C2318yes—
406#390C2311yescharacteristic
407#390C2318yes—
408#390C2311yescharacteristic
409#390C2312yes—
410#390C2311yescharacteristic
411#390C2314yes—
412#390C2312yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2314yes—
420#388C2314yes—
421#388C2318yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#386C2314yes—
436#386C2314yes—
437#386C2318yes—
438#386C2318yes—
439#386C2318yes—
440#386C2318yes—
441#386C2318yes—
442#386C2318yes—
443#386C2318yes—
444#386C2318yes—
445#386C2318yes—
446#386C2314yes—
447#386C2314yes—
448#386C2314yes—
449#386C2314yes—
450#386C2318yes—
451#386C2318yes—
452#385C2318yes—
453#385C2318yes—
454#385C2318yes—
455#385C2318yes—
456#385C2318yes—
457#385C2318yes—
458#385C2318yes—
459#382C2318yes—
460#382C2318yes—
461#382C2314yes—
462#382C2314yes—
463#381C2314yes—
464#381C2314yes—
465#381C2312yes—
466#381C2312yes—
467#380C2314yes—
468#380C2314yes—
469#380C2312yes—
470#380C2312yes—
471#380C2312yes—
472#380C2312yes—
473#379C2314yes—
474#379C2314yes—
475#379C2314yes—
476#379C2314yes—
477#379C2314yes—
478#379C2312yes—
479#379C2312yes—
480#379C2318yes—
481#379C2318yes—
482#379C2318yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
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—
510C25C2412yes—
511C25C2411yescharacteristic
512C25C2412yes—
513C25C2414yes—
514H(5,𝔽2)—464no—
515C2×#41—24no—
516C2×#41—24no—
517C2×#41—24no—
518C2×#41—24no—
519C2×#41—24no—
520C2×#41—24no—
521C2×#41—48no—
522C2×#41—48no—
523C2×#41—48no—
524C2×#41—48no—
525C2×#41—48no—
526C2×#41—48no—
527C2×#41—44no—
528C2×#41—44no—
529C2×#41—44no—
530C2×#41—44no—
531C2×#41—44no—
532C2×#41—44no—
533C2×#41—464no—
534C22×Q8—24no—
535C22×Q8—24no—
536C22×Q8—24no—
537C22×Q8C2412yes—
538C22×Q8C2412yes—
539C22×Q8C2411yescharacteristic
540C22×Q8C2411yescharacteristic
541C22×Q8C2414yes—
542C22×Q8C2414yes—
543C22×Q8C2414yes—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—24no—
547C22×D4—24no—
548C22×D4—24no—
549C22×D4—24no—
550C22×D4—44no—
551C22×D4—44no—
552C22×D4—44no—
553C22×D4—44no—
554C22×D4—44no—
555C22×D4—44no—
556C22×D4—48no—
557C22×D4—44no—
558C22×D4—44no—
559C22×D4—44no—
560C22×D4—44no—
561C22×D4—48no—
562C22×D4—48no—
563C22×D4—48no—
564C22×D4—48no—
565C22×D4—84no—
566C22×D4—84no—
567C22×D4C2412yes—
568C22×D4C2412yes—
569C22×D4C2412yes—
570C22×D4C2412yes—
571C22×D4C2411yescharacteristic
572C22×D4C2411yescharacteristic
573C22×D4C2412yes—
574C22×D4C2412yes—
575C22×D4C2418yes—
576C22×D4C2414yes—
577C22×D4C2414yes—
578C22×D4C2414yes—
579C22×D4C2418yes—
580C22×D4C2414yes—
581C22×D4C2418yes—
582C22×D4C2418yes—
583C22×D4C2414yes—
584C22×D4C2414yes—
585C22×D4C2418yes—
586C23×C4—24no—
587C23×C4—24no—
588C23×C4—24no—
589C23×C4—44no—
590C23×C4—44no—
591C23×C4—44no—
592C23×C4C2411yescharacteristic
593C23×C4C2412yes—
594C23×C4C2412yes—
595C23×C4C2412yes—
596C23×C4C2412yes—
597C23×C4C2412yes—
598C23×C4C2412yes—
599C23×C4C2412yes—
600C23×C4C2412yes—
601C23×C4C2418yes—
602C23×C4C2414yes—
603C23×C4C2411yescharacteristic
604C4⋊Q8—44no—
605C4⋊Q8—44no—
606C4⋊Q8—44no—
607C4⋊Q8—44no—
608C4⋊Q8—44no—
609C4⋊Q8—44no—
610#127—48no—
611#127—44no—
612#127—44no—
613#127—44no—
614#127—44no—
615#125—44no—
616#125—44no—
617#125—44no—
618#125—44no—
619#124—48no—
620#124—48no—
621#124—44no—
622#124—44no—
623#124—416no—
624#124—44no—
625#124—44no—
626#124—44no—
627#124—44no—
628#124—48no—
629#124—88no—
630#124—88no—
631#124—88no—
632#124—88no—
633#123—44no—
634#123—44no—
635#123—48no—
636#123—48no—
637C22⋊Q8—48no—
638C22⋊Q8—48no—
639C22⋊Q8—48no—
640C22⋊Q8—44no—
641C22⋊Q8—44no—
642C22⋊Q8—44no—
643C22⋊Q8—48no—
644C22⋊Q8—44no—
645#121—48no—
646#121—48no—
647#121—44no—
648#121—44no—
649#121—44no—
650#121—48no—
651#121—44no—
652#120—416no—
653#120—44no—
654#120—44no—
655#120—48no—
656#120—48no—
657#120—88no—
658#120—88no—
659C4×Q8—48no—
660C4×Q8—48no—
661C4×D4—48no—
662C4×D4—48no—
663#117—24no—
664#117—24no—
665#117—24no—
666#117—24no—
667#117—24no—
668#117—24no—
669C2×C4⋊C4—24no—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2418yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C22⋊C4—44no—
695C2×C22⋊C4—44no—
696C2×C22⋊C4—48no—
697C2×C22⋊C4—84no—
698C2×C22⋊C4C2412yes—
699C2×C22⋊C4C2412yes—
700C2×C22⋊C4C2412yes—
701C2×C22⋊C4C2412yes—
702C2×C22⋊C4C2412yes—
703C2×C22⋊C4C2412yes—
704C2×C22⋊C4C2412yes—
705C2×C22⋊C4C2412yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2412yes—
714C2×C22⋊C4C2412yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2418yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2418yes—
725C2×C22⋊C4C2418yes—
726C2×C22⋊C4C2418yes—
727C2×C22⋊C4C2418yes—
728C2×C22⋊C4C2418yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2418yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2418yes—
737C2×C22⋊C4C2418yes—
738C2×C22⋊C4C2418yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2418yes—
744C2×C22⋊C4C2418yes—
745C2×C22⋊C4C2418yes—
746C2×C22⋊C4C2418yes—
747C2×C42—24no—
748C2×C42—24no—
749C2×C42C2412yes—
750C2×C42C2412yes—
751C2×C42C2412yes—
752C2×C42C2412yes—
753C2×C42C2412yes—
754C2×C42C2412yes—
755C2×C42C2412yes—
756C2×C42C2412yes—
757C2×C42C2414yes—
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762C2×C42C2414yes—
763C2×C42C2414yes—
764C2×C42C2418yes—
765C2×C42C2414yes—
766#95C2412yes—
767#95C2412yes—
768#95C2412yes—
769#95C2412yes—
770#95C2418yes—
771#95C2418yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2418yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2418yes—
790#95C2418yes—
791#95C2418yes—
792#95C2418yes—
793#95C2418yes—
794#95C2418yes—
795C24—22no—
796C24—24no—
797C24—24no—
798C24—24no—
799C24—22no—
800C24—22no—
801C24—24no—
802C24—24no—
803C24—24no—
804C24—42no—
805C24—44no—
806C24—44no—
807C24—42no—
808C24—44no—
809C24—44no—
810C24—44no—
811C24—44no—
812C24—44no—
813C24—48no—
814C24—48no—
815C24C2512yes—
816C24C2512yes—
817C24C2514yes—
818C24C2512yes—
819C24C2514yes—
820C24C2511yescharacteristic
821#41—464no—
822#41—464no—
823#41—432no—
824#41—432no—
825#41—416no—
826#41—416no—
827C2×Q8—24no—
828C2×Q8—24no—
829C2×Q8—22no—
830C2×Q8—22no—
831C2×Q8—24no—
832C2×Q8—24no—
833C2×Q8—22no—
834C2×Q8—22no—
835C2×Q8—24no—
836C2×Q8—24no—
837C2×Q8—22no—
838C2×Q8—22no—
839C2×Q8—28no—
840C2×Q8—44no—
841C2×Q8—44no—
842C2×Q8—44no—
843C2×Q8—44no—
844C2×Q8—44no—
845C2×Q8—44no—
846C2×Q8—48no—
847C2×Q8—416no—
848C2×D4—24no—
849C2×D4—24no—
850C2×D4—24no—
851C2×D4—24no—
852C2×D4—24no—
853C2×D4—24no—
854C2×D4—24no—
855C2×D4—24no—
856C2×D4—24no—
857C2×D4—24no—
858C2×D4—22no—
859C2×D4—22no—
860C2×D4—24no—
861C2×D4—24no—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—24no—
865C2×D4—24no—
866C2×D4—24no—
867C2×D4—24no—
868C2×D4—24no—
869C2×D4—24no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—216no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—48no—
880C2×D4—48no—
881C2×D4—48no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—48no—
887C2×D4—48no—
888C2×D4—48no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—48no—
892C2×D4—48no—
893C2×D4—48no—
894C2×D4—48no—
895C2×D4—48no—
896C2×D4—44no—
897C2×D4—48no—
898C2×D4—44no—
899C2×D4—48no—
900C2×D4—48no—
901C2×D4—48no—
902C2×D4—48no—
903C2×D4—432no—
904C2×D4—464no—
905C2×D4—432no—
906C2×D4—432no—
907C2×D4—416no—
908C2×D4—416no—
909C2×D4—832no—
910C2×D4—816no—
911C22×C4—24no—
912C22×C4—22no—
913C22×C4—24no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—24no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—24no—
920C22×C4—24no—
921C22×C4—24no—
922C22×C4—24no—
923C22×C4—24no—
924C22×C4—24no—
925C22×C4—24no—
926C22×C4—24no—
927C22×C4—24no—
928C22×C4—24no—
929C22×C4—24no—
930C22×C4—24no—
931C22×C4—24no—
932C22×C4—24no—
933C22×C4—48no—
934C22×C4—48no—
935C22×C4—48no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—44no—
943C22×C4—432no—
944C22×C4—416no—
945C22×C4H(5,𝔽2)14yes—
946C22×C4H(5,𝔽2)14yes—
947C22×C4H(5,𝔽2)14yes—
948C22×C4C2512yes—
949C22×C4C2512yes—
950C22×C4C2514yes—
951C22×C4C2512yes—
952C22×C4C2512yes—
953C22×C4C2512yes—
954C22×C4C2514yes—
955C22×C4C2512yes—
956C22×C4C2512yes—
957C22×C4C2514yes—
958C22×C4C2514yes—
959C22×C4C2514yes—
960C22×C4C2512yes—
961C22×C4C2512yes—
962C22×C4C2514yes—
963C22×C4C2512yes—
964C22×C4C2512yes—
965C22×C4C2511yescharacteristic
966C22×C4C2511yescharacteristic
967C4⋊C4—24no—
968C4⋊C4—24no—
969C4⋊C4—22no—
970C4⋊C4—24no—
971C4⋊C4—22no—
972C4⋊C4—24no—
973C4⋊C4—24no—
974C4⋊C4—22no—
975C4⋊C4—24no—
976C4⋊C4—22no—
977C4⋊C4—44no—
978C4⋊C4—44no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—48no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C4⋊C4—44no—
991C22⋊C4—24no—
992C22⋊C4—24no—
993C22⋊C4—24no—
994C22⋊C4—24no—
995C22⋊C4—24no—
996C22⋊C4—24no—
997C22⋊C4—24no—
998C22⋊C4—24no—
999C22⋊C4—28no—
1000C22⋊C4—28no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—48no—
1004C22⋊C4—48no—
1005C22⋊C4—48no—
1006C22⋊C4—48no—
1007C22⋊C4—48no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—48no—
1013C22⋊C4—44no—
1014C22⋊C4—48no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—48no—
1019C22⋊C4—48no—
1020C22⋊C4—48no—
1021C22⋊C4—48no—
1022C22⋊C4—44no—
1023C22⋊C4—48no—
1024C22⋊C4—44no—
1025C22⋊C4—48no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—48no—
1029C22⋊C4—48no—
1030C22⋊C4—48no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—48no—
1035C22⋊C4—48no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4—44no—
1039C22⋊C4—48no—
1040C42—24no—
1041C42—24no—
1042C42—22no—
1043C42—22no—
1044C42—22no—
1045C42—22no—
1046C42—24no—
1047C42—24no—
1048C42—24no—
1049C42—24no—
1050C42—24no—
1051C42—24no—
1052C42—28no—
1053C42—44no—
1054C42—44no—
1055C42—44no—
1056C42—48no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—24no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—24no—
1067C23—24no—
1068C23—24no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—24no—
1073C23—24no—
1074C23—22no—
1075C23—22no—
1076C23—24no—
1077C23—24no—
1078C23—28no—
1079C23—28no—
1080C23—22no—
1081C23—28no—
1082C23—24no—
1083C23—24no—
1084C23—28no—
1085C23—22no—
1086C23—44no—
1087C23—416no—
1088C23—44no—
1089C23—416no—
1090C23—48no—
1091C23—44no—
1092C23—48no—
1093C23—84no—
1094C23—84no—
1095C23—84no—
1096C23—84no—
1097C23—88no—
1098C23—84no—
1099C23—88no—
1100C23—84no—
1101C23—88no—
1102C23—164no—
1103C23—164no—
1104C23—168no—
1105C23—168no—
1106C23C2×H(5,𝔽2)12yes—
1107C23C2×H(5,𝔽2)12yes—
1108C23C2×H(5,𝔽2)12yes—
1109C23C2611yescharacteristic
1110Q8—48no—
1111Q8—48no—
1112Q8—44no—
1113Q8—44no—
1114Q8—88no—
1115Q8—88no—
1116Q8—164no—
1117D4—416no—
1118D4—416no—
1119D4—432no—
1120D4—48no—
1121D4—48no—
1122D4—48no—
1123D4—48no—
1124D4—44no—
1125D4—44no—
1126D4—48no—
1127D4—48no—
1128D4—816no—
1129D4—88no—
1130D4—88no—
1131D4—816no—
1132D4—816no—
1133D4—164no—
1134D4—164no—
1135D4—168no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—22no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—28no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—48no—
1182C2×C4—432no—
1183C2×C4—416no—
1184C2×C4—44no—
1185C2×C4—48no—
1186C2×C4—48no—
1187C2×C4—48no—
1188C2×C4—48no—
1189C2×C4—48no—
1190C2×C4—84no—
1191C2×C4—84no—
1192C2×C4H(3,𝔽4)116yes—
1193C2×C4C2×H(5,𝔽2)12yes—
1194C2×C4C2×H(5,𝔽2)12yes—
1195C2×C4C2×H(5,𝔽2)12yes—
1196C2×C4C2×H(5,𝔽2)12yes—
1197C2×C4C2×H(5,𝔽2)12yes—
1198C2×C4C2×H(5,𝔽2)12yes—
1199C2×C4#58514yes—
1200C22—22no—
1201C22—22no—
1202C22—24no—
1203C22—24no—
1204C22—42no—
1205C22—44no—
1206C22—42no—
1207C22—44no—
1208C22—42no—
1209C22—42no—
1210C22—44no—
1211C22—42no—
1212C22—44no—
1213C22—42no—
1214C22—48no—
1215C22—42no—
1216C22—48no—
1217C22—44no—
1218C22—42no—
1219C22—44no—
1220C22—44no—
1221C22—42no—
1222C22—44no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—44no—
1227C22—44no—
1228C22—48no—
1229C22—42no—
1230C22—48no—
1231C22—88no—
1232C22—816no—
1233C22—168no—
1234C22—1616no—
1235C22C2×H(3,𝔽4)14yes—
1236C22C22×H(5,𝔽2)11yescharacteristic
1237C22C22×H(5,𝔽2)11yescharacteristic
1238C22C22×H(5,𝔽2)11yescharacteristic
1239C22C2×#58512yes—
1240C22H(7,𝔽2)12yes—
1241C4—24no—
1242C4—42no—
1243C4—42no—
1244C4—44no—
1245C4—42no—
1246C4—42no—
1247C4—42no—
1248C4—44no—
1249C4—44no—
1250C4—42no—
1251C4—42no—
1252C4—42no—
1253C4—44no—
1254C4—42no—
1255C4—42no—
1256C4—44no—
1257C4—44no—
1258C4C2×H(3,𝔽4)14yes—
1259C4C2×H(3,𝔽4)14yes—
1260C2—24no—
1261C2—84no—
1262C2—82no—
1263C2—82no—
1264C2—84no—
1265C2—82no—
1266C2C22×H(3,𝔽4)11yescharacteristic
1267C2#6283611yescharacteristic
1268C2#6287611yescharacteristic
1269C2#6292412yes—
1270C2#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. #53116C2semidirect
2. #53116C2semidirect
3. #53080C2semidirect
4. #53074C2semidirect
5. #52310C2semidirect
6. #46084C2semidirect
7. #46054C2semidirect
8. #46054C2semidirect
9. #46016C2semidirect
10. #45568C2semidirect
11. #35628C2semidirect
12. #35616C2semidirect
13. #35584C2semidirect
14. #35556C2semidirect
15. #35527C2semidirect
16. #35512C2semidirect
17. #35338C2semidirect
18. #35312C2semidirect
19. #35285C2semidirect
20. #35264C2semidirect
21. #35149C2semidirect
22. #35149C2semidirect
23. #34813C2semidirect
24. #34813C2semidirect
25. C2×#2431C2semidirect
27. C23×#41C22semidirect
28. C2×#544C22semidirect
33. C2×#533C22semidirect
34. C2×#533C22semidirect
40. #2862C22semidirect
41. #2861C22semidirect
42. #2861C22semidirect
43. #2861C22semidirect
44. #2858C22semidirect
45. #2858C22semidirect
46. #2849C22semidirect
47. #2849C22semidirect
48. #2828C22semidirect
49. #2828C22semidirect
50. #2828C22semidirect
51. #2828C22semidirect
52. #2824C22semidirect
53. #2824C22semidirect
54. #2824C22semidirect
55. #2819C22semidirect
56. #2819C22semidirect
57. #2812C22semidirect
58. #2804C22semidirect
59. #2782C22semidirect
60. #2782C22semidirect
61. #2753C22semidirect
62. #2753C22semidirect
63. #2753C22semidirect
64. #2753C22semidirect
65. #2753C22semidirect
66. #2753C22semidirect
67. #2733C22semidirect
68. #2733C22semidirect
69. #2712C22semidirect
70. #2712C22semidirect
71. #2712C22semidirect
72. #2684C22semidirect
73. #2684C22semidirect
74. #2684C22semidirect
75. #2670C22semidirect
76. #2670C22semidirect
77. #2670C22semidirect
78. #2642C22semidirect
79. #2641C22semidirect
80. #2641C22semidirect
81. #2640C22semidirect
82. #2640C22semidirect
83. #2640C22semidirect
84. #2613C22semidirect
85. #2613C22semidirect
86. #2592C22semidirect
87. #2592C22semidirect
88. #2592C22semidirect
89. #2592C22semidirect
90. #2568C22semidirect
91. #2561C22semidirect
92. #2561C22semidirect
93. #2548C22semidirect
94. #2548C22semidirect
95. #2548C22semidirect
96. #2492C22semidirect
97. #2492C22semidirect
98. #2492C22semidirect
99. #2492C22semidirect
100. #2491C22semidirect
101. #2491C22semidirect
102. #2491C22semidirect
103. #2491C22semidirect
104. #2491C22semidirect
105. #2491C22semidirect
106. #2490C22semidirect
107. #2490C22semidirect
108. #2490C22semidirect
109. #2490C22semidirect
110. #2490C22semidirect
111. #2490C22semidirect
112. #2489C22semidirect
113. #2489C22semidirect
114. #2489C22semidirect
115. #2489C22semidirect
116. #2488C22semidirect
117. #2488C22semidirect
118. #2488C22semidirect
119. #2488C22semidirect
120. #2472C22semidirect
121. #2472C22semidirect
122. #2472C22semidirect
123. #2472C22semidirect
124. #2435C22semidirect
125. #2435C22semidirect
126. #2435C22semidirect
127. #2435C22semidirect
128. #2435C22semidirect
129. #2433C22semidirect
130. #2433C22semidirect
131. #2433C22semidirect
132. #2432C22semidirect
133. #2432C22semidirect
134. #2432C22semidirect
135. #2432C22semidirect
136. #2432C22semidirect
137. #2431C22semidirect
138. #2431C22semidirect
139. #2431C22semidirect
140. #2431C22semidirect
141. #2431C22semidirect
142. #2431C22semidirect
143. #2431C22semidirect
144. #2431C22semidirect
145. #2431C22semidirect
146. #2408C22semidirect
147. #2408C22semidirect
148. #2407C22semidirect
149. #2407C22semidirect
150. #2407C22semidirect
151. #2407C22semidirect
152. #2407C22semidirect
153. #2407C22semidirect
158. #2398C22semidirect
159. #2398C22semidirect
160. C2×#392C22semidirect
161. #2379C22semidirect
162. #2375C22semidirect
165. #2310C22semidirect
166. #2310C22semidirect
170. #2309C22semidirect
171. #2309C22semidirect
172. C4×#124C22semidirect
173. C4×#124C22semidirect
178. C2×#391C22semidirect
179. C2×#390C22semidirect
180. C2×#386C22semidirect
181. #2280C22semidirect
182. #2280C22semidirect
183. #2274C22semidirect
184. C4×#117C22semidirect
185. C4×#117C22semidirect
186. C2×C4×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#531162
#530802
#530742
#523102
#460842
#460542
#460162
#455682
#356282
#356162
#355842
#355562
#355272
#355122
#353382
#353122
#352852
#352642
#351492
#348132
C2×#24312