Finite Group Databasebeta

← #8095540

Subgroups — #8095540

Order 512.

5998 conjugacy classes of subgroups.

The subgroup lattice has 1037 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53144C214yesmaximal, complemented
2#53116C214yesmaximal, complemented
3#53074C214yesmaximal, complemented
4#52990C214yesmaximal, complemented
5#52530C214yesmaximal, complemented
6#52395C214yesmaximal, complemented
7#46073C214yesmaximal, complemented
8#46054C214yesmaximal, complemented
9#46043C214yesmaximal, complemented
10#46031C218yesmaximal, complemented
11#46016C214yesmaximal, complemented
12#35676C211yesmaximal, characteristic, complemented
13#35660C212yesmaximal, complemented
14#35616C211yesmaximal, characteristic, complemented
15#35513C212yesmaximal, complemented
16#35312C212yesmaximal, complemented
17#35264C212yesmaximal, complemented
18#35158C212yesmaximal, complemented
19#34955C212yesmaximal, complemented
20C2×#2592C211yesmaximal, characteristic, complemented
21C22×2−1+4C2211yescharacteristic, complemented
22C22×H(5,𝔽2)C2211yescharacteristic
23C2×#544C2212yescomplemented
24C2×#537C2212yes—
25C2×#536C2212yes—
26C2×#535C2212yes—
27C2×#532C2212yes—
28C22×#124C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic, complemented
30#2862C2214yescomplemented
31#2861C2214yescomplemented
32#2861C2214yescomplemented
33#2858C2214yescomplemented
34#2850C2218yescomplemented
35#2840C2214yescomplemented
36#2835C2214yescomplemented
37#2832C2218yescomplemented
38#2832C2218yescomplemented
39#2832C2218yescomplemented
40#2828C2218yescomplemented
41#2828C2218yescomplemented
42#2824C2218yescomplemented
43#2824C2214yescomplemented
44#2824C2218yescomplemented
45#2819C2218yescomplemented
46#2812C2214yescomplemented
47#2804C2218yescomplemented
48#2785C2218yescomplemented
49#2782C2218yescomplemented
50#2782C2218yescomplemented
51#2763C2218yescomplemented
52#2763C2214yescomplemented
53#2753C2218yescomplemented
54#2753C2218yescomplemented
55#2753C2218yescomplemented
56#2753C2218yescomplemented
57#2753C2218yescomplemented
58#2736C2214yescomplemented
59#2736C2218yescomplemented
60#2733C2218yescomplemented
61#2712C2214yescomplemented
62#2712C2218yescomplemented
63#2712C2218yescomplemented
64#2684C2218yescomplemented
65#2684C2218yescomplemented
66#2684C2218yescomplemented
67#2670C2218yescomplemented
68#2670C2214yescomplemented
69#2642C2214yescomplemented
70#2641C2214yescomplemented
71#2640C2214yescomplemented
72#2640C2214yescomplemented
73#2639C2218yescomplemented
74#2592C2212yescomplemented
75#2592C2214yescomplemented
76#2592C2214yescomplemented
77#2592C2214yescomplemented
78#2592C2214yescomplemented
79#2592C2212yescomplemented
80#2592C2212yescomplemented
81#2592C2212yescomplemented
82#2591C2214yescomplemented
83#2591C2214yescomplemented
84#2568C2212yescomplemented
85#2568C2212yescomplemented
86#2548C2212yescomplemented
87#2548C2212yescomplemented
88#2504C2214yescomplemented
89#2492C2214yescomplemented
90#2492C2214yescomplemented
91#2492C2214yescomplemented
92#2492C2214yescomplemented
93#2491C2214yescomplemented
94#2491C2214yescomplemented
95#2491C2214yescomplemented
96#2491C2214yescomplemented
97#2490C2214yescomplemented
98#2490C2214yescomplemented
99#2490C2214yescomplemented
100#2490C2214yescomplemented
101#2489C2214yescomplemented
102#2489C2214yescomplemented
103#2489C2214yescomplemented
104#2489C2214yescomplemented
105#2488C2218yescomplemented
106#2488C2218yescomplemented
107#2472C2218yescomplemented
108#2472C2218yescomplemented
109#2436C2214yescomplemented
110#2436C2214yescomplemented
111#2436C2214yescomplemented
112#2436C2214yescomplemented
113#2435C2214yes—
114#2435C2214yes—
115#2435C2214yes—
116#2434C2214yescomplemented
117#2433C2214yes—
118#2432C2214yes—
119#2432C2214yes—
120#2432C2214yes—
121#2432C2214yescomplemented
122#2431C2214yes—
123#2431C2214yescomplemented
124#2431C2214yescomplemented
125#2431C2214yescomplemented
126#2430C2218yescomplemented
127#2430C2218yescomplemented
128#2410C2218yes—
129#2410C2218yes—
130#2409C2214yescomplemented
131#2409C2214yescomplemented
132#2408C2214yes—
133#2408C2214yes—
134#2407C2214yes—
135#2407C2214yes—
136#2407C2214yescomplemented
137#2407C2214yescomplemented
138#2405C2214yes—
139#2405C2214yes—
140#2404C2214yescomplemented
141#2404C2214yescomplemented
142#2398C2214yescomplemented
143#2398C2214yescomplemented
144C2×#397C2212yescomplemented
145C2×#393C2212yescomplemented
146#2379C2218yescomplemented
147#2375C2218yescomplemented
148#2311C2212yes—
149#2311C2212yescomplemented
150#2310C2211yescharacteristic, complemented
151#2309C2211yescharacteristic
152C4×#124C2214yescomplemented
153C4×#124C2214yescomplemented
154#2297C2212yes—
155#2297C2212yes—
156#2297C2212yescomplemented
157#2297C2212yescomplemented
158C2×#391C2212yescomplemented
159C2×#390C2212yes—
160C2×#388C2214yescomplemented
161C4×#117C2212yescomplemented
162C2×C4×C4⋊C4C2211yescharacteristic, complemented
163C2×2−1+4—44no—
164C2×2−1+4—48no—
165C2×H(5,𝔽2)—44no—
166C2×H(5,𝔽2)—48no—
167C22×#41C2312yes—
168C22×#41C2312yes—
169C22×#41C2314yes—
170C22×#41C2314yes—
171C22×#41C2314yes—
172C23×Q8C2311yescharacteristic
173C23×Q8C2314yes—
174C23×Q8C2311yescharacteristic
175C23×D4C2311yescharacteristic
176C23×D4C2314yes—
177C23×D4C2314yes—
178#544—48no—
179#537—48no—
180#536—48no—
181#535—48no—
182#532—48no—
183C2×C4⋊Q8C2312yes—
184C2×C4⋊Q8C2314yes—
185C2×C4⋊Q8C2314yes—
186C2×C4⋊Q8C2314yes—
187C2×#127C2314yes—
188C2×#127C2312yes—
189C2×#125C2314yes—
190C2×#125C2314yes—
191C2×#124—44no—
192C2×#124C2314yes—
193C2×#124C2318yes—
194C2×#124C2314yes—
195C2×#124C2314yes—
196C2×#124C2312yes—
197C2×#124C2312yes—
198C2×#124C2314yes—
199C2×#124C2314yes—
200C2×#124C2314yes—
201C2×#124C2318yes—
202C2×#124C2318yes—
203C2×#123C2318yes—
204C2×C22⋊Q8C2318yes—
205C2×C22⋊Q8C2314yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2314yes—
208C2×C22⋊Q8C2314yes—
209C2×#121C2314yes—
210C2×#121C2318yes—
211C2×#121C2314yes—
212C2×#121C2314yes—
213C2×#121C2314yes—
214C2×#121C2314yes—
215C2×#121C2314yes—
216C2×#120C2318yes—
217C2×#120C2318yes—
218C2×#120C2318yes—
219C2×C4×Q8—44no—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×D4C2314yes—
225C2×C4×D4C2314yes—
226C2×#117C2312yes—
227C2×#117C2312yes—
228C22×C4⋊C4C2312yes—
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2314yes—
233C22×C22⋊C4C2312yes—
234C22×C22⋊C4C2314yes—
235C22×C42C2311yescharacteristic
236C22×C42C2312yes—
237C22×C42C2312yes—
238#400C2314yes—
239#400C2314yes—
240#400C2314yes—
241#400C2314yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#397C2314yes—
249#397C2318yes—
250#397C2318yes—
251#397C2318yes—
252#397C2318yes—
253#397C2314yes—
254#397C2318yes—
255#397C2314yes—
256#397C2318yes—
257#397C2318yes—
258#397C2314yes—
259#397C2314yes—
260#397C2314yes—
261#395C2318yes—
262#395C2318yes—
263#394C2318yes—
264#394C2318yes—
265#394C2318yes—
266#394C2318yes—
267#394C2314yes—
268#394C2318yes—
269#394C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2314yes—
275#394C2314yes—
276#394C2318yes—
277#394C2318yes—
278#394C2318yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#394C2314yes—
283#393C2314yes—
284#393C2318yes—
285#393C2318yes—
286#393C2318yes—
287#393C2314yes—
288#393C2314yes—
289#393C2314yes—
290#393C2318yes—
291#393C2318yes—
292#393C2314yes—
293#393C2314yes—
294#393C2318yes—
295#393C2314yes—
296#393C2318yes—
297#393C2318yes—
298#393C2318yes—
299#393C2318yes—
300#393C2314yes—
301#392C2314yes—
302#392C2318yes—
303#392C2318yes—
304#392C2318yes—
305#392C2314yes—
306#392C2318yes—
307#392C2318yes—
308#392C2318yes—
309#392C2318yes—
310#391C2314yes—
311#391C2314yes—
312#391C2314yes—
313#391C2314yes—
314#391C2314yes—
315#391C2312yes—
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2312yes—
322#391C2312yes—
323#391C2314yes—
324#391C2318yes—
325#391C2318yes—
326#391C2314yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2318yes—
331#390C2314yes—
332#390C2314yes—
333#390C2314yes—
334#390C2314yes—
335#390C2318yes—
336#390C2318yes—
337#390C2314yes—
338#390C2314yes—
339#390C2314yes—
340#390C2314yes—
341#390C2312yes—
342#390C2312yes—
343#390C2312yes—
344#390C2312yes—
345#390C2312yes—
346#390C2312yes—
347#390C2312yes—
348#390C2312yes—
349#390C2318yes—
350#390C2314yes—
351#390C2314yes—
352#388C2314yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2314yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2314yes—
362#388C2314yes—
363#388C2314yes—
364#388C2314yes—
365#388C2314yes—
366#388C2314yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#386C2318yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2318yes—
381#386C2318yes—
382#386C2318yes—
383#386C2314yes—
384#386C2314yes—
385#386C2314yes—
386#386C2314yes—
387#386C2314yes—
388#386C2314yes—
389#386C2314yes—
390#386C2314yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#385C2314yes—
397#385C2318yes—
398#385C2318yes—
399#385C2314yes—
400#385C2318yes—
401#385C2318yes—
402#385C2318yes—
403#385C2318yes—
404#385C2318yes—
405#382C2318yes—
406#382C2314yes—
407#382C2314yes—
408#382C2318yes—
409#382C2318yes—
410#381C2314yes—
411#380C2314yes—
412#380C2314yes—
413#380C2314yes—
414#380C2314yes—
415#379C2314yes—
416#379C2314yes—
417#379C2318yes—
418#379C2318yes—
419#379C2318yes—
420#379C2314yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2312yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437#376C2314yes—
438C2×#95C2312yes—
439C2×#95C2314yes—
440C2×#95C2314yes—
441C43C2314yes—
442C25C2412yes—
443C25C2414yes—
4442−1+4—464no—
445H(5,𝔽2)—464no—
446C2×#41—28no—
447C2×#41—28no—
448C2×#41—28no—
449C2×#41—28no—
450C2×#41—28no—
451C2×#41—28no—
452C2×#41—48no—
453C2×#41—416no—
454C2×#41—48no—
455C2×#41—48no—
456C2×#41—48no—
457C2×#41—48no—
458C2×#41—48no—
459C2×#41—48no—
460C22×Q8—24no—
461C22×Q8—28no—
462C22×Q8—42no—
463C22×Q8—44no—
464C22×Q8—48no—
465C22×Q8—48no—
466C22×Q8—48no—
467C22×Q8C2414yes—
468C22×Q8C2412yes—
469C22×Q8C2412yes—
470C22×Q8C2411yescharacteristic
471C22×Q8C2412yes—
472C22×Q8C2411yescharacteristic
473C22×Q8C2418yes—
474C22×Q8C2414yes—
475C22×D4—24no—
476C22×D4—28no—
477C22×D4—48no—
478C22×D4—48no—
479C22×D4—48no—
480C22×D4—48no—
481C22×D4—416no—
482C22×D4C2414yes—
483C22×D4C2414yes—
484C22×D4C2414yes—
485C22×D4C2412yes—
486C22×D4C2412yes—
487C22×D4C2414yes—
488C22×D4C2414yes—
489C22×D4C2418yes—
490C22×D4C2418yes—
491C22×D4C2418yes—
492C22×D4C2418yes—
493C22×D4C2414yes—
494C23×C4C2412yes—
495C23×C4C2414yes—
496C23×C4C2414yes—
497C23×C4C2412yes—
498C23×C4C2412yes—
499C23×C4C2411yescharacteristic
500C23×C4C2414yes—
501C23×C4C2411yescharacteristic
502C23×C4C2414yes—
503C23×C4C2418yes—
504C23×C4C2411yescharacteristic
505C4⋊Q8—48no—
506C4⋊Q8—48no—
507C4⋊Q8—44no—
508C4⋊Q8—48no—
509#127—44no—
510#127—48no—
511#125—48no—
512#125—48no—
513#124—416no—
514#124—48no—
515#124—48no—
516#124—48no—
517#124—44no—
518#124—44no—
519#124—48no—
520#124—48no—
521#124—48no—
522#124—88no—
523#124—88no—
524#123—416no—
525C22⋊Q8—416no—
526C22⋊Q8—48no—
527C22⋊Q8—48no—
528C22⋊Q8—48no—
529C22⋊Q8—48no—
530#121—48no—
531#121—48no—
532#121—48no—
533#121—48no—
534#121—48no—
535#121—48no—
536#121—416no—
537#120—416no—
538#120—416no—
539#120—88no—
540C4×Q8—44no—
541C4×Q8—44no—
542C4×Q8—44no—
543C4×Q8—44no—
544C4×D4—48no—
545C4×D4—48no—
546#117—28no—
547#117—28no—
548C2×C4⋊C4—28no—
549C2×C4⋊C4—44no—
550C2×C4⋊C4—42no—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2411yescharacteristic
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2411yescharacteristic
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2418yes—
572C2×C22⋊C4—48no—
573C2×C22⋊C4—44no—
574C2×C22⋊C4—44no—
575C2×C22⋊C4—84no—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C42—24no—
619C2×C42—28no—
620C2×C42—82no—
621C2×C42C2414yes—
622C2×C42C2414yes—
623C2×C42C2412yes—
624C2×C42C2412yes—
625C2×C42C2412yes—
626C2×C42C2412yes—
627C2×C42C2412yes—
628C2×C42C2412yes—
629C2×C42C2414yes—
630C2×C42C2414yes—
631C2×C42C2414yes—
632C2×C42C2418yes—
633C2×C42C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2414yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2414yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2418yes—
661#95C2418yes—
662#95C2418yes—
663#95C2418yes—
664#95C2414yes—
665#95C2418yes—
666#95C2414yes—
667C24—24no—
668C24—28no—
669C24—48no—
670C24—44no—
671C24—44no—
672C24—42no—
673C24—42no—
674C24—48no—
675C24—44no—
676C24—44no—
677C24C2514yes—
678C24C2514yes—
679C24C2514yes—
680C24C2511yescharacteristic
681#41—464no—
682#41—464no—
683#41—464no—
684#41—432no—
685#41—432no—
686C2×Q8—28no—
687C2×Q8—24no—
688C2×Q8—24no—
689C2×Q8—28no—
690C2×Q8—24no—
691C2×Q8—28no—
692C2×Q8—24no—
693C2×Q8—24no—
694C2×Q8—24no—
695C2×Q8—24no—
696C2×Q8—24no—
697C2×Q8—41no—
698C2×Q8—42no—
699C2×Q8—41no—
700C2×Q8—48no—
701C2×Q8—44no—
702C2×Q8—42no—
703C2×Q8—42no—
704C2×Q8—48no—
705C2×Q8—48no—
706C2×Q8—48no—
707C2×Q8—416no—
708C2×Q8—464no—
709C2×Q8—416no—
710C2×D4—28no—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—28no—
716C2×D4—28no—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—28no—
720C2×D4—24no—
721C2×D4—28no—
722C2×D4—24no—
723C2×D4—24no—
724C2×D4—24no—
725C2×D4—28no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—44no—
730C2×D4—48no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—464no—
746C2×D4—464no—
747C2×D4—416no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—28no—
753C22×C4—24no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—28no—
758C22×C4—28no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—24no—
762C22×C4—41no—
763C22×C4—41no—
764C22×C4—44no—
765C22×C4—48no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—48no—
769C22×C4—48no—
770C22×C4—48no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4H(5,𝔽2)14yes—
776C22×C4H(5,𝔽2)18yes—
777C22×C4C2514yes—
778C22×C4C2514yes—
779C22×C4C2512yes—
780C22×C4C2511yescharacteristic
781C22×C4C2511yescharacteristic
782C22×C4C2512yes—
783C22×C4C2514yes—
784C22×C4C2514yes—
785C22×C4C2514yes—
786C22×C4C2518yes—
787C22×C4C2512yes—
788C22×C4C2512yes—
789C22×C4C2514yes—
790C22×C4C2514yes—
791C22×C4C2512yes—
792C22×C4C2512yes—
793C4⋊C4—28no—
794C4⋊C4—28no—
795C4⋊C4—24no—
796C4⋊C4—24no—
797C4⋊C4—24no—
798C4⋊C4—24no—
799C4⋊C4—42no—
800C4⋊C4—42no—
801C4⋊C4—42no—
802C4⋊C4—41no—
803C4⋊C4—42no—
804C4⋊C4—42no—
805C4⋊C4—41no—
806C4⋊C4—44no—
807C4⋊C4—44no—
808C4⋊C4—48no—
809C4⋊C4—48no—
810C4⋊C4—48no—
811C4⋊C4—48no—
812C4⋊C4—48no—
813C4⋊C4—48no—
814C22⋊C4—28no—
815C22⋊C4—28no—
816C22⋊C4—216no—
817C22⋊C4—28no—
818C22⋊C4—28no—
819C22⋊C4—48no—
820C22⋊C4—48no—
821C22⋊C4—44no—
822C22⋊C4—44no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4—44no—
826C22⋊C4—44no—
827C22⋊C4—44no—
828C22⋊C4—44no—
829C22⋊C4—44no—
830C22⋊C4—44no—
831C22⋊C4—44no—
832C22⋊C4—44no—
833C22⋊C4—44no—
834C22⋊C4—48no—
835C22⋊C4—48no—
836C22⋊C4—48no—
837C22⋊C4—44no—
838C22⋊C4—48no—
839C22⋊C4—48no—
840C22⋊C4—48no—
841C22⋊C4—48no—
842C22⋊C4—48no—
843C22⋊C4—48no—
844C22⋊C4—48no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—44no—
854C22⋊C4—48no—
855C22⋊C4—44no—
856C42—24no—
857C42—24no—
858C42—24no—
859C42—24no—
860C42—24no—
861C42—24no—
862C42—28no—
863C42—28no—
864C42—28no—
865C42—48no—
866C42—44no—
867C42—44no—
868C42—44no—
869C23—22no—
870C23—21no—
871C23—21no—
872C23—24no—
873C23—24no—
874C23—24no—
875C23—24no—
876C23—24no—
877C23—24no—
878C23—28no—
879C23—24no—
880C23—24no—
881C23—28no—
882C23—24no—
883C23—24no—
884C23—24no—
885C23—24no—
886C23—24no—
887C23—24no—
888C23—24no—
889C23—24no—
890C23—24no—
891C23—416no—
892C23—48no—
893C23—84no—
894C23—84no—
895C23—88no—
896C23—88no—
897C23—164no—
898C23—164no—
899C23—168no—
900C23—168no—
901C23C2×H(5,𝔽2)14yes—
902C23C2×H(5,𝔽2)12yes—
903C23C2611yescharacteristic
904Q8—44no—
905Q8—48no—
906Q8—44no—
907Q8—416no—
908Q8—416no—
909Q8—48no—
910Q8—48no—
911Q8—168no—
912D4—432no—
913D4—416no—
914D4—416no—
915D4—416no—
916D4—416no—
917D4—48no—
918D4—48no—
919D4—88no—
920D4—88no—
921D4—168no—
922D4—168no—
923D4—168no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—22no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—28no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—28no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—28no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—28no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—48no—
966C2×C4—44no—
967C2×C4—44no—
968C2×C4—416no—
969C2×C4—432no—
970C2×C4—48no—
971C2×C4—416no—
972C2×C4—416no—
973C2×C4—84no—
974C2×C4—88no—
975C2×C4H(3,𝔽4)116yes—
976C2×C4C2×H(5,𝔽2)14yes—
977C2×C4C2×H(5,𝔽2)14yes—
978C2×C4C2×H(5,𝔽2)14yes—
979C2×C4#58514yes—
980C22—22no—
981C22—22no—
982C22—24no—
983C22—24no—
984C22—44no—
985C22—44no—
986C22—44no—
987C22—44no—
988C22—44no—
989C22—44no—
990C22—44no—
991C22—48no—
992C22—44no—
993C22—44no—
994C22—44no—
995C22—44no—
996C22—44no—
997C22—44no—
998C22—44no—
999C22—44no—
1000C22—44no—
1001C22—48no—
1002C22—44no—
1003C22—168no—
1004C22—1616no—
1005C22C2×H(3,𝔽4)14yes—
1006C22C22×H(5,𝔽2)11yescharacteristic
1007C22C22×H(5,𝔽2)12yes—
1008C22C2×#58512yes—
1009C22H(7,𝔽2)11yescharacteristic
1010C222−1+611yescharacteristic
1011C4—24no—
1012C4—42no—
1013C4—41no—
1014C4—41no—
1015C4—42no—
1016C4—42no—
1017C4—42no—
1018C4—44no—
1019C4—44no—
1020C4—44no—
1021C4—44no—
1022C4—44no—
1023C4—48no—
1024C4—44no—
1025C4—44no—
1026C4C2×H(3,𝔽4)18yes—
1027C2—24no—
1028C2—84no—
1029C2—84no—
1030C2—84no—
1031C2C22×H(3,𝔽4)11yescharacteristic
1032C2#6282111yescharacteristic
1033C2#6287511yescharacteristic
1034C2#6293112yes—
1035C2#6296112yes—
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. #53116C2semidirect
3. #53074C2semidirect
4. #52990C2semidirect
5. #52530C2semidirect
6. #52395C2semidirect
7. #46073C2semidirect
8. #46054C2semidirect
9. #46043C2semidirect
10. #46031C2semidirect
11. #46016C2semidirect
12. #35676C2semidirect
13. #35660C2semidirect
14. #35616C2semidirect
15. #35513C2semidirect
16. #35312C2semidirect
17. #35264C2semidirect
18. #35158C2semidirect
19. #34955C2semidirect
20. C2×#2592C2semidirect
21. C22×2−1+4C22semidirect
23. C2×#544C22semidirect
29. C22×C4×Q8C22semidirect
30. #2862C22semidirect
31. #2861C22semidirect
32. #2861C22semidirect
33. #2858C22semidirect
34. #2850C22semidirect
35. #2840C22semidirect
36. #2835C22semidirect
37. #2832C22semidirect
38. #2832C22semidirect
39. #2832C22semidirect
40. #2828C22semidirect
41. #2828C22semidirect
42. #2824C22semidirect
43. #2824C22semidirect
44. #2824C22semidirect
45. #2819C22semidirect
46. #2812C22semidirect
47. #2804C22semidirect
48. #2785C22semidirect
49. #2782C22semidirect
50. #2782C22semidirect
51. #2763C22semidirect
52. #2763C22semidirect
53. #2753C22semidirect
54. #2753C22semidirect
55. #2753C22semidirect
56. #2753C22semidirect
57. #2753C22semidirect
58. #2736C22semidirect
59. #2736C22semidirect
60. #2733C22semidirect
61. #2712C22semidirect
62. #2712C22semidirect
63. #2712C22semidirect
64. #2684C22semidirect
65. #2684C22semidirect
66. #2684C22semidirect
67. #2670C22semidirect
68. #2670C22semidirect
69. #2642C22semidirect
70. #2641C22semidirect
71. #2640C22semidirect
72. #2640C22semidirect
73. #2639C22semidirect
74. #2592C22semidirect
75. #2592C22semidirect
76. #2592C22semidirect
77. #2592C22semidirect
78. #2592C22semidirect
79. #2592C22semidirect
80. #2592C22semidirect
81. #2592C22semidirect
82. #2591C22semidirect
83. #2591C22semidirect
84. #2568C22semidirect
85. #2568C22semidirect
86. #2548C22semidirect
87. #2548C22semidirect
88. #2504C22semidirect
89. #2492C22semidirect
90. #2492C22semidirect
91. #2492C22semidirect
92. #2492C22semidirect
93. #2491C22semidirect
94. #2491C22semidirect
95. #2491C22semidirect
96. #2491C22semidirect
97. #2490C22semidirect
98. #2490C22semidirect
99. #2490C22semidirect
100. #2490C22semidirect
101. #2489C22semidirect
102. #2489C22semidirect
103. #2489C22semidirect
104. #2489C22semidirect
105. #2488C22semidirect
106. #2488C22semidirect
107. #2472C22semidirect
108. #2472C22semidirect
109. #2436C22semidirect
110. #2436C22semidirect
111. #2436C22semidirect
112. #2436C22semidirect
116. #2434C22semidirect
121. #2432C22semidirect
123. #2431C22semidirect
124. #2431C22semidirect
125. #2431C22semidirect
126. #2430C22semidirect
127. #2430C22semidirect
130. #2409C22semidirect
131. #2409C22semidirect
136. #2407C22semidirect
137. #2407C22semidirect
140. #2404C22semidirect
141. #2404C22semidirect
142. #2398C22semidirect
143. #2398C22semidirect
144. C2×#397C22semidirect
145. C2×#393C22semidirect
146. #2379C22semidirect
147. #2375C22semidirect
149. #2311C22semidirect
150. #2310C22semidirect
152. C4×#124C22semidirect
153. C4×#124C22semidirect
156. #2297C22semidirect
157. #2297C22semidirect
158. C2×#391C22semidirect
160. C2×#388C22semidirect
161. C4×#117C22semidirect
162. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#531442
#531162
#530742
#529902
#525302
#523952
#460732
#460542
#460432
#460312
#460162
#356762
#356602
#356162
#355132
#353122
#352642
#351582
#349552
C2×#25922