Finite Group Databasebeta

← #8108046

Subgroups — #8108046

Order 512.

5368 conjugacy classes of subgroups.

The subgroup lattice has 1065 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53126C214yesmaximal, complemented
2#53125C212yesmaximal, complemented
3#52990C214yesmaximal, complemented
4#52985C212yesmaximal, complemented
5#45247C214yesmaximal, complemented
6#45188C214yesmaximal, complemented
7#45108C214yesmaximal, complemented
8#42982C212yesmaximal, complemented
9#42950C214yesmaximal, complemented
10#42872C214yesmaximal, complemented
11#42634C214yesmaximal, complemented
12#42611C214yesmaximal, complemented
13#42519C214yesmaximal, complemented
14#42487C212yesmaximal, complemented
15#36609C212yesmaximal, complemented
16#36129C212yesmaximal, complemented
17#36122C212yesmaximal, complemented
18#36121C212yesmaximal, complemented
19#35289C212yesmaximal, complemented
20#35285C211yesmaximal, characteristic, complemented
21#35283C211yesmaximal, characteristic, complemented
22#35277C212yesmaximal, complemented
23#34551C211yesmaximal, characteristic, complemented
24C2×#548C2214yescomplemented
25C2×#546C2214yes—
26C2×#542C2214yescomplemented
27C2×#533C2211yescharacteristic
28C2×#532C2212yes—
29C22×C4⋊Q8C2212yescomplemented
30C22×#127C2211yescharacteristic
31#2868C2211yescharacteristic, complemented
32#2862C2212yescomplemented
33#2862C2211yescharacteristic, complemented
34#2858C2212yes—
35#2858C2212yes—
36#2858C2212yes—
37#2857C2212yes—
38#2857C2212yescomplemented
39#2856C2212yes—
40#2840C2214yes—
41#2832C2218yescomplemented
42#2832C2218yescomplemented
43#2830C2214yescomplemented
44#2827C2218yescomplemented
45#2824C2218yescomplemented
46#2814C2218yescomplemented
47#2804C2214yescomplemented
48#2786C2218yescomplemented
49#2784C2214yescomplemented
50#2779C2218yescomplemented
51#2751C2218yescomplemented
52#2736C2218yes—
53#2735C2214yes—
54#2712C2218yescomplemented
55#2708C2218yescomplemented
56#2702C2218yescomplemented
57#2695C2218yescomplemented
58#2692C2218yescomplemented
59#2687C2218yescomplemented
60#2686C2218yescomplemented
61#2684C2218yes—
62#2684C2218yes—
63#2671C2218yescomplemented
64#2668C2214yes—
65#2653C2218yescomplemented
66#2648C2218yescomplemented
67#2647C2212yescomplemented
68#2641C2212yes—
69#2641C2212yes—
70#2640C2214yescomplemented
71#2640C2214yescomplemented
72#2640C2214yescomplemented
73#2630C2218yescomplemented
74#2628C2212yes—
75#2626C2218yes—
76#2620C2214yescomplemented
77#2592C2214yescomplemented
78#2592C2214yescomplemented
79#2580C2214yescomplemented
80#2563C2214yescomplemented
81#2563C2214yescomplemented
82#2557C2218yescomplemented
83#2555C2214yescomplemented
84#2550C2214yescomplemented
85#2548C2214yes—
86#2548C2214yes—
87#2547C2214yescomplemented
88#2547C2214yescomplemented
89#2545C2214yescomplemented
90#2544C2214yes—
91#2534C2218yes—
92#2513C2214yescomplemented
93#2513C2214yescomplemented
94#2512C2214yescomplemented
95#2512C2214yescomplemented
96#2511C2214yescomplemented
97#2504C2214yescomplemented
98#2504C2214yescomplemented
99#2492C2214yes—
100#2492C2214yes—
101#2491C2214yescomplemented
102#2491C2214yescomplemented
103#2491C2214yescomplemented
104#2491C2214yescomplemented
105#2480C2218yes—
106#2467C2218yescomplemented
107#2452C2214yescomplemented
108#2452C2214yescomplemented
109#2452C2214yescomplemented
110#2452C2214yescomplemented
111#2451C2214yescomplemented
112#2451C2214yescomplemented
113#2448C2214yescomplemented
114#2448C2214yescomplemented
115#2447C2214yescomplemented
116#2447C2214yescomplemented
117#2446C2214yescomplemented
118#2445C2214yes—
119#2445C2214yes—
120#2442C2214yescomplemented
121#2439C2214yes—
122#2437C2214yes—
123#2436C2214yescomplemented
124#2436C2214yescomplemented
125#2436C2214yescomplemented
126#2435C2214yes—
127#2435C2214yes—
128#2435C2214yes—
129#2432C2214yescomplemented
130#2431C2214yes—
131#2429C2214yes—
132#2428C2214yes—
133#2428C2214yes—
134#2427C2218yescomplemented
135#2423C2214yes—
136#2422C2214yescomplemented
137#2422C2214yescomplemented
138#2417C2214yes—
139#2416C2214yescomplemented
140#2416C2214yescomplemented
141#2409C2214yes—
142#2408C2214yes—
143#2408C2214yes—
144#2402C2211yescharacteristic, complemented
145#2402C2212yescomplemented
146#2401C2212yes—
147#2401C2212yescomplemented
148#2401C2212yescomplemented
149#2398C2212yes—
150#2398C2211yescharacteristic, complemented
151#2396C2211yescharacteristic
152#2396C2212yescomplemented
153#2395C2212yes—
154#2395C2212yes—
155#2395C2212yescomplemented
156#2392C2212yes—
157#2392C2211yescharacteristic
158#2367C2214yescomplemented
159#2367C2214yescomplemented
160#2361C2214yescomplemented
161#2361C2214yescomplemented
162#2360C2214yescomplemented
163#2357C2214yescomplemented
164#2352C2214yes—
165Q8×C22⋊C4C2214yescomplemented
166D4×C22⋊C4C2214yes—
167D4×C22⋊C4C2214yes—
168#2331C2212yescomplemented
169#2326C2214yescomplemented
170#2314C2212yes—
171#2311C2214yescomplemented
172#2311C2214yescomplemented
173#2309C2212yes—
174#2309C2212yes—
175C4×C4⋊Q8C2212yescomplemented
176C4×C4⋊Q8C2212yescomplemented
177C4×#127C2212yes—
178C42×Q8C2211yescharacteristic, complemented
179C42×D4C2212yes—
180C42×D4C2211yescharacteristic, complemented
181C4×#117C2211yescharacteristic
182C4×#117C2212yescomplemented
183C22×#41C2314yes—
184C23×Q8C2314yes—
185C23×D4C2312yes—
186C23×D4C2314yes—
187#548—416no—
188#546—416no—
189#542—416no—
190#533—44no—
191#532—48no—
192C2×C4⋊Q8—48no—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2314yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2314yes—
198C2×C4⋊Q8C2314yes—
199C2×C4⋊Q8C2314yes—
200C2×#127—44no—
201C2×#127C2312yes—
202C2×#127C2312yes—
203C2×#127C2314yes—
204C2×#126C2318yes—
205C2×#125C2312yes—
206C2×#124C2314yes—
207C2×#124C2314yes—
208C2×#124C2314yes—
209C2×#124C2314yes—
210C2×#124C2314yes—
211C2×#124C2314yes—
212C2×#124C2314yes—
213C2×#124C2318yes—
214C2×#124C2318yes—
215C2×#123C2318yes—
216C2×#123C2318yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2318yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2318yes—
222C2×#121C2314yes—
223C2×#121C2314yes—
224C2×#121C2314yes—
225C2×#121C2314yes—
226C2×#121C2314yes—
227C2×#121C2318yes—
228C2×#121C2318yes—
229C2×#120C2318yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2314yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2318yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2312yes—
248C2×#117C2312yes—
249C2×#117C2311yescharacteristic
250C2×#117C2312yes—
251C22×C4⋊C4C2314yes—
252C22×C4⋊C4C2314yes—
253C22×C22⋊C4C2318yes—
254C22×C42C2312yes—
255C22×C42C2311yescharacteristic
256#401C2312yes—
257#400C2318yes—
258#400C2318yes—
259#400C2312yes—
260#400C2312yes—
261#400C2312yes—
262#400C2314yes—
263#400C2312yes—
264#400C2312yes—
265#400C2312yes—
266#400C2311yescharacteristic
267#400C2312yes—
268#399C2318yes—
269#399C2314yes—
270#399C2311yescharacteristic
271#399C2312yes—
272#398C2318yes—
273#398C2318yes—
274#398C2311yescharacteristic
275#398C2318yes—
276#398C2312yes—
277#398C2312yes—
278#398C2312yes—
279#398C2312yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#397C2311yescharacteristic
290#397C2312yes—
291#397C2312yes—
292#397C2312yes—
293#397C2312yes—
294#397C2312yes—
295#397C2312yes—
296#397C2312yes—
297#397C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2318yes—
301#396C2312yes—
302#396C2318yes—
303#396C2318yes—
304#396C2312yes—
305#396C2312yes—
306#395C2314yes—
307#395C2318yes—
308#395C2311yescharacteristic
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2318yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2312yes—
322#394C2312yes—
323#394C2312yes—
324#394C2311yescharacteristic
325#394C2312yes—
326#393C2318yes—
327#393C2318yes—
328#393C2318yes—
329#393C2318yes—
330#393C2312yes—
331#393C2318yes—
332#393C2318yes—
333#393C2318yes—
334#393C2318yes—
335#393C2318yes—
336#393C2311yescharacteristic
337#393C2318yes—
338#393C2314yes—
339#392C2318yes—
340#392C2311yescharacteristic
341#392C2318yes—
342#391C2314yes—
343#391C2314yes—
344#391C2314yes—
345#391C2314yes—
346#391C2314yes—
347#391C2314yes—
348#391C2318yes—
349#391C2318yes—
350#391C2314yes—
351#391C2314yes—
352#391C2314yes—
353#391C2318yes—
354#391C2314yes—
355#390C2314yes—
356#390C2314yes—
357#390C2314yes—
358#390C2314yes—
359#390C2314yes—
360#390C2314yes—
361#390C2314yes—
362#390C2314yes—
363#390C2314yes—
364#390C2314yes—
365#390C2314yes—
366#390C2318yes—
367#390C2314yes—
368#390C2314yes—
369#390C2314yes—
370#390C2314yes—
371#390C2314yes—
372#390C2314yes—
373#390C2314yes—
374#390C2314yes—
375#390C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#386C2318yes—
402#386C2318yes—
403#386C2318yes—
404#386C2318yes—
405#386C2318yes—
406#386C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2318yes—
410#386C2318yes—
411#386C2318yes—
412#385C2318yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#384C2312yes—
420#384C2312yes—
421#384C2314yes—
422#382C2312yes—
423#382C2312yes—
424#382C2314yes—
425#382C2314yes—
426#381C2318yes—
427#380C2318yes—
428#380C2318yes—
429#380C2318yes—
430#380C2318yes—
431#380C2314yes—
432#380C2314yes—
433#380C2314yes—
434#380C2318yes—
435#380C2314yes—
436#379C2314yes—
437#379C2314yes—
438#379C2318yes—
439#379C2318yes—
440#379C2318yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2312yes—
461C4×C22⋊C4C2312yes—
462C4×C22⋊C4C2312yes—
463C4×C22⋊C4C2312yes—
464C4×C22⋊C4C2318yes—
465C4×C22⋊C4C2318yes—
466C4×C22⋊C4C2312yes—
467C4×C22⋊C4C2312yes—
468C4×C22⋊C4C2312yes—
469C4×C22⋊C4C2312yes—
470C4×C22⋊C4C2312yes—
471C4×C22⋊C4C2312yes—
472C4×C22⋊C4C2312yes—
473C4×C22⋊C4C2312yes—
474C4×C22⋊C4C2312yes—
475C4×C22⋊C4C2312yes—
476C4×C22⋊C4C2312yes—
477C4×C22⋊C4C2312yes—
478#376C2312yes—
479#376C2311yescharacteristic
480#376C2312yes—
481#376C2311yescharacteristic
482C43C2312yes—
483C43C2311yescharacteristic
484C43C2311yescharacteristic
485C25C2414yes—
486C2×#41—216no—
487C2×#41—48no—
488C2×#41—48no—
489C22×Q8—48no—
490C22×Q8—48no—
491C22×Q8—48no—
492C22×Q8C2414yes—
493C22×Q8C2414yes—
494C22×Q8C2411yescharacteristic
495C22×Q8C2414yes—
496C22×Q8C2418yes—
497C22×D4—28no—
498C22×D4—44no—
499C22×D4—48no—
500C22×D4—48no—
501C22×D4—44no—
502C22×D4—48no—
503C22×D4C2414yes—
504C22×D4C2414yes—
505C22×D4C2414yes—
506C22×D4C2412yes—
507C22×D4C2411yescharacteristic
508C22×D4C2418yes—
509C22×D4C2418yes—
510C22×D4C2414yes—
511C22×D4C2418yes—
512C23×C4C2412yes—
513C23×C4C2412yes—
514C23×C4C2412yes—
515C23×C4C2412yes—
516C23×C4C2411yescharacteristic
517C23×C4C2418yes—
518C23×C4C2418yes—
519C23×C4C2418yes—
520C4⋊Q8—28no—
521C4⋊Q8—28no—
522C4⋊Q8—48no—
523C4⋊Q8—48no—
524C4⋊Q8—44no—
525C4⋊Q8—48no—
526C4⋊Q8—48no—
527#127—28no—
528#127—48no—
529#127—44no—
530#126—416no—
531#125—44no—
532#124—48no—
533#124—48no—
534#124—48no—
535#124—48no—
536#124—48no—
537#124—48no—
538#124—48no—
539#124—416no—
540#124—416no—
541#123—416no—
542#123—416no—
543C22⋊Q8—216no—
544C22⋊Q8—416no—
545C22⋊Q8—416no—
546C22⋊Q8—48no—
547C22⋊Q8—48no—
548#121—216no—
549#121—416no—
550#121—416no—
551#121—48no—
552#121—48no—
553#121—48no—
554#121—48no—
555#120—416no—
556C4×Q8—42no—
557C4×Q8—44no—
558C4×Q8—48no—
559C4×Q8—48no—
560C4×Q8—48no—
561C4×D4—28no—
562C4×D4—28no—
563C4×D4—28no—
564C4×D4—48no—
565C4×D4—48no—
566C4×D4—48no—
567C4×D4—48no—
568C4×D4—48no—
569C4×D4—42no—
570C4×D4—44no—
571C4×D4—416no—
572#117—28no—
573#117—24no—
574#117—44no—
575#117—42no—
576#117—44no—
577C2×C4⋊C4—48no—
578C2×C4⋊C4—48no—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2414yes—
612C2×C22⋊C4—416no—
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2412yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2412yes—
619C2×C22⋊C4C2412yes—
620C2×C22⋊C4C2412yes—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2411yescharacteristic
628C2×C22⋊C4C2411yescharacteristic
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2412yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C42—24no—
653C2×C42—28no—
654C2×C42C2412yes—
655C2×C42C2411yescharacteristic
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2412yes—
665C2×C42C2412yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2411yescharacteristic
673C2×C42C2414yes—
674C2×C42C2418yes—
675C2×C42C2418yes—
676C2×C42C2411yescharacteristic
677#95C2412yes—
678#95C2412yes—
679#95C2412yes—
680#95C2412yes—
681#95C2412yes—
682#95C2412yes—
683#95C2412yes—
684#95C2412yes—
685#95C2412yes—
686#95C2412yes—
687#95C2412yes—
688#95C2412yes—
689#95C2412yes—
690#95C2411yescharacteristic
691#95C2412yes—
692#95C2412yes—
693#95C2412yes—
694#95C2412yes—
695#95C2412yes—
696#95C2412yes—
697#95C2412yes—
698#95C2411yescharacteristic
699#95C2412yes—
700#95C2418yes—
701#95C2418yes—
702#95C2418yes—
703#95C2412yes—
704#95C2411yescharacteristic
705#95C2411yescharacteristic
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2414yes—
711#95C2418yes—
712#95C2414yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718C24—28no—
719C24—44no—
720C24—48no—
721C24—48no—
722C24—44no—
723C24C2518yes—
724C24C2512yes—
725C24C2511yescharacteristic
726#41—832no—
727C2×Q8—28no—
728C2×Q8—28no—
729C2×Q8—28no—
730C2×Q8—28no—
731C2×Q8—28no—
732C2×Q8—28no—
733C2×Q8—42no—
734C2×Q8—41no—
735C2×Q8—48no—
736C2×Q8—48no—
737C2×Q8—48no—
738C2×Q8—48no—
739C2×Q8—44no—
740C2×Q8—832no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—24no—
744C2×D4—216no—
745C2×D4—216no—
746C2×D4—28no—
747C2×D4—28no—
748C2×D4—28no—
749C2×D4—28no—
750C2×D4—28no—
751C2×D4—28no—
752C2×D4—28no—
753C2×D4—28no—
754C2×D4—28no—
755C2×D4—28no—
756C2×D4—42no—
757C2×D4—41no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—44no—
763C2×D4—48no—
764C2×D4—44no—
765C2×D4—48no—
766C2×D4—48no—
767C2×D4—816no—
768C2×D4—832no—
769C22×C4—24no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—216no—
783C22×C4—48no—
784C22×C4—48no—
785C22×C4—48no—
786C22×C4—48no—
787C22×C4—48no—
788C22×C4—48no—
789C22×C4—48no—
790C22×C4—48no—
791C22×C4H(5,𝔽2)18yes—
792C22×C42−1+414yes—
793C22×C4C2512yes—
794C22×C4C2511yescharacteristic
795C22×C4C2512yes—
796C22×C4C2512yes—
797C22×C4C2512yes—
798C22×C4C2512yes—
799C22×C4C2518yes—
800C22×C4C2512yes—
801C22×C4C2512yes—
802C22×C4C2512yes—
803C22×C4C2511yescharacteristic
804C22×C4C2511yescharacteristic
805C22×C4C2512yes—
806C22×C4C2518yes—
807C22×C4C2518yes—
808C22×C4C2511yescharacteristic
809C22×C4C2512yes—
810C22×C4C2511yescharacteristic
811C22×C4C2512yes—
812C22×C4C2511yescharacteristic
813C4⋊C4—28no—
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—28no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—28no—
822C4⋊C4—28no—
823C4⋊C4—216no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—28no—
827C4⋊C4—48no—
828C4⋊C4—48no—
829C4⋊C4—42no—
830C4⋊C4—42no—
831C4⋊C4—41no—
832C4⋊C4—41no—
833C4⋊C4—41no—
834C4⋊C4—42no—
835C4⋊C4—42no—
836C4⋊C4—42no—
837C4⋊C4—42no—
838C4⋊C4—42no—
839C4⋊C4—41no—
840C4⋊C4—48no—
841C4⋊C4—48no—
842C4⋊C4—48no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C4⋊C4—44no—
846C22⋊C4—24no—
847C22⋊C4—24no—
848C22⋊C4—24no—
849C22⋊C4—24no—
850C22⋊C4—216no—
851C22⋊C4—24no—
852C22⋊C4—24no—
853C22⋊C4—24no—
854C22⋊C4—216no—
855C22⋊C4—24no—
856C22⋊C4—24no—
857C22⋊C4—48no—
858C22⋊C4—48no—
859C22⋊C4—42no—
860C22⋊C4—42no—
861C22⋊C4—41no—
862C22⋊C4—41no—
863C22⋊C4—44no—
864C22⋊C4—48no—
865C22⋊C4—42no—
866C22⋊C4—42no—
867C22⋊C4—42no—
868C22⋊C4—48no—
869C22⋊C4—48no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—48no—
881C22⋊C4—48no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C42—24no—
886C42—24no—
887C42—24no—
888C42—24no—
889C42—22no—
890C42—24no—
891C42—24no—
892C42—24no—
893C42—24no—
894C42—22no—
895C42—22no—
896C42—24no—
897C42—24no—
898C42—22no—
899C42—24no—
900C42—22no—
901C42—24no—
902C42—24no—
903C42—24no—
904C42—44no—
905C42—48no—
906C42—48no—
907C42H(5,𝔽2)14yes—
908C23—22no—
909C23—22no—
910C23—21no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—21no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—28no—
919C23—28no—
920C23—28no—
921C23—28no—
922C23—28no—
923C23—28no—
924C23—28no—
925C23—88no—
926C23—816no—
927C23—816no—
928C23—164no—
929C23—164no—
930C23C2×H(5,𝔽2)14yes—
931C23C2×2−1+412yes—
932C23C2611yescharacteristic
933Q8—44no—
934Q8—416no—
935Q8—416no—
936Q8—816no—
937Q8—164no—
938D4—44no—
939D4—48no—
940D4—416no—
941D4—416no—
942D4—416no—
943D4—88no—
944D4—816no—
945D4—816no—
946D4—816no—
947C2×C4—21no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—21no—
951C2×C4—216no—
952C2×C4—28no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—28no—
965C2×C4—28no—
966C2×C4—28no—
967C2×C4—28no—
968C2×C4—28no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—28no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—22no—
989C2×C4—21no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—28no—
993C2×C4—28no—
994C2×C4—28no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—48no—
998C2×C4—48no—
999C2×C4—48no—
1000C2×C4—816no—
1001C2×C4—816no—
1002C2×C4—168no—
1003C2×C4C2×H(5,𝔽2)14yes—
1004C2×C4C2×H(5,𝔽2)14yes—
1005C2×C4C2×H(5,𝔽2)14yes—
1006C2×C4C2×H(5,𝔽2)12yes—
1007C2×C4C2×2−1+412yes—
1008C2×C4C2×2−1+412yes—
1009C2×C4#58514yes—
1010C2×C4#58512yes—
1011C22—24no—
1012C22—22no—
1013C22—24no—
1014C22—24no—
1015C22—24no—
1016C22—42no—
1017C22—42no—
1018C22—42no—
1019C22—41no—
1020C22—42no—
1021C22—42no—
1022C22—41no—
1023C22—48no—
1024C22—48no—
1025C22—48no—
1026C22—48no—
1027C22—48no—
1028C22—48no—
1029C22—48no—
1030C22—1616no—
1031C22C22×H(5,𝔽2)11yescharacteristic
1032C22C22×H(5,𝔽2)12yes—
1033C22C22×2−1+411yescharacteristic
1034C22C2×#58512yes—
1035C22C2×#58511yescharacteristic
1036C4—24no—
1037C4—22no—
1038C4—42no—
1039C4—42no—
1040C4—48no—
1041C4—48no—
1042C4—42no—
1043C4—42no—
1044C4—48no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—42no—
1049C4—42no—
1050C4—42no—
1051C4—41no—
1052C4—41no—
1053C4—42no—
1054C4#355818yes—
1055C4#356114yes—
1056C2—44no—
1057C2—42no—
1058C2—88no—
1059C2C2×#355812yes—
1060C2C2×#356111yescharacteristic
1061C2#6283411yescharacteristic
1062C2#6283512yes—
1063C2#6283911yescharacteristic
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. #53126C2semidirect
2. #53125C2semidirect
3. #52990C2semidirect
4. #52985C2semidirect
5. #45247C2semidirect
6. #45188C2semidirect
7. #45108C2semidirect
8. #42982C2semidirect
9. #42950C2semidirect
10. #42872C2semidirect
11. #42634C2semidirect
12. #42611C2semidirect
13. #42519C2semidirect
14. #42487C2semidirect
15. #36609C2semidirect
16. #36129C2semidirect
17. #36122C2semidirect
18. #36121C2semidirect
19. #35289C2semidirect
20. #35285C2semidirect
21. #35283C2semidirect
22. #35277C2semidirect
23. #34551C2semidirect
24. C2×#548C22semidirect
26. C2×#542C22semidirect
29. C22×C4⋊Q8C22semidirect
31. #2868C22semidirect
32. #2862C22semidirect
33. #2862C22semidirect
38. #2857C22semidirect
41. #2832C22semidirect
42. #2832C22semidirect
43. #2830C22semidirect
44. #2827C22semidirect
45. #2824C22semidirect
46. #2814C22semidirect
47. #2804C22semidirect
48. #2786C22semidirect
49. #2784C22semidirect
50. #2779C22semidirect
51. #2751C22semidirect
54. #2712C22semidirect
55. #2708C22semidirect
56. #2702C22semidirect
57. #2695C22semidirect
58. #2692C22semidirect
59. #2687C22semidirect
60. #2686C22semidirect
63. #2671C22semidirect
65. #2653C22semidirect
66. #2648C22semidirect
67. #2647C22semidirect
70. #2640C22semidirect
71. #2640C22semidirect
72. #2640C22semidirect
73. #2630C22semidirect
76. #2620C22semidirect
77. #2592C22semidirect
78. #2592C22semidirect
79. #2580C22semidirect
80. #2563C22semidirect
81. #2563C22semidirect
82. #2557C22semidirect
83. #2555C22semidirect
84. #2550C22semidirect
87. #2547C22semidirect
88. #2547C22semidirect
89. #2545C22semidirect
92. #2513C22semidirect
93. #2513C22semidirect
94. #2512C22semidirect
95. #2512C22semidirect
96. #2511C22semidirect
97. #2504C22semidirect
98. #2504C22semidirect
101. #2491C22semidirect
102. #2491C22semidirect
103. #2491C22semidirect
104. #2491C22semidirect
106. #2467C22semidirect
107. #2452C22semidirect
108. #2452C22semidirect
109. #2452C22semidirect
110. #2452C22semidirect
111. #2451C22semidirect
112. #2451C22semidirect
113. #2448C22semidirect
114. #2448C22semidirect
115. #2447C22semidirect
116. #2447C22semidirect
117. #2446C22semidirect
120. #2442C22semidirect
123. #2436C22semidirect
124. #2436C22semidirect
125. #2436C22semidirect
129. #2432C22semidirect
134. #2427C22semidirect
136. #2422C22semidirect
137. #2422C22semidirect
139. #2416C22semidirect
140. #2416C22semidirect
144. #2402C22semidirect
145. #2402C22semidirect
147. #2401C22semidirect
148. #2401C22semidirect
150. #2398C22semidirect
152. #2396C22semidirect
155. #2395C22semidirect
158. #2367C22semidirect
159. #2367C22semidirect
160. #2361C22semidirect
161. #2361C22semidirect
162. #2360C22semidirect
163. #2357C22semidirect
165. Q8×C22⋊C4C22semidirect
168. #2331C22semidirect
169. #2326C22semidirect
171. #2311C22semidirect
172. #2311C22semidirect
175. C4×C4⋊Q8C22semidirect
176. C4×C4⋊Q8C22semidirect
178. C42×Q8C22semidirect
180. C42×D4C22semidirect
182. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#531262
#531252
#529902
#529852
#452472
#451882
#451082
#429822
#429502
#428722
#426342
#426112
#425192
#424872
#366092
#361292
#361222
#361212
#352892
#352852
#352832
#352772
#345512