Finite Group Databasebeta

← #7657915

Subgroups — #7657915

Order 512.

8290 conjugacy classes of subgroups.

The subgroup lattice has 1067 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3524C211yesmaximal, characteristic, complemented
2C2×D4×#41C211yesmaximal, characteristic, complemented
3#42683C213yesmaximal, complemented
4#42679C213yesmaximal, complemented
5#42484C213yesmaximal, complemented
6#42480C213yesmaximal, complemented
7#42443C216yesmaximal, complemented
8#42438C216yesmaximal, complemented
9#39887C216yesmaximal, complemented
10#39886C216yesmaximal, complemented
11#37616C213yesmaximal, complemented
12#37544C213yesmaximal, complemented
13#36429C212yesmaximal, complemented
14#36428C212yesmaximal, complemented
15#36066C211yesmaximal, characteristic, complemented
16#36049C211yesmaximal, characteristic, complemented
17#35927C211yesmaximal, characteristic, complemented
18#35910C211yesmaximal, characteristic, complemented
19#35831C212yesmaximal, complemented
20#35771C212yesmaximal, complemented
21#35236C213yesmaximal, complemented
22#34593C213yesmaximal, complemented
23#34193C211yesmaximal, characteristic, complemented
24C23×#41C2212yes—
25#3524—216no—
26C2×#559C2213yescomplemented
27C2×#557C2211yescharacteristic, complemented
28C2×#555C2213yescomplemented
29C2×#553C2213yescomplemented
30C2×#552C2213yescomplemented
31D4×#41—216no—
32C2×#550C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#550C2212yescomplemented
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2212yescomplemented
37C2×#548C2211yescharacteristic
38C2×#548C2212yes—
39C2×#548C2211yescharacteristic, complemented
40C2×#548C2212yescomplemented
41C2×#548C2212yescomplemented
42C2×#547C2213yes—
43C2×#546C2216yes—
44C2×D42C2213yes—
45C2×#542C2213yescomplemented
46C2×#540C2213yescomplemented
47C2×#532C2213yes—
48C2×#529C2213yescomplemented
49C2×#529C2213yescomplemented
50C2×#525C2216yes—
51C2×#520C2211yescharacteristic, complemented
52C2×#519C2211yescharacteristic, complemented
53C2×C4×#41C2211yescharacteristic
54C22×C4×D4C2213yes—
55#2848C2216yescomplemented
56#2847C2216yescomplemented
57#2813C22112yescomplemented
58#2813C2216yescomplemented
59#2813C2216yescomplemented
60#2718C22112yescomplemented
61#2710C22112yescomplemented
62#2706C22112yescomplemented
63#2703C22112yescomplemented
64#2685C22112yescomplemented
65#2678C22112yescomplemented
66#2670C22112yescomplemented
67#2669C22112yescomplemented
68#2658C2213yescomplemented
69#2657C2213yescomplemented
70#2642C2213yescomplemented
71#2641C2213yescomplemented
72#2636C2211yescharacteristic
73#2636C2213yes—
74#2636C2213yescomplemented
75#2636C2213yescomplemented
76#2636C2216yescomplemented
77#2635C2216yescomplemented
78#2635C2216yescomplemented
79#2633C2216yescomplemented
80#2631C2216yescomplemented
81#2626C2216yescomplemented
82#2623C2213yescomplemented
83#2623C2213yescomplemented
84#2620C2216yescomplemented
85#2620C2216yescomplemented
86#2620C2216yescomplemented
87#2619C2216yescomplemented
88#2617C2216yescomplemented
89#2613C2213yes—
90#2613C2213yes—
91#2598C22112yescomplemented
92#2568C2213yescomplemented
93#2566C2216yescomplemented
94#2562C2213yes—
95#2562C2213yescomplemented
96#2548C2213yescomplemented
97#2545C2216yescomplemented
98#2544C2216yescomplemented
99#2544C2216yescomplemented
100#2542C2213yescomplemented
101#2542C2216yescomplemented
102#2541C2216yescomplemented
103#2541C2213yescomplemented
104#2540C2213yes—
105#2540C2216yescomplemented
106#2540C2213yescomplemented
107#2540C2216yescomplemented
108#2538C2216yescomplemented
109#2537C2216yescomplemented
110#2492C2216yescomplemented
111#2491C2216yescomplemented
112#2490C2216yescomplemented
113#2489C2216yescomplemented
114#2487C2216yescomplemented
115#2435C2216yescomplemented
116#2433C2216yescomplemented
117#2432C2216yescomplemented
118#2432C2216yescomplemented
119#2431C2216yescomplemented
120#2431C2216yescomplemented
121#2429C2216yescomplemented
122#2428C2216yescomplemented
123#2427C2216yescomplemented
124#2426C2216yescomplemented
125#2417C2216yescomplemented
126#2416C2216yescomplemented
127#2415C2216yescomplemented
128#2414C2216yescomplemented
129#2411C22112yescomplemented
130#2408C2216yes—
131#2408C2216yescomplemented
132#2408C2216yescomplemented
133#2407C2216yescomplemented
134#2407C2216yescomplemented
135#2407C2216yescomplemented
136#2407C2216yescomplemented
137#2398C2213yes—
138#2398C2213yescomplemented
139#2397C2213yes—
140#2397C2213yescomplemented
141#2392C2216yescomplemented
142#2392C2216yescomplemented
143#2354C2216yescomplemented
144Q8×C4⋊C4C2212yescomplemented
145#2347C2216yescomplemented
146#2341C2212yes—
147#2341C2212yescomplemented
148#2341C2212yescomplemented
149Q8×C22⋊C4C2212yescomplemented
150Q8×C22⋊C4C2212yescomplemented
151#2324C22112yescomplemented
152#2319C2213yescomplemented
153#2319C2213yescomplemented
154C4×#120C2216yescomplemented
155C4×#120C2216yescomplemented
156#2285C2213yescomplemented
157#2283C2213yescomplemented
158#2276C2211yescharacteristic, complemented
159#2276C2211yescharacteristic, complemented
160C22×#41—216no—
161C22×#41—48no—
162C22×#41—48no—
163C22×#41C2312yes—
164C22×#41C2311yescharacteristic
165C22×#41C2311yescharacteristic
166C22×#41C2316yes—
167C22×#41C2316yes—
168C23×Q8C2312yes—
169C23×Q8C2311yescharacteristic
170C23×D4C2316yes—
171C23×D4C2313yes—
172C24×C4C2316yes—
173#559—224no—
174#557—28no—
175#555—224no—
176#553—224no—
177#552—224no—
178#550—28no—
179#550—28no—
180#550—48no—
181D4×Q8—28no—
182D4×Q8—48no—
183#548—28no—
184#548—216no—
185#548—28no—
186#548—48no—
187#548—48no—
188#547—224no—
189#546—248no—
190D42—224no—
191#542—224no—
192#540—224no—
193#532—224no—
194C2×C4⋊Q8C2313yes—
195C2×C4⋊Q8C2313yes—
196C2×C4⋊Q8C2316yes—
197C2×#127C2313yes—
198C2×#127C2313yes—
199C2×#127C2316yes—
200C2×#127C2316yes—
201#529—224no—
202#529—224no—
203C2×#126C2311yescharacteristic
204C2×#126C2313yes—
205C2×#126C2316yes—
206C2×#125C2313yes—
207C2×#125C2313yes—
208C2×#125C2313yes—
209C2×#124C2316yes—
210C2×#124C2313yes—
211C2×#124C2313yes—
212C2×#124C2316yes—
213C2×#124C2313yes—
214C2×#124C2316yes—
215C2×#124C2316yes—
216C2×#124C2316yes—
217#525—248no—
218C2×#123C2313yes—
219C2×#123C2313yes—
220C2×#123C2316yes—
221C2×#123C23112yes—
222C2×#123C2316yes—
223C2×C22⋊Q8C2313yes—
224C2×C22⋊Q8C2313yes—
225C2×C22⋊Q8C2316yes—
226C2×C22⋊Q8C2316yes—
227C2×C22⋊Q8C2313yes—
228C2×C22⋊Q8C2316yes—
229C2×C22⋊Q8C2316yes—
230C2×C22⋊Q8C2316yes—
231C2×C22⋊Q8C2316yes—
232C2×#121C2313yes—
233C2×#121C2313yes—
234C2×#121C2316yes—
235C2×#121C2316yes—
236C2×#121C2313yes—
237C2×#121C2313yes—
238C2×#121C2316yes—
239C2×#121C2316yes—
240C2×#121C2316yes—
241C2×#121C2313yes—
242C2×#121C23112yes—
243C2×#121C2316yes—
244C2×#121C2316yes—
245C2×#121C2316yes—
246C2×#121C2316yes—
247C2×#120C23112yes—
248C2×#120C2316yes—
249C2×#120C2316yes—
250C2×#120C23112yes—
251#520—28no—
252#519—28no—
253C4×#41D4116yescomplemented
254C2×C4×Q8C2313yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2313yes—
260C2×C4×Q8C2313yes—
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2311yescharacteristic
263C2×C4×D4—224no—
264C2×C4×D4C2313yes—
265C2×C4×D4C2313yes—
266C2×C4×D4C2316yes—
267C2×C4×D4C2316yes—
268C2×C4×D4C2316yes—
269C2×C4×D4C2311yescharacteristic
270C2×C4×D4C2313yes—
271C2×C4×D4C2316yes—
272C2×C4×D4C2313yes—
273C2×C4×D4C2313yes—
274C2×C4×D4C2313yes—
275C2×C4×D4C2313yes—
276C2×C4×D4C2313yes—
277C2×C4×D4C2316yes—
278C2×C4×D4C2316yes—
279C2×C4×D4C2316yes—
280C2×C4×D4C2316yes—
281C2×C4×D4C2313yes—
282C2×C4×D4C2313yes—
283C2×#117C2316yes—
284C2×#117C2313yes—
285C2×#117C2313yes—
286C2×#117C2313yes—
287C2×#117C2316yes—
288C2×#117C2313yes—
289C22×C4⋊C4C2313yes—
290C22×C4⋊C4C2313yes—
291C22×C22⋊C4C2316yes—
292C22×C42C2313yes—
293#400C2316yes—
294#400C2313yes—
295#400C2313yes—
296#400C23112yes—
297#400C2311yescharacteristic
298#400C2313yes—
299#399C23112yes—
300#399C2311yescharacteristic
301#399C2313yes—
302#399C2313yes—
303#399C2313yes—
304#399C2316yes—
305#399C2316yes—
306#399C2316yes—
307#398C2316yes—
308#398C2316yes—
309#397C2316yes—
310#397C2316yes—
311#397C2316yes—
312#397C2316yes—
313#396C23112yes—
314#396C23112yes—
315#396C2316yes—
316#396C23112yes—
317#396C2312yes—
318#396C2316yes—
319#396C2316yes—
320#394C2313yes—
321#394C2316yes—
322#394C23112yes—
323#394C2311yescharacteristic
324#394C2316yes—
325#394C2316yes—
326#394C2313yes—
327#394C2313yes—
328#394C2312yes—
329#394C2316yes—
330#394C2316yes—
331#394C2316yes—
332#394C23112yes—
333#394C23112yes—
334#394C23112yes—
335#394C23112yes—
336#394C23112yes—
337#394C23112yes—
338#394C23112yes—
339#393C2316yes—
340#393C2316yes—
341#392C23112yes—
342#392C2311yescharacteristic
343#392C2316yes—
344#392C2316yes—
345#392C2313yes—
346#392C2313yes—
347#392C2313yes—
348#392C2316yes—
349#392C2316yes—
350#392C23112yes—
351#392C23112yes—
352#392C2316yes—
353#392C23112yes—
354#392C23112yes—
355#391C2316yes—
356#391C2316yes—
357#391C2316yes—
358#391C2316yes—
359#391C2316yes—
360#390C2316yes—
361#390C2316yes—
362#390C2316yes—
363#390C2316yes—
364#390C23112yes—
365#390C23112yes—
366#390C23112yes—
367#390C2316yes—
368#390C2316yes—
369#390C2316yes—
370#390C2316yes—
371#390C2316yes—
372#389C2316yes—
373#389C2316yes—
374#389C23112yes—
375#388C23112yes—
376#388C23112yes—
377#388C23112yes—
378#388C23112yes—
379#388C23112yes—
380#388C23112yes—
381#386C2316yes—
382#386C23112yes—
383#386C23112yes—
384#386C2316yes—
385#386C23112yes—
386#386C23112yes—
387#386C2316yes—
388#386C2316yes—
389#386C2312yes—
390#386C2316yes—
391#385C2316yes—
392#385C23112yes—
393#385C2316yes—
394#385C23112yes—
395#385C2316yes—
396#385C2316yes—
397#385C2316yes—
398#385C2312yes—
399#384C2316yes—
400#384C2316yes—
401#383C2316yes—
402#382C2316yes—
403#382C2311yescharacteristic
404#382C2313yes—
405#381C2313yes—
406#381C2313yes—
407#380C2316yes—
408#380C2316yes—
409#380C2316yes—
410#380C2316yes—
411#380C2316yes—
412#380C23112yes—
413#380C2316yes—
414#380C2316yes—
415#379C23112yes—
416#379C2316yes—
417#379C2316yes—
418C4×C4⋊C4C2313yes—
419C4×C4⋊C4C2313yes—
420C4×C4⋊C4C2316yes—
421C4×C4⋊C4C2316yes—
422C4×C4⋊C4C2316yes—
423C4×C4⋊C4C2316yes—
424C4×C22⋊C4C2316yes—
425C4×C22⋊C4C2316yes—
426C4×C22⋊C4C2316yes—
427C4×C22⋊C4C2316yes—
428C4×C22⋊C4C2316yes—
429#376C2313yes—
430#376C2313yes—
431C25C2416yes—
432C2×#41—24no—
433C2×#41—28no—
434C2×#41—28no—
435C2×#41—28no—
436C2×#41—28no—
437C2×#41—28no—
438C2×#41—224no—
439C2×#41—224no—
440C2×#41—412no—
441C2×#41—412no—
442C2×#41—412no—
443C2×#41—412no—
444C2×#41—4128no—
445C2×#41C2×D418yes—
446C22×Q8—24no—
447C22×Q8—28no—
448C22×Q8—28no—
449C22×Q8—28no—
450C22×Q8—28no—
451C22×Q8C2413yes—
452C22×Q8C2416yes—
453C22×Q8C2413yes—
454C22×Q8C2411yescharacteristic
455C22×D4—224no—
456C22×D4—212no—
457C22×D4—412no—
458C22×D4—412no—
459C22×D4—412no—
460C22×D4C2411yescharacteristic
461C22×D4C2413yes—
462C22×D4C2416yes—
463C22×D4C2416yes—
464C22×D4C2413yes—
465C22×D4C2412yes—
466C22×D4C2413yes—
467C22×D4C2416yes—
468C22×D4C2413yes—
469C22×D4C2416yes—
470C22×D4C2416yes—
471C22×D4C2413yes—
472C22×D4C2413yes—
473C22×D4C24112yes—
474C22×D4C2416yes—
475C22×D4C2416yes—
476C22×D4C24112yes—
477C23×C4—224no—
478C23×C4—412no—
479C23×C4—412no—
480C23×C4C2413yes—
481C23×C4C2413yes—
482C23×C4C2416yes—
483C23×C4C2416yes—
484C23×C4C2413yes—
485C23×C4C2416yes—
486C23×C4C2416yes—
487C23×C4C2412yes—
488C23×C4C2416yes—
489C23×C4C2413yes—
490C23×C4C2413yes—
491C4⋊Q8—212no—
492C4⋊Q8—212no—
493C4⋊Q8—412no—
494#127—212no—
495#127—212no—
496#127—412no—
497#127—86no—
498#126—224no—
499#126—24no—
500#126—212no—
501#125—212no—
502#125—212no—
503#125—212no—
504#124—212no—
505#124—224no—
506#124—212no—
507#124—212no—
508#124—224no—
509#124—412no—
510#124—412no—
511#124—86no—
512#123—224no—
513#123—212no—
514#123—212no—
515#123—248no—
516#123—224no—
517C22⋊Q8—212no—
518C22⋊Q8—212no—
519C22⋊Q8—224no—
520C22⋊Q8—224no—
521C22⋊Q8—212no—
522C22⋊Q8—412no—
523C22⋊Q8—412no—
524C22⋊Q8—412no—
525C22⋊Q8—412no—
526#121—212no—
527#121—212no—
528#121—212no—
529#121—212no—
530#121—224no—
531#121—224no—
532#121—224no—
533#121—224no—
534#121—212no—
535#121—224no—
536#121—424no—
537#121—412no—
538#121—412no—
539#121—412no—
540#121—412no—
541#120—248no—
542#120—412no—
543#120—412no—
544#120—812no—
545C4×Q8—24no—
546C4×Q8—24no—
547C4×Q8—28no—
548C4×Q8—28no—
549C4×Q8—212no—
550C4×Q8—212no—
551C4×Q8—212no—
552C4×Q8C2×D418yes—
553C4×Q8C2×D418yes—
554C4×D4—212no—
555C4×D4—212no—
556C4×D4—224no—
557C4×D4—212no—
558C4×D4—24no—
559C4×D4—224no—
560C4×D4—212no—
561C4×D4—212no—
562C4×D4—224no—
563C4×D4—212no—
564C4×D4—212no—
565C4×D4—224no—
566C4×D4—212no—
567C4×D4—412no—
568C4×D4—412no—
569C4×D4—412no—
570C4×D4—412no—
571C4×D4C2×D4124yes—
572C4×D4C2×D4124yes—
573#117—212no—
574#117—212no—
575#117—212no—
576#117—224no—
577#117—86no—
578#117C2×D4124yes—
579C2×C4⋊C4—212no—
580C2×C4⋊C4—212no—
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2413yes—
583C2×C4⋊C4C2413yes—
584C2×C4⋊C4C2416yes—
585C2×C4⋊C4C2413yes—
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2413yes—
588C2×C4⋊C4C2413yes—
589C2×C4⋊C4C2413yes—
590C2×C4⋊C4C2413yes—
591C2×C4⋊C4C2416yes—
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2413yes—
594C2×C4⋊C4C2416yes—
595C2×C4⋊C4C2413yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2416yes—
598C2×C4⋊C4C2416yes—
599C2×C4⋊C4C2413yes—
600C2×C4⋊C4C2416yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2416yes—
603C2×C4⋊C4C2416yes—
604C2×C4⋊C4C2416yes—
605C2×C4⋊C4C24112yes—
606C2×C4⋊C4C24112yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2413yes—
609C2×C4⋊C4C2413yes—
610C2×C22⋊C4—224no—
611C2×C22⋊C4C2412yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2411yescharacteristic
616C2×C22⋊C4C2413yes—
617C2×C22⋊C4C2413yes—
618C2×C22⋊C4C2413yes—
619C2×C22⋊C4C2413yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2411yescharacteristic
622C2×C22⋊C4C2413yes—
623C2×C22⋊C4C2411yescharacteristic
624C2×C22⋊C4C24112yes—
625C2×C22⋊C4C2413yes—
626C2×C22⋊C4C2416yes—
627C2×C22⋊C4C2413yes—
628C2×C22⋊C4C2412yes—
629C2×C22⋊C4C2416yes—
630C2×C22⋊C4C24112yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2416yes—
634C2×C22⋊C4C2416yes—
635C2×C22⋊C4C2416yes—
636C2×C22⋊C4C2416yes—
637C2×C22⋊C4C2416yes—
638C2×C22⋊C4C2416yes—
639C2×C22⋊C4C2416yes—
640C2×C22⋊C4C24112yes—
641C2×C22⋊C4C2416yes—
642C2×C22⋊C4C2416yes—
643C2×C22⋊C4C2416yes—
644C2×C22⋊C4C2416yes—
645C2×C22⋊C4C24112yes—
646C2×C22⋊C4C24112yes—
647C2×C22⋊C4C24112yes—
648C2×C22⋊C4C2416yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2416yes—
651C2×C22⋊C4C2416yes—
652C2×C42C2×D4124yes—
653C2×C42C2416yes—
654C2×C42C2413yes—
655C2×C42C2413yes—
656C2×C42C2416yes—
657C2×C42C2416yes—
658C2×C42C2416yes—
659C2×C42C2416yes—
660C2×C42C2413yes—
661C2×C42C2413yes—
662C2×C42C2413yes—
663C2×C42C2411yescharacteristic
664#95C2411yescharacteristic
665#95C2411yescharacteristic
666#95C2413yes—
667#95C2413yes—
668#95C2416yes—
669#95C2416yes—
670#95C2412yes—
671#95C2412yes—
672#95C2412yes—
673#95C2416yes—
674#95C2416yes—
675#95C2416yes—
676#95C2416yes—
677#95C2416yes—
678#95C2416yes—
679#95C2416yes—
680#95C2416yes—
681#95C2416yes—
682#95C24112yes—
683#95C24112yes—
684C24—212no—
685C24—212no—
686C24—46no—
687C24—46no—
688C24—46no—
689C24—46no—
690C24—46no—
691C24C2516yes—
692C24C2511yescharacteristic
693C24C2513yes—
694C24C2513yes—
695C24C2512yes—
696#41—232no—
697#41—496no—
698#41—496no—
699#41—416no—
700#41—432no—
701C2×Q8—26no—
702C2×Q8—212no—
703C2×Q8—26no—
704C2×Q8—212no—
705C2×Q8—212no—
706C2×Q8—212no—
707C2×Q8—43no—
708C2×Q8—43no—
709C2×Q8—416no—
710C2×Q8—432no—
711C2×Q8C22×D414yes—
712C2×Q8H(5,𝔽2)18yes—
713C2×D4—24no—
714C2×D4—224no—
715C2×D4—24no—
716C2×D4—212no—
717C2×D4—26no—
718C2×D4—212no—
719C2×D4—26no—
720C2×D4—212no—
721C2×D4—22no—
722C2×D4—212no—
723C2×D4—26no—
724C2×D4—26no—
725C2×D4—212no—
726C2×D4—212no—
727C2×D4—26no—
728C2×D4—212no—
729C2×D4—212no—
730C2×D4—212no—
731C2×D4—212no—
732C2×D4—42no—
733C2×D4—46no—
734C2×D4—46no—
735C2×D4—412no—
736C2×D4—412no—
737C2×D4—42no—
738C2×D4—46no—
739C2×D4—46no—
740C2×D4—46no—
741C2×D4—46no—
742C2×D4—46no—
743C2×D4—46no—
744C2×D4—46no—
745C2×D4—46no—
746C2×D4—46no—
747C2×D4—46no—
748C2×D4—43no—
749C2×D4—46no—
750C2×D4—46no—
751C2×D4—43no—
752C2×D4—46no—
753C2×D4—46no—
754C2×D4—412no—
755C2×D4—412no—
756C2×D4—412no—
757C2×D4—448no—
758C2×D4—496no—
759C2×D4C22×D4112yes—
760C22×C4—212no—
761C22×C4—212no—
762C22×C4—26no—
763C22×C4—26no—
764C22×C4—24no—
765C22×C4—212no—
766C22×C4—212no—
767C22×C4—212no—
768C22×C4—212no—
769C22×C4—212no—
770C22×C4—212no—
771C22×C4—212no—
772C22×C4—212no—
773C22×C4—212no—
774C22×C4—212no—
775C22×C4—43no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—46no—
779C22×C4—46no—
780C22×C4—46no—
781C22×C4—46no—
782C22×C4—43no—
783C22×C4—46no—
784C22×C4—412no—
785C22×C4—496no—
786C22×C4C22×D4112yes—
787C22×C4C22×D4112yes—
788C22×C4C22×D4112yes—
789C22×C4C2512yes—
790C22×C4C2512yes—
791C22×C4C2516yes—
792C22×C4C2511yescharacteristic
793C22×C4C2513yes—
794C22×C4C2511yescharacteristic
795C22×C4C2513yes—
796C22×C4C2512yes—
797C22×C4C2516yes—
798C22×C4C2516yes—
799C22×C4C2513yes—
800C22×C4C2511yescharacteristic
801C22×C4C2511yescharacteristic
802C22×C4C2511yescharacteristic
803C22×C4C2513yes—
804C22×C4C2513yes—
805C22×C4C2511yescharacteristic
806C22×C4C2513yes—
807C4⋊C4—22no—
808C4⋊C4—26no—
809C4⋊C4—26no—
810C4⋊C4—212no—
811C4⋊C4—26no—
812C4⋊C4—22no—
813C4⋊C4—26no—
814C4⋊C4—26no—
815C4⋊C4—26no—
816C4⋊C4—26no—
817C4⋊C4—212no—
818C4⋊C4—22no—
819C4⋊C4—26no—
820C4⋊C4—212no—
821C4⋊C4—26no—
822C4⋊C4—22no—
823C4⋊C4—26no—
824C4⋊C4—212no—
825C4⋊C4—212no—
826C4⋊C4—42no—
827C4⋊C4—46no—
828C4⋊C4—42no—
829C4⋊C4—46no—
830C4⋊C4—46no—
831C4⋊C4—46no—
832C4⋊C4—412no—
833C4⋊C4—412no—
834C4⋊C4C22×D4112yes—
835C4⋊C4C22×D4112yes—
836C22⋊C4—26no—
837C22⋊C4—212no—
838C22⋊C4—26no—
839C22⋊C4—24no—
840C22⋊C4—212no—
841C22⋊C4—24no—
842C22⋊C4—212no—
843C22⋊C4—212no—
844C22⋊C4—212no—
845C22⋊C4—22no—
846C22⋊C4—26no—
847C22⋊C4—26no—
848C22⋊C4—26no—
849C22⋊C4—26no—
850C22⋊C4—212no—
851C22⋊C4—22no—
852C22⋊C4—26no—
853C22⋊C4—22no—
854C22⋊C4—224no—
855C22⋊C4—46no—
856C22⋊C4—42no—
857C22⋊C4—412no—
858C22⋊C4—42no—
859C22⋊C4—42no—
860C22⋊C4—46no—
861C22⋊C4—46no—
862C22⋊C4—46no—
863C22⋊C4—46no—
864C22⋊C4—46no—
865C22⋊C4—46no—
866C22⋊C4—46no—
867C22⋊C4—46no—
868C22⋊C4—46no—
869C22⋊C4—46no—
870C22⋊C4—46no—
871C22⋊C4—412no—
872C22⋊C4—412no—
873C22⋊C4—412no—
874C22⋊C4—412no—
875C22⋊C4—46no—
876C22⋊C4C22×D4124yes—
877C42—212no—
878C42—26no—
879C42—26no—
880C42—212no—
881C42—212no—
882C42—46no—
883C42—46no—
884C42C22×D414yes—
885C42C22×D4112yes—
886C42C22×D4112yes—
887C42C22×D4112yes—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—26no—
892C23—26no—
893C23—22no—
894C23—23no—
895C23—22no—
896C23—22no—
897C23—23no—
898C23—23no—
899C23—21no—
900C23—26no—
901C23—22no—
902C23—26no—
903C23—26no—
904C23—26no—
905C23—26no—
906C23—26no—
907C23—26no—
908C23—22no—
909C23—26no—
910C23—21no—
911C23—23no—
912C23—26no—
913C23—21no—
914C23—23no—
915C23—424no—
916C23—424no—
917C23—812no—
918C23—812no—
919C23—812no—
920C23—812no—
921C23—812no—
922C23C23×D416yes—
923C23#58514yes—
924C23C2611yescharacteristic
925Q8—412no—
926Q8—424no—
927Q8—86no—
928Q8#535116yes—
929D4—28no—
930D4—224no—
931D4—424no—
932D4—412no—
933D4—48no—
934D4—448no—
935D4—424no—
936D4—412no—
937D4—86no—
938D4—812no—
939D4—86no—
940D4—86no—
941D4—812no—
942D4—812no—
943D4—812no—
944D4—812no—
945D4—1612no—
946C2×C4—22no—
947C2×C4—26no—
948C2×C4—22no—
949C2×C4—23no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—23no—
953C2×C4—224no—
954C2×C4—21no—
955C2×C4—23no—
956C2×C4—21no—
957C2×C4—23no—
958C2×C4—23no—
959C2×C4—21no—
960C2×C4—22no—
961C2×C4—26no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—26no—
965C2×C4—26no—
966C2×C4—22no—
967C2×C4—26no—
968C2×C4—22no—
969C2×C4—26no—
970C2×C4—22no—
971C2×C4—26no—
972C2×C4—26no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—26no—
976C2×C4—22no—
977C2×C4—26no—
978C2×C4—26no—
979C2×C4—26no—
980C2×C4—23no—
981C2×C4—21no—
982C2×C4—22no—
983C2×C4—23no—
984C2×C4—21no—
985C2×C4—22no—
986C2×C4—412no—
987C2×C4—412no—
988C2×C4—48no—
989C2×C4—424no—
990C2×C4—424no—
991C2×C4—424no—
992C2×C4—424no—
993C2×C4—412no—
994C2×C4—412no—
995C2×C4—812no—
996C2×C4C23×D416yes—
997C2×C4C23×D412yes—
998C2×C4C23×D412yes—
999C2×C4C23×D412yes—
1000C2×C4C23×D416yes—
1001C2×C4C23×D416yes—
1002C2×C4C2×H(5,𝔽2)112yes—
1003C22—26no—
1004C22—24no—
1005C22—26no—
1006C22—24no—
1007C22—24no—
1008C22—26no—
1009C22—42no—
1010C22—46no—
1011C22—42no—
1012C22—46no—
1013C22—42no—
1014C22—42no—
1015C22—43no—
1016C22—46no—
1017C22—41no—
1018C22—41no—
1019C22—43no—
1020C22—46no—
1021C22—42no—
1022C22—46no—
1023C22—46no—
1024C22—46no—
1025C22—42no—
1026C22—46no—
1027C22—46no—
1028C22—46no—
1029C22—41no—
1030C22—46no—
1031C22—43no—
1032C22—848no—
1033C22C24×D411yescharacteristic
1034C22C22×H(5,𝔽2)12yes—
1035C22C2×#58512yes—
1036C22H(7,𝔽2)11yescharacteristic
1037C222−1+611yescharacteristic
1038C4—22no—
1039C4—26no—
1040C4—22no—
1041C4—26no—
1042C4—22no—
1043C4—43no—
1044C4—41no—
1045C4—43no—
1046C4—41no—
1047C4—42no—
1048C4—42no—
1049C4—46no—
1050C4—46no—
1051C4—41no—
1052C4—42no—
1053C4—46no—
1054C4—43no—
1055C4C2×#535112yes—
1056C2—46no—
1057C2—44no—
1058C2—83no—
1059C2—81no—
1060C2—86no—
1061C2C22×#53511yescharacteristic
1062C2#6281111yescharacteristic
1063C2#6285311yescharacteristic
1064C2#6289712yes—
1065C2#6289912yes—
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. C2×#3524C2semidirect
2. C2×D4×#41C2semidirect
3. #42683C2semidirect
4. #42679C2semidirect
5. #42484C2semidirect
6. #42480C2semidirect
7. #42443C2semidirect
8. #42438C2semidirect
9. #39887C2semidirect
10. #39886C2semidirect
11. #37616C2semidirect
12. #37544C2semidirect
13. #36429C2semidirect
14. #36428C2semidirect
15. #36066C2semidirect
16. #36049C2semidirect
17. #35927C2semidirect
18. #35910C2semidirect
19. #35831C2semidirect
20. #35771C2semidirect
21. #35236C2semidirect
22. #34593C2semidirect
23. #34193C2semidirect
26. C2×#559C22semidirect
27. C2×#557C22semidirect
28. C2×#555C22semidirect
29. C2×#553C22semidirect
30. C2×#552C22semidirect
34. C2×#550C22semidirect
36. C2×D4×Q8C22semidirect
39. C2×#548C22semidirect
40. C2×#548C22semidirect
41. C2×#548C22semidirect
45. C2×#542C22semidirect
46. C2×#540C22semidirect
48. C2×#529C22semidirect
49. C2×#529C22semidirect
51. C2×#520C22semidirect
52. C2×#519C22semidirect
55. #2848C22semidirect
56. #2847C22semidirect
57. #2813C22semidirect
58. #2813C22semidirect
59. #2813C22semidirect
60. #2718C22semidirect
61. #2710C22semidirect
62. #2706C22semidirect
63. #2703C22semidirect
64. #2685C22semidirect
65. #2678C22semidirect
66. #2670C22semidirect
67. #2669C22semidirect
68. #2658C22semidirect
69. #2657C22semidirect
70. #2642C22semidirect
71. #2641C22semidirect
74. #2636C22semidirect
75. #2636C22semidirect
76. #2636C22semidirect
77. #2635C22semidirect
78. #2635C22semidirect
79. #2633C22semidirect
80. #2631C22semidirect
81. #2626C22semidirect
82. #2623C22semidirect
83. #2623C22semidirect
84. #2620C22semidirect
85. #2620C22semidirect
86. #2620C22semidirect
87. #2619C22semidirect
88. #2617C22semidirect
91. #2598C22semidirect
92. #2568C22semidirect
93. #2566C22semidirect
95. #2562C22semidirect
96. #2548C22semidirect
97. #2545C22semidirect
98. #2544C22semidirect
99. #2544C22semidirect
100. #2542C22semidirect
101. #2542C22semidirect
102. #2541C22semidirect
103. #2541C22semidirect
105. #2540C22semidirect
106. #2540C22semidirect
107. #2540C22semidirect
108. #2538C22semidirect
109. #2537C22semidirect
110. #2492C22semidirect
111. #2491C22semidirect
112. #2490C22semidirect
113. #2489C22semidirect
114. #2487C22semidirect
115. #2435C22semidirect
116. #2433C22semidirect
117. #2432C22semidirect
118. #2432C22semidirect
119. #2431C22semidirect
120. #2431C22semidirect
121. #2429C22semidirect
122. #2428C22semidirect
123. #2427C22semidirect
124. #2426C22semidirect
125. #2417C22semidirect
126. #2416C22semidirect
127. #2415C22semidirect
128. #2414C22semidirect
129. #2411C22semidirect
131. #2408C22semidirect
132. #2408C22semidirect
133. #2407C22semidirect
134. #2407C22semidirect
135. #2407C22semidirect
136. #2407C22semidirect
138. #2398C22semidirect
140. #2397C22semidirect
141. #2392C22semidirect
142. #2392C22semidirect
143. #2354C22semidirect
144. Q8×C4⋊C4C22semidirect
145. #2347C22semidirect
147. #2341C22semidirect
148. #2341C22semidirect
149. Q8×C22⋊C4C22semidirect
150. Q8×C22⋊C4C22semidirect
151. #2324C22semidirect
152. #2319C22semidirect
153. #2319C22semidirect
154. C4×#120C22semidirect
155. C4×#120C22semidirect
156. #2285C22semidirect
157. #2283C22semidirect
158. #2276C22semidirect
159. #2276C22semidirect
253. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35242
C2×D4×#412
#426832
#426792
#424842
#424802
#424432
#424382
#398872
#398862
#376162
#375442
#364292
#364282
#360662
#360492
#359272
#359102
#358312
#357712
#352362
#345932
#341932