Finite Group Databasebeta

← #7652940

Subgroups — #7652940

Order 512.

8662 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3486C211yesmaximal, characteristic, complemented
2C22×#548C211yesmaximal, characteristic, complemented
3#42797C216yesmaximal, complemented
4#42796C216yesmaximal, complemented
5#39743C216yesmaximal, complemented
6#39723C213yesmaximal, complemented
7#39595C213yesmaximal, complemented
8#39166C216yesmaximal, complemented
9#39135C213yesmaximal, complemented
10#39123C213yesmaximal, complemented
11#37439C213yesmaximal, complemented
12#36578C211yesmaximal, characteristic, complemented
13#36576C212yesmaximal, complemented
14Q8×#123C211yesmaximal, characteristic, complemented
15#36434C212yesmaximal, complemented
16#36429C211yesmaximal, characteristic, complemented
17#36428C211yesmaximal, characteristic, complemented
18#35801C212yesmaximal, complemented
19#35757C212yesmaximal, complemented
20#35078C213yesmaximal, complemented
21#35077C213yesmaximal, complemented
22#34957C213yesmaximal, complemented
23C2×Q8×C22⋊C4C211yesmaximal, characteristic, complemented
24C22×2−1+4C2211yescharacteristic, complemented
25C23×#41C2211yescharacteristic
26C24×Q8C2211yescharacteristic
27#3486—216no—
28C2×#550C2212yescomplemented
29C2×D4×Q8C2211yescharacteristic
30C2×D4×Q8C2213yes—
31C2×D4×Q8C2211yescharacteristic, complemented
32C2×D4×Q8C2213yescomplemented
33C2×#548—216no—
34C2×#548C2213yes—
35C2×#548C2216yes—
36C2×#548C2211yescharacteristic
37C2×#548C2216yes—
38C2×#548C2212yes—
39C2×#548C2212yes—
40C2×#548C2213yescomplemented
41C2×#548C2211yescharacteristic, complemented
42C2×#548C2212yescomplemented
43C2×#536C2213yescomplemented
44C2×#536C2213yescomplemented
45C22×#124C2213yes—
46C2×#525C2213yes—
47C2×#525C2213yes—
48C22×C22⋊Q8C2213yes—
49C22×#121C2213yes—
50C2×#519C2211yescharacteristic, complemented
51C22×C4×Q8C2211yescharacteristic
52C22×C4×Q8C2212yescomplemented
53C22×C4×D4C2213yes—
54#2856C2216yescomplemented
55#2855C2213yes—
56#2854C2213yes—
57#2850C2216yescomplemented
58#2848C2213yes—
59#2847C2213yes—
60#2813C2216yescomplemented
61#2813C2216yescomplemented
62#2733C22112yescomplemented
63#2732C22112yescomplemented
64#2731C22112yescomplemented
65#2730C22112yescomplemented
66#2730C22112yescomplemented
67#2730C22112yescomplemented
68#2729C22112yescomplemented
69#2728C22112yescomplemented
70#2661C22112yescomplemented
71#2656C2216yescomplemented
72#2639C2216yescomplemented
73#2630C22112yescomplemented
74#2626C2216yes—
75#2624C2216yescomplemented
76#2617C2216yes—
77#2615C2216yescomplemented
78#2602C2216yescomplemented
79#2602C2216yescomplemented
80#2591C2213yes—
81#2583C2213yes—
82#2579C2216yes—
83#2564C2216yescomplemented
84#2561C2213yes—
85#2548C2216yescomplemented
86#2545C2216yescomplemented
87#2543C22112yescomplemented
88#2543C2216yescomplemented
89#2539C2213yes—
90#2538C2216yescomplemented
91#2536C2216yescomplemented
92#2534C2216yes—
93#2504C2213yes—
94#2502C2213yes—
95#2500C2216yescomplemented
96#2487C2213yes—
97#2487C2213yes—
98#2485C2216yescomplemented
99#2448C2216yescomplemented
100#2448C2216yescomplemented
101#2448C2216yescomplemented
102#2446C2216yescomplemented
103#2436C2216yescomplemented
104#2435C2213yes—
105#2433C2213yes—
106#2432C2216yescomplemented
107#2431C2216yescomplemented
108#2431C2216yescomplemented
109#2431C2216yescomplemented
110#2429C2216yescomplemented
111#2426C2216yescomplemented
112#2426C2216yescomplemented
113#2426C2216yescomplemented
114#2423C2216yescomplemented
115#2423C2216yescomplemented
116#2421C2216yescomplemented
117#2421C2216yescomplemented
118#2417C2216yescomplemented
119#2416C2216yescomplemented
120#2416C2216yescomplemented
121#2416C2216yescomplemented
122#2412C2213yes—
123#2412C2211yescharacteristic
124#2410C2216yes—
125#2410C2213yes—
126#2410C2213yes—
127#2409C2216yescomplemented
128#2408C2213yes—
129#2408C2213yes—
130#2407C2216yescomplemented
131#2407C2216yescomplemented
132#2407C2216yescomplemented
133#2407C2216yescomplemented
134#2395C2216yescomplemented
135#2388C2216yescomplemented
136#2351C2212yescomplemented
137Q8×C4⋊C4C2212yescomplemented
138#2341C2212yescomplemented
139#2341C2212yescomplemented
140#2341C2212yescomplemented
141Q8×C22⋊C4C2213yes—
142Q8×C22⋊C4C2211yescharacteristic
143Q8×C22⋊C4C2211yescharacteristic
144Q8×C22⋊C4C2213yes—
145Q8×C22⋊C4C2216yescomplemented
146Q8×C22⋊C4C2212yescomplemented
147Q8×C22⋊C4C2212yescomplemented
148#2325C22112yescomplemented
149#2321C2216yes—
150#2321C2216yes—
151C4×#123C2213yes—
152C4×#123C2213yes—
153C4×#121C2216yescomplemented
154C4×#121C2216yescomplemented
155C4×#120C2213yes—
156C4×#120C2213yes—
157C2×#391C2216yescomplemented
158C2×#380C2213yes—
159C2×C4×C22⋊C4C2213yes—
160C2×2−1+4—28no—
161C2×2−1+4—48no—
162C22×#41—28no—
163C22×#41—48no—
164C22×#41C2312yes—
165C22×#41C2311yescharacteristic
166C22×#41C2316yes—
167C22×#41C2313yes—
168C22×#41C2313yes—
169C22×#41C2313yes—
170C23×Q8—48no—
171C23×Q8D4116yescomplemented
172C23×Q8C2311yescharacteristic
173C23×Q8C2311yescharacteristic
174C23×Q8C2311yescharacteristic
175C23×Q8C2311yescharacteristic
176C23×Q8C2313yes—
177C23×Q8C2313yes—
178C23×Q8C2313yes—
179C23×Q8C2313yes—
180C23×D4C2313yes—
181C23×D4C2313yes—
182C24×C4C2313yes—
183C24×C4C2313yes—
184#550—48no—
185D4×Q8—28no—
186D4×Q8—224no—
187D4×Q8—28no—
188D4×Q8—224no—
189#548—216no—
190#548—216no—
191#548—248no—
192#548—248no—
193#548—28no—
194#548—224no—
195#548—28no—
196#548—224no—
197#548—48no—
198#536—224no—
199#536—224no—
200C2×C4⋊Q8C2313yes—
201C2×C4⋊Q8C2313yes—
202C2×C4⋊Q8C2316yes—
203C2×#127C2316yes—
204C2×#124—224no—
205C2×#124C2316yes—
206C2×#124C2316yes—
207C2×#124C23112yes—
208C2×#124C2313yes—
209C2×#124C2313yes—
210C2×#124C2316yes—
211C2×#124C2316yes—
212#525—224no—
213#525—224no—
214C2×#123C2313yes—
215C2×#123C2313yes—
216C2×#123C2316yes—
217C2×#123C2311yescharacteristic
218C2×#123C2313yes—
219C2×C22⋊Q8—224no—
220C2×C22⋊Q8C2313yes—
221C2×C22⋊Q8C2313yes—
222C2×C22⋊Q8C2313yes—
223C2×C22⋊Q8C2313yes—
224C2×C22⋊Q8C2313yes—
225C2×C22⋊Q8C2313yes—
226C2×C22⋊Q8C2316yes—
227C2×C22⋊Q8C2316yes—
228C2×C22⋊Q8C23112yes—
229C2×C22⋊Q8C2313yes—
230C2×C22⋊Q8C2313yes—
231C2×C22⋊Q8C2316yes—
232C2×C22⋊Q8C2316yes—
233C2×C22⋊Q8C2316yes—
234C2×#121—224no—
235C2×#121C2313yes—
236C2×#121C2313yes—
237C2×#121C2316yes—
238C2×#121C2313yes—
239C2×#121C2316yes—
240C2×#121C2316yes—
241C2×#121C2313yes—
242C2×#121C2316yes—
243C2×#121C23112yes—
244C2×#121C2316yes—
245C2×#121C2316yes—
246C2×#121C2316yes—
247C2×#121C2316yes—
248C2×#121C2316yes—
249C2×#120C2313yes—
250C2×#120C2313yes—
251C2×#120C2311yescharacteristic
252C2×#120C2316yes—
253C2×#120C2313yes—
254#519—28no—
255C2×C4×Q8—28no—
256C2×C4×Q8—48no—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2316yes—
263C2×C4×Q8C2313yes—
264C2×C4×Q8C2313yes—
265C2×C4×Q8C2316yes—
266C2×C4×Q8C2316yes—
267C2×C4×D4—224no—
268C2×C4×D4C2316yes—
269C2×C4×D4C2316yes—
270C2×C4×D4C2316yes—
271C2×C4×D4C2316yes—
272C2×C4×D4C2316yes—
273C2×C4×D4C2316yes—
274C2×C4×D4C2313yes—
275C2×C4×D4C2313yes—
276C2×C4×D4C2313yes—
277C2×C4×D4C2313yes—
278C2×C4×D4C2316yes—
279C2×C4×D4C2316yes—
280C2×#117C2313yes—
281C2×#117C2313yes—
282C22×C4⋊C4C2313yes—
283C22×C4⋊C4C2313yes—
284C22×C4⋊C4C2316yes—
285C22×C22⋊C4C2313yes—
286C22×C22⋊C4C2316yes—
287C22×C22⋊C4C2311yescharacteristic
288C22×C22⋊C4C2311yescharacteristic
289C22×C22⋊C4C2313yes—
290C22×C42C2313yes—
291C22×C42C2316yes—
292#400C2316yes—
293#400C2316yes—
294#400C2316yes—
295#399C2316yes—
296#399C23112yes—
297#399C2316yes—
298#399C2316yes—
299#398C23112yes—
300#398C2316yes—
301#398C23112yes—
302#397C2316yes—
303#397C2312yes—
304#397C2316yes—
305#397C23112yes—
306#397C23112yes—
307#396C23112yes—
308#396C23112yes—
309#396C23112yes—
310#396C23112yes—
311#395C2316yes—
312#394C2316yes—
313#394C2312yes—
314#394C2316yes—
315#394C2316yes—
316#394C2316yes—
317#394C23112yes—
318#394C23112yes—
319#394C23112yes—
320#394C23112yes—
321#394C2316yes—
322#394C2316yes—
323#394C23112yes—
324#393C2316yes—
325#393C23112yes—
326#392C2316yes—
327#392C2316yes—
328#392C23112yes—
329#392C23112yes—
330#392C2316yes—
331#392C2316yes—
332#392C2316yes—
333#392C23112yes—
334#391C2316yes—
335#391C2316yes—
336#391C2316yes—
337#391C2316yes—
338#391C2316yes—
339#391C23112yes—
340#391C23112yes—
341#391C2316yes—
342#390C23112yes—
343#390C23112yes—
344#390C2316yes—
345#390C2316yes—
346#390C2316yes—
347#390C2316yes—
348#390C2316yes—
349#390C2316yes—
350#390C2316yes—
351#390C2316yes—
352#389C2316yes—
353#389C2316yes—
354#389C2316yes—
355#389C2316yes—
356#389C2316yes—
357#389C2316yes—
358#388C2316yes—
359#388C2316yes—
360#388C23112yes—
361#388C23112yes—
362#388C23112yes—
363#388C23112yes—
364#388C23112yes—
365#388C23112yes—
366#388C2316yes—
367#388C2316yes—
368#388C2316yes—
369#388C2316yes—
370#387C2316yes—
371#387C2316yes—
372#387C23112yes—
373#387C23112yes—
374#386C2316yes—
375#386C2316yes—
376#386C2313yes—
377#386C2316yes—
378#386C23112yes—
379#386C23112yes—
380#386C2313yes—
381#386C2316yes—
382#386C23112yes—
383#386C23112yes—
384#386C23112yes—
385#386C2311yescharacteristic
386#386C2313yes—
387#386C2316yes—
388#386C2316yes—
389#386C2312yes—
390#385C2316yes—
391#385C2316yes—
392#385C2313yes—
393#385C2316yes—
394#385C2313yes—
395#385C23112yes—
396#385C23112yes—
397#385C2311yescharacteristic
398#385C2313yes—
399#384C2316yes—
400#382C2316yes—
401#381C2311yescharacteristic
402#381C2313yes—
403#380C2312yes—
404#380C2316yes—
405#380C2316yes—
406#380C2313yes—
407#380C2316yes—
408#380C2313yes—
409#380C2316yes—
410#380C2316yes—
411#380C2316yes—
412#380C2316yes—
413#380C2316yes—
414#379C2313yes—
415#379C2313yes—
416#379C2316yes—
417C4×C4⋊C4C2316yes—
418C4×C4⋊C4C2316yes—
419C4×C22⋊C4C2313yes—
420C4×C22⋊C4C2313yes—
421C4×C22⋊C4C2313yes—
422C4×C22⋊C4C2313yes—
423C4×C22⋊C4C2316yes—
424C4×C22⋊C4C2316yes—
425C4×C22⋊C4C2316yes—
426C4×C22⋊C4C2316yes—
427C4×C22⋊C4C2316yes—
428C4×C22⋊C4C2316yes—
429C2×#95C2316yes—
430C2×#95C2316yes—
431C25C2411yescharacteristic
432C25C2413yes—
4332−1+4—464no—
434C2×#41—224no—
435C2×#41—28no—
436C2×#41—212no—
437C2×#41—24no—
438C2×#41—28no—
439C2×#41—28no—
440C2×#41—28no—
441C2×#41—212no—
442C2×#41—212no—
443C2×#41—412no—
444C2×#41—412no—
445C2×#41—412no—
446C2×#41—412no—
447C2×#41—412no—
448C2×#41—464no—
449C22×Q8—28no—
450C22×Q8—28no—
451C22×Q8—28no—
452C22×Q8—212no—
453C22×Q8—24no—
454C22×Q8—28no—
455C22×Q8—412no—
456C22×Q8—412no—
457C22×Q8—412no—
458C22×Q8—412no—
459C22×Q8—464no—
460C22×Q8C2×D418yes—
461C22×Q8C2×D418yes—
462C22×Q8C2×D418yes—
463C22×Q8C2×D4124yes—
464C22×Q8C2×D4124yes—
465C22×Q8C2×D4124yes—
466C22×Q8C2413yes—
467C22×Q8C2413yes—
468C22×Q8C2413yes—
469C22×Q8C2413yes—
470C22×Q8C2413yes—
471C22×Q8C2416yes—
472C22×Q8C2411yescharacteristic
473C22×D4—212no—
474C22×D4—212no—
475C22×D4—412no—
476C22×D4—412no—
477C22×D4C2413yes—
478C22×D4C2411yescharacteristic
479C22×D4C2413yes—
480C22×D4C2411yescharacteristic
481C22×D4C2416yes—
482C22×D4C2416yes—
483C22×D4C2413yes—
484C22×D4C2416yes—
485C22×D4C2416yes—
486C22×D4C2411yescharacteristic
487C22×D4C2413yes—
488C22×D4C2416yes—
489C22×D4C2413yes—
490C22×D4C2416yes—
491C22×D4C24112yes—
492C23×C4—212no—
493C23×C4—412no—
494C23×C4—412no—
495C23×C4C2×D4124yes—
496C23×C4C2411yescharacteristic
497C23×C4C2413yes—
498C23×C4C2413yes—
499C23×C4C2416yes—
500C23×C4C2412yes—
501C23×C4C2413yes—
502C23×C4C2413yes—
503C23×C4C2413yes—
504C23×C4C2413yes—
505C23×C4C2411yescharacteristic
506C23×C4C2416yes—
507C23×C4C2416yes—
508C23×C4C2416yes—
509C23×C4C2413yes—
510C23×C4C2413yes—
511C23×C4C2413yes—
512C4⋊Q8—212no—
513C4⋊Q8—212no—
514C4⋊Q8—224no—
515#127—412no—
516#124—224no—
517#124—224no—
518#124—248no—
519#124—212no—
520#124—212no—
521#124—224no—
522#124—412no—
523#123—212no—
524#123—212no—
525#123—224no—
526#123—24no—
527#123—46no—
528C22⋊Q8—224no—
529C22⋊Q8—224no—
530C22⋊Q8—248no—
531C22⋊Q8—212no—
532C22⋊Q8—212no—
533C22⋊Q8—212no—
534C22⋊Q8—212no—
535C22⋊Q8—224no—
536C22⋊Q8—224no—
537C22⋊Q8—212no—
538C22⋊Q8—212no—
539C22⋊Q8—212no—
540C22⋊Q8—212no—
541C22⋊Q8—412no—
542#121—224no—
543#121—224no—
544#121—224no—
545#121—224no—
546#121—212no—
547#121—212no—
548#121—212no—
549#121—212no—
550#121—412no—
551#121—412no—
552#121—412no—
553#121—412no—
554#121—412no—
555#121—424no—
556#120—212no—
557#120—24no—
558#120—212no—
559#120—412no—
560#120—46no—
561C4×Q8—224no—
562C4×Q8—28no—
563C4×Q8—212no—
564C4×Q8—212no—
565C4×Q8—24no—
566C4×Q8—24no—
567C4×Q8—28no—
568C4×Q8—28no—
569C4×Q8—412no—
570C4×Q8—412no—
571C4×D4—224no—
572C4×D4—224no—
573C4×D4—224no—
574C4×D4—224no—
575C4×D4—212no—
576C4×D4—212no—
577C4×D4—212no—
578C4×D4—212no—
579C4×D4—224no—
580C4×D4—224no—
581C4×D4—412no—
582C4×D4—412no—
583#117—212no—
584#117—212no—
585C2×C4⋊C4—212no—
586C2×C4⋊C4—212no—
587C2×C4⋊C4—412no—
588C2×C4⋊C4C2416yes—
589C2×C4⋊C4C2416yes—
590C2×C4⋊C4C2416yes—
591C2×C4⋊C4C2416yes—
592C2×C4⋊C4C2416yes—
593C2×C4⋊C4C2416yes—
594C2×C4⋊C4C2413yes—
595C2×C4⋊C4C2413yes—
596C2×C4⋊C4C2413yes—
597C2×C4⋊C4C2413yes—
598C2×C4⋊C4C2416yes—
599C2×C4⋊C4C2413yes—
600C2×C4⋊C4C2413yes—
601C2×C4⋊C4C2416yes—
602C2×C4⋊C4C2413yes—
603C2×C4⋊C4C2413yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C24112yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2416yes—
608C2×C4⋊C4C2416yes—
609C2×C4⋊C4C2416yes—
610C2×C4⋊C4C24112yes—
611C2×C4⋊C4C2416yes—
612C2×C22⋊C4—24no—
613C2×C22⋊C4—212no—
614C2×C22⋊C4—224no—
615C2×C22⋊C4—24no—
616C2×C22⋊C4—46no—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2412yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2413yes—
622C2×C22⋊C4C2413yes—
623C2×C22⋊C4C24112yes—
624C2×C22⋊C4C24112yes—
625C2×C22⋊C4C2411yescharacteristic
626C2×C22⋊C4C2412yes—
627C2×C22⋊C4C2411yescharacteristic
628C2×C22⋊C4C2413yes—
629C2×C22⋊C4C2413yes—
630C2×C22⋊C4C2411yescharacteristic
631C2×C22⋊C4C2413yes—
632C2×C22⋊C4C2411yescharacteristic
633C2×C22⋊C4C2416yes—
634C2×C22⋊C4C2413yes—
635C2×C22⋊C4C2413yes—
636C2×C22⋊C4C2413yes—
637C2×C22⋊C4C2413yes—
638C2×C22⋊C4C2416yes—
639C2×C22⋊C4C2416yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2416yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2416yes—
644C2×C22⋊C4C2416yes—
645C2×C22⋊C4C2416yes—
646C2×C22⋊C4C2416yes—
647C2×C22⋊C4C24112yes—
648C2×C22⋊C4C24112yes—
649C2×C22⋊C4C2416yes—
650C2×C22⋊C4C2416yes—
651C2×C22⋊C4C2416yes—
652C2×C22⋊C4C2416yes—
653C2×C22⋊C4C24112yes—
654C2×C22⋊C4C24112yes—
655C2×C22⋊C4C2416yes—
656C2×C22⋊C4C2411yescharacteristic
657C2×C42—212no—
658C2×C42—412no—
659C2×C42C2413yes—
660C2×C42C2413yes—
661C2×C42C2416yes—
662C2×C42C2416yes—
663C2×C42C2416yes—
664C2×C42C2416yes—
665C2×C42C2416yes—
666C2×C42C2416yes—
667C2×C42C2416yes—
668#95C2416yes—
669#95C2416yes—
670#95C2416yes—
671#95C2416yes—
672#95C2416yes—
673#95C24112yes—
674#95C2416yes—
675#95C2412yes—
676#95C2412yes—
677#95C2412yes—
678#95C2416yes—
679#95C2416yes—
680#95C2416yes—
681#95C2416yes—
682#95C2416yes—
683#95C2412yes—
684#95C2416yes—
685#95C2416yes—
686#95C2416yes—
687#95C24112yes—
688#95C24112yes—
689C24—22no—
690C24—22no—
691C24—24no—
692C24—26no—
693C24—26no—
694C24—26no—
695C24—42no—
696C24—46no—
697C24—46no—
698C24C22×D414yes—
699C24C2516yes—
700C24C2511yescharacteristic
701C24C2513yes—
702C24C2511yescharacteristic
703C24C2511yescharacteristic
704C24C2511yescharacteristic
705#41—448no—
706#41—448no—
707#41—496no—
708#41—448no—
709#41—432no—
710#41—416no—
711C2×Q8—232no—
712C2×Q8—232no—
713C2×Q8—232no—
714C2×Q8—26no—
715C2×Q8—26no—
716C2×Q8—212no—
717C2×Q8—212no—
718C2×Q8—212no—
719C2×Q8—212no—
720C2×Q8—412no—
721C2×Q8—46no—
722C2×Q8—448no—
723C2×Q8—448no—
724C2×Q8—448no—
725C2×Q8—448no—
726C2×Q8—416no—
727C2×Q8C22×D4112yes—
728C2×Q8C22×D4112yes—
729C2×Q8C22×D4112yes—
730C2×Q8C22×D4124yes—
731C2×Q8C22×D414yes—
732C2×Q8H(5,𝔽2)18yes—
733C2×D4—22no—
734C2×D4—26no—
735C2×D4—26no—
736C2×D4—22no—
737C2×D4—212no—
738C2×D4—212no—
739C2×D4—22no—
740C2×D4—26no—
741C2×D4—26no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—26no—
745C2×D4—212no—
746C2×D4—24no—
747C2×D4—212no—
748C2×D4—212no—
749C2×D4—212no—
750C2×D4—212no—
751C2×D4—26no—
752C2×D4—26no—
753C2×D4—212no—
754C2×D4—212no—
755C2×D4—212no—
756C2×D4—212no—
757C2×D4—46no—
758C2×D4—46no—
759C2×D4—412no—
760C2×D4—46no—
761C2×D4—42no—
762C2×D4—46no—
763C2×D4—448no—
764C2×D4—46no—
765C2×D4—46no—
766C2×D4—46no—
767C2×D4—46no—
768C2×D4—46no—
769C2×D4—412no—
770C2×D4—412no—
771C2×D4—412no—
772C2×D4—448no—
773C22×C4—212no—
774C22×C4—212no—
775C22×C4—212no—
776C22×C4—22no—
777C22×C4—26no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—24no—
781C22×C4—22no—
782C22×C4—212no—
783C22×C4—212no—
784C22×C4—212no—
785C22×C4—212no—
786C22×C4—26no—
787C22×C4—26no—
788C22×C4—212no—
789C22×C4—212no—
790C22×C4—212no—
791C22×C4—212no—
792C22×C4—24no—
793C22×C4—448no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—46no—
797C22×C4—46no—
798C22×C4—46no—
799C22×C4—46no—
800C22×C4—46no—
801C22×C4—46no—
802C22×C4—412no—
803C22×C4—46no—
804C22×C4—46no—
805C22×C4—448no—
806C22×C4C22×D4112yes—
807C22×C4C22×D4112yes—
808C22×C4C22×D4112yes—
809C22×C4C22×D4112yes—
810C22×C4C22×D4112yes—
811C22×C4C22×D4112yes—
812C22×C4C2512yes—
813C22×C4C2516yes—
814C22×C4C2516yes—
815C22×C4C2512yes—
816C22×C4C2513yes—
817C22×C4C2511yescharacteristic
818C22×C4C2516yes—
819C22×C4C2511yescharacteristic
820C22×C4C2513yes—
821C22×C4C2512yes—
822C22×C4C2511yescharacteristic
823C22×C4C2513yes—
824C22×C4C2513yes—
825C22×C4C2513yes—
826C22×C4C2513yes—
827C22×C4C2512yes—
828C22×C4C2513yes—
829C4⋊C4—212no—
830C4⋊C4—212no—
831C4⋊C4—212no—
832C4⋊C4—212no—
833C4⋊C4—26no—
834C4⋊C4—26no—
835C4⋊C4—26no—
836C4⋊C4—26no—
837C4⋊C4—212no—
838C4⋊C4—26no—
839C4⋊C4—26no—
840C4⋊C4—212no—
841C4⋊C4—26no—
842C4⋊C4—26no—
843C4⋊C4—212no—
844C4⋊C4—212no—
845C4⋊C4—24no—
846C4⋊C4—412no—
847C4⋊C4—42no—
848C4⋊C4—46no—
849C4⋊C4—46no—
850C4⋊C4—46no—
851C4⋊C4—412no—
852C4⋊C4—46no—
853C22⋊C4—24no—
854C22⋊C4—24no—
855C22⋊C4—22no—
856C22⋊C4—26no—
857C22⋊C4—26no—
858C22⋊C4—22no—
859C22⋊C4—26no—
860C22⋊C4—22no—
861C22⋊C4—22no—
862C22⋊C4—26no—
863C22⋊C4—26no—
864C22⋊C4—212no—
865C22⋊C4—212no—
866C22⋊C4—224no—
867C22⋊C4—224no—
868C22⋊C4—212no—
869C22⋊C4—26no—
870C22⋊C4—26no—
871C22⋊C4—26no—
872C22⋊C4—26no—
873C22⋊C4—212no—
874C22⋊C4—24no—
875C22⋊C4—212no—
876C22⋊C4—24no—
877C22⋊C4—46no—
878C22⋊C4—42no—
879C22⋊C4—46no—
880C22⋊C4—46no—
881C22⋊C4—46no—
882C22⋊C4—46no—
883C22⋊C4—412no—
884C22⋊C4—46no—
885C22⋊C4—46no—
886C22⋊C4—412no—
887C22⋊C4—412no—
888C22⋊C4—46no—
889C22⋊C4—46no—
890C22⋊C4—412no—
891C22⋊C4—46no—
892C22⋊C42−1+414yescomplemented
893C42—212no—
894C42—212no—
895C42—212no—
896C42—26no—
897C42—26no—
898C42—212no—
899C42—212no—
900C42—46no—
901C42—46no—
902C23—22no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—21no—
909C23—21no—
910C23—22no—
911C23—28no—
912C23—28no—
913C23—21no—
914C23—23no—
915C23—26no—
916C23—26no—
917C23—22no—
918C23—26no—
919C23—26no—
920C23—21no—
921C23—26no—
922C23—23no—
923C23—26no—
924C23—22no—
925C23—26no—
926C23—23no—
927C23—26no—
928C23—26no—
929C23—21no—
930C23—44no—
931C23—48no—
932C23—48no—
933C23—412no—
934C23—412no—
935C23—412no—
936C23—812no—
937C23—812no—
938C23C23×D412yes—
939C23C23×D412yes—
940C23C23×D412yes—
941C23C2×2−1+412yes—
942C23#58514yes—
943C23#58512yes—
944C23C2611yescharacteristic
945Q8—224no—
946Q8—224no—
947Q8—224no—
948Q8—424no—
949Q8—412no—
950Q8—412no—
951Q8#534116yes—
952D4—424no—
953D4—412no—
954D4—424no—
955D4—44no—
956D4—412no—
957D4—412no—
958D4—44no—
959D4—424no—
960D4—412no—
961D4—44no—
962D4—424no—
963D4—412no—
964D4—812no—
965D4—812no—
966D4—1612no—
967C2×C4—22no—
968C2×C4—26no—
969C2×C4—26no—
970C2×C4—26no—
971C2×C4—22no—
972C2×C4—224no—
973C2×C4—224no—
974C2×C4—224no—
975C2×C4—22no—
976C2×C4—23no—
977C2×C4—21no—
978C2×C4—23no—
979C2×C4—21no—
980C2×C4—26no—
981C2×C4—22no—
982C2×C4—21no—
983C2×C4—23no—
984C2×C4—22no—
985C2×C4—26no—
986C2×C4—26no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—26no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—23no—
993C2×C4—22no—
994C2×C4—21no—
995C2×C4—26no—
996C2×C4—26no—
997C2×C4—22no—
998C2×C4—21no—
999C2×C4—23no—
1000C2×C4—26no—
1001C2×C4—22no—
1002C2×C4—26no—
1003C2×C4—22no—
1004C2×C4—26no—
1005C2×C4—26no—
1006C2×C4—26no—
1007C2×C4—412no—
1008C2×C4—412no—
1009C2×C4—412no—
1010C2×C4—48no—
1011C2×C4—424no—
1012C2×C4—424no—
1013C2×C4—44no—
1014C2×C4—412no—
1015C2×C4—44no—
1016C2×C4—424no—
1017C2×C4—412no—
1018C2×C4—412no—
1019C2×C4—812no—
1020C2×C4C23×D416yes—
1021C2×C4C23×D416yes—
1022C2×C4C23×D416yes—
1023C2×C4C23×D416yes—
1024C2×C4C2×H(5,𝔽2)112yes—
1025C2×C4C2×2−1+414yes—
1026C22—24no—
1027C22—24no—
1028C22—24no—
1029C22—24no—
1030C22—22no—
1031C22—22no—
1032C22—22no—
1033C22—22no—
1034C22—22no—
1035C22—22no—
1036C22—22no—
1037C22—416no—
1038C22—42no—
1039C22—42no—
1040C22—46no—
1041C22—46no—
1042C22—42no—
1043C22—46no—
1044C22—42no—
1045C22—46no—
1046C22—46no—
1047C22—46no—
1048C22—41no—
1049C22—43no—
1050C22—46no—
1051C22—46no—
1052C22—43no—
1053C22—41no—
1054C22—43no—
1055C22—41no—
1056C22—46no—
1057C22—824no—
1058C22#348714yes—
1059C22#349714yes—
1060C22C24×D411yescharacteristic
1061C22C22×H(5,𝔽2)12yes—
1062C22C22×2−1+411yescharacteristic
1063C22C2×#58512yes—
1064C22C2×#58511yescharacteristic
1065C4—24no—
1066C4—26no—
1067C4—26no—
1068C4—26no—
1069C4—42no—
1070C4—46no—
1071C4—46no—
1072C4—42no—
1073C4—43no—
1074C4—41no—
1075C4—46no—
1076C4—43no—
1077C4—41no—
1078C4—42no—
1079C4—41no—
1080C4—43no—
1081C4C2×#534112yes—
1082C2—24no—
1083C2—24no—
1084C2—42no—
1085C2—83no—
1086C2—81no—
1087C2—86no—
1088C2C22×#53411yescharacteristic
1089C2C2×#349711yescharacteristic
1090C2C2×#348711yescharacteristic
1091C2#6301512yes—
1092C2#6302012yes—
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×#3486C2semidirect
2. C22×#548C2semidirect
3. #42797C2semidirect
4. #42796C2semidirect
5. #39743C2semidirect
6. #39723C2semidirect
7. #39595C2semidirect
8. #39166C2semidirect
9. #39135C2semidirect
10. #39123C2semidirect
11. #37439C2semidirect
12. #36578C2semidirect
13. #36576C2semidirect
14. Q8×#123C2semidirect
15. #36434C2semidirect
16. #36429C2semidirect
17. #36428C2semidirect
18. #35801C2semidirect
19. #35757C2semidirect
20. #35078C2semidirect
21. #35077C2semidirect
22. #34957C2semidirect
23. C2×Q8×C22⋊C4C2semidirect
24. C22×2−1+4C22semidirect
28. C2×#550C22semidirect
31. C2×D4×Q8C22semidirect
32. C2×D4×Q8C22semidirect
40. C2×#548C22semidirect
41. C2×#548C22semidirect
42. C2×#548C22semidirect
43. C2×#536C22semidirect
44. C2×#536C22semidirect
50. C2×#519C22semidirect
52. C22×C4×Q8C22semidirect
54. #2856C22semidirect
57. #2850C22semidirect
60. #2813C22semidirect
61. #2813C22semidirect
62. #2733C22semidirect
63. #2732C22semidirect
64. #2731C22semidirect
65. #2730C22semidirect
66. #2730C22semidirect
67. #2730C22semidirect
68. #2729C22semidirect
69. #2728C22semidirect
70. #2661C22semidirect
71. #2656C22semidirect
72. #2639C22semidirect
73. #2630C22semidirect
75. #2624C22semidirect
77. #2615C22semidirect
78. #2602C22semidirect
79. #2602C22semidirect
83. #2564C22semidirect
85. #2548C22semidirect
86. #2545C22semidirect
87. #2543C22semidirect
88. #2543C22semidirect
90. #2538C22semidirect
91. #2536C22semidirect
95. #2500C22semidirect
98. #2485C22semidirect
99. #2448C22semidirect
100. #2448C22semidirect
101. #2448C22semidirect
102. #2446C22semidirect
103. #2436C22semidirect
106. #2432C22semidirect
107. #2431C22semidirect
108. #2431C22semidirect
109. #2431C22semidirect
110. #2429C22semidirect
111. #2426C22semidirect
112. #2426C22semidirect
113. #2426C22semidirect
114. #2423C22semidirect
115. #2423C22semidirect
116. #2421C22semidirect
117. #2421C22semidirect
118. #2417C22semidirect
119. #2416C22semidirect
120. #2416C22semidirect
121. #2416C22semidirect
127. #2409C22semidirect
130. #2407C22semidirect
131. #2407C22semidirect
132. #2407C22semidirect
133. #2407C22semidirect
134. #2395C22semidirect
135. #2388C22semidirect
136. #2351C22semidirect
137. Q8×C4⋊C4C22semidirect
138. #2341C22semidirect
139. #2341C22semidirect
140. #2341C22semidirect
145. Q8×C22⋊C4C22semidirect
146. Q8×C22⋊C4C22semidirect
147. Q8×C22⋊C4C22semidirect
148. #2325C22semidirect
153. C4×#121C22semidirect
154. C4×#121C22semidirect
157. C2×#391C22semidirect
171. C23×Q8D4semidirect
892. C22⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×#34862
C22×#5482
#427972
#427962
#397432
#397232
#395952
#391662
#391352
#391232
#374392
#365782
#365762
Q8×#1232
#364342
#364292
#364282
#358012
#357572
#350782
#350772
#349572
C2×Q8×C22⋊C42