Finite Group Databasebeta

← #7693002

Subgroups — #7693002

Order 512.

10875 conjugacy classes of subgroups.

The subgroup lattice has 1149 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3499C211yesmaximal, characteristic, complemented
2C2×#3497C211yesmaximal, characteristic, complemented
3C2×#3497C212yesmaximal, complemented
4#59654C213yesmaximal, complemented
5#59128C216yesmaximal, complemented
6#59127C213yesmaximal, complemented
7#59051C213yesmaximal, complemented
8#45245C216yesmaximal, complemented
9#44884C216yesmaximal, complemented
10#39341C213yesmaximal, complemented
11#39340C213yesmaximal, complemented
12#39335C216yesmaximal, complemented
13Q8×#121C211yesmaximal, characteristic, complemented
14#36465C211yesmaximal, characteristic, complemented
15#36455C211yesmaximal, characteristic, complemented
16#36434C212yesmaximal, complemented
17#36125C213yesmaximal, complemented
18#36122C213yesmaximal, complemented
19#35757C212yesmaximal, complemented
20#35687C212yesmaximal, complemented
21#34925C213yesmaximal, complemented
22C4×D4×Q8C211yesmaximal, characteristic, complemented
23C4×#548C211yesmaximal, characteristic, complemented
24C22×2−1+4C2212yes—
25C22×2−1+4C2212yes—
26#3499—216no—
27#3497—216no—
28#3497—232no—
29C2×#550C2213yes—
30C2×#550C2216yes—
31C2×#550C2211yescharacteristic
32C2×#550C2212yes—
33C2×D4×Q8C2213yes—
34C2×D4×Q8C2212yes—
35C2×D4×Q8C2216yes—
36C2×D4×Q8C2212yes—
37C2×D4×Q8C2211yescharacteristic
38C2×D4×Q8C2211yescharacteristic
39C2×#548C2216yes—
40C2×#548C2216yes—
41C2×#548C2212yes—
42C2×#548C2212yes—
43C2×#548C2216yes—
44C2×#548C2212yes—
45C2×#548C2211yescharacteristic
46C2×#547C2213yes—
47C2×#547C2213yes—
48C2×#547C2216yes—
49C2×#537C2216yes—
50C2×#537C2216yes—
51C2×#537C2216yes—
52C2×#536C2216yes—
53C2×#532C2213yes—
54C2×#532C2216yes—
55C2×#532C2216yes—
56C2×#532C2213yes—
57C2×#532C2213yes—
58C22×C4⋊Q8C2213yes—
59C2×C4×#41C2211yescharacteristic
60C22×C4×Q8C2212yes—
61C22×C4×Q8C2211yescharacteristic
62#2858C2213yes—
63#2857C2213yes—
64#2856C2213yes—
65#2850C2216yes—
66#2681C22112yes—
67#2677C22112yes—
68#2676C22112yes—
69#2675C22112yes—
70#2673C22112yes—
71#2672C22112yes—
72#2671C22112yes—
73#2616C2216yes—
74#2615C2216yes—
75#2555C2216yes—
76#2555C2216yes—
77#2551C2213yes—
78#2546C2213yes—
79#2545C2216yes—
80#2542C2213yes—
81#2541C2213yes—
82#2541C2213yes—
83#2541C2213yes—
84#2541C2213yes—
85#2540C2216yes—
86#2540C2216yes—
87#2538C2213yes—
88#2537C2213yes—
89#2537C2213yes—
90#2536C2216yes—
91#2491C2213yes—
92#2491C2213yes—
93#2491C2216yes—
94#2491C2216yes—
95#2464C22112yes—
96#2464C22112yes—
97#2461C22112yes—
98#2456C22112yes—
99#2452C2216yes—
100#2452C2216yes—
101#2449C22112yes—
102#2440C2216yes—
103#2436C2216yes—
104#2434C2216yes—
105#2432C2216yes—
106#2432C2216yes—
107#2431C2216yes—
108#2431C2216yes—
109#2429C2216yes—
110#2429C2216yes—
111#2428C2216yes—
112#2428C2213yes—
113#2428C2216yes—
114#2428C2216yes—
115#2428C2216yes—
116#2428C2211yescharacteristic
117#2426C2216yes—
118#2417C2216yes—
119#2417C2216yes—
120#2416C2216yes—
121#2416C2216yes—
122#2416C2216yes—
123#2414C2216yes—
124#2409C2216yes—
125#2409C2216yes—
126#2407C2216yes—
127#2407C2216yes—
128#2407C2216yes—
129#2407C2216yes—
130#2388C2216yes—
131#2388C2216yes—
132#2367C2213yes—
133#2365C2213yes—
134#2362C2213yes—
135#2361C2216yes—
136#2361C2216yes—
137#2361C2216yes—
138#2361C2213yes—
139#2360C2216yes—
140#2352C2213yes—
141#2351C2211yescharacteristic
142Q8×C4⋊C4C2211yescharacteristic
143D4×C4⋊C4C2213yes—
144#2341C2212yes—
145#2341C2211yescharacteristic
146Q8×C22⋊C4C2212yes—
147Q8×C22⋊C4C2211yescharacteristic
148Q8×C22⋊C4C2212yes—
149C4×C4⋊Q8C2213yes—
150C4×#127C2213yes—
151C4×#124C2213yes—
152C4×C22⋊Q8C2213yes—
153C4×C22⋊Q8C2216yes—
154C4×#121C2216yes—
155C4×#121C2213yes—
156C4×#121C2213yes—
157C4×#121C2213yes—
158C42×Q8C2211yescharacteristic
159C42×D4C2213yes—
160C42×D4C2213yes—
161C2×2−1+4—216no—
162C2×2−1+4—216no—
163C2×2−1+4—216no—
164C2×2−1+4—216no—
165C2×2−1+4—48no—
166C2×2−1+4—48no—
167C22×#41C2312yes—
168C22×#41C2316yes—
169C22×#41C2316yes—
170C22×#41C2316yes—
171C22×#41C2316yes—
172C22×#41C2316yes—
173C22×#41C2316yes—
174C22×#41C2311yescharacteristic
175C23×Q8C2312yes—
176C23×Q8C2316yes—
177C23×Q8C2316yes—
178C23×Q8C2312yes—
179C23×Q8C2311yescharacteristic
180#550—216no—
181#550—248no—
182#550—28no—
183#550—224no—
184D4×Q8—216no—
185D4×Q8—216no—
186D4×Q8—224no—
187D4×Q8—248no—
188D4×Q8—28no—
189D4×Q8D4116yescomplemented
190#548—216no—
191#548—248no—
192#548—248no—
193#548—216no—
194#548—248no—
195#548—48no—
196#548D4116yescomplemented
197#547—224no—
198#547—248no—
199#547—224no—
200#537—248no—
201#537—248no—
202#537—248no—
203#536—248no—
204#532—224no—
205#532—248no—
206#532—224no—
207#532—248no—
208#532—224no—
209C2×C4⋊Q8—224no—
210C2×C4⋊Q8C2313yes—
211C2×C4⋊Q8C2313yes—
212C2×C4⋊Q8C2316yes—
213C2×C4⋊Q8C2316yes—
214C2×C4⋊Q8C2316yes—
215C2×C4⋊Q8C2316yes—
216C2×C4⋊Q8C2313yes—
217C2×C4⋊Q8C2313yes—
218C2×#127C2313yes—
219C2×#127C2316yes—
220C2×#127C2311yescharacteristic
221C2×#127C2313yes—
222C2×#127C2316yes—
223C2×#127C2313yes—
224C2×#124C2316yes—
225C2×#124C2316yes—
226C2×#124C2316yes—
227C2×#124C2316yes—
228C2×#124C2316yes—
229C2×#124C2316yes—
230C2×#124C2316yes—
231C2×#124C2313yes—
232C2×#123C23112yes—
233C2×#123C23112yes—
234C2×C22⋊Q8C2316yes—
235C2×C22⋊Q8C2316yes—
236C2×C22⋊Q8C2316yes—
237C2×C22⋊Q8C2316yes—
238C2×C22⋊Q8C2316yes—
239C2×C22⋊Q8C23112yes—
240C2×C22⋊Q8C2316yes—
241C2×C22⋊Q8C2316yes—
242C2×C22⋊Q8C23112yes—
243C2×C22⋊Q8C23112yes—
244C2×C22⋊Q8C2316yes—
245C2×C22⋊Q8C2316yes—
246C2×C22⋊Q8C2313yes—
247C2×#121C2316yes—
248C2×#121C2316yes—
249C2×#121C2313yes—
250C2×#121C2316yes—
251C2×#121C2316yes—
252C2×#121C2316yes—
253C2×#121C2316yes—
254C2×#121C23112yes—
255C2×#121C2313yes—
256C2×#121C2316yes—
257C2×#121C2316yes—
258C2×#121C23112yes—
259C2×#121C2316yes—
260C2×#121C2311yescharacteristic
261C2×#121C2312yes—
262C2×#121C2316yes—
263C2×#121C2316yes—
264C2×#121C2313yes—
265C2×#121C2313yes—
266C2×#121C23112yes—
267C2×#121C23112yes—
268C2×#121C2311yescharacteristic
269C2×#121C2316yes—
270C2×#121C2316yes—
271C2×#121C2316yes—
272C2×#121C2316yes—
273C2×#121C2313yes—
274C4×#41—28no—
275C2×C4×Q8—28no—
276C2×C4×Q8—216no—
277C2×C4×Q8C2316yes—
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2316yes—
283C2×C4×Q8C2313yes—
284C2×C4×Q8C2313yes—
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×D4C2313yes—
288C2×C4×D4C2316yes—
289C2×C4×D4C2313yes—
290C2×C4×D4C2316yes—
291C2×C4×D4C23112yes—
292C2×C4×D4C2313yes—
293C2×C4×D4C2316yes—
294C2×C4×D4C23112yes—
295C2×C4×D4C2316yes—
296C2×C4×D4C2316yes—
297C2×C4×D4C2316yes—
298C2×C4×D4C2316yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2311yescharacteristic
301C2×C4×D4C2316yes—
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2313yes—
306C2×C4×D4C2313yes—
307C2×#117C2313yes—
308C22×C4⋊C4C2316yes—
309C22×C4⋊C4C2313yes—
310C22×C4⋊C4C2316yes—
311C22×C4⋊C4C2316yes—
312C22×C42C2316yes—
313C22×C42C2313yes—
314C22×C42C2313yes—
315#399C23112yes—
316#398C23112yes—
317#398C23112yes—
318#396C23112yes—
319#396C23112yes—
320#396C23112yes—
321#395C23112yes—
322#395C2316yes—
323#395C2316yes—
324#394C2316yes—
325#394C23112yes—
326#394C23112yes—
327#394C2312yes—
328#394C2316yes—
329#394C2316yes—
330#394C2316yes—
331#394C2316yes—
332#394C23112yes—
333#394C23112yes—
334#393C23112yes—
335#393C2316yes—
336#393C2316yes—
337#392C2316yes—
338#392C23112yes—
339#392C23112yes—
340#392C2312yes—
341#392C2316yes—
342#392C2316yes—
343#392C2316yes—
344#392C2316yes—
345#392C23112yes—
346#392C23112yes—
347#391C2316yes—
348#391C2316yes—
349#391C2316yes—
350#391C2313yes—
351#391C2316yes—
352#391C2313yes—
353#390C2311yescharacteristic
354#390C2313yes—
355#390C2316yes—
356#390C2316yes—
357#390C2316yes—
358#390C2316yes—
359#390C2313yes—
360#390C2313yes—
361#390C2313yes—
362#390C2316yes—
363#390C2316yes—
364#390C2316yes—
365#390C2316yes—
366#390C2316yes—
367#390C2313yes—
368#389C2316yes—
369#389C2316yes—
370#389C2316yes—
371#389C2316yes—
372#389C2316yes—
373#389C2313yes—
374#389C2313yes—
375#389C2313yes—
376#389C2316yes—
377#389C2311yescharacteristic
378#388C23112yes—
379#388C23112yes—
380#388C2316yes—
381#388C2316yes—
382#388C2316yes—
383#388C2316yes—
384#388C2316yes—
385#388C2316yes—
386#388C2316yes—
387#387C2316yes—
388#387C23112yes—
389#386C2316yes—
390#386C23112yes—
391#386C2316yes—
392#386C23112yes—
393#386C23112yes—
394#386C23112yes—
395#386C23112yes—
396#386C2316yes—
397#386C2316yes—
398#386C2312yes—
399#385C23112yes—
400#385C2316yes—
401#385C23112yes—
402#385C23112yes—
403#385C23112yes—
404#385C23112yes—
405#384C2313yes—
406#384C2313yes—
407#382C2313yes—
408#380C2316yes—
409#380C2313yes—
410#380C2316yes—
411#380C2313yes—
412#380C2316yes—
413#380C2313yes—
414#380C2316yes—
415#380C2316yes—
416#380C2313yes—
417C4×C4⋊C4C2313yes—
418C4×C4⋊C4C2316yes—
419C4×C4⋊C4C2313yes—
420C4×C4⋊C4C2313yes—
421C4×C4⋊C4C2313yes—
422C4×C4⋊C4C2313yes—
423C4×C4⋊C4C2313yes—
424C4×C4⋊C4C2313yes—
425C4×C4⋊C4C2313yes—
426C4×C4⋊C4C2313yes—
427C4×C22⋊C4C2316yes—
428C4×C22⋊C4C2313yes—
429C4×C22⋊C4C2316yes—
430C4×C22⋊C4C2313yes—
431C4×C22⋊C4C2316yes—
432C4×C22⋊C4C2313yes—
433C4×C22⋊C4C2316yes—
434C4×C22⋊C4C2313yes—
435C4×C22⋊C4C2313yes—
436C4×C22⋊C4C2316yes—
437C4×C22⋊C4C2311yescharacteristic
438C4×C22⋊C4C2316yes—
439C43C2313yes—
4402−1+4—4128no—
4412−1+4—4128no—
442C2×#41—24no—
443C2×#41—224no—
444C2×#41—224no—
445C2×#41—224no—
446C2×#41—28no—
447C2×#41—28no—
448C2×#41—24no—
449C2×#41—28no—
450C2×#41—224no—
451C2×#41—224no—
452C2×#41—224no—
453C2×#41—224no—
454C2×#41—224no—
455C2×#41—224no—
456C2×#41—224no—
457C2×#41—224no—
458C2×#41—224no—
459C2×#41—412no—
460C2×#41—412no—
461C2×#41—412no—
462C2×#41—412no—
463C2×#41—412no—
464C2×#41—412no—
465C2×#41C2×D418yes—
466C22×Q8—28no—
467C22×Q8—24no—
468C22×Q8—28no—
469C22×Q8—24no—
470C22×Q8—224no—
471C22×Q8—224no—
472C22×Q8—224no—
473C22×Q8—28no—
474C22×Q8—28no—
475C22×Q8—28no—
476C22×Q8—224no—
477C22×Q8—412no—
478C22×Q8—412no—
479C22×Q8C2×D4116yes—
480C22×Q8C2×D418yes—
481C22×Q8C2416yes—
482C22×Q8C2416yes—
483C22×Q8C2416yes—
484C22×Q8C2416yes—
485C22×Q8C2413yes—
486C22×Q8C2411yescharacteristic
487C22×D4C2411yescharacteristic
488C22×D4C2413yes—
489C22×D4C2416yes—
490C22×D4C2412yes—
491C22×D4C2416yes—
492C22×D4C2412yes—
493C22×D4C2412yes—
494C22×D4C2416yes—
495C22×D4C2416yes—
496C22×D4C2416yes—
497C22×D4C2416yes—
498C22×D4C2412yes—
499C22×D4C2411yescharacteristic
500C22×D4C2413yes—
501C22×D4C24112yes—
502C22×D4C2416yes—
503C22×D4C2416yes—
504C22×D4C2416yes—
505C22×D4C2416yes—
506C22×D4C2413yes—
507C23×C4C2413yes—
508C23×C4C2416yes—
509C23×C4C2416yes—
510C23×C4C2411yescharacteristic
511C23×C4C2413yes—
512C23×C4C24112yes—
513C23×C4C24112yes—
514C23×C4C2412yes—
515C23×C4C2416yes—
516C23×C4C2413yes—
517C23×C4C2413yes—
518C23×C4C2416yes—
519C23×C4C2413yes—
520C4⋊Q8—224no—
521C4⋊Q8—224no—
522C4⋊Q8—212no—
523C4⋊Q8—224no—
524C4⋊Q8—224no—
525C4⋊Q8—212no—
526C4⋊Q8—212no—
527C4⋊Q8C2×D4124yes—
528#127—24no—
529#127—224no—
530#127—224no—
531#127—212no—
532#127—212no—
533#127—46no—
534#124—224no—
535#124—224no—
536#124—224no—
537#124—224no—
538#124—224no—
539#124—224no—
540#124—412no—
541#124C2×D4124yes—
542#123—248no—
543#123—248no—
544C22⋊Q8—224no—
545C22⋊Q8—224no—
546C22⋊Q8—224no—
547C22⋊Q8—224no—
548C22⋊Q8—224no—
549C22⋊Q8—224no—
550C22⋊Q8—248no—
551C22⋊Q8—248no—
552C22⋊Q8—224no—
553C22⋊Q8—248no—
554C22⋊Q8—412no—
555C22⋊Q8C2×D4148yes—
556C22⋊Q8C2×D4124yes—
557#121—24no—
558#121—224no—
559#121—212no—
560#121—224no—
561#121—248no—
562#121—224no—
563#121—224no—
564#121—212no—
565#121—224no—
566#121—224no—
567#121—212no—
568#121—224no—
569#121—224no—
570#121—212no—
571#121—24no—
572#121—224no—
573#121—28no—
574#121—248no—
575#121—224no—
576#121—224no—
577#121—248no—
578#121—248no—
579#121—412no—
580#121—412no—
581#121—412no—
582#121—412no—
583#121C2×D4124yes—
584C4×Q8—24no—
585C4×Q8—28no—
586C4×Q8—24no—
587C4×Q8—24no—
588C4×Q8—212no—
589C4×Q8—224no—
590C4×Q8—224no—
591C4×Q8—212no—
592C4×Q8C2×D418yes—
593C4×Q8C2×D418yes—
594C4×D4—224no—
595C4×D4—224no—
596C4×D4—224no—
597C4×D4—224no—
598C4×D4—212no—
599C4×D4—224no—
600C4×D4—224no—
601C4×D4—24no—
602C4×D4—248no—
603C4×D4—248no—
604C4×D4—212no—
605C4×D4—212no—
606C4×D4—224no—
607C4×D4—212no—
608C4×D4—46no—
609C4×D4—46no—
610C4×D4—412no—
611C4×D4—46no—
612C4×D4C2×D4124yes—
613C4×D4C2×D4124yes—
614#117—212no—
615C2×C4⋊C4—224no—
616C2×C4⋊C4—212no—
617C2×C4⋊C4—224no—
618C2×C4⋊C4—224no—
619C2×C4⋊C4C2413yes—
620C2×C4⋊C4C2416yes—
621C2×C4⋊C4C2413yes—
622C2×C4⋊C4C2416yes—
623C2×C4⋊C4C2416yes—
624C2×C4⋊C4C24112yes—
625C2×C4⋊C4C2416yes—
626C2×C4⋊C4C24112yes—
627C2×C4⋊C4C2413yes—
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2416yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2413yes—
632C2×C4⋊C4C2413yes—
633C2×C4⋊C4C2416yes—
634C2×C4⋊C4C2416yes—
635C2×C4⋊C4C24112yes—
636C2×C4⋊C4C2413yes—
637C2×C4⋊C4C2416yes—
638C2×C4⋊C4C2413yes—
639C2×C4⋊C4C2416yes—
640C2×C4⋊C4C2413yes—
641C2×C4⋊C4C2413yes—
642C2×C4⋊C4C2413yes—
643C2×C4⋊C4C2416yes—
644C2×C4⋊C4C2413yes—
645C2×C4⋊C4C2411yescharacteristic
646C2×C22⋊C4C2416yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2416yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2416yes—
651C2×C22⋊C4C2411yescharacteristic
652C2×C22⋊C4C2416yes—
653C2×C22⋊C4C2416yes—
654C2×C22⋊C4C24112yes—
655C2×C22⋊C4C2416yes—
656C2×C22⋊C4C24112yes—
657C2×C22⋊C4C2416yes—
658C2×C22⋊C4C2416yes—
659C2×C22⋊C4C2416yes—
660C2×C22⋊C4C2416yes—
661C2×C22⋊C4C2416yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2416yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2416yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2416yes—
668C2×C22⋊C4C2416yes—
669C2×C22⋊C4C2413yes—
670C2×C22⋊C4C2413yes—
671C2×C22⋊C4C2413yes—
672C2×C22⋊C4C24112yes—
673C2×C22⋊C4C2416yes—
674C2×C22⋊C4C24112yes—
675C2×C22⋊C4C2416yes—
676C2×C22⋊C4C2413yes—
677C2×C22⋊C4C2411yescharacteristic
678C2×C22⋊C4C2416yes—
679C2×C22⋊C4C2416yes—
680C2×C42—212no—
681C2×C42—224no—
682C2×C42—212no—
683C2×C42C2413yes—
684C2×C42C2413yes—
685C2×C42C2413yes—
686C2×C42C2416yes—
687C2×C42C2413yes—
688C2×C42C2413yes—
689C2×C42C2416yes—
690C2×C42C2416yes—
691C2×C42C2413yes—
692C2×C42C2413yes—
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2413yes—
696C2×C42C2413yes—
697C2×C42C2413yes—
698C2×C42C2413yes—
699#95C2411yescharacteristic
700#95C2411yescharacteristic
701#95C2412yes—
702#95C2413yes—
703#95C2413yes—
704#95C2413yes—
705#95C2413yes—
706#95C2416yes—
707#95C2416yes—
708#95C2416yes—
709#95C2416yes—
710#95C2416yes—
711#95C2416yes—
712#95C2416yes—
713#95C2416yes—
714#95C2416yes—
715#95C24112yes—
716#95C24112yes—
717C24C2512yes—
718C24C2516yes—
719C24C2513yes—
720C24C2512yes—
721C24C2511yescharacteristic
722#41—232no—
723#41—496no—
724#41—496no—
725#41—496no—
726#41—496no—
727#41—496no—
728#41—496no—
729#41—432no—
730C2×Q8—264no—
731C2×Q8—232no—
732C2×Q8—26no—
733C2×Q8—212no—
734C2×Q8—212no—
735C2×Q8—212no—
736C2×Q8—212no—
737C2×Q8—212no—
738C2×Q8—212no—
739C2×Q8—212no—
740C2×Q8—212no—
741C2×Q8—26no—
742C2×Q8—212no—
743C2×Q8—46no—
744C2×Q8—46no—
745C2×Q8—496no—
746C2×Q8—496no—
747C2×Q8—432no—
748C2×Q8C22×D4124yes—
749C2×Q8C22×D4112yes—
750C2×Q8C22×D414yes—
751C2×Q8C22×D414yes—
752C2×Q8H(5,𝔽2)14yes—
753C2×D4—24no—
754C2×D4—24no—
755C2×D4—212no—
756C2×D4—24no—
757C2×D4—24no—
758C2×D4—212no—
759C2×D4—212no—
760C2×D4—212no—
761C2×D4—212no—
762C2×D4—212no—
763C2×D4—24no—
764C2×D4—212no—
765C2×D4—224no—
766C2×D4—26no—
767C2×D4—22no—
768C2×D4—26no—
769C2×D4—24no—
770C2×D4—212no—
771C2×D4—212no—
772C2×D4—212no—
773C2×D4—212no—
774C2×D4—212no—
775C2×D4—212no—
776C2×D4—212no—
777C2×D4—26no—
778C2×D4—212no—
779C2×D4—22no—
780C2×D4—212no—
781C2×D4—24no—
782C2×D4—22no—
783C2×D4—26no—
784C2×D4—22no—
785C2×D4—24no—
786C2×D4—26no—
787C2×D4—22no—
788C2×D4—43no—
789C2×D4—43no—
790C2×D4—42no—
791C2×D4—46no—
792C2×D4—42no—
793C2×D4—42no—
794C2×D4—46no—
795C2×D4—46no—
796C2×D4—46no—
797C2×D4—46no—
798C2×D4—42no—
799C2×D4—46no—
800C2×D4—46no—
801C2×D4—46no—
802C2×D4—412no—
803C2×D4—412no—
804C2×D4—46no—
805C2×D4—46no—
806C2×D4—46no—
807C2×D4—46no—
808C2×D4—46no—
809C2×D4—46no—
810C2×D4C22×D414yes—
811C2×D4C22×D4112yes—
812C2×D4C22×D4112yes—
813C22×C4—26no—
814C22×C4—212no—
815C22×C4—26no—
816C22×C4—212no—
817C22×C4—26no—
818C22×C4—26no—
819C22×C4—224no—
820C22×C4—24no—
821C22×C4—22no—
822C22×C4—26no—
823C22×C4—26no—
824C22×C4—224no—
825C22×C4—224no—
826C22×C4—224no—
827C22×C4—212no—
828C22×C4—212no—
829C22×C4—212no—
830C22×C4—212no—
831C22×C4—212no—
832C22×C4—212no—
833C22×C4—24no—
834C22×C4—26no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—26no—
838C22×C4—26no—
839C22×C4—26no—
840C22×C4—212no—
841C22×C4—42no—
842C22×C4—43no—
843C22×C4—412no—
844C22×C4—412no—
845C22×C4—46no—
846C22×C4—43no—
847C22×C4—46no—
848C22×C4—43no—
849C22×C4C22×D4112yes—
850C22×C4C22×D4124yes—
851C22×C4C22×D4112yes—
852C22×C4C2513yes—
853C22×C4C2511yescharacteristic
854C22×C4C2513yes—
855C22×C4C2511yescharacteristic
856C22×C4C2513yes—
857C22×C4C2516yes—
858C22×C4C2512yes—
859C22×C4C2516yes—
860C22×C4C2511yescharacteristic
861C22×C4C2513yes—
862C22×C4C2513yes—
863C22×C4C2511yescharacteristic
864C22×C4C2516yes—
865C22×C4C2513yes—
866C22×C4C2512yes—
867C22×C4C2511yescharacteristic
868C22×C4C2513yes—
869C22×C4C2511yescharacteristic
870C4⋊C4—212no—
871C4⋊C4—26no—
872C4⋊C4—212no—
873C4⋊C4—224no—
874C4⋊C4—26no—
875C4⋊C4—212no—
876C4⋊C4—224no—
877C4⋊C4—212no—
878C4⋊C4—26no—
879C4⋊C4—24no—
880C4⋊C4—212no—
881C4⋊C4—22no—
882C4⋊C4—212no—
883C4⋊C4—224no—
884C4⋊C4—212no—
885C4⋊C4—26no—
886C4⋊C4—26no—
887C4⋊C4—26no—
888C4⋊C4—43no—
889C4⋊C4—46no—
890C4⋊C4—46no—
891C4⋊C4C22×D4112yes—
892C4⋊C4C22×D4112yes—
893C4⋊C4C22×D4112yes—
894C4⋊C4C22×D4124yes—
895C4⋊C4C22×D4112yes—
896C4⋊C42−1+414yescomplemented
897C22⋊C4—24no—
898C22⋊C4—212no—
899C22⋊C4—212no—
900C22⋊C4—212no—
901C22⋊C4—212no—
902C22⋊C4—212no—
903C22⋊C4—212no—
904C22⋊C4—24no—
905C22⋊C4—212no—
906C22⋊C4—224no—
907C22⋊C4—212no—
908C22⋊C4—212no—
909C22⋊C4—224no—
910C22⋊C4—212no—
911C22⋊C4—212no—
912C22⋊C4—24no—
913C22⋊C4—24no—
914C22⋊C4—212no—
915C22⋊C4—22no—
916C22⋊C4—212no—
917C22⋊C4—46no—
918C22⋊C4—43no—
919C22⋊C4—46no—
920C22⋊C4—43no—
921C22⋊C4—43no—
922C22⋊C4—42no—
923C22⋊C4—46no—
924C22⋊C4—46no—
925C22⋊C4—412no—
926C22⋊C4—412no—
927C22⋊C4C22×D4112yes—
928C22⋊C4C22×D4124yes—
929C22⋊C4C22×D414yes—
930C22⋊C4C22×D4124yes—
931C42—22no—
932C42—26no—
933C42—26no—
934C42—26no—
935C42—212no—
936C42—26no—
937C42—212no—
938C42—212no—
939C42—26no—
940C42—26no—
941C42—22no—
942C42—26no—
943C42—43no—
944C42—43no—
945C42C22×D4112yes—
946C42C22×D4112yes—
947C23—23no—
948C23—22no—
949C23—21no—
950C23—21no—
951C23—22no—
952C23—23no—
953C23—22no—
954C23—23no—
955C23—21no—
956C23—21no—
957C23—21no—
958C23—22no—
959C23—23no—
960C23—23no—
961C23—22no—
962C23—23no—
963C23—21no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—26no—
968C23—26no—
969C23—26no—
970C23—22no—
971C23—22no—
972C23—26no—
973C23—26no—
974C23—22no—
975C23—26no—
976C23—22no—
977C23—22no—
978C23—26no—
979C23C23×D412yes—
980C23C23×D414yes—
981C23C23×D416yes—
982C23C2611yescharacteristic
983Q8—248no—
984Q8—224no—
985Q8—424no—
986Q8—424no—
987Q8—424no—
988Q8D42116yes—
989D4—224no—
990D4—28no—
991D4—412no—
992D4—424no—
993D4—48no—
994D4—48no—
995D4—48no—
996D4—424no—
997D4—424no—
998D4—424no—
999D4—48no—
1000D4—424no—
1001D4—424no—
1002D4—44no—
1003D4—412no—
1004D4—812no—
1005D4—812no—
1006D4—812no—
1007D4—824no—
1008D4—812no—
1009C2×C4—22no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—26no—
1013C2×C4—23no—
1014C2×C4—21no—
1015C2×C4—23no—
1016C2×C4—26no—
1017C2×C4—21no—
1018C2×C4—23no—
1019C2×C4—23no—
1020C2×C4—23no—
1021C2×C4—21no—
1022C2×C4—23no—
1023C2×C4—21no—
1024C2×C4—22no—
1025C2×C4—248no—
1026C2×C4—224no—
1027C2×C4—224no—
1028C2×C4—21no—
1029C2×C4—23no—
1030C2×C4—23no—
1031C2×C4—26no—
1032C2×C4—22no—
1033C2×C4—26no—
1034C2×C4—22no—
1035C2×C4—26no—
1036C2×C4—21no—
1037C2×C4—23no—
1038C2×C4—26no—
1039C2×C4—22no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—23no—
1043C2×C4—23no—
1044C2×C4—21no—
1045C2×C4—26no—
1046C2×C4—23no—
1047C2×C4—23no—
1048C2×C4—26no—
1049C2×C4—21no—
1050C2×C4—23no—
1051C2×C4—23no—
1052C2×C4—48no—
1053C2×C4—412no—
1054C2×C4—448no—
1055C2×C4—448no—
1056C2×C4—424no—
1057C2×C4—424no—
1058C2×C4—44no—
1059C2×C4—412no—
1060C2×C4—86no—
1061C2×C4—812no—
1062C2×C4C23×D412yes—
1063C2×C4C23×D416yes—
1064C2×C4C23×D416yes—
1065C2×C4C23×D412yes—
1066C2×C4C23×D4112yes—
1067C2×C4C23×D416yes—
1068C2×C4C23×D416yes—
1069C2×C4C23×D416yes—
1070C2×C4C23×D412yes—
1071C2×C4C2×H(5,𝔽2)16yes—
1072C2×C4C2×2−1+414yes—
1073C2×C4C2×2−1+412yes—
1074C2×C4#58512yes—
1075C2×C4#58512yes—
1076C22—26no—
1077C22—22no—
1078C22—24no—
1079C22—24no—
1080C22—22no—
1081C22—26no—
1082C22—22no—
1083C22—24no—
1084C22—26no—
1085C22—42no—
1086C22—43no—
1087C22—41no—
1088C22—43no—
1089C22—41no—
1090C22—42no—
1091C22—41no—
1092C22—43no—
1093C22—42no—
1094C22—41no—
1095C22—42no—
1096C22—43no—
1097C22—42no—
1098C22—46no—
1099C22—42no—
1100C22—46no—
1101C22—42no—
1102C22—46no—
1103C22—46no—
1104C22—42no—
1105C22—42no—
1106C22—46no—
1107C22—42no—
1108C22—46no—
1109C22—46no—
1110C22—42no—
1111C22C24×D411yescharacteristic
1112C22C24×D411yescharacteristic
1113C22C22×H(5,𝔽2)11yescharacteristic
1114C22C22×2−1+411yescharacteristic
1115C22C2×#58511yescharacteristic
1116C22C2×#58511yescharacteristic
1117C222−1+611yescharacteristic
1118C4—22no—
1119C4—24no—
1120C4—22no—
1121C4—26no—
1122C4—26no—
1123C4—22no—
1124C4—26no—
1125C4—212no—
1126C4—43no—
1127C4—41no—
1128C4—43no—
1129C4—41no—
1130C4—46no—
1131C4—43no—
1132C4—42no—
1133C4—46no—
1134C4C2×D42112yes—
1135C4#349714yescomplemented
1136C2—42no—
1137C2—46no—
1138C2—44no—
1139C2—82no—
1140C2—86no—
1141C2C22×D4211yescharacteristic
1142C2C2×#349711yescharacteristic
1143C2#6281211yescharacteristic
1144C2#6292211yescharacteristic
1145C2D4×2−1+411yescharacteristic
1146C2#6300211yescharacteristic
1147C2#6303911yescharacteristic
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×#3499C2semidirect
2. C2×#3497C2semidirect
3. C2×#3497C2semidirect
4. #59654C2semidirect
5. #59128C2semidirect
6. #59127C2semidirect
7. #59051C2semidirect
8. #45245C2semidirect
9. #44884C2semidirect
10. #39341C2semidirect
11. #39340C2semidirect
12. #39335C2semidirect
13. Q8×#121C2semidirect
14. #36465C2semidirect
15. #36455C2semidirect
16. #36434C2semidirect
17. #36125C2semidirect
18. #36122C2semidirect
19. #35757C2semidirect
20. #35687C2semidirect
21. #34925C2semidirect
22. C4×D4×Q8C2semidirect
23. C4×#548C2semidirect
189. D4×Q8D4semidirect
196. #548D4semidirect
896. C4⋊C42−1+4semidirect
1135. C4#3497semidirect

Maximal subgroups

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

subgroupindex
C2×#34992
C2×#34972
#596542
#591282
#591272
#590512
#452452
#448842
#393412
#393402
#393352
Q8×#1212
#364652
#364552
#364342
#361252
#361222
#357572
#356872
#349252
C4×D4×Q82
C4×#5482