Finite Group Databasebeta

← #7693602

Subgroups — #7693602

Order 512.

11369 conjugacy classes of subgroups.

The subgroup lattice has 1171 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3500C212yesmaximal, complemented
2C2×#3498C211yesmaximal, characteristic, complemented
3C2×#3497C211yesmaximal, characteristic, complemented
4#59412C213yesmaximal, complemented
5#59131C216yesmaximal, complemented
6#59124C213yesmaximal, complemented
7#59035C213yesmaximal, complemented
8#45093C216yesmaximal, complemented
9#44868C216yesmaximal, complemented
10#39343C213yesmaximal, complemented
11#39342C213yesmaximal, complemented
12#39334C216yesmaximal, complemented
13#36576C211yesmaximal, characteristic, complemented
14#36465C211yesmaximal, characteristic, complemented
15#36444C211yesmaximal, characteristic, complemented
16#36430C212yesmaximal, complemented
17#36121C213yesmaximal, complemented
18D4×#124C213yesmaximal, complemented
19#36082C212yesmaximal, complemented
20#35757C212yesmaximal, complemented
21#34925C213yesmaximal, complemented
22C4×#550C211yesmaximal, characteristic, complemented
23C4×#548C211yesmaximal, characteristic, complemented
24C22×2−1+4C2212yescomplemented
25C22×H(5,𝔽2)C2212yes—
26#3500—232no—
27#3498—216no—
28#3497—216no—
29C2×#550C2212yes—
30C2×#550C2211yescharacteristic
31C2×#550C2211yescharacteristic
32C2×#550C2213yescomplemented
33C2×D4×Q8C2213yescomplemented
34C2×D4×Q8C2211yescharacteristic, complemented
35C2×#548C2212yes—
36C2×#548C2211yescharacteristic
37C2×#548C2216yescomplemented
38C2×#548C2212yescomplemented
39C2×#548C2212yescomplemented
40C2×#548C2212yescomplemented
41C2×#548C2212yescomplemented
42C2×#546C2216yescomplemented
43C2×#546C2216yescomplemented
44C2×#546C2216yescomplemented
45C2×#546C2216yescomplemented
46C2×D42C2213yes—
47C2×D42C2213yes—
48C2×D42C2216yes—
49C2×#537C2216yescomplemented
50C2×#536C2216yescomplemented
51C2×#535C2216yes—
52C2×#535C2216yescomplemented
53C2×#532C2213yes—
54C2×#532C2213yescomplemented
55C2×#532C2213yescomplemented
56C2×#532C2216yescomplemented
57C22×#127C2213yes—
58C22×#124C2216yescomplemented
59C2×C4×#41C2211yescharacteristic
60C2×C4×#41C2212yescomplemented
61C22×C4×Q8C2211yescharacteristic, complemented
62#2858C2213yescomplemented
63#2857C2213yescomplemented
64#2856C2213yescomplemented
65#2850C2216yescomplemented
66#2678C22112yescomplemented
67#2674C22112yescomplemented
68#2673C22112yescomplemented
69#2672C22112yescomplemented
70#2670C22112yescomplemented
71#2669C22112yescomplemented
72#2668C22112yescomplemented
73#2616C2216yescomplemented
74#2615C2216yescomplemented
75#2555C2216yescomplemented
76#2555C2216yescomplemented
77#2551C2213yescomplemented
78#2548C2213yescomplemented
79#2547C2213yescomplemented
80#2544C2216yescomplemented
81#2542C2213yescomplemented
82#2541C2213yescomplemented
83#2541C2213yescomplemented
84#2541C2213yescomplemented
85#2540C2216yescomplemented
86#2540C2216yescomplemented
87#2538C2213yescomplemented
88#2537C2213yescomplemented
89#2537C2213yescomplemented
90#2535C2216yescomplemented
91#2491C2213yescomplemented
92#2491C2216yescomplemented
93#2491C2216yescomplemented
94#2491C2211yescharacteristic, complemented
95#2472C22112yescomplemented
96#2472C22112yescomplemented
97#2445C2216yescomplemented
98#2445C2216yescomplemented
99#2436C2216yescomplemented
100#2435C2216yescomplemented
101#2435C2216yescomplemented
102#2435C2216yescomplemented
103#2433C2216yescomplemented
104#2431C2216yescomplemented
105#2431C2216yescomplemented
106#2428C2213yescomplemented
107#2428C2213yescomplemented
108#2428C2216yescomplemented
109#2428C2216yescomplemented
110#2428C2216yescomplemented
111#2427C2216yescomplemented
112#2427C2216yescomplemented
113#2426C2216yescomplemented
114#2424C22112yescomplemented
115#2422C2216yescomplemented
116#2418C22112yescomplemented
117#2416C2216yescomplemented
118#2415C2216yescomplemented
119#2415C2216yescomplemented
120#2414C2216yescomplemented
121#2410C22112yescomplemented
122#2409C2216yescomplemented
123#2408C2216yescomplemented
124#2408C2216yescomplemented
125#2408C2216yescomplemented
126#2408C2216yescomplemented
127#2408C2216yescomplemented
128#2407C2216yescomplemented
129#2407C2216yescomplemented
130#2388C2216yescomplemented
131#2388C2216yescomplemented
132#2367C2213yescomplemented
133#2366C2213yescomplemented
134#2363C2216yescomplemented
135#2362C2213yescomplemented
136#2361C2213yescomplemented
137#2354C2213yescomplemented
138#2352C2213yescomplemented
139#2351C2211yescharacteristic, complemented
140Q8×C4⋊C4C2211yescharacteristic, complemented
141#2341C2211yescharacteristic
142#2341C2212yescomplemented
143#2341C2212yescomplemented
144Q8×C22⋊C4C2212yescomplemented
145Q8×C22⋊C4C2211yescharacteristic, complemented
146D4×C22⋊C4C2216yescomplemented
147D4×C22⋊C4C2216yescomplemented
148D4×C22⋊C4C2216yescomplemented
149C4×#127C2213yescomplemented
150C4×#127C2213yescomplemented
151C4×#124C2213yescomplemented
152C4×C22⋊Q8C2213yescomplemented
153C4×#121C2216yescomplemented
154C4×#121C2213yescomplemented
155C4×#121C2213yescomplemented
156C4×#121C2213yescomplemented
157C4×#121C2216yescomplemented
158C42×Q8C2211yescharacteristic, complemented
159C42×D4C2213yescomplemented
160C42×D4C2213yescomplemented
161C2×2−1+4—216no—
162C2×2−1+4—216no—
163C2×2−1+4—48no—
164C2×H(5,𝔽2)—216no—
165C2×H(5,𝔽2)—216no—
166C2×H(5,𝔽2)—48no—
167C22×#41C2312yes—
168C22×#41C2316yes—
169C22×#41C2316yes—
170C22×#41C2316yes—
171C22×#41C2316yes—
172C22×#41C2311yescharacteristic
173C22×#41C2312yes—
174C23×Q8C2312yes—
175C23×Q8C2316yes—
176C23×Q8C2311yescharacteristic
177C23×D4C2316yes—
178C23×D4C2316yes—
179C23×D4C2316yes—
180C23×D4C2316yes—
181C23×D4C2316yes—
182#550—216no—
183#550—224no—
184#550—28no—
185#550D4116yescomplemented
186D4×Q8—28no—
187D4×Q8—224no—
188#548—216no—
189#548—216no—
190#548—216no—
191#548—248no—
192#548—216no—
193#548—48no—
194#548D4116yescomplemented
195#546—248no—
196#546—248no—
197#546—248no—
198#546—248no—
199D42—224no—
200D42—248no—
201D42—224no—
202#537—248no—
203#536—248no—
204#535—248no—
205#535—248no—
206#532—224no—
207#532—224no—
208#532—224no—
209#532—248no—
210C2×C4⋊Q8C2313yes—
211C2×C4⋊Q8C2316yes—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2313yes—
214C2×#127—224no—
215C2×#127C2313yes—
216C2×#127C2316yes—
217C2×#127C2313yes—
218C2×#127C2316yes—
219C2×#127C2316yes—
220C2×#127C2313yes—
221C2×#127C2313yes—
222C2×#127C2313yes—
223C2×#124—248no—
224C2×#124C2316yes—
225C2×#124C2316yes—
226C2×#124C23112yes—
227C2×#124C2316yes—
228C2×#124C2316yes—
229C2×#124C2316yes—
230C2×#124C2316yes—
231C2×#124C2312yes—
232C2×#124C2316yes—
233C2×#124C2316yes—
234C2×#124C2313yes—
235C2×#123C23112yes—
236C2×#123C23112yes—
237C2×C22⋊Q8C2316yes—
238C2×C22⋊Q8C2316yes—
239C2×C22⋊Q8C2316yes—
240C2×C22⋊Q8C2316yes—
241C2×C22⋊Q8C2316yes—
242C2×C22⋊Q8C23112yes—
243C2×C22⋊Q8C2316yes—
244C2×C22⋊Q8C2313yes—
245C2×#121C2316yes—
246C2×#121C2316yes—
247C2×#121C2316yes—
248C2×#121C2313yes—
249C2×#121C2316yes—
250C2×#121C2316yes—
251C2×#121C2316yes—
252C2×#121C23112yes—
253C2×#121C2316yes—
254C2×#121C2316yes—
255C2×#121C2316yes—
256C2×#121C2316yes—
257C2×#121C2316yes—
258C2×#121C2316yes—
259C2×#121C2313yes—
260C2×#121C2313yes—
261C2×#121C2311yescharacteristic
262C2×#121C2316yes—
263C2×#121C2316yes—
264C2×#121C2313yes—
265C2×#121C2316yes—
266C2×#121C2316yes—
267C2×#121C2313yes—
268C2×#121C2316yes—
269C2×#121C2316yes—
270C2×#121C2313yes—
271C2×#120C23112yes—
272C2×#120C23112yes—
273C2×#120C23112yes—
274C2×#120C23112yes—
275C2×#120C23112yes—
276C4×#41—28no—
277C4×#41—216no—
278C2×C4×Q8—28no—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2313yes—
284C2×C4×Q8C2313yes—
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×D4C2316yes—
288C2×C4×D4C2313yes—
289C2×C4×D4C2316yes—
290C2×C4×D4C2313yes—
291C2×C4×D4C2316yes—
292C2×C4×D4C2316yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2316yes—
295C2×C4×D4C2316yes—
296C2×C4×D4C2316yes—
297C2×C4×D4C2316yes—
298C2×C4×D4C2316yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2316yes—
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2316yes—
306C2×C4×D4C2313yes—
307C2×C4×D4C2313yes—
308C2×#117C2313yes—
309C2×#117C2316yes—
310C22×C4⋊C4C2313yes—
311C22×C22⋊C4C23112yes—
312C22×C22⋊C4C23112yes—
313C22×C42C2316yes—
314C22×C42C2313yes—
315C22×C42C2313yes—
316#399C23112yes—
317#397C23112yes—
318#397C23112yes—
319#396C23112yes—
320#395C2316yes—
321#395C2316yes—
322#394C23112yes—
323#394C23112yes—
324#394C23112yes—
325#394C2312yes—
326#394C2316yes—
327#394C2316yes—
328#394C2316yes—
329#394C2316yes—
330#394C2316yes—
331#394C23112yes—
332#394C23112yes—
333#394C23112yes—
334#394C23112yes—
335#393C23112yes—
336#393C2312yes—
337#393C2316yes—
338#392C2316yes—
339#392C23112yes—
340#392C23112yes—
341#392C2316yes—
342#392C2316yes—
343#392C2316yes—
344#392C2316yes—
345#392C2316yes—
346#392C23112yes—
347#392C23112yes—
348#391C2316yes—
349#391C2316yes—
350#391C2313yes—
351#391C2313yes—
352#390C2311yescharacteristic
353#390C2313yes—
354#390C2316yes—
355#390C2316yes—
356#390C2316yes—
357#390C2316yes—
358#390C2316yes—
359#390C2313yes—
360#390C2316yes—
361#390C2316yes—
362#390C2316yes—
363#390C2316yes—
364#390C2316yes—
365#390C2313yes—
366#390C2313yes—
367#390C2316yes—
368#390C2316yes—
369#390C2316yes—
370#390C2316yes—
371#390C2311yescharacteristic
372#389C2313yes—
373#389C2316yes—
374#389C2316yes—
375#389C2313yes—
376#389C2313yes—
377#389C2316yes—
378#389C2313yes—
379#388C2316yes—
380#388C23112yes—
381#388C2316yes—
382#388C23112yes—
383#388C2316yes—
384#388C2316yes—
385#388C2316yes—
386#388C2316yes—
387#388C2312yes—
388#387C2316yes—
389#386C2316yes—
390#386C23112yes—
391#386C23112yes—
392#386C23112yes—
393#386C23112yes—
394#386C23112yes—
395#386C2316yes—
396#386C23112yes—
397#386C2316yes—
398#386C2316yes—
399#386C2316yes—
400#385C2316yes—
401#385C23112yes—
402#384C2313yes—
403#384C2313yes—
404#382C2313yes—
405#380C2313yes—
406#380C2316yes—
407#380C2316yes—
408#380C2313yes—
409#380C2316yes—
410#380C2313yes—
411#380C2316yes—
412#380C2316yes—
413#380C2316yes—
414#380C2311yescharacteristic
415#379C23112yes—
416#379C23112yes—
417#379C23112yes—
418C4×C4⋊C4C2313yes—
419C4×C4⋊C4C2313yes—
420C4×C4⋊C4C2313yes—
421C4×C4⋊C4C2313yes—
422C4×C4⋊C4C2313yes—
423C4×C4⋊C4C2313yes—
424C4×C4⋊C4C2313yes—
425C4×C4⋊C4C2313yes—
426C4×C4⋊C4C2311yescharacteristic
427C4×C22⋊C4C2313yes—
428C4×C22⋊C4C2313yes—
429C4×C22⋊C4C2316yes—
430C4×C22⋊C4C2313yes—
431C4×C22⋊C4C2316yes—
432C4×C22⋊C4C2313yes—
433C4×C22⋊C4C2316yes—
434C4×C22⋊C4C2316yes—
435C4×C22⋊C4C2313yes—
436C4×C22⋊C4C2316yes—
437C4×C22⋊C4C2311yescharacteristic
438C4×C22⋊C4C2316yes—
439C43C2313yes—
440C25C24112yes—
4412−1+4—4128no—
442H(5,𝔽2)—4128no—
443C2×#41—24no—
444C2×#41—28no—
445C2×#41—224no—
446C2×#41—28no—
447C2×#41—28no—
448C2×#41—24no—
449C2×#41—28no—
450C2×#41—28no—
451C2×#41—224no—
452C2×#41—224no—
453C2×#41—224no—
454C2×#41—224no—
455C2×#41—224no—
456C2×#41—224no—
457C2×#41—224no—
458C2×#41—412no—
459C2×#41—412no—
460C2×#41—412no—
461C2×#41—412no—
462C2×#41C2×D418yes—
463C2×#41C2×D4116yes—
464C22×Q8—24no—
465C22×Q8—24no—
466C22×Q8—224no—
467C22×Q8—28no—
468C22×Q8—28no—
469C22×Q8—28no—
470C22×Q8—224no—
471C22×Q8—412no—
472C22×Q8C2×D418yescomplemented
473C22×Q8C2416yes—
474C22×Q8C2416yes—
475C22×Q8C2412yes—
476C22×Q8C2413yes—
477C22×Q8C2411yescharacteristic
478C22×D4—224no—
479C22×D4—224no—
480C22×D4—224no—
481C22×D4—224no—
482C22×D4—224no—
483C22×D4—224no—
484C22×D4—224no—
485C22×D4—224no—
486C22×D4—412no—
487C22×D4—412no—
488C22×D4—412no—
489C22×D4—412no—
490C22×D4—412no—
491C22×D4—412no—
492C22×D4—86no—
493C22×D4C2411yescharacteristic
494C22×D4C2413yes—
495C22×D4C2416yes—
496C22×D4C2416yes—
497C22×D4C2416yes—
498C22×D4C2416yes—
499C22×D4C2416yes—
500C22×D4C2416yes—
501C22×D4C2412yes—
502C22×D4C2416yes—
503C22×D4C2413yes—
504C22×D4C2413yes—
505C22×D4C2416yes—
506C22×D4C2416yes—
507C22×D4C2416yes—
508C22×D4C2416yes—
509C22×D4C2416yes—
510C22×D4C2416yes—
511C22×D4C24112yes—
512C22×D4C2416yes—
513C22×D4C2413yes—
514C22×D4C2416yes—
515C23×C4C2416yes—
516C23×C4C2416yes—
517C23×C4C2411yescharacteristic
518C23×C4C2413yes—
519C23×C4C24112yes—
520C23×C4C2413yes—
521C23×C4C2413yes—
522C23×C4C2416yes—
523C23×C4C2413yes—
524C23×C4C2416yes—
525C23×C4C2416yes—
526C23×C4C2413yes—
527C4⋊Q8—24no—
528C4⋊Q8—224no—
529C4⋊Q8—212no—
530C4⋊Q8—212no—
531#127—212no—
532#127—224no—
533#127—224no—
534#127—224no—
535#127—212no—
536#127—212no—
537#127—46no—
538#127C2×D4124yes—
539#124—224no—
540#124—224no—
541#124—224no—
542#124—224no—
543#124—248no—
544#124—28no—
545#124—224no—
546#124—224no—
547#124—224no—
548#124—412no—
549#124C2×D4124yescomplemented
550#123—248no—
551#123—248no—
552C22⋊Q8—224no—
553C22⋊Q8—224no—
554C22⋊Q8—224no—
555C22⋊Q8—224no—
556C22⋊Q8—224no—
557C22⋊Q8—248no—
558C22⋊Q8—412no—
559C22⋊Q8C2×D4124yescomplemented
560#121—212no—
561#121—224no—
562#121—212no—
563#121—224no—
564#121—224no—
565#121—224no—
566#121—224no—
567#121—248no—
568#121—224no—
569#121—224no—
570#121—24no—
571#121—212no—
572#121—224no—
573#121—224no—
574#121—224no—
575#121—224no—
576#121—224no—
577#121—224no—
578#121—224no—
579#121—412no—
580#121—46no—
581#121—46no—
582#121—412no—
583#121—86no—
584#121C2×D4148yes—
585#121C2×D4124yescomplemented
586#120—248no—
587#120—248no—
588#120—248no—
589#120—248no—
590#120—812no—
591C4×Q8—24no—
592C4×Q8—28no—
593C4×Q8—24no—
594C4×Q8—24no—
595C4×Q8—212no—
596C4×Q8—212no—
597C4×Q8C2×D418yes—
598C4×Q8C2×D418yescomplemented
599C4×D4—224no—
600C4×D4—224no—
601C4×D4—224no—
602C4×D4—224no—
603C4×D4—224no—
604C4×D4—224no—
605C4×D4—212no—
606C4×D4—224no—
607C4×D4—212no—
608C4×D4—224no—
609C4×D4—212no—
610C4×D4—224no—
611C4×D4—212no—
612C4×D4—46no—
613C4×D4—46no—
614C4×D4—46no—
615C4×D4—412no—
616C4×D4—46no—
617C4×D4—86no—
618C4×D4C2×D4124yes—
619C4×D4C2×D4124yescomplemented
620#117—212no—
621#117—224no—
622C2×C4⋊C4—212no—
623C2×C4⋊C4C2413yes—
624C2×C4⋊C4C2416yes—
625C2×C4⋊C4C2413yes—
626C2×C4⋊C4C2416yes—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2413yes—
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2413yes—
632C2×C4⋊C4C2413yes—
633C2×C4⋊C4C2416yes—
634C2×C4⋊C4C2416yes—
635C2×C4⋊C4C2416yes—
636C2×C4⋊C4C2416yes—
637C2×C4⋊C4C2416yes—
638C2×C4⋊C4C2413yes—
639C2×C4⋊C4C2416yes—
640C2×C4⋊C4C2416yes—
641C2×C4⋊C4C2413yes—
642C2×C4⋊C4C2413yes—
643C2×C4⋊C4C2413yes—
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2413yes—
646C2×C22⋊C4—248no—
647C2×C22⋊C4—248no—
648C2×C22⋊C4C2416yes—
649C2×C22⋊C4C2416yes—
650C2×C22⋊C4C2416yes—
651C2×C22⋊C4C24112yes—
652C2×C22⋊C4C24112yes—
653C2×C22⋊C4C24112yes—
654C2×C22⋊C4C2416yes—
655C2×C22⋊C4C24112yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2416yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2411yescharacteristic
662C2×C22⋊C4C2416yes—
663C2×C22⋊C4C2416yes—
664C2×C22⋊C4C2416yes—
665C2×C22⋊C4C24112yes—
666C2×C22⋊C4C2416yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C24112yes—
670C2×C22⋊C4C2416yes—
671C2×C22⋊C4C2413yes—
672C2×C22⋊C4C2413yes—
673C2×C22⋊C4C2416yes—
674C2×C22⋊C4C2416yes—
675C2×C22⋊C4C2413yes—
676C2×C22⋊C4C2416yes—
677C2×C22⋊C4C24112yes—
678C2×C22⋊C4C24112yes—
679C2×C22⋊C4C2416yes—
680C2×C22⋊C4C2416yes—
681C2×C22⋊C4C2416yes—
682C2×C22⋊C4C2413yes—
683C2×C22⋊C4C2416yes—
684C2×C22⋊C4C2411yescharacteristic
685C2×C22⋊C4C2416yes—
686C2×C42—212no—
687C2×C42—224no—
688C2×C42—212no—
689C2×C42C2413yes—
690C2×C42C2416yes—
691C2×C42C2416yes—
692C2×C42C2413yes—
693C2×C42C2411yescharacteristic
694C2×C42C2413yes—
695C2×C42C2413yes—
696C2×C42C2413yes—
697C2×C42C2413yes—
698C2×C42C2413yes—
699C2×C42C2412yes—
700C2×C42C2411yescharacteristic
701C2×C42C2413yes—
702C2×C42C2413yes—
703C2×C42C2413yes—
704C2×C42C2413yes—
705#95C2412yes—
706#95C2411yescharacteristic
707#95C2411yescharacteristic
708#95C2412yes—
709#95C2413yes—
710#95C2416yes—
711#95C2413yes—
712#95C2413yes—
713#95C2416yes—
714#95C2413yes—
715#95C2416yes—
716#95C2416yes—
717#95C2416yes—
718#95C2416yes—
719#95C2416yes—
720#95C2416yes—
721#95C24112yes—
722C24—224no—
723C24—224no—
724C24—412no—
725C24—412no—
726C24—412no—
727C24—412no—
728C24—412no—
729C24C2516yes—
730C24C2512yes—
731C24C2513yes—
732C24C2516yes—
733C24C2511yescharacteristic
734#41—232no—
735#41—264no—
736#41—496no—
737#41—496no—
738#41—496no—
739#41—496no—
740#41—432no—
741C2×Q8—232no—
742C2×Q8—26no—
743C2×Q8—212no—
744C2×Q8—212no—
745C2×Q8—212no—
746C2×Q8—212no—
747C2×Q8—24no—
748C2×Q8—24no—
749C2×Q8—26no—
750C2×Q8—212no—
751C2×Q8—46no—
752C2×Q8—42no—
753C2×Q8—496no—
754C2×Q8—432no—
755C2×Q8C22×D4112yes—
756C2×Q8C22×D414yes—
757C2×Q8C22×D414yes—
758C2×Q8H(5,𝔽2)14yes—
759C2×D4—212no—
760C2×D4—212no—
761C2×D4—212no—
762C2×D4—212no—
763C2×D4—212no—
764C2×D4—212no—
765C2×D4—212no—
766C2×D4—212no—
767C2×D4—24no—
768C2×D4—212no—
769C2×D4—212no—
770C2×D4—212no—
771C2×D4—224no—
772C2×D4—26no—
773C2×D4—212no—
774C2×D4—22no—
775C2×D4—26no—
776C2×D4—212no—
777C2×D4—212no—
778C2×D4—24no—
779C2×D4—212no—
780C2×D4—212no—
781C2×D4—212no—
782C2×D4—212no—
783C2×D4—212no—
784C2×D4—26no—
785C2×D4—212no—
786C2×D4—212no—
787C2×D4—26no—
788C2×D4—26no—
789C2×D4—22no—
790C2×D4—212no—
791C2×D4—26no—
792C2×D4—22no—
793C2×D4—26no—
794C2×D4—496no—
795C2×D4—496no—
796C2×D4—43no—
797C2×D4—43no—
798C2×D4—46no—
799C2×D4—46no—
800C2×D4—46no—
801C2×D4—46no—
802C2×D4—46no—
803C2×D4—46no—
804C2×D4—42no—
805C2×D4—46no—
806C2×D4—46no—
807C2×D4—46no—
808C2×D4—46no—
809C2×D4—46no—
810C2×D4—46no—
811C2×D4—46no—
812C2×D4—46no—
813C2×D4—46no—
814C2×D4—46no—
815C2×D4—46no—
816C2×D4—46no—
817C2×D4—46no—
818C2×D4—46no—
819C2×D4—46no—
820C2×D4—412no—
821C2×D4—412no—
822C2×D4—496no—
823C2×D4—848no—
824C2×D4—848no—
825C2×D4C22×D4112yes—
826C2×D4C22×D4124yes—
827C2×D4C22×D4112yes—
828C2×D4C22×D4124yes—
829C2×D4C22×D4112yes—
830C22×C4—26no—
831C22×C4—26no—
832C22×C4—212no—
833C22×C4—26no—
834C22×C4—212no—
835C22×C4—26no—
836C22×C4—224no—
837C22×C4—22no—
838C22×C4—26no—
839C22×C4—26no—
840C22×C4—224no—
841C22×C4—212no—
842C22×C4—212no—
843C22×C4—212no—
844C22×C4—212no—
845C22×C4—212no—
846C22×C4—212no—
847C22×C4—22no—
848C22×C4—26no—
849C22×C4—26no—
850C22×C4—22no—
851C22×C4—26no—
852C22×C4—212no—
853C22×C4—212no—
854C22×C4—26no—
855C22×C4—43no—
856C22×C4—412no—
857C22×C4—46no—
858C22×C4—46no—
859C22×C4—43no—
860C22×C4—46no—
861C22×C4—46no—
862C22×C4—43no—
863C22×C4C22×D4124yes—
864C22×C4C22×D4112yes—
865C22×C4C22×D4112yes—
866C22×C4C2513yes—
867C22×C4C2512yes—
868C22×C4C2513yes—
869C22×C4C2511yescharacteristic
870C22×C4C2516yes—
871C22×C4C2513yes—
872C22×C4C2511yescharacteristic
873C22×C4C2516yes—
874C22×C4C2512yes—
875C22×C4C2511yescharacteristic
876C22×C4C2513yes—
877C22×C4C2513yes—
878C22×C4C2512yes—
879C22×C4C2511yescharacteristic
880C22×C4C2513yes—
881C22×C4C2511yescharacteristic
882C22×C4C2513yes—
883C22×C4C2511yescharacteristic
884C4⋊C4—212no—
885C4⋊C4—26no—
886C4⋊C4—26no—
887C4⋊C4—212no—
888C4⋊C4—24no—
889C4⋊C4—22no—
890C4⋊C4—26no—
891C4⋊C4—212no—
892C4⋊C4—212no—
893C4⋊C4—212no—
894C4⋊C4—212no—
895C4⋊C4—212no—
896C4⋊C4—26no—
897C4⋊C4—22no—
898C4⋊C4—26no—
899C4⋊C4—26no—
900C4⋊C4—43no—
901C4⋊C4—46no—
902C4⋊C4—46no—
903C4⋊C4C22×D4112yes—
904C4⋊C4C22×D4112yes—
905C4⋊C4C22×D414yes—
906C4⋊C4C22×D4112yes—
907C22⋊C4—212no—
908C22⋊C4—224no—
909C22⋊C4—24no—
910C22⋊C4—212no—
911C22⋊C4—212no—
912C22⋊C4—224no—
913C22⋊C4—212no—
914C22⋊C4—212no—
915C22⋊C4—224no—
916C22⋊C4—224no—
917C22⋊C4—212no—
918C22⋊C4—224no—
919C22⋊C4—24no—
920C22⋊C4—24no—
921C22⋊C4—24no—
922C22⋊C4—212no—
923C22⋊C4—212no—
924C22⋊C4—212no—
925C22⋊C4—22no—
926C22⋊C4—24no—
927C22⋊C4—46no—
928C22⋊C4—46no—
929C22⋊C4—43no—
930C22⋊C4—43no—
931C22⋊C4—43no—
932C22⋊C4—42no—
933C22⋊C4—46no—
934C22⋊C4—412no—
935C22⋊C4—46no—
936C22⋊C4—412no—
937C22⋊C4—46no—
938C22⋊C4—46no—
939C22⋊C4—46no—
940C22⋊C4—412no—
941C22⋊C4C22×D4112yes—
942C22⋊C4C22×D4124yes—
943C22⋊C4C22×D4124yes—
944C22⋊C4C22×D414yes—
945C42—24no—
946C42—22no—
947C42—26no—
948C42—212no—
949C42—212no—
950C42—26no—
951C42—26no—
952C42—26no—
953C42—26no—
954C42—26no—
955C42—22no—
956C42—26no—
957C42—43no—
958C42—43no—
959C42C22×D4112yes—
960C42C22×D4112yes—
961C23—26no—
962C23—23no—
963C23—21no—
964C23—21no—
965C23—26no—
966C23—23no—
967C23—21no—
968C23—21no—
969C23—23no—
970C23—23no—
971C23—26no—
972C23—26no—
973C23—21no—
974C23—23no—
975C23—26no—
976C23—26no—
977C23—23no—
978C23—21no—
979C23—26no—
980C23—22no—
981C23—22no—
982C23—26no—
983C23—26no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—26no—
988C23—26no—
989C23—22no—
990C23—26no—
991C23—26no—
992C23—22no—
993C23—448no—
994C23—824no—
995C23—824no—
996C23—824no—
997C23—824no—
998C23—1612no—
999C23—1612no—
1000C23C23×D416yes—
1001C23C23×D4112yes—
1002C23C23×D412yes—
1003C23C2611yescharacteristic
1004Q8—224no—
1005Q8—424no—
1006Q8—48no—
1007Q8—424no—
1008Q8D42116yes—
1009D4—224no—
1010D4—248no—
1011D4—224no—
1012D4—424no—
1013D4—412no—
1014D4—424no—
1015D4—424no—
1016D4—424no—
1017D4—48no—
1018D4—424no—
1019D4—424no—
1020D4—424no—
1021D4—424no—
1022D4—44no—
1023D4—412no—
1024D4—812no—
1025D4—812no—
1026D4—812no—
1027D4—812no—
1028D4—812no—
1029D4—824no—
1030D4—812no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—22no—
1034C2×C4—23no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—23no—
1038C2×C4—23no—
1039C2×C4—21no—
1040C2×C4—23no—
1041C2×C4—23no—
1042C2×C4—21no—
1043C2×C4—23no—
1044C2×C4—21no—
1045C2×C4—224no—
1046C2×C4—248no—
1047C2×C4—224no—
1048C2×C4—21no—
1049C2×C4—22no—
1050C2×C4—26no—
1051C2×C4—23no—
1052C2×C4—23no—
1053C2×C4—22no—
1054C2×C4—26no—
1055C2×C4—26no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—23no—
1059C2×C4—26no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—23no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—23no—
1068C2×C4—26no—
1069C2×C4—21no—
1070C2×C4—23no—
1071C2×C4—23no—
1072C2×C4—23no—
1073C2×C4—23no—
1074C2×C4—26no—
1075C2×C4—412no—
1076C2×C4—448no—
1077C2×C4—424no—
1078C2×C4—424no—
1079C2×C4—44no—
1080C2×C4—412no—
1081C2×C4—86no—
1082C2×C4—812no—
1083C2×C4—812no—
1084C2×C4C23×D412yes—
1085C2×C4C23×D416yes—
1086C2×C4C23×D416yes—
1087C2×C4C23×D416yes—
1088C2×C4C23×D414yes—
1089C2×C4C23×D412yes—
1090C2×C4C23×D416yes—
1091C2×C4C23×D416yes—
1092C2×C4C23×D412yes—
1093C2×C4C2×H(5,𝔽2)16yes—
1094C2×C4#58512yes—
1095C2×C4#58512yes—
1096C2×C4#58512yes—
1097C22—212no—
1098C22—22no—
1099C22—26no—
1100C22—212no—
1101C22—22no—
1102C22—26no—
1103C22—22no—
1104C22—212no—
1105C22—26no—
1106C22—43no—
1107C22—41no—
1108C22—46no—
1109C22—41no—
1110C22—46no—
1111C22—43no—
1112C22—41no—
1113C22—43no—
1114C22—46no—
1115C22—41no—
1116C22—46no—
1117C22—43no—
1118C22—46no—
1119C22—42no—
1120C22—42no—
1121C22—46no—
1122C22—42no—
1123C22—46no—
1124C22—46no—
1125C22—42no—
1126C22—42no—
1127C22—46no—
1128C22—42no—
1129C22—46no—
1130C22—42no—
1131C22—46no—
1132C22—1648no—
1133C22C24×D411yescharacteristic
1134C22C24×D411yescharacteristic
1135C22C22×H(5,𝔽2)11yescharacteristic
1136C22C2×#58511yescharacteristic
1137C22C2×#58511yescharacteristic
1138C22C2×#58511yescharacteristic
1139C22H(7,𝔽2)11yescharacteristic
1140C4—22no—
1141C4—26no—
1142C4—22no—
1143C4—26no—
1144C4—22no—
1145C4—24no—
1146C4—26no—
1147C4—43no—
1148C4—46no—
1149C4—41no—
1150C4—41no—
1151C4—43no—
1152C4—42no—
1153C4—43no—
1154C4—42no—
1155C4—46no—
1156C4C2×D42112yes—
1157C4#350014yescomplemented
1158C2—42no—
1159C2—412no—
1160C2—46no—
1161C2—82no—
1162C2—86no—
1163C2C22×D4211yescharacteristic
1164C2C2×#350011yescharacteristic
1165C2#6281211yescharacteristic
1166C2#6292311yescharacteristic
1167C2#6298711yescharacteristic
1168C2#6300311yescharacteristic
1169C2#6303511yescharacteristic
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×#3500C2semidirect
2. C2×#3498C2semidirect
3. C2×#3497C2semidirect
4. #59412C2semidirect
5. #59131C2semidirect
6. #59124C2semidirect
7. #59035C2semidirect
8. #45093C2semidirect
9. #44868C2semidirect
10. #39343C2semidirect
11. #39342C2semidirect
12. #39334C2semidirect
13. #36576C2semidirect
14. #36465C2semidirect
15. #36444C2semidirect
16. #36430C2semidirect
17. #36121C2semidirect
18. D4×#124C2semidirect
19. #36082C2semidirect
20. #35757C2semidirect
21. #34925C2semidirect
22. C4×#550C2semidirect
23. C4×#548C2semidirect
24. C22×2−1+4C22semidirect
32. C2×#550C22semidirect
33. C2×D4×Q8C22semidirect
34. C2×D4×Q8C22semidirect
37. C2×#548C22semidirect
38. C2×#548C22semidirect
39. C2×#548C22semidirect
40. C2×#548C22semidirect
41. C2×#548C22semidirect
42. C2×#546C22semidirect
43. C2×#546C22semidirect
44. C2×#546C22semidirect
45. C2×#546C22semidirect
49. C2×#537C22semidirect
50. C2×#536C22semidirect
52. C2×#535C22semidirect
54. C2×#532C22semidirect
55. C2×#532C22semidirect
56. C2×#532C22semidirect
58. C22×#124C22semidirect
60. C2×C4×#41C22semidirect
61. C22×C4×Q8C22semidirect
62. #2858C22semidirect
63. #2857C22semidirect
64. #2856C22semidirect
65. #2850C22semidirect
66. #2678C22semidirect
67. #2674C22semidirect
68. #2673C22semidirect
69. #2672C22semidirect
70. #2670C22semidirect
71. #2669C22semidirect
72. #2668C22semidirect
73. #2616C22semidirect
74. #2615C22semidirect
75. #2555C22semidirect
76. #2555C22semidirect
77. #2551C22semidirect
78. #2548C22semidirect
79. #2547C22semidirect
80. #2544C22semidirect
81. #2542C22semidirect
82. #2541C22semidirect
83. #2541C22semidirect
84. #2541C22semidirect
85. #2540C22semidirect
86. #2540C22semidirect
87. #2538C22semidirect
88. #2537C22semidirect
89. #2537C22semidirect
90. #2535C22semidirect
91. #2491C22semidirect
92. #2491C22semidirect
93. #2491C22semidirect
94. #2491C22semidirect
95. #2472C22semidirect
96. #2472C22semidirect
97. #2445C22semidirect
98. #2445C22semidirect
99. #2436C22semidirect
100. #2435C22semidirect
101. #2435C22semidirect
102. #2435C22semidirect
103. #2433C22semidirect
104. #2431C22semidirect
105. #2431C22semidirect
106. #2428C22semidirect
107. #2428C22semidirect
108. #2428C22semidirect
109. #2428C22semidirect
110. #2428C22semidirect
111. #2427C22semidirect
112. #2427C22semidirect
113. #2426C22semidirect
114. #2424C22semidirect
115. #2422C22semidirect
116. #2418C22semidirect
117. #2416C22semidirect
118. #2415C22semidirect
119. #2415C22semidirect
120. #2414C22semidirect
121. #2410C22semidirect
122. #2409C22semidirect
123. #2408C22semidirect
124. #2408C22semidirect
125. #2408C22semidirect
126. #2408C22semidirect
127. #2408C22semidirect
128. #2407C22semidirect
129. #2407C22semidirect
130. #2388C22semidirect
131. #2388C22semidirect
132. #2367C22semidirect
133. #2366C22semidirect
134. #2363C22semidirect
135. #2362C22semidirect
136. #2361C22semidirect
137. #2354C22semidirect
138. #2352C22semidirect
139. #2351C22semidirect
140. Q8×C4⋊C4C22semidirect
142. #2341C22semidirect
143. #2341C22semidirect
144. Q8×C22⋊C4C22semidirect
145. Q8×C22⋊C4C22semidirect
146. D4×C22⋊C4C22semidirect
147. D4×C22⋊C4C22semidirect
148. D4×C22⋊C4C22semidirect
149. C4×#127C22semidirect
150. C4×#127C22semidirect
151. C4×#124C22semidirect
152. C4×C22⋊Q8C22semidirect
153. C4×#121C22semidirect
154. C4×#121C22semidirect
155. C4×#121C22semidirect
156. C4×#121C22semidirect
157. C4×#121C22semidirect
158. C42×Q8C22semidirect
159. C42×D4C22semidirect
160. C42×D4C22semidirect
185. #550D4semidirect
194. #548D4semidirect
472. C22×Q8C2×D4semidirect
549. #124C2×D4semidirect
559. C22⋊Q8C2×D4semidirect
585. #121C2×D4semidirect
598. C4×Q8C2×D4semidirect
619. C4×D4C2×D4semidirect
1157. C4#3500semidirect

Maximal subgroups

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

subgroupindex
C2×#35002
C2×#34982
C2×#34972
#594122
#591312
#591242
#590352
#450932
#448682
#393432
#393422
#393342
#365762
#364652
#364442
#364302
#361212
D4×#1242
#360822
#357572
#349252
C4×#5502
C4×#5482