Finite Group Databasebeta

← #7632636

Subgroups — #7632636

Order 512.

11151 conjugacy classes of subgroups.

The subgroup lattice has 1191 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3500C211yesmaximal, characteristic, complemented
2C2×#3489C211yesmaximal, characteristic, complemented
3C2×#3488C211yesmaximal, characteristic, complemented
4C2×C4×2−1+4C211yesmaximal, characteristic, complemented
5#36576C212yesmaximal, complemented
6#36434C212yesmaximal, complemented
7#36258C216yesmaximal, complemented
8#36218C216yesmaximal, complemented
9#36018C212yesmaximal, complemented
10#35821C216yesmaximal, complemented
11#35771C212yesmaximal, complemented
12#35728C216yesmaximal, complemented
13#35677C213yesmaximal, complemented
14#35661C213yesmaximal, complemented
15#35564C213yesmaximal, complemented
16#35563C213yesmaximal, complemented
17#35256C213yesmaximal, complemented
18#35153C213yesmaximal, complemented
19#34743C213yesmaximal, complemented
20C2×#2426C213yesmaximal, complemented
21#34258C211yesmaximal, characteristic, complemented
22#34250C211yesmaximal, characteristic, complemented
23C22⋊C4×#41C211yesmaximal, characteristic, complemented
24C22×2−1+4C2211yescharacteristic
25C22×H(5,𝔽2)C2211yescharacteristic
26C23×#41C2211yescharacteristic
27#3500—216no—
28#3489—216no—
29#3488—216no—
30C2×#550C2212yes—
31C2×D4×Q8C2212yescomplemented
32C2×#548C2212yes—
33C2×#548C2212yescomplemented
34C2×#548C2212yescomplemented
35C2×#548C2212yescomplemented
36C2×#547C2216yescomplemented
37C2×#546C2216yes—
38C2×#546C2216yescomplemented
39C2×#546C2216yescomplemented
40C2×#546C2216yescomplemented
41C2×D42C2216yes—
42C2×#537C2213yes—
43C2×#537C2213yescomplemented
44C2×#536C2213yescomplemented
45C2×#536C2213yescomplemented
46C2×#535C2213yes—
47C2×#535C2213yescomplemented
48C2×#532C2213yescomplemented
49C22×#124C2213yescomplemented
50C2×#525C2213yes—
51C2×#525C2213yescomplemented
52C22×C22⋊Q8C2213yescomplemented
53C22×#121C2213yes—
54C4×2−1+4—216no—
55C2×#520C2211yescharacteristic
56C2×#520C2211yescharacteristic
57C2×#520C2216yescomplemented
58C2×#520C2213yescomplemented
59C2×#519C2213yescomplemented
60C2×#519C2212yescomplemented
61C2×C4×#41C2211yescharacteristic
62C2×C4×#41C2211yescharacteristic
63C2×C4×#41C2216yescomplemented
64C2×C4×#41C2213yescomplemented
65C22×C4×Q8C2213yescomplemented
66C22×C4×Q8C2212yescomplemented
67#2856C2216yescomplemented
68#2854C22112yescomplemented
69#2850C2216yescomplemented
70#2620C2216yescomplemented
71#2619C2216yescomplemented
72#2618C22112yescomplemented
73#2548C2216yescomplemented
74#2548C2216yescomplemented
75#2545C2216yescomplemented
76#2545C2216yescomplemented
77#2543C22112yescomplemented
78#2538C2216yescomplemented
79#2538C2216yescomplemented
80#2536C2216yescomplemented
81#2536C2216yescomplemented
82#2534C22112yescomplemented
83#2429C2213yescomplemented
84#2429C2216yescomplemented
85#2429C2213yescomplemented
86#2429C2216yescomplemented
87#2429C2216yescomplemented
88#2428C2213yescomplemented
89#2428C2213yescomplemented
90#2428C2216yescomplemented
91#2427C2211yescharacteristic, complemented
92#2427C2213yescomplemented
93#2426C2216yescomplemented
94#2426C2216yescomplemented
95#2426C2216yescomplemented
96#2426C2216yescomplemented
97#2426C2216yescomplemented
98#2426C2216yescomplemented
99#2426C2216yescomplemented
100#2426C2213yescomplemented
101#2426C2216yescomplemented
102#2426C2216yescomplemented
103#2426C2216yescomplemented
104#2426C2213yescomplemented
105#2426C2216yescomplemented
106#2425C2216yescomplemented
107#2425C2216yescomplemented
108#2424C22112yescomplemented
109#2424C2216yescomplemented
110#2424C22112yescomplemented
111#2424C2216yescomplemented
112#2417C2216yescomplemented
113#2416C2216yescomplemented
114#2416C2216yescomplemented
115#2416C22112yescomplemented
116#2416C2216yescomplemented
117#2415C2216yescomplemented
118#2414C2216yescomplemented
119#2414C2216yescomplemented
120#2414C2216yescomplemented
121#2413C22112yescomplemented
122#2411C22112yescomplemented
123#2411C22112yescomplemented
124#2411C22112yescomplemented
125#2408C22112yescomplemented
126#2392C2216yescomplemented
127#2392C2216yescomplemented
128C2×#396C2216yescomplemented
129C2×#394C2216yescomplemented
130#2351C2212yescomplemented
131Q8×C4⋊C4C2212yescomplemented
132#2349C2216yescomplemented
133D4×C4⋊C4C2216yescomplemented
134#2341C2211yescharacteristic, complemented
135#2341C2211yescharacteristic, complemented
136#2341C2212yescomplemented
137#2341C2212yescomplemented
138Q8×C22⋊C4C2211yescharacteristic, complemented
139Q8×C22⋊C4C2211yescharacteristic, complemented
140#2339C2213yescomplemented
141#2339C2213yescomplemented
142D4×C22⋊C4C2213yescomplemented
143D4×C22⋊C4C2213yescomplemented
144D4×C22⋊C4C2216yescomplemented
145D4×C22⋊C4C2216yescomplemented
146#2317C2213yescomplemented
147#2316C2213yescomplemented
148#2311C2213yescomplemented
149#2309C2213yescomplemented
150C4×#121C2216yescomplemented
151C4×#121C2216yescomplemented
152#2297C2213yescomplemented
153#2297C2213yescomplemented
154#2297C2213yescomplemented
155#2296C2213yescomplemented
156C2×#390C2216yescomplemented
157C2×#390C2213yescomplemented
158C2×#389C2213yescomplemented
159C2×#388C2216yescomplemented
160#2280C2213yescomplemented
161C2×C4×C22⋊C4C2213yescomplemented
162C2×2−1+4—28no—
163C2×2−1+4—28no—
164C2×2−1+4D4116yescomplemented
165C2×H(5,𝔽2)—28no—
166C2×H(5,𝔽2)—28no—
167C2×H(5,𝔽2)—28no—
168C22×#41—28no—
169C22×#41—28no—
170C22×#41—28no—
171C22×#41C2313yes—
172C22×#41C2311yescharacteristic
173C22×#41C2313yes—
174C22×#41C2313yes—
175C22×#41C2312yes—
176C22×#41C2313yes—
177C22×#41C2316yes—
178C22×#41C2311yescharacteristic
179C23×Q8C2311yescharacteristic
180C23×Q8C2313yes—
181C23×Q8C2312yes—
182C23×D4C2313yes—
183C23×D4C2313yes—
184C23×D4C2316yes—
185C23×D4C2316yes—
186C24×C4C2313yes—
187#550—216no—
188D4×Q8—216no—
189#548—216no—
190#548—216no—
191#548—216no—
192#548—216no—
193#547—248no—
194#546—248no—
195#546—248no—
196#546—248no—
197#546—248no—
198D42—248no—
199#537—224no—
200#537—224no—
201#536—224no—
202#536—224no—
203#535—224no—
204#535—224no—
205#532—224no—
206C2×C4⋊Q8C2313yes—
207C2×C4⋊Q8C2316yes—
208C2×#127C2316yes—
209C2×#127C2313yes—
210C2×#124—224no—
211C2×#124C2316yes—
212C2×#124C2313yes—
213C2×#124C2316yes—
214C2×#124C2316yes—
215C2×#124C2316yes—
216C2×#124C2311yescharacteristic
217C2×#124C2316yes—
218#525—224no—
219#525—224no—
220C2×#123C23112yes—
221C2×#123C23112yes—
222C2×#123C2316yes—
223C2×#123C2316yes—
224C2×C22⋊Q8—224no—
225C2×C22⋊Q8C2316yes—
226C2×C22⋊Q8C2313yes—
227C2×C22⋊Q8C2316yes—
228C2×C22⋊Q8C2316yes—
229C2×C22⋊Q8C2316yes—
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2313yes—
232C2×C22⋊Q8C2313yes—
233C2×C22⋊Q8C2316yes—
234C2×C22⋊Q8C2316yes—
235C2×C22⋊Q8C2316yes—
236C2×#121—224no—
237C2×#121C2316yes—
238C2×#121C23112yes—
239C2×#121C2316yes—
240C2×#121C2316yes—
241C2×#121C2313yes—
242C2×#121C2316yes—
243C2×#121C2316yes—
244C2×#121C2316yes—
245C2×#121C2313yes—
246C2×#121C2311yescharacteristic
247C2×#121C2313yes—
248C2×#121C2316yes—
249C2×#121C2316yes—
250C2×#121C23112yes—
251C2×#121C2316yes—
252C2×#121C2316yes—
253C2×#121C2316yes—
254C2×#121C23112yes—
255C2×#120C2316yes—
256C2×#120C23112yes—
257C2×#120C2316yes—
258C2×#120C23112yes—
259#520—28no—
260#520—248no—
261#520—224no—
262#520D4116yescomplemented
263#519—216no—
264#519—224no—
265C4×#41—28no—
266C4×#41—28no—
267C4×#41—248no—
268C4×#41—224no—
269C2×C4×Q8—216no—
270C2×C4×Q8—224no—
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2313yes—
277C2×C4×Q8C2316yes—
278C2×C4×Q8C2316yes—
279C2×C4×Q8C2316yes—
280C2×C4×Q8C2316yes—
281C2×C4×Q8C2313yes—
282C2×C4×Q8C2316yes—
283C2×C4×Q8C2312yes—
284C2×C4×D4C2313yes—
285C2×C4×D4C2313yes—
286C2×C4×D4C2316yes—
287C2×C4×D4C2313yes—
288C2×C4×D4C2313yes—
289C2×C4×D4C2316yes—
290C2×C4×D4C2316yes—
291C2×C4×D4C2316yes—
292C2×C4×D4C2316yes—
293C2×C4×D4C2316yes—
294C2×C4×D4C2316yes—
295C2×C4×D4C2316yes—
296C2×C4×D4C2311yescharacteristic
297C2×C4×D4C23112yes—
298C2×C4×D4C2316yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2316yes—
301C2×#117C2313yes—
302C2×#117C2313yes—
303C2×#117C2313yes—
304C2×#117C2316yes—
305C2×#117C23112yes—
306C2×#117C2316yes—
307C2×#117C2313yes—
308C22×C4⋊C4C2313yes—
309C22×C4⋊C4C2316yes—
310C22×C4⋊C4C2316yes—
311C22×C4⋊C4C2316yes—
312C22×C4⋊C4C2316yes—
313C22×C4⋊C4C2313yes—
314C22×C22⋊C4C2316yes—
315C22×C22⋊C4C2316yes—
316C22×C22⋊C4C2316yes—
317C22×C22⋊C4C2316yes—
318C22×C22⋊C4C2313yes—
319C22×C22⋊C4C2313yes—
320C22×C22⋊C4C2316yes—
321C22×C22⋊C4C2316yes—
322C22×C42C2316yes—
323C22×C42C2316yes—
324C22×C42C2313yes—
325C22×C42C2313yes—
326#398C2316yes—
327#398C23112yes—
328#398C2316yes—
329#397C2312yes—
330#397C2316yes—
331#396C2316yes—
332#396C23112yes—
333#396C23112yes—
334#396C23112yes—
335#396C23112yes—
336#396C2316yes—
337#396C23112yes—
338#396C23112yes—
339#396C2316yes—
340#396C2316yes—
341#394C23112yes—
342#394C23112yes—
343#394C23112yes—
344#394C2316yes—
345#394C23112yes—
346#394C2316yes—
347#394C23112yes—
348#394C23112yes—
349#394C2312yes—
350#394C2316yes—
351#394C2316yes—
352#394C2316yes—
353#392C2316yes—
354#392C23112yes—
355#392C2316yes—
356#391C2313yes—
357#391C2313yes—
358#391C2313yes—
359#391C2313yes—
360#391C2313yes—
361#391C2311yescharacteristic
362#390C2313yes—
363#390C2316yes—
364#390C2316yes—
365#390C2316yes—
366#390C2316yes—
367#390C2313yes—
368#390C2313yes—
369#390C2316yes—
370#390C2313yes—
371#390C2313yes—
372#390C23112yes—
373#390C23112yes—
374#390C23112yes—
375#390C23112yes—
376#390C2316yes—
377#390C23112yes—
378#390C2316yes—
379#390C2313yes—
380#389C2313yes—
381#389C2316yes—
382#389C2316yes—
383#389C2316yes—
384#389C2313yes—
385#389C2316yes—
386#389C23112yes—
387#389C2316yes—
388#389C2316yes—
389#389C2316yes—
390#389C2313yes—
391#389C2311yescharacteristic
392#388C23112yes—
393#388C23112yes—
394#388C2316yes—
395#388C23112yes—
396#388C23112yes—
397#388C2316yes—
398#388C2316yes—
399#388C23112yes—
400#388C23112yes—
401#388C2316yes—
402#386C23112yes—
403#386C2316yes—
404#386C2316yes—
405#386C2316yes—
406#386C2316yes—
407#386C2316yes—
408#386C2316yes—
409#386C2316yes—
410#386C23112yes—
411#386C2316yes—
412#386C2316yes—
413#386C2312yes—
414#385C23112yes—
415#385C2316yes—
416#385C2316yes—
417#384C2316yes—
418#382C2316yes—
419#381C2316yes—
420#380C2316yes—
421#380C2316yes—
422#380C23112yes—
423#380C2313yes—
424#380C2313yes—
425#380C2313yes—
426#380C2313yes—
427#380C2316yes—
428#380C2312yes—
429#379C23112yes—
430#379C2316yes—
431C4×C4⋊C4C2316yes—
432C4×C4⋊C4C2316yes—
433C4×C22⋊C4C2313yes—
434C4×C22⋊C4C2313yes—
435C4×C22⋊C4C2316yes—
436C4×C22⋊C4C2316yes—
437C4×C22⋊C4C2313yes—
438C4×C22⋊C4C2313yes—
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2313yes—
441C4×C22⋊C4C2313yes—
442C4×C22⋊C4C2313yes—
443C4×C22⋊C4C2316yes—
444C2×#95C2313yes—
445C2×#95C2313yes—
446C2×#95C2316yes—
447C25C2413yes—
448C25C2416yes—
4492−1+4—2128no—
450H(5,𝔽2)—464no—
451C2×#41—24no—
452C2×#41—28no—
453C2×#41—28no—
454C2×#41—24no—
455C2×#41—24no—
456C2×#41—28no—
457C2×#41—224no—
458C2×#41—212no—
459C2×#41—212no—
460C2×#41—224no—
461C2×#41—212no—
462C2×#41—212no—
463C2×#41—212no—
464C2×#41—212no—
465C2×#41—212no—
466C2×#41—212no—
467C2×#41—212no—
468C2×#41—212no—
469C2×#41—212no—
470C2×#41—464no—
471C2×#41C2×D418yes—
472C2×#41C2×D418yes—
473C2×#41C2×D4124yescomplemented
474C2×#41C2×D4148yescomplemented
475C2×#41#4118yes—
476C22×Q8—28no—
477C22×Q8—28no—
478C22×Q8—24no—
479C22×Q8—24no—
480C22×Q8—24no—
481C22×Q8—212no—
482C22×Q8—212no—
483C22×Q8C2×D4124yescomplemented
484C22×Q8C2×D4116yescomplemented
485C22×Q8C2413yes—
486C22×Q8C2411yescharacteristic
487C22×Q8C2413yes—
488C22×Q8C2416yes—
489C22×Q8C2411yescharacteristic
490C22×D4—212no—
491C22×D4—224no—
492C22×D4—212no—
493C22×D4—224no—
494C22×D4—212no—
495C22×D4—224no—
496C22×D4—212no—
497C22×D4—212no—
498C22×D4—224no—
499C22×D4—212no—
500C22×D4—412no—
501C22×D4—86no—
502C22×D4C2416yes—
503C22×D4C2416yes—
504C22×D4C2413yes—
505C22×D4C2416yes—
506C22×D4C2413yes—
507C22×D4C2412yes—
508C22×D4C2416yes—
509C22×D4C2416yes—
510C22×D4C2411yescharacteristic
511C22×D4C2416yes—
512C22×D4C2416yes—
513C22×D4C2416yes—
514C22×D4C2416yes—
515C22×D4C24112yes—
516C22×D4C2413yes—
517C23×C4—212no—
518C23×C4—212no—
519C23×C4—212no—
520C23×C4C2413yes—
521C23×C4C2413yes—
522C23×C4C2413yes—
523C23×C4C2416yes—
524C23×C4C2411yescharacteristic
525C23×C4C2413yes—
526C23×C4C2413yes—
527C23×C4C2412yes—
528C23×C4C2416yes—
529C23×C4C2416yes—
530C23×C4C2416yes—
531C23×C4C2413yes—
532C23×C4C2413yes—
533C23×C4C2413yes—
534C23×C4C2416yes—
535C23×C4C2416yes—
536C23×C4C2413yes—
537C4⋊Q8—212no—
538C4⋊Q8—224no—
539#127—212no—
540#127—224no—
541#124—212no—
542#124—224no—
543#124—224no—
544#124—224no—
545#124—224no—
546#124—24no—
547#124—224no—
548#123—224no—
549#123—248no—
550#123—248no—
551#123—224no—
552C22⋊Q8—212no—
553C22⋊Q8—224no—
554C22⋊Q8—224no—
555C22⋊Q8—224no—
556C22⋊Q8—212no—
557C22⋊Q8—224no—
558C22⋊Q8—224no—
559C22⋊Q8—224no—
560C22⋊Q8—24no—
561C22⋊Q8—212no—
562C22⋊Q8—224no—
563#121—24no—
564#121—212no—
565#121—224no—
566#121—224no—
567#121—248no—
568#121—224no—
569#121—224no—
570#121—248no—
571#121—224no—
572#121—212no—
573#121—224no—
574#121—224no—
575#121—224no—
576#121—212no—
577#121—224no—
578#121—412no—
579#121—412no—
580#121—812no—
581#120—224no—
582#120—248no—
583#120—224no—
584#120—248no—
585C4×Q8—24no—
586C4×Q8—24no—
587C4×Q8—24no—
588C4×Q8—24no—
589C4×Q8—28no—
590C4×Q8—224no—
591C4×Q8—212no—
592C4×Q8—224no—
593C4×Q8—224no—
594C4×Q8—212no—
595C4×Q8—224no—
596C4×Q8—224no—
597C4×Q8C2×D4116yes—
598C4×D4—212no—
599C4×D4—212no—
600C4×D4—212no—
601C4×D4—212no—
602C4×D4—224no—
603C4×D4—248no—
604C4×D4—224no—
605C4×D4—224no—
606C4×D4—224no—
607C4×D4—224no—
608C4×D4—24no—
609C4×D4—212no—
610C4×D4—224no—
611C4×D4—224no—
612C4×D4—224no—
613C4×D4—224no—
614C4×D4C2×D4148yes—
615#117—212no—
616#117—212no—
617#117—212no—
618#117—224no—
619#117—248no—
620#117—224no—
621#117C2×D4124yes—
622C2×C4⋊C4—224no—
623C2×C4⋊C4—212no—
624C2×C4⋊C4—224no—
625C2×C4⋊C4—224no—
626C2×C4⋊C4—86no—
627C2×C4⋊C4C2×D4124yes—
628C2×C4⋊C4C2413yes—
629C2×C4⋊C4C2416yes—
630C2×C4⋊C4C24112yes—
631C2×C4⋊C4C2413yes—
632C2×C4⋊C4C2416yes—
633C2×C4⋊C4C2416yes—
634C2×C4⋊C4C24112yes—
635C2×C4⋊C4C2413yes—
636C2×C4⋊C4C2416yes—
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2413yes—
639C2×C4⋊C4C2413yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2416yes—
642C2×C4⋊C4C2416yes—
643C2×C4⋊C4C2416yes—
644C2×C4⋊C4C2416yes—
645C2×C4⋊C4C2416yes—
646C2×C4⋊C4C24112yes—
647C2×C4⋊C4C2416yes—
648C2×C4⋊C4C2416yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2416yes—
651C2×C4⋊C4C2413yes—
652C2×C4⋊C4C2411yescharacteristic
653C2×C22⋊C4—224no—
654C2×C22⋊C4—224no—
655C2×C22⋊C4—224no—
656C2×C22⋊C4—224no—
657C2×C22⋊C4—46no—
658C2×C22⋊C4—412no—
659C2×C22⋊C4—46no—
660C2×C22⋊C4—86no—
661C2×C22⋊C4C2411yescharacteristic
662C2×C22⋊C4C2411yescharacteristic
663C2×C22⋊C4C2416yes—
664C2×C22⋊C4C2416yes—
665C2×C22⋊C4C2416yes—
666C2×C22⋊C4C2416yes—
667C2×C22⋊C4C2416yes—
668C2×C22⋊C4C24112yes—
669C2×C22⋊C4C24112yes—
670C2×C22⋊C4C24112yes—
671C2×C22⋊C4C24112yes—
672C2×C22⋊C4C2413yes—
673C2×C22⋊C4C2413yes—
674C2×C22⋊C4C2416yes—
675C2×C22⋊C4C2416yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2416yes—
678C2×C22⋊C4C2416yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2416yes—
684C2×C22⋊C4C2416yes—
685C2×C22⋊C4C2416yes—
686C2×C22⋊C4C2416yes—
687C2×C22⋊C4C2416yes—
688C2×C22⋊C4C24112yes—
689C2×C22⋊C4C2413yes—
690C2×C22⋊C4C2413yes—
691C2×C22⋊C4C2413yes—
692C2×C22⋊C4C2413yes—
693C2×C22⋊C4C24112yes—
694C2×C22⋊C4C2416yes—
695C2×C22⋊C4C2416yes—
696C2×C22⋊C4C2416yes—
697C2×C22⋊C4C2416yes—
698C2×C22⋊C4C2416yes—
699C2×C42—224no—
700C2×C42—212no—
701C2×C42—212no—
702C2×C42—224no—
703C2×C42C2413yes—
704C2×C42C2413yes—
705C2×C42C24112yes—
706C2×C42C2416yes—
707C2×C42C2413yes—
708C2×C42C2416yes—
709C2×C42C2413yes—
710C2×C42C2413yes—
711C2×C42C2413yes—
712C2×C42C2411yescharacteristic
713C2×C42C2416yes—
714C2×C42C2411yescharacteristic
715C2×C42C2416yes—
716#95C2411yescharacteristic
717#95C2411yescharacteristic
718#95C2416yes—
719#95C2413yes—
720#95C2413yes—
721#95C2413yes—
722#95C2413yes—
723#95C2413yes—
724#95C2413yes—
725#95C24112yes—
726#95C2412yes—
727#95C2412yes—
728#95C2416yes—
729#95C2416yes—
730#95C2416yes—
731#95C2416yes—
732#95C2412yes—
733#95C2416yes—
734#95C2416yes—
735C24—26no—
736C24—26no—
737C24—26no—
738C24—26no—
739C24—212no—
740C24—212no—
741C24—212no—
742C24—43no—
743C24—43no—
744C24—43no—
745C24—46no—
746C24—46no—
747C24—46no—
748C24—46no—
749C24C2516yes—
750C24C2513yes—
751C24C2512yes—
752C24C2511yescharacteristic
753C24C2513yes—
754#41—2192no—
755#41—296no—
756#41—416no—
757#41—432no—
758#41—448no—
759#41—448no—
760#41—448no—
761#41#121164yescomplemented
762C2×Q8—264no—
763C2×Q8—296no—
764C2×Q8—26no—
765C2×Q8—212no—
766C2×Q8—22no—
767C2×Q8—26no—
768C2×Q8—26no—
769C2×Q8—22no—
770C2×Q8—212no—
771C2×Q8—26no—
772C2×Q8—26no—
773C2×Q8—22no—
774C2×Q8—416no—
775C2×Q8C22×D4112yes—
776C2×Q8C22×D4124yes—
777C2×Q8C22×D414yes—
778C2×Q8C22×D414yes—
779C2×Q8C2×#4114yes—
780C2×D4—212no—
781C2×D4—212no—
782C2×D4—24no—
783C2×D4—212no—
784C2×D4—212no—
785C2×D4—212no—
786C2×D4—212no—
787C2×D4—212no—
788C2×D4—212no—
789C2×D4—24no—
790C2×D4—212no—
791C2×D4—212no—
792C2×D4—212no—
793C2×D4—212no—
794C2×D4—22no—
795C2×D4—212no—
796C2×D4—26no—
797C2×D4—212no—
798C2×D4—26no—
799C2×D4—212no—
800C2×D4—26no—
801C2×D4—26no—
802C2×D4—212no—
803C2×D4—224no—
804C2×D4—22no—
805C2×D4—212no—
806C2×D4—26no—
807C2×D4—26no—
808C2×D4—46no—
809C2×D4—42no—
810C2×D4—46no—
811C2×D4—46no—
812C2×D4—46no—
813C2×D4—46no—
814C2×D4—46no—
815C2×D4—46no—
816C2×D4—412no—
817C2×D4—412no—
818C2×D4—46no—
819C2×D4—46no—
820C2×D4—448no—
821C2×D4—496no—
822C2×D4—448no—
823C2×D4—848no—
824C2×D4C22×D4124yes—
825C2×D4C22×D414yes—
826C2×D4C22×D4112yes—
827C2×D4C22×D4112yes—
828C2×D4C2×#41112yes—
829C22×C4—212no—
830C22×C4—212no—
831C22×C4—212no—
832C22×C4—212no—
833C22×C4—26no—
834C22×C4—26no—
835C22×C4—26no—
836C22×C4—26no—
837C22×C4—26no—
838C22×C4—26no—
839C22×C4—26no—
840C22×C4—212no—
841C22×C4—24no—
842C22×C4—26no—
843C22×C4—26no—
844C22×C4—212no—
845C22×C4—26no—
846C22×C4—26no—
847C22×C4—212no—
848C22×C4—22no—
849C22×C4—26no—
850C22×C4—22no—
851C22×C4—26no—
852C22×C4—22no—
853C22×C4—26no—
854C22×C4—26no—
855C22×C4—26no—
856C22×C4—212no—
857C22×C4—26no—
858C22×C4—24no—
859C22×C4—212no—
860C22×C4—46no—
861C22×C4—42no—
862C22×C4—43no—
863C22×C4—46no—
864C22×C4—43no—
865C22×C4—43no—
866C22×C4—43no—
867C22×C4—46no—
868C22×C4—43no—
869C22×C4—46no—
870C22×C4—43no—
871C22×C4—46no—
872C22×C4—46no—
873C22×C4—43no—
874C22×C4—448no—
875C22×C4C22×D4124yes—
876C22×C4C22×D4124yes—
877C22×C4C22×D4124yes—
878C22×C4C22×D4112yes—
879C22×C4C22×D4112yes—
880C22×C4C2×#41112yes—
881C22×C4C2511yescharacteristic
882C22×C4C2513yes—
883C22×C4C2511yescharacteristic
884C22×C4C2513yes—
885C22×C4C2512yes—
886C22×C4C2513yes—
887C22×C4C2511yescharacteristic
888C22×C4C2511yescharacteristic
889C22×C4C2513yes—
890C22×C4C2512yes—
891C22×C4C2513yes—
892C22×C4C2516yes—
893C22×C4C2512yes—
894C22×C4C2516yes—
895C22×C4C2516yes—
896C22×C4C2511yescharacteristic
897C22×C4C2511yescharacteristic
898C22×C4C2513yes—
899C4⋊C4—212no—
900C4⋊C4—224no—
901C4⋊C4—26no—
902C4⋊C4—26no—
903C4⋊C4—212no—
904C4⋊C4—212no—
905C4⋊C4—224no—
906C4⋊C4—212no—
907C4⋊C4—26no—
908C4⋊C4—22no—
909C4⋊C4—26no—
910C4⋊C4—26no—
911C4⋊C4—24no—
912C4⋊C4—212no—
913C4⋊C4—212no—
914C4⋊C4—212no—
915C4⋊C4—212no—
916C4⋊C4—46no—
917C4⋊C4—412no—
918C4⋊C4—42no—
919C4⋊C4—46no—
920C4⋊C4—46no—
921C4⋊C4C22×D4124yes—
922C4⋊C4C22×D4112yes—
923C4⋊C4C22×D414yes—
924C22⋊C4—212no—
925C22⋊C4—212no—
926C22⋊C4—212no—
927C22⋊C4—24no—
928C22⋊C4—24no—
929C22⋊C4—24no—
930C22⋊C4—212no—
931C22⋊C4—22no—
932C22⋊C4—26no—
933C22⋊C4—212no—
934C22⋊C4—212no—
935C22⋊C4—212no—
936C22⋊C4—212no—
937C22⋊C4—224no—
938C22⋊C4—224no—
939C22⋊C4—224no—
940C22⋊C4—224no—
941C22⋊C4—212no—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—212no—
945C22⋊C4—212no—
946C22⋊C4—212no—
947C22⋊C4—22no—
948C22⋊C4—212no—
949C22⋊C4—26no—
950C22⋊C4—43no—
951C22⋊C4—43no—
952C22⋊C4—43no—
953C22⋊C4—412no—
954C22⋊C4—43no—
955C22⋊C4—46no—
956C22⋊C4—412no—
957C22⋊C4—46no—
958C22⋊C4—46no—
959C22⋊C4—46no—
960C22⋊C4—46no—
961C22⋊C4C22×D4124yes—
962C42—212no—
963C42—22no—
964C42—26no—
965C42—22no—
966C42—224no—
967C42—212no—
968C42—26no—
969C42—26no—
970C42—26no—
971C42—26no—
972C42—26no—
973C42—212no—
974C42C22×D4124yes—
975C23—23no—
976C23—23no—
977C23—23no—
978C23—23no—
979C23—21no—
980C23—22no—
981C23—21no—
982C23—21no—
983C23—22no—
984C23—21no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—21no—
989C23—22no—
990C23—21no—
991C23—23no—
992C23—26no—
993C23—26no—
994C23—23no—
995C23—23no—
996C23—26no—
997C23—26no—
998C23—23no—
999C23—23no—
1000C23—26no—
1001C23—26no—
1002C23—23no—
1003C23—23no—
1004C23—26no—
1005C23—412no—
1006C23—412no—
1007C23—412no—
1008C23—412no—
1009C23—424no—
1010C23—86no—
1011C23—86no—
1012C23—86no—
1013C23—812no—
1014C23—812no—
1015C23—812no—
1016C23—812no—
1017C23—812no—
1018C23—812no—
1019C23C23×D414yes—
1020C23C23×D416yes—
1021C23C23×D416yes—
1022C23C22×#4116yes—
1023C23#58512yes—
1024C23C2611yescharacteristic
1025Q8—248no—
1026Q8—224no—
1027Q8—412no—
1028Q8—44no—
1029Q8C2×#121116yes—
1030D4—248no—
1031D4—28no—
1032D4—424no—
1033D4—48no—
1034D4—424no—
1035D4—424no—
1036D4—424no—
1037D4—412no—
1038D4—412no—
1039D4—812no—
1040D4—824no—
1041D4—812no—
1042D4—812no—
1043D4—812no—
1044D4C2×#121148yes—
1045C2×C4—21no—
1046C2×C4—26no—
1047C2×C4—26no—
1048C2×C4—22no—
1049C2×C4—26no—
1050C2×C4—26no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—248no—
1054C2×C4—248no—
1055C2×C4—23no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—23no—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—23no—
1062C2×C4—23no—
1063C2×C4—26no—
1064C2×C4—21no—
1065C2×C4—23no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—23no—
1070C2×C4—21no—
1071C2×C4—22no—
1072C2×C4—23no—
1073C2×C4—21no—
1074C2×C4—23no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—26no—
1078C2×C4—23no—
1079C2×C4—23no—
1080C2×C4—23no—
1081C2×C4—22no—
1082C2×C4—21no—
1083C2×C4—23no—
1084C2×C4—26no—
1085C2×C4—23no—
1086C2×C4—21no—
1087C2×C4—23no—
1088C2×C4—22no—
1089C2×C4—23no—
1090C2×C4—21no—
1091C2×C4—424no—
1092C2×C4—48no—
1093C2×C4—412no—
1094C2×C4—412no—
1095C2×C4—44no—
1096C2×C4—412no—
1097C2×C4—412no—
1098C2×C4—412no—
1099C2×C4—424no—
1100C2×C4—812no—
1101C2×C4—86no—
1102C2×C4—86no—
1103C2×C4—86no—
1104C2×C4—812no—
1105C2×C4C2×#121148yes—
1106C2×C4C23×D414yes—
1107C2×C4C23×D4112yes—
1108C2×C4C23×D4112yes—
1109C2×C4C23×D416yes—
1110C2×C4C23×D412yes—
1111C2×C4C23×D412yes—
1112C2×C4C23×D416yes—
1113C2×C4C22×#4116yes—
1114C2×C4C22×#4112yes—
1115C2×C4#58512yes—
1116C22—26no—
1117C22—26no—
1118C22—26no—
1119C22—26no—
1120C22—26no—
1121C22—26no—
1122C22—22no—
1123C22—22no—
1124C22—24no—
1125C22—24no—
1126C22—22no—
1127C22—24no—
1128C22—42no—
1129C22—42no—
1130C22—41no—
1131C22—41no—
1132C22—42no—
1133C22—42no—
1134C22—41no—
1135C22—41no—
1136C22—46no—
1137C22—43no—
1138C22—43no—
1139C22—46no—
1140C22—46no—
1141C22—43no—
1142C22—43no—
1143C22—46no—
1144C22—43no—
1145C22—46no—
1146C22—43no—
1147C22—46no—
1148C22—43no—
1149C22—46no—
1150C22—824no—
1151C22—1624no—
1152C22C22×#121112yes—
1153C22C24×D411yescharacteristic
1154C22C24×D411yescharacteristic
1155C22C23×#4111yescharacteristic
1156C22C2×#58511yescharacteristic
1157C22C2×#58511yescharacteristic
1158C22H(7,𝔽2)11yescharacteristic
1159C222−1+611yescharacteristic
1160C4—212no—
1161C4—22no—
1162C4—24no—
1163C4—212no—
1164C4—43no—
1165C4—41no—
1166C4—43no—
1167C4—41no—
1168C4—43no—
1169C4—42no—
1170C4—41no—
1171C4—46no—
1172C4—43no—
1173C4—41no—
1174C4—42no—
1175C4—43no—
1176C4C22×#121112yes—
1177C4C22×#12114yes—
1178C2—212no—
1179C2—44no—
1180C2—42no—
1181C2—83no—
1182C2—86no—
1183C2C23×#12111yescharacteristic
1184C2#6281011yescharacteristic
1185C2#6285711yescharacteristic
1186C2#6298711yescharacteristic
1187C2#6300211yescharacteristic
1188C2#6300211yescharacteristic
1189C2#6300311yescharacteristic
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×#3489C2semidirect
3. C2×#3488C2semidirect
4. C2×C4×2−1+4C2semidirect
5. #36576C2semidirect
6. #36434C2semidirect
7. #36258C2semidirect
8. #36218C2semidirect
9. #36018C2semidirect
10. #35821C2semidirect
11. #35771C2semidirect
12. #35728C2semidirect
13. #35677C2semidirect
14. #35661C2semidirect
15. #35564C2semidirect
16. #35563C2semidirect
17. #35256C2semidirect
18. #35153C2semidirect
19. #34743C2semidirect
20. C2×#2426C2semidirect
21. #34258C2semidirect
22. #34250C2semidirect
23. C22⋊C4×#41C2semidirect
31. C2×D4×Q8C22semidirect
33. C2×#548C22semidirect
34. C2×#548C22semidirect
35. C2×#548C22semidirect
36. C2×#547C22semidirect
38. C2×#546C22semidirect
39. C2×#546C22semidirect
40. C2×#546C22semidirect
43. C2×#537C22semidirect
44. C2×#536C22semidirect
45. C2×#536C22semidirect
47. C2×#535C22semidirect
48. C2×#532C22semidirect
49. C22×#124C22semidirect
51. C2×#525C22semidirect
52. C22×C22⋊Q8C22semidirect
57. C2×#520C22semidirect
58. C2×#520C22semidirect
59. C2×#519C22semidirect
60. C2×#519C22semidirect
63. C2×C4×#41C22semidirect
64. C2×C4×#41C22semidirect
65. C22×C4×Q8C22semidirect
66. C22×C4×Q8C22semidirect
67. #2856C22semidirect
68. #2854C22semidirect
69. #2850C22semidirect
70. #2620C22semidirect
71. #2619C22semidirect
72. #2618C22semidirect
73. #2548C22semidirect
74. #2548C22semidirect
75. #2545C22semidirect
76. #2545C22semidirect
77. #2543C22semidirect
78. #2538C22semidirect
79. #2538C22semidirect
80. #2536C22semidirect
81. #2536C22semidirect
82. #2534C22semidirect
83. #2429C22semidirect
84. #2429C22semidirect
85. #2429C22semidirect
86. #2429C22semidirect
87. #2429C22semidirect
88. #2428C22semidirect
89. #2428C22semidirect
90. #2428C22semidirect
91. #2427C22semidirect
92. #2427C22semidirect
93. #2426C22semidirect
94. #2426C22semidirect
95. #2426C22semidirect
96. #2426C22semidirect
97. #2426C22semidirect
98. #2426C22semidirect
99. #2426C22semidirect
100. #2426C22semidirect
101. #2426C22semidirect
102. #2426C22semidirect
103. #2426C22semidirect
104. #2426C22semidirect
105. #2426C22semidirect
106. #2425C22semidirect
107. #2425C22semidirect
108. #2424C22semidirect
109. #2424C22semidirect
110. #2424C22semidirect
111. #2424C22semidirect
112. #2417C22semidirect
113. #2416C22semidirect
114. #2416C22semidirect
115. #2416C22semidirect
116. #2416C22semidirect
117. #2415C22semidirect
118. #2414C22semidirect
119. #2414C22semidirect
120. #2414C22semidirect
121. #2413C22semidirect
122. #2411C22semidirect
123. #2411C22semidirect
124. #2411C22semidirect
125. #2408C22semidirect
126. #2392C22semidirect
127. #2392C22semidirect
128. C2×#396C22semidirect
129. C2×#394C22semidirect
130. #2351C22semidirect
131. Q8×C4⋊C4C22semidirect
132. #2349C22semidirect
133. D4×C4⋊C4C22semidirect
134. #2341C22semidirect
135. #2341C22semidirect
136. #2341C22semidirect
137. #2341C22semidirect
138. Q8×C22⋊C4C22semidirect
139. Q8×C22⋊C4C22semidirect
140. #2339C22semidirect
141. #2339C22semidirect
142. D4×C22⋊C4C22semidirect
143. D4×C22⋊C4C22semidirect
144. D4×C22⋊C4C22semidirect
145. D4×C22⋊C4C22semidirect
146. #2317C22semidirect
147. #2316C22semidirect
148. #2311C22semidirect
149. #2309C22semidirect
150. C4×#121C22semidirect
151. C4×#121C22semidirect
152. #2297C22semidirect
153. #2297C22semidirect
154. #2297C22semidirect
155. #2296C22semidirect
156. C2×#390C22semidirect
157. C2×#390C22semidirect
158. C2×#389C22semidirect
159. C2×#388C22semidirect
160. #2280C22semidirect
161. C2×C4×C22⋊C4C22semidirect
164. C2×2−1+4D4semidirect
262. #520D4semidirect
473. C2×#41C2×D4semidirect
474. C2×#41C2×D4semidirect
483. C22×Q8C2×D4semidirect
484. C22×Q8C2×D4semidirect
761. #41#121semidirect

Maximal subgroups

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

subgroupindex
C2×#35002
C2×#34892
C2×#34882
C2×C4×2−1+42
#365762
#364342
#362582
#362182
#360182
#358212
#357712
#357282
#356772
#356612
#355642
#355632
#352562
#351532
#347432
C2×#24262
#342582
#342502
C22⋊C4×#412