Finite Group Databasebeta

← #28329055

Subgroups — #28329055

Order 13568.

1974 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20291262C214yesmaximal
2#20291252C214yesmaximal
3#20291249C212yesmaximal, complemented
4#20291244C212yesmaximal, complemented
5#20291235C212yesmaximal, complemented
6Q8×C4⋊#6157C212yesmaximal, complemented
7#20291215C214yesmaximal, complemented
8#20291209C214yesmaximal, complemented
9#20291202C212yesmaximal
10#20291193C211yesmaximal, characteristic
11C22⋊Q8×#6157C212yesmaximal
12#20291175C211yesmaximal, characteristic
13#541×D53C211yesmaximal, characteristic
14C2×Q8×#6157C2212yes—
15C2×Q8×#6157C2212yes—
16C2×#13133296C2211yescharacteristic
17C22×C4×#6157C2211yescharacteristic
18(C2×#6157)⋊Q8C2212yes—
19(C2×#6157)⋊Q8C2212yes—
20#16811574C2212yes—
21#16811574C2212yes—
22#16811574C2212yes—
23#16811574C2214yes—
24#16811574C2212yes—
25#16811574C2214yes—
26#16811574C2214yes—
27#16811574C2214yes—
28#16811574C2214yes—
29#16811573C2214yes—
30#16811573C2214yes—
31#16811573C2214yes—
32#16811572C2214yes—
33#16811572C2214yes—
34#16811572C2214yes—
35#16811572C2214yes—
36#16811572C2214yes—
37#16811572C2214yes—
38#16811572C2214yes—
39#16811572C2214yes—
40#16811572C2214yes—
41#16811570C2212yes—
42#16811570C2212yes—
43#16811570C2214yes—
44#16811569C2211yescharacteristic
45#16811569C2214yes—
46#16811568C2214yes—
47#16811567C2211yescharacteristic
48#16811565C2212yes—
49C4⋊C4×#6157C2214yes—
50C4⋊C4×#6157C2212yes—
51C4⋊C4×#6157C2212yes—
52C4⋊C4×#6157C2214yes—
53C4⋊C4×#6157C2214yes—
54C4×C4⋊#6157C2212yes—
55C4×C4⋊#6157C2212yes—
56C4×C4⋊#6157C2212yes—
57C4×C4⋊#6157C2214yes—
58C22⋊C4×#6157C2214yes—
59#16811559C2214yes—
60#16811236C411yescharacteristic, complemented
61#16811235C411yescharacteristic, complemented
62#16811234C411yescharacteristic, complemented
63#16811233C412yescomplemented
64#16811232C414yescomplemented
65#16811231C412yescomplemented
66#16811230C414yescomplemented
67C4⋊Q8×D53C2211yescharacteristic
68#126×D53C2214yes—
69#125×D53C2214yes—
70#125×D53C2211yescharacteristic
71C22⋊Q8×D53C2212yes—
72C4×Q8×D53C2212yes—
73#117×D53C2211yescharacteristic
74C53×#541C411yescharacteristic, complemented
75C23×#6157C2311yescharacteristic
76C23×#6157C2311yescharacteristic
77Q8×#6157—44no—
78Q8×#6157—44no—
79#13133296—42no—
80C2×C4⋊#6157C2312yes—
81C2×C4⋊#6157C2312yes—
82C2×C4⋊#6157C2312yes—
83C2×C4⋊#6157C2312yes—
84C2×C4⋊#6157C2312yes—
85C2×C4⋊#6157C2314yes—
86C2×C4⋊#6157C2312yes—
87C2×C4⋊#6157C2314yes—
88C2×C4⋊#6157C2314yes—
89C2×C4⋊#6157C2314yes—
90C2×C4⋊#6157C2314yes—
91C2×C4⋊#6157C2311yescharacteristic
92C2×C4⋊#6157C2311yescharacteristic
93C2×C22⋊#6157C2314yes—
94C2×C22⋊#6157C2312yes—
95C2×C4×#6157—42no—
96C2×C4×#6157C2314yes—
97C2×C4×#6157C2312yes—
98C2×C4×#6157C2312yes—
99C2×C4×#6157C2314yes—
100C2×C4×#6157C2314yes—
101C2×C4×#6157C2314yes—
102C2×C4×#6157C2314yes—
103C2×C4×#6157C2312yes—
104(C2×#6157)⋊C4C2312yes—
105(C2×#6157)⋊C4C2314yes—
106(C2×#6157)⋊C4C2314yes—
107(C2×#6157)⋊C4C2314yes—
108(C2×#6157)⋊C4C2314yes—
109(C2×#6157)⋊C4C2312yes—
110(C2×#6157)⋊C4C2312yes—
111(C2×#6157)⋊C4C2312yes—
112(C2×#6157)⋊C4C2314yes—
113(C2×#6157)⋊C4C2314yes—
114(C2×#6157)⋊C4C2314yes—
115(C2×#6157)⋊C4C2314yes—
116(C2×#6157)⋊C4C2314yes—
117(C2×#6157)⋊C4C2314yes—
118(C2×#6157)⋊C4C2314yes—
119C2×Q8×D53C2312yes—
120C22×C4×D53C2311yescharacteristic
121#13133217C2×C411yescharacteristic, complemented
122#13133216C2×C414yescomplemented
123#13133215C2×C412yescomplemented
124#13133212C2×C414yes—
125#13133212C2×C414yes—
126#13133212C2×C414yes—
127#13133211C2×C414yes—
128#13133210C2×C414yes—
129#13133210C2×C414yes—
130#13133210C2×C414yes—
131#13133209C2×C414yescomplemented
132#13133209C2×C411yescharacteristic, complemented
133#13133208C2×C414yescomplemented
134#13133208C2×C412yescomplemented
135#13133208C2×C414yescomplemented
136#13133207C2×C414yescomplemented
137#13133207C2×C414yescomplemented
138#13133207C2×C414yescomplemented
139#13133207C2×C414yescomplemented
140#13133207C2×C414yescomplemented
141#13133197C2×C412yes—
142#13133196C2×C412yes—
143#13133195C2×C414yes—
144#13133194C2×C414yes—
145#13133193C2×C412yes—
146Q8×Dic53C2×C412yescomplemented
147C4×Dic106C2×C414yescomplemented
148C4×Dic106C2×C412yescomplemented
149#13133182C2×C414yescomplemented
150#13133182C2×C412yescomplemented
151#13133176C2×C411yescharacteristic
152#13133175C2×C412yes—
153#13133174C2×C411yescharacteristic
154#13133174C2×C411yescharacteristic
155#13133173C2×C412yes—
156C4⋊C4×D53C2312yes—
157C4⋊C4×D53C2314yes—
158C4⋊C4×D53C2314yes—
159C4⋊C4×D53C2314yes—
160C4⋊C4×D53C2312yes—
161C4⋊C4×D53C2314yes—
162C22⋊C4×D53C2314yes—
163C22⋊C4×D53C2312yes—
164C42×D53C2314yes—
165C42×D53C2311yescharacteristic
166C42×D53C2311yescharacteristic
167C4⋊Q8×C53C2×C411yescharacteristic, complemented
168#126×C53C2×C414yes—
169#125×C53C2×C414yescomplemented
170#125×C53C2×C411yescharacteristic, complemented
171C22⋊Q8×C53C2×C412yes—
172C4×Q8×C53C2×C412yescomplemented
173#117×C53C2×C411yescharacteristic
174C23×D53C2411yescharacteristic
175C22×#6157—24no—
176C22×#6157—41no—
177C22×#6157—41no—
178C22×#6157—42no—
179C22×#6157C2414yes—
180C22×#6157C2412yes—
181C22×#6157C2412yes—
182C22×#6157C2412yes—
183C22×#6157C2414yes—
184C22×#6157C2412yes—
185C2×Q8×C53C22×C412yes—
186C22×C4×C53C22×C411yescharacteristic
187C22×Dic53C22×C411yescharacteristic
188Q8×D53—24no—
189Q8×D53—24no—
190C2×C4×D53—22no—
191C2×C4×D53—22no—
192C2×C4×D53C22×C411yescharacteristic
193C2×C4×D53C22×C411yescharacteristic
194C2×C4×D53C2412yes—
195C2×C4×D53C2414yes—
196C2×C4×D53C2412yes—
197C2×C4×D53C2414yes—
198C2×C4×D53C2411yescharacteristic
199C2×C4×D53C2411yescharacteristic
200C2×Dic106C22×C414yes—
201C2×Dic106C22×C412yes—
202C22⋊#6157—44no—
203C22⋊#6157—42no—
204C4⋊#6157—24no—
205C4⋊#6157—24no—
206C4⋊#6157—24no—
207C4⋊#6157—24no—
208C4⋊#6157—42no—
209C4⋊#6157—44no—
210C4⋊#6157—44no—
211C4⋊#6157—42no—
212C4⋊#6157—44no—
213C4⋊#6157—41no—
214C4⋊#6157—41no—
215C4⋊#6157—44no—
216C4⋊#6157—44no—
217C4×#6157—28no—
218C4×#6157—24no—
219C4×#6157—24no—
220C4×#6157—42no—
221C4×#6157—44no—
222C4×#6157—44no—
223C4×#6157—44no—
224C4×#6157—44no—
225C4⋊C4×C53C22×C412yes—
226C4⋊C4×C53C22×C412yes—
227C4⋊C4×C53C22×C414yes—
228C4⋊C4×C53C22×C414yes—
229C4⋊C4×C53C22×C414yes—
230C4⋊C4×C53C22×C414yes—
231C22⋊C4×C53C22×C412yes—
232C22⋊C4×C53C22×C414yes—
233C42×C53C22×C411yescharacteristic
234C42×C53C22×C411yescharacteristic
235C42×C53C22×C414yes—
236C22⋊Dic53C22×C412yes—
237C22⋊Dic53C22×C414yes—
238#11719921C22×C412yes—
239#11719921C22×C412yes—
240#11719921C22×C414yes—
241#11719921C22×C414yes—
242C4⋊Dic53C22×C412yes—
243C4⋊Dic53C22×C412yes—
244C4⋊Dic53C22×C414yes—
245C4⋊Dic53C22×C414yes—
246C4⋊Dic53C22×C414yes—
247C4⋊Dic53C22×C414yes—
248#11719919C22×C412yes—
249#11719919C22×C412yes—
250#11719919C22×C414yes—
251#11719919C22×C414yes—
252#11719919C22×C414yes—
253#11719919C22×C414yes—
254#11719919C22×C414yes—
255#11719919C22×C414yes—
256#11719919C22×C414yes—
257#11719919C22×C414yes—
258#11719919C22×C414yes—
259C4×Dic53C22×C412yes—
260C4×Dic53C22×C412yes—
261C4×Dic53C22×C411yescharacteristic
262C4×Dic53C22×C411yescharacteristic
263C4×Dic53C22×C414yes—
264C4×Dic53C22×C414yes—
265C4×Dic53C22×C414yes—
266C23×C53C23×C411yescharacteristic
267C22×D53—21no—
268C22×D53—21no—
269C22×D53—22no—
270C22×D53—22no—
271C22×D53C23×C411yescharacteristic
272C22×D53C2511yescharacteristic
273C2×#6157—22no—
274C2×#6157—22no—
275C2×#6157—22no—
276C2×#6157—22no—
277C2×#6157—22no—
278C2×#6157—24no—
279C2×#6157—24no—
280C2×#6157—22no—
281C2×#6157—22no—
282C2×#6157—24no—
283C2×#6157—22no—
284C2×#6157—24no—
285C2×#6157—24no—
286C2×#6157—22no—
287C2×#6157—24no—
288C2×#6157—22no—
289C2×#6157—22no—
290C2×#6157—44no—
291C2×#6157—44no—
292C2×#61572−1+414yes—
293Q8×C53—24no—
294C2×C4×C53—22no—
295C2×C4×C53C23×C414yes—
296C2×C4×C53C23×C411yescharacteristic
297C2×C4×C53C23×C412yes—
298C2×C4×C53C23×C412yes—
299C2×C4×C53C23×C414yes—
300C2×C4×C53C23×C411yescharacteristic
301C2×Dic53—22no—
302C2×Dic53C23×C414yes—
303C2×Dic53C23×C411yescharacteristic
304C2×Dic53C23×C412yes—
305C2×Dic53C23×C412yes—
306C2×Dic53C23×C414yes—
307C2×Dic53C23×C411yescharacteristic
308C4×D53—21no—
309C4×D53—24no—
310C4×D53—24no—
311C4×D53—22no—
312C4×D53—22no—
313C4×D53—21no—
314C4×D53—24no—
315C4×D53—22no—
316C4×D53—24no—
317C4×D53—22no—
318C4×D53—22no—
319C4×D53—22no—
320C4×D53H(5,𝔽2)12yes—
321C4×D532−1+412yes—
322Dic106—24no—
323Dic106—28no—
324#34420—531nomaximal, Sylow
325C22×C53—21no—
326C22×C53—22no—
327C22×C53C24×C411yescharacteristic
328C2×D53—21no—
329C2×D53—22no—
330C2×D53—41no—
331C2×D53—41no—
332C2×D53—42no—
333C2×D53C2×H(5,𝔽2)11yescharacteristic
334C2×D53C2×2−1+412yes—
335C2×D53C2×2−1+411yescharacteristic
336C2×D53#58512yes—
337#6157—24no—
338#6157—42no—
339#6157—42no—
340#6157—44no—
341#6157—42no—
342#6157—44no—
343C4×C53—24no—
344C4×C53—21no—
345C4×C53—24no—
346C4×C53—22no—
347C4×C53—22no—
348C4×C53#52012yes—
349Dic53—24no—
350Dic53—21no—
351Dic53—24no—
352Dic53—22no—
353Dic53—22no—
354Dic53#52012yes—
355C2×#541—531no—
356#2383—534no—
357#2373—534no—
358#2370—532no—
359#2365—532no—
360#2356—532no—
361Q8×C4⋊C4—532no—
362#2336—534no—
363#2330—534no—
364#2323—532no—
365#2314—531no—
366C4×C22⋊Q8—532no—
367#2296—531no—
368C2×C53—41no—
369C2×C53C2×#52011yescharacteristic
370C2×C53C4×2−1+412yes—
371D53—41no—
372D53#353811yescharacteristic
373D53#353911yescharacteristic
374D53#355512yes—
375#541—531no—
376#541—534no—
377#541—534no—
378#541—531no—
379#541—532no—
380#541—532no—
381#541—531no—
382#541#615711yescharacteristic, complemented
383C2×C4⋊Q8—531no—
384C2×#126—534no—
385C2×#125—534no—
386C2×#125—531no—
387C2×C22⋊Q8—532no—
388C2×C4×Q8—532no—
389C2×C4×Q8—532no—
390C2×C4×Q8—532no—
391C2×#117—531no—
392C2×#117—531no—
393C22×C42—531no—
394#391—532no—
395#391—532no—
396#389—534no—
397#389—532no—
398#389—532no—
399#389—534no—
400#389—534no—
401#389—534no—
402#389—532no—
403#389—534no—
404#389—532no—
405#388—534no—
406#388—534no—
407#388—534no—
408#387—534no—
409#387—534no—
410#387—534no—
411#387—534no—
412#387—534no—
413#387—534no—
414#387—534no—
415#387—534no—
416#387—534no—
417#385—532no—
418#385—532no—
419#385—534no—
420#384—531no—
421#384—534no—
422#383—534no—
423#382—531no—
424#380—532no—
425C4×C4⋊C4—532no—
426C4×C4⋊C4—532no—
427C4×C4⋊C4—534no—
428C4×C4⋊C4—534no—
429C4×C4⋊C4—534no—
430C4×C4⋊C4—534no—
431C4×C4⋊C4—532no—
432C4×C4⋊C4—532no—
433C4×C4⋊C4—532no—
434C4×C22⋊C4—534no—
435#376—534no—
436C53#3442011yescharacteristic, complemented, Sylow
437C22×Q8—532no—
438C23×C4—531no—
439C23×C4—531no—
440C23×C4—531no—
441C4⋊Q8—532no—
442C4⋊Q8—534no—
443C4⋊Q8—531no—
444C4⋊Q8C2×#615711yescharacteristic, complemented
445#126—534no—
446#126—534no—
447#126—534no—
448#126—534no—
449#126—534no—
450#126—534no—
451#126—534no—
452#126C2×#615714yes—
453#125—534no—
454#125—534no—
455#125—534no—
456#125—534no—
457#125—534no—
458#125—532no—
459#125—534no—
460#125—534no—
461#125—531no—
462#125—534no—
463#125C2×#615711yescharacteristic, complemented
464#125C2×#615714yescomplemented
465C22⋊Q8—532no—
466C22⋊Q8—532no—
467C22⋊Q8—534no—
468C22⋊Q8—532no—
469C22⋊Q8—534no—
470C22⋊Q8C2×#615712yes—
471C4×Q8—532no—
472C4×Q8—534no—
473C4×Q8—532no—
474C4×Q8—534no—
475C4×Q8—532no—
476C4×Q8—2124no—
477C4×Q8—2124no—
478C4×Q8C2×#615712yescomplemented
479#117—531no—
480#117—532no—
481#117—532no—
482#117—531no—
483#117—531no—
484#117—2122no—
485#117C2×#615711yescharacteristic
486C2×C4⋊C4—532no—
487C2×C4⋊C4—532no—
488C2×C4⋊C4—534no—
489C2×C4⋊C4—534no—
490C2×C4⋊C4—534no—
491C2×C4⋊C4—534no—
492C2×C4⋊C4—532no—
493C2×C4⋊C4—532no—
494C2×C4⋊C4—532no—
495C2×C4⋊C4—532no—
496C2×C4⋊C4—531no—
497C2×C4⋊C4—531no—
498C2×C4⋊C4—534no—
499C2×C4⋊C4—534no—
500C2×C4⋊C4—532no—
501C2×C4⋊C4—534no—
502C2×C4⋊C4—534no—
503C2×C4⋊C4—534no—
504C2×C4⋊C4—532no—
505C2×C22⋊C4—532no—
506C2×C22⋊C4—534no—
507C2×C22⋊C4—532no—
508C2×C22⋊C4—534no—
509C2×C42—531no—
510C2×C42—531no—
511C2×C42—534no—
512C2×C42—532no—
513C2×C42—532no—
514C2×C42—534no—
515C2×C42—534no—
516C2×C42—534no—
517C2×C42—534no—
518C2×C42—534no—
519C2×C42—532no—
520C2×C42—2122no—
521#95—532no—
522#95—534no—
523#95—534no—
524#95—534no—
525#95—534no—
526#95—532no—
527#95—534no—
528#95—532no—
529#95—534no—
530#95—534no—
531#95—534no—
532#95—534no—
533#95—532no—
534#95—534no—
535#95—534no—
536C24—531no—
537C2×Q8—534no—
538C2×Q8—532no—
539C2×Q8—1064no—
540C2×Q8—1064no—
541C2×Q8C22×#615712yes—
542C22×C4—531no—
543C22×C4—532no—
544C22×C4—531no—
545C22×C4—531no—
546C22×C4—531no—
547C22×C4—532no—
548C22×C4—534no—
549C22×C4—532no—
550C22×C4—534no—
551C22×C4—531no—
552C22×C4—534no—
553C22×C4—532no—
554C22×C4—532no—
555C22×C4—532no—
556C22×C4—534no—
557C22×C4—1062no—
558C22×C4—1062no—
559C22×C4—1064no—
560C22×C4—2121no—
561C22×C4—2121no—
562C22×C4—2122no—
563C22×C4C22×#615711yescharacteristic
564C4⋊C4—532no—
565C4⋊C4—532no—
566C4⋊C4—532no—
567C4⋊C4—534no—
568C4⋊C4—532no—
569C4⋊C4—534no—
570C4⋊C4—534no—
571C4⋊C4—534no—
572C4⋊C4—534no—
573C4⋊C4—534no—
574C4⋊C4—534no—
575C4⋊C4—534no—
576C4⋊C4—534no—
577C4⋊C4—534no—
578C4⋊C4—534no—
579C4⋊C4—534no—
580C4⋊C4—534no—
581C4⋊C4—1064no—
582C4⋊C4—1064no—
583C4⋊C4—1064no—
584C4⋊C4—1064no—
585C4⋊C4—2122no—
586C4⋊C4—2124no—
587C4⋊C4—2124no—
588C4⋊C4—2122no—
589C4⋊C4—2124no—
590C4⋊C4—2121no—
591C4⋊C4—2121no—
592C4⋊C4—2124no—
593C4⋊C4—2124no—
594C4⋊C4C22×#615712yes—
595C4⋊C4C22×#615712yes—
596C4⋊C4C22×#615714yes—
597C4⋊C4C22×#615714yes—
598C4⋊C4C22×#615714yes—
599C4⋊C4C22×#615714yes—
600C22⋊C4—532no—
601C22⋊C4—534no—
602C22⋊C4—532no—
603C22⋊C4—532no—
604C22⋊C4—534no—
605C22⋊C4—534no—
606C22⋊C4—2124no—
607C22⋊C4—2122no—
608C22⋊C4C22×#615712yes—
609C22⋊C4C22×#615714yes—
610C42—532no—
611C42—531no—
612C42—532no—
613C42—531no—
614C42—534no—
615C42—534no—
616C42—534no—
617C42—1068no—
618C42—1064no—
619C42—1064no—
620C42—2124no—
621C42—2124no—
622C42—2122no—
623C42—2124no—
624C42—2124no—
625C42C22×#615711yescharacteristic
626C42C22×#615711yescharacteristic
627C42C22×#615714yes—
628C23—531no—
629C23—531no—
630C23—1061no—
631C23—1062no—
632C23—1061no—
633C23—1062no—
634C23C23×#615711yescharacteristic
635Q8—24no—
636Q8—1068no—
637Q8—1064no—
638C2×C4—22no—
639C2×C4—531no—
640C2×C4—532no—
641C2×C4—532no—
642C2×C4—534no—
643C2×C4—532no—
644C2×C4—532no—
645C2×C4—534no—
646C2×C4—534no—
647C2×C4—531no—
648C2×C4—1062no—
649C2×C4—1064no—
650C2×C4—1061no—
651C2×C4—1064no—
652C2×C4—1062no—
653C2×C4—1064no—
654C2×C4—1062no—
655C2×C4—1062no—
656C2×C4—1062no—
657C2×C4—1061no—
658C2×C4—1064no—
659C2×C4—1062no—
660C2×C4—1062no—
661C2×C4—1062no—
662C2×C4—1062no—
663C2×C4—1062no—
664C2×C4—1062no—
665C2×C4—1062no—
666C2×C4—1064no—
667C2×C4—1064no—
668C2×C4—1064no—
669C2×C4—1062no—
670C2×C4—1064no—
671C2×C4—1064no—
672C2×C4—1064no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1062no—
676C2×C4—1062no—
677C2×C4—1062no—
678C2×C4—2124no—
679C2×C4—2124no—
680C2×C4C23×#615712yes—
681C2×C4C23×#615712yes—
682C2×C4C23×#615714yes—
683C2×C4C23×#615714yes—
684C2×C4C23×#615711yescharacteristic
685C2×C4C23×#615711yescharacteristic
686C22—21no—
687C22—22no—
688C22—531no—
689C22—531no—
690C22—532no—
691C22—532no—
692C22—1061no—
693C22—1062no—
694C22—2121no—
695C22—2121no—
696C22—2122no—
697C22C24×#615711yescharacteristic
698C4—21no—
699C4—24no—
700C4—24no—
701C4—22no—
702C4—22no—
703C4—532no—
704C4—1064no—
705C4—1061no—
706C4—1064no—
707C4—1062no—
708C4—1064no—
709C4—1062no—
710C4—2122no—
711C4—2122no—
712C4—2122no—
713C4—2124no—
714C4—2124no—
715C4#1681169212yes—
716C2—41no—
717C2—531no—
718C2—531no—
719C2—532no—
720C2—2121no—
721C2C2×#1681169211yescharacteristic
722C22−1+4×#615712yes—
subgroupG/H
center, FrattiniC22C24×#6157
commutator, socleC22×C53C24×C4
FittingC53×#541C4
prime radicalC23×D53C24
cosocleC22×D53C25
hypercenter#541#6157
hypocenterC53#34420
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #541

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #20291249C2semidirect
4. #20291244C2semidirect
5. #20291235C2semidirect
6. Q8×C4⋊#6157C2semidirect
7. #20291215C2semidirect
8. #20291209C2semidirect
60. #16811236C4semidirect
61. #16811235C4semidirect
62. #16811234C4semidirect
63. #16811233C4semidirect
64. #16811232C4semidirect
65. #16811231C4semidirect
66. #16811230C4semidirect
74. C53×#541C4semidirect
121. #13133217C2×C4semidirect
122. #13133216C2×C4semidirect
123. #13133215C2×C4semidirect
131. #13133209C2×C4semidirect
132. #13133209C2×C4semidirect
133. #13133208C2×C4semidirect
134. #13133208C2×C4semidirect
135. #13133208C2×C4semidirect
136. #13133207C2×C4semidirect
137. #13133207C2×C4semidirect
138. #13133207C2×C4semidirect
139. #13133207C2×C4semidirect
140. #13133207C2×C4semidirect
146. Q8×Dic53C2×C4semidirect
147. C4×Dic106C2×C4semidirect
148. C4×Dic106C2×C4semidirect
149. #13133182C2×C4semidirect
150. #13133182C2×C4semidirect
167. C4⋊Q8×C53C2×C4semidirect
169. #125×C53C2×C4semidirect
170. #125×C53C2×C4semidirect
172. C4×Q8×C53C2×C4semidirect
382. #541#6157semidirect
436. C53#34420semidirect
444. C4⋊Q8C2×#6157semidirect
463. #125C2×#6157semidirect
464. #125C2×#6157semidirect
478. C4×Q8C2×#6157semidirect

Maximal subgroups

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

subgroupindex
#202912622
#202912522
#202912492
#202912442
#202912352
Q8×C4⋊#61572
#202912152
#202912092
#202912022
#202911932
C22⋊Q8×#61572
#202911752
#541×D532
#3442053