Finite Group Databasebeta

← #14738621

Subgroups — #14738621

Order 2816.

648 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079834C211yesmaximal, characteristic, complemented
2#13079631C211yesmaximal, characteristic
3C2×#10622307C211yesmaximal, characteristic, complemented
4#13068156C212yesmaximal, complemented
5#13068149C212yesmaximal, complemented
6#13068032C212yesmaximal, complemented
7#13068025C212yesmaximal, complemented
8#13067379C211yesmaximal, characteristic, complemented
9#13067341C211yesmaximal, characteristic, complemented
10#13067329C211yesmaximal, characteristic, complemented
11C11×#2966C211yesmaximal, characteristic, complemented
12C11×#529C2211yescharacteristic
13C2×#66927C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C11×#446C2211yescharacteristic, complemented
16C8×Q8×C11C2211yescharacteristic, complemented
17C11×#436C2211yescharacteristic, complemented
18C11×#435—21no—
19C8×D4×C11—21no—
20C8×D4×C11C2211yescharacteristic, complemented
21C11×#433—21no—
22C11×#432C2211yescharacteristic
23C11×#405—21no—
24C2×C4×C8×C11C2211yescharacteristic
25C2×#66885—21no—
26C2×#66885—21no—
27#10622680—21no—
28#10622678—21no—
29#10622671—21no—
30#10622668—21no—
31#10622659—21no—
32#10622656—21no—
33#10622649—21no—
34#10622646—21no—
35#10622640C2212yes—
36#10622634C2212yescomplemented
37#10622628C2212yes—
38#10622621C2212yescomplemented
39#10622539C2211yescharacteristic
40#10622539C2211yescharacteristic
41#10622307—21no—
42#10622307—21no—
43#10622307C2212yes—
44#10622307C2212yes—
45#10622123C2212yes—
46#10622123C2212yes—
47#10622119C2212yescomplemented
48#10622119C2212yescomplemented
49#10622096C2212yescomplemented
50#10622095C2212yescomplemented
51C22×D44—21no—
52C22×D44—21no—
53C22×D44—21no—
54C22×Dic22—21no—
55C2×C11×M16—21no—
56C22×C8×C11—21no—
57C22×C8×C11D411yescharacteristic
58C22×C8×C11D411yescharacteristic
59C11×#126—21no—
60C11×#125D411yescharacteristic
61C11×#124D411yescharacteristic
62C11×#123—21no—
63C11×C22⋊Q8D411yescharacteristic
64C11×#121D411yescharacteristic
65C4×Q8×C11C2311yescharacteristic
66C4×D4×C11—21no—
67C4×D4×C11C2311yescharacteristic
68C11×#117—21no—
69C2×C42×C11C2311yescharacteristic
70C2×#4325—22no—
71C2×#4323—22no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74#66927—21no—
75#66927—21no—
76#66927—21no—
77#66927C2312yes—
78#66922—21no—
79#66922—21no—
80#66922—21no—
81#66922C2312yes—
82C11×C4⋊C8—21no—
83C11×C4⋊C8—21no—
84C11×C4⋊C8C2311yescharacteristic
85C11×C4⋊C8C2311yescharacteristic
86C11×C22⋊C8—21no—
87C11×C22⋊C8—21no—
88C11×C22⋊C8—21no—
89C11×#97—21no—
90C11×#97—21no—
91C4×C8×C11—21no—
92C4×C8×C11D411yescharacteristic
93C4×C8×C11D411yescharacteristic
94C4×C8×C11C2311yescharacteristic
95C4×C8×C11C2311yescharacteristic
96#66899—22no—
97#66896—22no—
98C22⋊(C11⋊C8)—21no—
99C22⋊(C11⋊C8)—21no—
100#66885—22no—
101#66885—22no—
102#66885—22no—
103#66885—22no—
104#66873—22no—
105#66873—22no—
106#66872—22no—
107#66871—22no—
108C4⋊(C11⋊C8)C2312yes—
109C4⋊(C11⋊C8)C2312yes—
110#66867—21no—
111#66867—21no—
112#19362—111nomaximal, Sylow
113C23×D11—41no—
114C2×Q8×C11C2×D411yescharacteristic
115C2×D4×C11—21no—
116C2×D4×C11C2×D411yescharacteristic
117C22×C4×C11—21no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11#4111yescharacteristic
121C22×Dic11—41no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—22no—
125C2×D44—42no—
126C2×D44—42no—
127C2×D44—41no—
128C2×D44—41no—
129C2×D44—41no—
130C2×D44—82no—
131C2×D44—82no—
132C2×Dic22—22no—
133C2×Dic22—41no—
134C2×Dic22—82no—
135C11×M16—42no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—41no—
139C2×C8×C11—41no—
140C2×C8×C11—42no—
141C2×C8×C11C2×D411yescharacteristic
142C2×C8×C11C2×D411yescharacteristic
143C2×C8×C11C2×D411yescharacteristic
144C2×C8×C11C2×D411yescharacteristic
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4C2×D411yescharacteristic
150C11×C4⋊C4C2×D411yescharacteristic
151C11×C22⋊C4—21no—
152C11×C22⋊C4—21no—
153C11×C22⋊C4—21no—
154C11×C22⋊C4—21no—
155C11×C22⋊C4—21no—
156C42×C11—21no—
157C42×C11C2×D411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11#4111yescharacteristic
160C42×C11C2411yescharacteristic
161#4325—82no—
162#4323—82no—
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165C4⋊Dic11—41no—
166C4⋊Dic11—41no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169#3238—111no—
170#3217—111no—
171C2×#486—111no—
172#2966D1111yescharacteristic, complemented
173#1698—112no—
174#1697—112no—
175#1678—112no—
176#1677—112no—
177#1568—111no—
178#1558—111no—
179#1555—111no—
180C23×C11—21no—
181C23×C11#12111yescharacteristic
182C22×D11—42no—
183C22×D11—82no—
184C22×D11—82no—
185C22×D11—82no—
186Q8×C11—22no—
187D4×C11—22no—
188D4×C11—42no—
189C2×C4×C11—22no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×Dic11—42no—
205C2×Dic11—82no—
206D44—42no—
207D44—42no—
208D44—42no—
209D44—42no—
210D44—82no—
211D44—82no—
212D44—82no—
213D44—82no—
214Dic22—82no—
215Dic22—82no—
216C8×C11—21no—
217C8×C11—21no—
218C8×C11—21no—
219C8×C11—21no—
220C8×C11—41no—
221C8×C11—41no—
222C11⋊C8—42no—
223C11⋊C8—42no—
224C2×C4⋊Q8—111no—
225C2×#127—111no—
226#529C2×D1111yescharacteristic
227#501—221no—
228#496—221no—
229#490—221no—
230#489—221no—
231#486—112no—
232#486—112no—
233#486—221no—
234#486—221no—
235#483—221no—
236#480—221no—
237#477—112no—
238#476—112no—
239#460—112no—
240#459—112no—
241#450—221no—
242#447—221no—
243#446C2×D1111yescharacteristic, complemented
244C8×Q8C2×D1111yescharacteristic, complemented
245#436C2×D1111yescharacteristic, complemented
246#435—21no—
247C8×D4—21no—
248C8×D4C2×D1111yescharacteristic, complemented
249#433—21no—
250#432—111no—
251#432—111no—
252#432C2×D1111yescharacteristic
253C2×#102—221no—
254C2×#102—221no—
255#405—21no—
256C2×C4×C8C2×D1111yescharacteristic
257#335—112no—
258#334—112no—
259#333—112no—
260#333—112no—
261#331—112no—
262#331—112no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—41no—
266C22×C11—41no—
267C22×C11—41no—
268C22×C11#47212yes—
269C22×C11C2×#12111yescharacteristic
270C2×D11—82no—
271C2×D11—82no—
272C2×D11—82no—
273C2×D11—164no—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—41no—
279C4×C11—41no—
280C4×C11—41no—
281C4×C11#57511yescharacteristic
282C4×C11#57511yescharacteristic
283C4×C11#57712yes—
284Dic11—82no—
285C22×Q8—221no—
286C22×D4—221no—
287C22×D4—221no—
288C22×D4—221no—
289C2×SD16—222no—
290C2×D8—222no—
291C2×M16—21no—
292C22×C8—21no—
293C22×C8C22⋊D1111yescharacteristic
294C22×C8C22⋊D1111yescharacteristic
295C4⋊Q8—112no—
296C4⋊Q8—221no—
297C4⋊Q8—221no—
298C4⋊Q8—221no—
299#127—112no—
300#127—221no—
301#127—221no—
302#127—221no—
303#126—21no—
304#125D4411yescharacteristic
305#124D4411yescharacteristic
306#123—21no—
307C22⋊Q8D4411yescharacteristic
308#121D4411yescharacteristic
309C4×Q8C22×D1111yescharacteristic
310C4×D4—21no—
311C4×D4C22×D1111yescharacteristic
312#117—21no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4—221no—
315C2×C42C22×D1111yescharacteristic
316#107—222no—
317#106—222no—
318C4⋊C8—21no—
319C4⋊C8—21no—
320C4⋊C8—112no—
321C4⋊C8—112no—
322C4⋊C8C22×D1111yescharacteristic
323C4⋊C8C22×D1111yescharacteristic
324#103—222no—
325#102—222no—
326#102—222no—
327#102—222no—
328#102—222no—
329#102—222no—
330#102—222no—
331#102—222no—
332C22⋊C8—21no—
333C22⋊C8—21no—
334C22⋊C8—21no—
335C22⋊C8—221no—
336C22⋊C8—221no—
337#97—21no—
338#97—21no—
339#97—221no—
340#97—221no—
341C4×C8—21no—
342C4×C8C22⋊D1111yescharacteristic
343C4×C8C22⋊D1111yescharacteristic
344C4×C8C22×D1111yescharacteristic
345C4×C8C22×D1111yescharacteristic
346C2×C11—22no—
347C2×C11—81no—
348C2×C11#304011yescharacteristic
349C2×C11#305711yescharacteristic
350C2×C11C2×#47211yescharacteristic
351D11—162no—
352C24—441no—
353C2×Q8—222no—
354C2×Q8—441no—
355C2×Q8—882no—
356C2×Q8C2×D4411yescharacteristic
357C2×D4—21no—
358C2×D4—222no—
359C2×D4—222no—
360C2×D4—222no—
361C2×D4—442no—
362C2×D4—442no—
363C2×D4—441no—
364C2×D4—441no—
365C2×D4—441no—
366C2×D4—882no—
367C2×D4—882no—
368C2×D4C2×D4411yescharacteristic
369C22×C4—21no—
370C22×C4—441no—
371C22×C4C2×D4411yescharacteristic
372C22×C4#433911yescharacteristic
373C22×C4C2×C22⋊D1111yescharacteristic
374SD16—882no—
375D8—882no—
376M16—42no—
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—41no—
380C2×C8—41no—
381C2×C8—42no—
382C2×C8—222no—
383C2×C8—222no—
384C2×C8C2×C22⋊D1111yescharacteristic
385C2×C8C2×C22⋊D1111yescharacteristic
386C2×C8C2×C22⋊D1111yescharacteristic
387C2×C8C2×C22⋊D1111yescharacteristic
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—222no—
393C4⋊C4—222no—
394C4⋊C4—441no—
395C4⋊C4—441no—
396C4⋊C4C2×D4411yescharacteristic
397C4⋊C4C2×D4411yescharacteristic
398C22⋊C4—21no—
399C22⋊C4—21no—
400C22⋊C4—21no—
401C22⋊C4—21no—
402C22⋊C4—21no—
403C42—21no—
404C42C2×D4411yescharacteristic
405C42#433911yescharacteristic
406C42C2×C22⋊D1111yescharacteristic
407C42C23×D1111yescharacteristic
408C11#1936211yescharacteristic, complemented, Sylow
409C23—21no—
410C23—442no—
411C23—882no—
412C23—882no—
413C23—882no—
414C23#6698311yescharacteristic
415Q8—22no—
416Q8—882no—
417Q8—882no—
418D4—22no—
419D4—42no—
420D4—442no—
421D4—442no—
422D4—442no—
423D4—442no—
424D4—882no—
425D4—882no—
426D4—882no—
427D4—882no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—442no—
438C2×C4—882no—
439C2×C4#6698311yescharacteristic
440C2×C4#6698311yescharacteristic
441C2×C4#6698311yescharacteristic
442C2×C4C22×D4411yescharacteristic
443C2×C4C2×#433911yescharacteristic
444C2×C4C22×C22⋊D1111yescharacteristic
445C8—21no—
446C8—21no—
447C8—21no—
448C8—21no—
449C8—41no—
450C8—41no—
451C8—442no—
452C8—442no—
453C22—21no—
454C22—21no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—882no—
459C22—882no—
460C22—882no—
461C22—1764no—
462C22#1062275512yes—
463C22C2×#6698311yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—882no—
472C4#1062328212yes—
473C4#1062335311yescharacteristic
474C4#1062335311yescharacteristic
475C2—22no—
476C2—81no—
477C2—1762no—
478C2#1307811011yescharacteristic
479C2#1307825511yescharacteristic
480C2C2×#1062275511yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2966C2
socleC22×C11C2×#121
prime radical#13079631C2
hypercenter#2966D11
hypocenterC11#19362
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2966

Complements

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

NH ≅ G/Ntype
1. #13079834C2semidirect
3. C2×#10622307C2semidirect
4. #13068156C2semidirect
5. #13068149C2semidirect
6. #13068032C2semidirect
7. #13068025C2semidirect
8. #13067379C2semidirect
9. #13067341C2semidirect
10. #13067329C2semidirect
11. C11×#2966C2semidirect
15. C11×#446C22semidirect
16. C8×Q8×C11C22semidirect
17. C11×#436C22semidirect
20. C8×D4×C11C22semidirect
36. #10622634C22semidirect
38. #10622621C22semidirect
47. #10622119C22semidirect
48. #10622119C22semidirect
49. #10622096C22semidirect
50. #10622095C22semidirect
172. #2966D11semidirect
243. #446C2×D11semidirect
244. C8×Q8C2×D11semidirect
245. #436C2×D11semidirect
248. C8×D4C2×D11semidirect
408. C11#19362semidirect

Maximal subgroups

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

subgroupindex
#130798342
#130796312
C2×#106223072
#130681562
#130681492
#130680322
#130680252
#130673792
#130673412
#130673292
C11×#29662
#1936211