Finite Group Databasebeta

← #13078717

Subgroups — #13078717

Order 1408.

444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623259C211yesmaximal, characteristic, complemented
2C4×D4×D11C211yesmaximal, characteristic
3C11×#474C211yesmaximal, characteristic, complemented
4#10622700C211yesmaximal, characteristic, complemented
5#10622632C211yesmaximal, characteristic, complemented
6#10622502C212yesmaximal, complemented
7#10622497C212yesmaximal, complemented
8#10622454C211yesmaximal, characteristic, complemented
9#10622448C211yesmaximal, characteristic, complemented
10#10622389C212yesmaximal
11#10622370C212yesmaximal, complemented
12C2×D4×D11C2211yescharacteristic
13C22×C4×D11—21no—
14C11×C4⋊Q8C2211yescharacteristic, complemented
15C4×D4×C11C2211yescharacteristic
16#66999—21no—
17Q8×Dic11—21no—
18D4×Dic11C2211yescharacteristic
19C2×#4324C2212yes—
20C4×C22⋊D11—21no—
21C2×#4314C2212yes—
22#66950C2212yes—
23#66946C2211yescharacteristic
24#66945—21no—
25C4⋊C4×D11C2211yescharacteristic
26#66943—21no—
27#66940C2212yescomplemented
28(C22⋊D11)⋊C4—21no—
29C22⋊C4×D11—21no—
30C4×D44C2211yescharacteristic
31C42×D11C2211yescharacteristic
32#66922C2211yescharacteristic, complemented
33C11×#107C2212yescomplemented
34C11×C4⋊C8C2211yescharacteristic, complemented
35C11×#102C2212yes—
36(C2×D11)⋊C8C2212yes—
37#66880C2212yescomplemented
38#66879C2212yescomplemented
39#66874C2212yescomplemented
40#66873C2212yes—
41#66871C2212yescomplemented
42C4⋊(C11⋊C8)C2211yescharacteristic, complemented
43C23×D11—21no—
44C2×Q8×C11—21no—
45C2×D4×C11C2311yescharacteristic
46C22×C4×C11—21no—
47C2×C22⋊D11—21no—
48C22×Dic11—21no—
49D4×D11—22no—
50D4×D11—22no—
51C2×D44C2311yescharacteristic
52C2×C4×D11—21no—
53C2×C4×D11—21no—
54C2×C4×D11—21no—
55C2×C4×D11—44no—
56C2×C4×D11D411yescharacteristic
57C2×C4×D11D411yescharacteristic
58C2×C4×D11C2311yescharacteristic
59C2×Dic22C2312yes—
60C2×C8×C11C2312yes—
61C11×C4⋊C4—21no—
62C11×C4⋊C4C2312yes—
63C11×C4⋊C4C2311yescharacteristic
64C11×C22⋊C4—21no—
65C42×C11C2311yescharacteristic
66C22⋊Dic11—21no—
67#4324—24no—
68(C2×D11)⋊C4—21no—
69(C2×D11)⋊C4—22no—
70(C2×D11)⋊C4—21no—
71C4⋊Dic11—22no—
72C4⋊Dic11—21no—
73C4⋊Dic11—21no—
74C4⋊Dic11C2311yescharacteristic
75Dic11⋊C4—21no—
76Dic11⋊C4—22no—
77C4×Dic11—22no—
78C4×Dic11D411yescharacteristic
79C4×Dic11D411yescharacteristic
80C4×Dic11C2311yescharacteristic
81C2×C11⋊C8C2312yes—
82#4314—24no—
83#3110—111nomaximal, Sylow
84C23×C11—21no—
85C22×D11—24no—
86C22×D11—21no—
87C22×D11—42no—
88C22×D11—42no—
89C22×D11C2×D411yescharacteristic
90Q8×C11—42no—
91D4×C11—21no—
92D4×C11#4112yes—
93C2×C4×C11—22no—
94C2×C4×C11—21no—
95C2×C4×C11—42no—
96C2×C4×C11C2×D411yescharacteristic
97C2×C4×C11C2×D411yescharacteristic
98C2×C4×C11C2411yescharacteristic
99C22⋊D11—24no—
100C2×Dic11—22no—
101C2×Dic11—21no—
102C2×Dic11—42no—
103C2×Dic11C2×D411yescharacteristic
104C2×Dic11C2×D411yescharacteristic
105C2×Dic11C2×D411yescharacteristic
106D44—21no—
107D44#4112yes—
108C4×D11—22no—
109C4×D11—22no—
110C4×D11—21no—
111C4×D11—21no—
112C4×D11—42no—
113C4×D11—42no—
114C4×D11—42no—
115Dic22—22no—
116Dic22—22no—
117C8×C11—22no—
118C11⋊C8—22no—
119#533—111no—
120C2×C4×D4—111no—
121#484—112no—
122#474—111no—
123#474D1111yescharacteristic, complemented
124#461—111no—
125#461—111no—
126#450—112no—
127#440—112no—
128#440—112no—
129#432—111no—
130C22×C11—22no—
131C22×C11—41no—
132C22×C11—41no—
133C22×C11C22×D411yescharacteristic
134C2×D11—21no—
135C2×D11—21no—
136C2×D11—22no—
137C2×D11—48no—
138C2×D11—41no—
139C2×D11—41no—
140C2×D11#13712yes—
141C4×C11—21no—
142C4×C11—41no—
143C4×C11—42no—
144C4×C11AGL(1,ℤ/8)12yes—
145C4×C11C2×#4111yescharacteristic
146C4×C11C2×#4111yescharacteristic
147Dic11—21no—
148Dic11—21no—
149Dic11—21no—
150Dic11—42no—
151Dic11—41no—
152C22×D4—111no—
153C23×C4—221no—
154C2×SD16—112no—
155C2×SD16—112no—
156C4⋊Q8—111no—
157C4⋊Q8C2×D1111yescharacteristic, complemented
158#125—221no—
159C22⋊Q8—112no—
160C22⋊Q8—221no—
161C4×Q8—112no—
162C4×Q8—221no—
163C4×D4—111no—
164C4×D4—111no—
165C4×D4—111no—
166C4×D4—221no—
167C4×D4—221no—
168C4×D4C2×D1111yescharacteristic
169#117—221no—
170C2×C4⋊C4—111no—
171C2×C22⋊C4—221no—
172C2×C42—111no—
173#107—112no—
174#107C2×D1112yescomplemented
175C4⋊C8—111no—
176C4⋊C8C2×D1111yescharacteristic, complemented
177#103—112no—
178#103—112no—
179#102—112no—
180#102C2×D1112yes—
181C22⋊C8—112no—
182#97—112no—
183C2×C11—42no—
184C2×C11#52511yescharacteristic
185C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
186C2×C11C2×#13711yescharacteristic
187D11—22no—
188D11—42no—
189C24—221no—
190C2×Q8—21no—
191C2×Q8—112no—
192C2×D4—111no—
193C2×D4—221no—
194C2×D4—222no—
195C2×D4—222no—
196C2×D4C22×D1111yescharacteristic
197C22×C4—21no—
198C22×C4—111no—
199C22×C4—111no—
200C22×C4—111no—
201C22×C4—221no—
202C22×C4—221no—
203C22×C4—221no—
204C22×C4—221no—
205C22×C4—444no—
206SD16—224no—
207SD16—224no—
208C2×C8—112no—
209C2×C8C22×D1112yes—
210C4⋊C4—21no—
211C4⋊C4—111no—
212C4⋊C4—221no—
213C4⋊C4—222no—
214C4⋊C4—222no—
215C4⋊C4—221no—
216C4⋊C4—221no—
217C4⋊C4C22×D1112yes—
218C4⋊C4C22×D1111yescharacteristic
219C22⋊C4—21no—
220C22⋊C4—221no—
221C22⋊C4—222no—
222C22⋊C4—221no—
223C22⋊C4—221no—
224C42—111no—
225C42—111no—
226C42—111no—
227C42—222no—
228C42C22×D1111yescharacteristic
229C11#311011yescharacteristic, complemented, Sylow
230C23—21no—
231C23—111no—
232C23—224no—
233C23—221no—
234C23—442no—
235C23—442no—
236Q8—42no—
237Q8—222no—
238Q8—222no—
239D4—21no—
240D4—112no—
241D4—224no—
242D4—221no—
243D4#434312yes—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—111no—
248C2×C4—111no—
249C2×C4—111no—
250C2×C4—222no—
251C2×C4—222no—
252C2×C4—221no—
253C2×C4—221no—
254C2×C4—222no—
255C2×C4—221no—
256C2×C4—442no—
257C2×C4—442no—
258C2×C4—442no—
259C2×C4—442no—
260C2×C4D4×D1111yescharacteristic
261C2×C4D4×D1111yescharacteristic
262C2×C4C23×D1111yescharacteristic
263C8—22no—
264C8—222no—
265C22—22no—
266C22—41no—
267C22—41no—
268C22—112no—
269C22—221no—
270C22—221no—
271C22—222no—
272C22—448no—
273C22—441no—
274C22—441no—
275C22C2×D4×D1111yescharacteristic
276C4—21no—
277C4—41no—
278C4—42no—
279C4—221no—
280C4—221no—
281C4—221no—
282C4—441no—
283C4—442no—
284C4#6696412yes—
285C4C2×#434311yescharacteristic
286C4#41×D1111yescharacteristic
287C2—42no—
288C2—222no—
289C2—442no—
290C2#1062315811yescharacteristic
291C2C2×#6696411yescharacteristic
292C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#474C2
socleC22×C11C22×D4
prime radicalC2×D4×D11C22
hypercenter#474D11
hypocenterC11#3110
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #10623259C2semidirect
3. C11×#474C2semidirect
4. #10622700C2semidirect
5. #10622632C2semidirect
6. #10622502C2semidirect
7. #10622497C2semidirect
8. #10622454C2semidirect
9. #10622448C2semidirect
11. #10622370C2semidirect
14. C11×C4⋊Q8C22semidirect
27. #66940C22semidirect
32. #66922C22semidirect
33. C11×#107C22semidirect
34. C11×C4⋊C8C22semidirect
37. #66880C22semidirect
38. #66879C22semidirect
39. #66874C22semidirect
41. #66871C22semidirect
42. C4⋊(C11⋊C8)C22semidirect
123. #474D11semidirect
157. C4⋊Q8C2×D11semidirect
174. #107C2×D11semidirect
176. C4⋊C8C2×D11semidirect
229. C11#3110semidirect

Maximal subgroups

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

subgroupindex
#106232592
C4×D4×D112
C11×#4742
#106227002
#106226322
#106225022
#106224972
#106224542
#106224482
#106223892
#106223702
#311011