Finite Group Databasebeta

← #13079436

Subgroups — #13079436

Order 1408.

410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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
1D11×C22⋊Q8C212yesmaximal
2C11×#470C211yesmaximal, characteristic, complemented
3#10622799C212yesmaximal, complemented
4#10622750C211yesmaximal, characteristic, complemented
5#10622739C211yesmaximal, characteristic
6#10622665C212yesmaximal, complemented
7#10622475C212yesmaximal, complemented
8#10622421C212yesmaximal, complemented
9#10622418C212yesmaximal, complemented
10C2×Q8×D11C2212yes—
11C22×C4×D11C2211yescharacteristic
12C2×C11×Q16C2211yescharacteristic, complemented
13C2×C11×M16C2211yescharacteristic
14C11×C22⋊Q8C2212yes—
15#66999C2212yes—
16C2×#4326C2212yescomplemented
17#66977C2212yes—
18C2×#4318C2211yescharacteristic
19C2×Dic44C2211yescharacteristic, complemented
20#66950C2212yes—
21#66949—22no—
22C4⋊C4×D11—22no—
23C4⋊C4×D11C2212yes—
24C22⋊C4×D11—22no—
25#66931—22no—
26C11×#106C2211yescharacteristic, complemented
27C11×#103C2212yescomplemented
28#66899C2212yescomplemented
29(C2×D11)⋊C8C2212yes—
30(C2×D11)⋊C8C2212yes—
31#66881C2211yescharacteristic, complemented
32#66880C2212yescomplemented
33#66874C2212yescomplemented
34#66872C2212yescomplemented
35C23×D11D411yescharacteristic
36C2×Q8×C11C2312yes—
37C22×C4×C11C2311yescharacteristic
38C22×Dic11D411yescharacteristic
39Q8×D11—42no—
40Q8×D11—42no—
41C2×C4×D11—22no—
42C2×C4×D11—22no—
43C2×C4×D11—41no—
44C2×C4×D11—41no—
45C2×C4×D11D412yes—
46C2×C4×D11C2312yes—
47C2×Dic22—22no—
48C2×Dic22C2312yes—
49C11×Q16—41no—
50C11×M16—41no—
51C2×C8×C11C2311yescharacteristic
52C2×C8×C11C2311yescharacteristic
53C11×C4⋊C4—22no—
54C11×C4⋊C4C2312yes—
55C11×C22⋊C4—22no—
56C22⋊Dic11—22no—
57#4326—42no—
58(C2×D11)⋊C4—22no—
59(C2×D11)⋊C4—22no—
60C4⋊Dic11—22no—
61C4⋊Dic11C2312yes—
62Dic11⋊C4—22no—
63Dic11⋊C4—22no—
64Dic11⋊C4—22no—
65#4318—41no—
66C2×C11⋊C8C2312yes—
67Dic44—41no—
68#3195—111nomaximal, Sylow
69C23×C11C2×D411yescharacteristic
70C22×D11—24no—
71C22×D11—41no—
72C22×D11C2×D412yes—
73Q8×C11—22no—
74Q8×C11—22no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11C2×D411yescharacteristic
80C2×C4×C11C2411yescharacteristic
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—41no—
84C2×Dic11C2×D412yes—
85C4×D11—22no—
86C4×D11—22no—
87C4×D11—42no—
88C4×D11—44no—
89C4×D11—44no—
90Dic22—22no—
91Dic22—22no—
92Dic22—44no—
93C8×C11—21no—
94C8×C11—21no—
95C11⋊C8—22no—
96C2×C22⋊Q8—112no—
97#483—112no—
98#483—112no—
99#470—111no—
100#470—112no—
101#470D1111yescharacteristic, complemented
102#451—112no—
103#451—112no—
104#407—111no—
105C22×C11—21no—
106C22×C11—22no—
107C22×C11C22×D411yescharacteristic
108C2×D11—22no—
109C2×D11—22no—
110C2×D11—44no—
111C2×D11#13714yes—
112C4×C11—21no—
113C4×C11—42no—
114C4×C11—42no—
115C4×C11H(5,𝔽2)11yescharacteristic
116C4×C11H(5,𝔽2)11yescharacteristic
117Dic11—22no—
118Dic11—42no—
119Dic11—42no—
120C22×Q8—112no—
121C23×C4—111no—
122C2×Q16—112no—
123C2×Q16—111no—
124C2×Q16C2×D1111yescharacteristic, complemented
125C2×M16—111no—
126C2×M16C2×D1111yescharacteristic
127C22⋊Q8—112no—
128C22⋊Q8—112no—
129C22⋊Q8—112no—
130C22⋊Q8—222no—
131C22⋊Q8—222no—
132C22⋊Q8C2×D1112yes—
133C2×C4⋊C4—112no—
134C2×C4⋊C4—222no—
135C2×C22⋊C4—222no—
136#106—111no—
137#106—112no—
138#106C2×D1111yescharacteristic, complemented
139#103—112no—
140#103—112no—
141#103—112no—
142#103C2×D1112yescomplemented
143C22⋊C8—112no—
144C22⋊C8—112no—
145C2×C11—41no—
146C2×C11#53411yescharacteristic
147C2×C11C2×#13712yes—
148D11—24no—
149C24—111no—
150C2×Q8—112no—
151C2×Q8—222no—
152C2×Q8—442no—
153C2×Q8—442no—
154C2×Q8C22×D1112yes—
155C22×C4—111no—
156C22×C4—112no—
157C22×C4—112no—
158C22×C4—222no—
159C22×C4—222no—
160C22×C4—441no—
161C22×C4—441no—
162C22×C4C22×D1111yescharacteristic
163Q16—41no—
164Q16—441no—
165Q16—442no—
166M16—41no—
167M16—441no—
168C2×C8—112no—
169C2×C8C22×D1111yescharacteristic
170C2×C8C22×D1111yescharacteristic
171C4⋊C4—22no—
172C4⋊C4—112no—
173C4⋊C4—222no—
174C4⋊C4—222no—
175C4⋊C4—222no—
176C4⋊C4—222no—
177C4⋊C4C22×D1112yes—
178C22⋊C4—22no—
179C22⋊C4—222no—
180C22⋊C4—222no—
181C22⋊C4—222no—
182C11#319511yescharacteristic, complemented, Sylow
183C23—112no—
184C23—224no—
185C23—441no—
186C23D4×D1111yescharacteristic
187Q8—22no—
188Q8—22no—
189Q8—222no—
190Q8—222no—
191Q8—444no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—112no—
197C2×C4—222no—
198C2×C4—222no—
199C2×C4—222no—
200C2×C4—222no—
201C2×C4—442no—
202C2×C4—444no—
203C2×C4—444no—
204C2×C4—441no—
205C2×C4D4×D1111yescharacteristic
206C2×C4C23×D1111yescharacteristic
207C8—21no—
208C8—21no—
209C8—222no—
210C22—22no—
211C22—21no—
212C22—114no—
213C22—222no—
214C22—222no—
215C22—444no—
216C22C2×D4×D1111yescharacteristic
217C4—21no—
218C4—42no—
219C4—42no—
220C4—222no—
221C4—442no—
222C4—442no—
223C4#6703711yescharacteristic
224C4#6704211yescharacteristic
225C2—41no—
226C2—224no—
227C2#1062313611yescharacteristic
228C2D11×#13712yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#470C2
socleC22×C11C22×D4
prime radicalC23×D11D4
hypercenter#470D11
hypocenterC11#3195
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. C11×#470C2semidirect
3. #10622799C2semidirect
4. #10622750C2semidirect
6. #10622665C2semidirect
7. #10622475C2semidirect
8. #10622421C2semidirect
9. #10622418C2semidirect
12. C2×C11×Q16C22semidirect
16. C2×#4326C22semidirect
19. C2×Dic44C22semidirect
26. C11×#106C22semidirect
27. C11×#103C22semidirect
28. #66899C22semidirect
31. #66881C22semidirect
32. #66880C22semidirect
33. #66874C22semidirect
34. #66872C22semidirect
101. #470D11semidirect
124. C2×Q16C2×D11semidirect
138. #106C2×D11semidirect
142. #103C2×D11semidirect
182. C11#3195semidirect

Maximal subgroups

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

subgroupindex
D11×C22⋊Q82
C11×#4702
#106227992
#106227502
#106227392
#106226652
#106224752
#106224212
#106224182
#319511