Finite Group Databasebeta

← #13079560

Subgroups — #13079560

Order 1408.

384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 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
2D11×C4⋊Q8C211yesmaximal, characteristic
3C11×#494C211yesmaximal, characteristic, complemented
4#10622799C214yesmaximal
5#10622795C214yesmaximal, complemented
6#10622705C211yesmaximal, characteristic, complemented
7#10622694C211yesmaximal, characteristic, complemented
8#10622298C211yesmaximal, characteristic
9#10622294C211yesmaximal, characteristic, complemented
10C2×Q8×D11C2212yes—
11C2×C11×Q16C2214yes—
12C11×C4⋊Q8C2211yescharacteristic
13C11×C4⋊Q8C2211yescharacteristic
14#66999C2212yes—
15Q8×Dic11C2212yes—
16#66997C2212yes—
17C2×#4326C2214yes—
18#66950—21no—
19#66945—21no—
20C4⋊C4×D11—21no—
21C4⋊C4×D11—21no—
22#66943—21no—
23#66941—21no—
24#66941—21no—
25#66940—21no—
26C42×D11C2211yescharacteristic
27#66922C2211yescharacteristic
28#66922C2211yescharacteristic
29C4×C8×C11C2211yescharacteristic
30#66899C2214yes—
31(C2×D11)⋊C8C2212yes—
32#66880C2214yes—
33Dic11⋊C8C2212yes—
34C4×C11⋊C8C2211yescharacteristic
35C2×Q8×C11C2312yes—
36C2×Q8×C11C2312yes—
37Q8×D11—44no—
38C2×C4×D11—22no—
39C2×C4×D11D411yescharacteristic
40C2×C4×D11D411yescharacteristic
41C2×C4×D11C2311yescharacteristic
42C2×Dic22—22no—
43C2×Dic22—21no—
44C2×Dic22C2312yes—
45C11×Q16—44no—
46C2×C8×C11C2312yes—
47C11×C4⋊C4—21no—
48C11×C4⋊C4—21no—
49C11×C4⋊C4—21no—
50C11×C4⋊C4—21no—
51C42×C11C2311yescharacteristic
52#4326—44no—
53(C2×D11)⋊C4—22no—
54C4⋊Dic11—22no—
55C4⋊Dic11—21no—
56C4⋊Dic11—21no—
57C4⋊Dic11—21no—
58C4⋊Dic11C2312yes—
59Dic11⋊C4—22no—
60Dic11⋊C4—22no—
61Dic11⋊C4—22no—
62C4×Dic11—22no—
63C4×Dic11D411yescharacteristic
64C4×Dic11D411yescharacteristic
65C4×Dic11C2311yescharacteristic
66C2×C11⋊C8C2312yes—
67#3209—111nomaximal, Sylow
68C22×D11C2×D411yescharacteristic
69Q8×C11—24no—
70Q8×C11—24no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11C2×D411yescharacteristic
75C2×C4×C11C2411yescharacteristic
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11C2×D411yescharacteristic
79C2×Dic11C2×D411yescharacteristic
80C2×Dic11C2×D411yescharacteristic
81C4×D11—22no—
82C4×D11—22no—
83C4×D11—44no—
84C4×D11Q1614yescomplemented
85Dic22—24no—
86Dic22—44no—
87Dic22—42no—
88C8×C11—22no—
89C11⋊C8—22no—
90#533—111no—
91C2×C4⋊Q8—111no—
92#494—111no—
93#494D1111yescharacteristic, complemented
94#487—111no—
95#487—111no—
96#462—114no—
97#451—114no—
98#431—111no—
99C22×C11C22×D411yescharacteristic
100C2×D11—21no—
101C2×D11—21no—
102C2×D11C2×Q1612yes—
103C4×C11—42no—
104C4×C11—42no—
105C4×C11C2×Q1612yes—
106C4×C11#13712yes—
107C4×C11H(5,𝔽2)12yes—
108Dic11—21no—
109Dic11—21no—
110Dic11—42no—
111Dic11—42no—
112Dic11C2×Q1612yes—
113C22×Q8—112no—
114C2×Q16—114no—
115C2×Q16C2×D1114yes—
116C4⋊Q8—112no—
117C4⋊Q8—111no—
118C4⋊Q8—111no—
119C4⋊Q8—221no—
120C4⋊Q8—221no—
121C4⋊Q8C2×D1111yescharacteristic
122C4⋊Q8C2×D1111yescharacteristic
123#125—221no—
124C22⋊Q8—112no—
125C22⋊Q8—221no—
126C4×Q8—112no—
127C4×Q8—221no—
128#117—221no—
129C2×C4⋊C4—221no—
130C2×C4⋊C4—221no—
131C2×C42—111no—
132C4⋊C8—112no—
133#103—114no—
134#103—114no—
135C22⋊C8—112no—
136C4×C8—111no—
137C4×C8C2×D1111yescharacteristic
138C2×C11#53511yescharacteristic
139C2×C11C22×Q1611yescharacteristic
140C2×C11C2×#13711yescharacteristic
141D11—22no—
142C2×Q8—112no—
143C2×Q8—222no—
144C2×Q8—221no—
145C2×Q8—444no—
146C2×Q8C22×D1112yes—
147C2×Q8C22×D1112yes—
148C22×C4—111no—
149C22×C4—111no—
150C22×C4—111no—
151C22×C4—222no—
152Q16—44no—
153Q16—444no—
154C2×C8—112no—
155C2×C8C22×D1112yes—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—112no—
161C4⋊C4—222no—
162C4⋊C4—222no—
163C4⋊C4—222no—
164C4⋊C4—222no—
165C4⋊C4—221no—
166C4⋊C4—221no—
167C4⋊C4—221no—
168C22⋊C4—222no—
169C42—111no—
170C42—111no—
171C42—111no—
172C42—222no—
173C42C22×D1111yescharacteristic
174C11#320911yescharacteristic, complemented, Sylow
175C23—111no—
176Q8—24no—
177Q8—24no—
178Q8—224no—
179Q8—444no—
180Q8—442no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—111no—
184C2×C4—114no—
185C2×C4—111no—
186C2×C4—111no—
187C2×C4—222no—
188C2×C4—222no—
189C2×C4—222no—
190C2×C4—222no—
191C2×C4—444no—
192C2×C4D4×D1111yescharacteristic
193C2×C4D4×D1111yescharacteristic
194C2×C4C23×D1111yescharacteristic
195C8—22no—
196C8—222no—
197C22—112no—
198C22—221no—
199C22—221no—
200C22C2×D4×D1111yescharacteristic
201C4—42no—
202C4—42no—
203C4—112no—
204C4—221no—
205C4—221no—
206C4—442no—
207C4—442no—
208C4Q16×D1112yes—
209C4#6697112yes—
210C4#6703712yes—
211C2—222no—
212C2#1062324611yescharacteristic
213C2C2×Q16×D1111yescharacteristic
214C2C2×#6697111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#494C2
socleC22×C11C22×D4
prime radicalC22×D11C2×D4
hypercenter#494D11
hypocenterC11#3209
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
3. C11×#494C2semidirect
5. #10622795C2semidirect
6. #10622705C2semidirect
7. #10622694C2semidirect
9. #10622294C2semidirect
84. C4×D11Q16semidirect
93. #494D11semidirect
174. C11#3209semidirect

Maximal subgroups

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

subgroupindex
#106232592
D11×C4⋊Q82
C11×#4942
#106227992
#106227952
#106227052
#106226942
#106222982
#106222942
#320911