Finite Group Databasebeta

← #13080007

Subgroups — #13080007

Order 1408.

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

normal subgroups only

This group has 342 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
1C11×#533C211yesmaximal, characteristic
2#10623001C211yesmaximal, characteristic
3#10622707C212yesmaximal, complemented
4#10622703C212yesmaximal, complemented
5#10622665C214yesmaximal
6#10622644C212yesmaximal, complemented
7#10622633C212yesmaximal, complemented
8#10622537C211yesmaximal, characteristic
9C11×C4⋊Q8C2211yescharacteristic
10C11×C4⋊Q8C2211yescharacteristic
11C11×#125—21no—
12C11×C22⋊Q8—21no—
13C11×C22⋊Q8C2212yes—
14C4×Q8×C11—21no—
15C4×Q8×C11C2212yes—
16C11×#117—21no—
17C2×C42×C11C2211yescharacteristic
18C2×#4326C2214yes—
19#66979—21no—
20#66977—21no—
21#66977C2212yes—
22C2×#4318C2212yes—
23#66923—21no—
24#66922C2211yescharacteristic
25#66922C2211yescharacteristic
26C4×Dic22—21no—
27C4×Dic22C2212yes—
28#66899C2214yes—
29#66874C2214yes—
30#66872C2214yes—
31C4⋊(C11⋊C8)C2212yes—
32C4⋊(C11⋊C8)C2212yes—
33C2×Q8×C11—21no—
34C2×Q8×C11C2312yes—
35C22×C4×C11D411yescharacteristic
36C22×C4×C11D411yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C2×Dic22—21no—
39C2×Dic22C2312yes—
40C11×C4⋊C4—21no—
41C11×C4⋊C4—21no—
42C11×C4⋊C4—21no—
43C11×C4⋊C4—22no—
44C11×C4⋊C4—22no—
45C11×C4⋊C4C2312yes—
46C11×C22⋊C4—22no—
47C42×C11—22no—
48C42×C11D411yescharacteristic
49C42×C11D411yescharacteristic
50C42×C11C2311yescharacteristic
51C42×C11C2311yescharacteristic
52C22⋊Dic11—22no—
53#4326—44no—
54C4⋊Dic11—21no—
55C4⋊Dic11—21no—
56C4⋊Dic11—21no—
57C4⋊Dic11C2312yes—
58Dic11⋊C4—22no—
59Dic11⋊C4—22no—
60C4×Dic11—22no—
61#4318—42no—
62C2×C11⋊C8C2314yes—
63#3255—111nomaximal, Sylow
64C23×C11C2×D411yescharacteristic
65Q8×C11—22no—
66Q8×C11—22no—
67Q8×C11—42no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11C2×D411yescharacteristic
75C2×C4×C11C2×D411yescharacteristic
76C2×C4×C11C2×D411yescharacteristic
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11C2×D411yescharacteristic
79C2×C4×C11C2411yescharacteristic
80C2×Dic11—22no—
81C2×Dic11—22no—
82Dic22—22no—
83Dic22—22no—
84Dic22—42no—
85C11⋊C8—24no—
86#533—111no—
87#533D1111yescharacteristic
88#475—112no—
89#475—112no—
90#470—114no—
91#462—112no—
92#462—112no—
93#423—111no—
94C22×C11—21no—
95C22×C11—21no—
96C22×C11—21no—
97C22×C11C22×D411yescharacteristic
98C4×C11—21no—
99C4×C11—21no—
100C4×C11—21no—
101C4×C11—42no—
102C4×C11—42no—
103C4×C11#13712yes—
104C4×C11#13712yes—
105C4×C11H(5,𝔽2)11yescharacteristic
106C4×C112−1+411yescharacteristic
107Dic11—42no—
108Dic11—42no—
109C2×Q16—114no—
110C2×M16—112no—
111C4⋊Q8—111no—
112C4⋊Q8—111no—
113C4⋊Q8C2×D1111yescharacteristic
114C4⋊Q8C2×D1111yescharacteristic
115#125—21no—
116#125—221no—
117C22⋊Q8—21no—
118C22⋊Q8—112no—
119C22⋊Q8—221no—
120C22⋊Q8C2×D1112yes—
121C4×Q8—21no—
122C4×Q8—112no—
123C4×Q8—221no—
124C4×Q8C2×D1112yes—
125#117—21no—
126#117—221no—
127C2×C42C2×D1111yescharacteristic
128#106—114no—
129C4⋊C8—112no—
130C4⋊C8—112no—
131#103—114no—
132#103—114no—
133C2×C11—41no—
134C2×C11#53711yescharacteristic
135C2×C11C2×#13711yescharacteristic
136C2×C11C2×#13711yescharacteristic
137C2×Q8—21no—
138C2×Q8—112no—
139C2×Q8—221no—
140C2×Q8C22×D1112yes—
141C22×C4C22⋊D1111yescharacteristic
142C22×C4C22⋊D1111yescharacteristic
143C22×C4C22×D1111yescharacteristic
144Q16—444no—
145M16—442no—
146C2×C8—114no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—112no—
153C4⋊C4—221no—
154C4⋊C4—221no—
155C4⋊C4—222no—
156C4⋊C4—222no—
157C4⋊C4—221no—
158C4⋊C4C22×D1112yes—
159C22⋊C4—22no—
160C22⋊C4—222no—
161C42—22no—
162C42—222no—
163C42C22⋊D1111yescharacteristic
164C42C22⋊D1111yescharacteristic
165C42C22×D1111yescharacteristic
166C42C22×D1111yescharacteristic
167C11#325511yescharacteristic, complemented, Sylow
168C23C2×C22⋊D1111yescharacteristic
169Q8—22no—
170Q8—22no—
171Q8—42no—
172Q8—222no—
173Q8—222no—
174Q8—442no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—222no—
182C2×C4—222no—
183C2×C4C2×C22⋊D1111yescharacteristic
184C2×C4C2×C22⋊D1111yescharacteristic
185C2×C4C2×C22⋊D1111yescharacteristic
186C2×C4C2×C22⋊D1111yescharacteristic
187C2×C4C2×C22⋊D1111yescharacteristic
188C2×C4C23×D1111yescharacteristic
189C8—224no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22C22×C22⋊D1111yescharacteristic
194C4—21no—
195C4—21no—
196C4—21no—
197C4—42no—
198C4—42no—
199C4—442no—
200C4—442no—
201C4#6699512yes—
202C4#6700412yes—
203C4#6704211yescharacteristic
204C4#6704311yescharacteristic
205C2—41no—
206C2C2×#6699511yescharacteristic
207C2C2×#6700411yescharacteristic
208C2#1062336411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#533C2
socleC22×C11C22×D4
prime radicalC23×C11C2×D4
hypercenter#533D11
hypocenterC11#3255
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
3. #10622707C2semidirect
4. #10622703C2semidirect
6. #10622644C2semidirect
7. #10622633C2semidirect
167. C11#3255semidirect

Maximal subgroups

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

subgroupindex
C11×#5332
#106230012
#106227072
#106227032
#106226652
#106226442
#106226332
#106225372
#325511