Finite Group Databasebeta

← #13079511

Subgroups — #13079511

Order 1408.

378 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 117 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#10623356C212yesmaximal
2C11×#408C211yesmaximal, characteristic
3#10622750C212yesmaximal, complemented
4#10622729C212yesmaximal, complemented
5#10622352C214yesmaximal, complemented
6#10622336C214yesmaximal, complemented
7C2×C11×#41C2211yescharacteristic
8C22×Dic22C2212yes—
9C2×C11×M16C2211yescharacteristic
10C22×C8×C11C2211yescharacteristic
11#66997—22no—
12#66989—22no—
13#66988—22no—
14#66988—22no—
15#66979C2212yes—
16#66977C2214yes—
17#66977C2214yes—
18C2×Dic44C2212yes—
19C2×Dic44C2212yes—
20C11×C22⋊C8C2214yes—
21#66882C2212yes—
22#66881C2212yes—
23#66880C2214yes—
24#66880C2214yes—
25C11×#41—41no—
26C11×#41—41no—
27C2×Q8×C11D411yescharacteristic
28C2×D4×C11D411yescharacteristic
29C2×D4×C11D412yes—
30C22×C4×C11C2312yes—
31C22×C4×C11C2311yescharacteristic
32C22×Dic11—22no—
33C2×Dic22—22no—
34C2×Dic22—42no—
35C2×Dic22—42no—
36C2×Dic22C2314yes—
37C11×M16—41no—
38C2×C8×C11—41no—
39C2×C8×C11C2312yes—
40C2×C8×C11C2312yes—
41C22⋊Dic11—24no—
42C22⋊Dic11—24no—
43C22⋊Dic11—22no—
44C4⋊Dic11C2314yes—
45Dic11⋊C4—24no—
46Dic11⋊C4—24no—
47C4×Dic11—22no—
48Dic44—42no—
49Dic44—42no—
50#3202—111nomaximal, Sylow
51C23×C11C2×D411yescharacteristic
52C23×C11C2×D412yes—
53Q8×C11—41no—
54D4×C11—41no—
55D4×C11—42no—
56C2×C4×C11—21no—
57C2×C4×C11—21no—
58C2×C4×C11—22no—
59C2×C4×C11—22no—
60C2×C4×C11C2×D412yes—
61C2×C4×C11C2×D411yescharacteristic
62C2×C4×C11C2411yescharacteristic
63C2×Dic11—24no—
64C2×Dic11—24no—
65C2×Dic11—44no—
66Dic22—24no—
67Dic22—24no—
68Dic22—44no—
69C8×C11—22no—
70C8×C11—22no—
71#536—112no—
72#485—114no—
73#470—112no—
74#467—112no—
75#451—114no—
76#408D1111yescharacteristic
77C22×C11—21no—
78C22×C11—22no—
79C22×C11—22no—
80C22×C11—24no—
81C22×C11C22×D411yescharacteristic
82C4×C11—21no—
83C4×C11—22no—
84C4×C11H(5,𝔽2)11yescharacteristic
85C4×C11H(5,𝔽2)11yescharacteristic
86Dic11—44no—
87Dic11—44no—
88C2×#41C2×D1111yescharacteristic
89C22×Q8—112no—
90C2×Q16—112no—
91C2×Q16—112no—
92C2×M16C2×D1111yescharacteristic
93C22×C8C2×D1111yescharacteristic
94C4⋊Q8—222no—
95#124—222no—
96#123—222no—
97#123—222no—
98C22⋊Q8—114no—
99C22⋊Q8—114no—
100#117—112no—
101#107—112no—
102#106—112no—
103#103—114no—
104#103—114no—
105C22⋊C8C2×D1114yes—
106C2×C11—41no—
107C2×C11—42no—
108C2×C11#53411yescharacteristic
109C2×C11#57812yes—
110#41—41no—
111#41—41no—
112C2×Q8—114no—
113C2×Q8—222no—
114C2×Q8—442no—
115C2×Q8—442no—
116C2×Q8D4411yescharacteristic
117C2×D4D4411yescharacteristic
118C2×D4D4412yes—
119C22×C4—222no—
120C22×C4C22×D1112yes—
121C22×C4C22×D1111yescharacteristic
122Q16—442no—
123Q16—442no—
124M16—41no—
125C2×C8—41no—
126C2×C8C22×D1112yes—
127C2×C8C22×D1112yes—
128C4⋊C4—114no—
129C4⋊C4—224no—
130C4⋊C4—224no—
131C22⋊C4—222no—
132C22⋊C4—224no—
133C22⋊C4—224no—
134C42—222no—
135C11#320211yescharacteristic, complemented, Sylow
136C23C2×D4411yescharacteristic
137C23C2×D4412yes—
138Q8—41no—
139Q8—224no—
140Q8—224no—
141Q8—444no—
142D4—42no—
143D4—41no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—224no—
149C2×C4—224no—
150C2×C4—444no—
151C2×C4C2×D4412yes—
152C2×C4C2×D4411yescharacteristic
153C2×C4C23×D1111yescharacteristic
154C8—22no—
155C8—22no—
156C22—22no—
157C22—21no—
158C22—22no—
159C22—24no—
160C22C22×D4411yescharacteristic
161C4—22no—
162C4—21no—
163C4—444no—
164C4—444no—
165C4#6703711yescharacteristic
166C4#6703711yescharacteristic
167C2—42no—
168C2—41no—
169C2#1062302411yescharacteristic
170C2#1062328412yes—
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#408C2
socleC22×C11C22×D4
prime radicalC2×C11×#41C22
hypercenter#408D11
hypocenterC11#3202
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
3. #10622750C2semidirect
4. #10622729C2semidirect
5. #10622352C2semidirect
6. #10622336C2semidirect
135. C11#3202semidirect

Maximal subgroups

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

subgroupindex
#106233562
C11×#4082
#106227502
#106227292
#106223522
#106223362
#320211