Finite Group Databasebeta

← #13070288

Subgroups — #13070288

Order 1408.

270 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 73 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×#535C211yesmaximal, characteristic
2#10622853C212yesmaximal, complemented
3#10622183C214yesmaximal, complemented
4C2×C11×#41C2211yescharacteristic
5C22×D4×C11C411yescharacteristic, complemented
6C11×#127C2212yes—
7C11×#124C412yescomplemented
8C11×#121—22no—
9C11×#120—22no—
10C11×#117C411yescharacteristic, complemented
11#66979—22no—
12#66898—22no—
13#66898C2214yescomplemented
14C24×C11—21no—
15C11×#41—42no—
16C2×Q8×C11C2×C411yescharacteristic
17C2×D4×C11—24no—
18C2×D4×C11—21no—
19C2×D4×C11—42no—
20C2×D4×C11C2×C412yes—
21C2×D4×C11D412yes—
22C2×D4×C11C2311yescharacteristic
23C22×C4×C11C2×C411yescharacteristic
24C22×C4×C11D412yes—
25C11×C4⋊C4—21no—
26C11×C22⋊C4—21no—
27C11×C22⋊C4—24no—
28C42×C11C2×C412yes—
29C22⋊Dic11—24no—
30C4⋊Dic11—42no—
31C4×Dic11—42no—
32#2128—111nomaximal, Sylow
33C23×C11—22no—
34C23×C11—42no—
35C23×C11—82no—
36C23×C11C22⋊C411yescharacteristic
37C23×C11C2×D412yes—
38Q8×C11—41no—
39D4×C11—42no—
40D4×C11—41no—
41D4×C11—42no—
42D4×C11—42no—
43D4×C11—84no—
44C2×C4×C11—22no—
45C2×C4×C11—22no—
46C2×C4×C11—22no—
47C2×C4×C11—22no—
48C2×C4×C11C22⋊C412yes—
49C2×C4×C11C22⋊C411yescharacteristic
50C2×C4×C11C22×C411yescharacteristic
51C2×Dic11—44no—
52#535D1111yescharacteristic
53#410—112no—
54#353—114no—
55C22×C11—21no—
56C22×C11—22no—
57C22×C11—42no—
58C22×C11—41no—
59C22×C11—44no—
60C22×C11—42no—
61C22×C11—84no—
62C22×C11C2×C22⋊C411yescharacteristic
63C4×C11—22no—
64C4×C11—21no—
65C4×C11—42no—
66C4×C11#9912yes—
67Dic11—84no—
68C2×#41C2×D1111yescharacteristic
69C22×D4Dic1111yescharacteristic, complemented
70#127C2×D1112yes—
71#124Dic1112yescomplemented
72#121—22no—
73#120—22no—
74#117—222no—
75#117Dic1111yescharacteristic, complemented
76#99—114no—
77#99—222no—
78C2×C11—21no—
79C2×C11—42no—
80C2×C11—41no—
81C2×C11—82no—
82C2×C11C2×#9911yescharacteristic
83C24—21no—
84#41—42no—
85C2×Q8C2×Dic1111yescharacteristic
86C2×D4—24no—
87C2×D4—21no—
88C2×D4—42no—
89C2×D4C2×Dic1112yes—
90C2×D4C22⋊D1112yes—
91C2×D4C22×D1111yescharacteristic
92C22×C4C2×Dic1111yescharacteristic
93C22×C4C22⋊D1112yes—
94C4⋊C4—21no—
95C4⋊C4—442no—
96C22⋊C4—21no—
97C22⋊C4—24no—
98C22⋊C4—224no—
99C42—442no—
100C42C2×Dic1112yes—
101C11#212811yescharacteristic, complemented, Sylow
102C23—22no—
103C23—42no—
104C23—82no—
105C23C22⋊Dic1111yescharacteristic
106C23C2×C22⋊D1112yes—
107Q8—41no—
108D4—41no—
109D4—42no—
110D4—42no—
111D4—42no—
112D4—84no—
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—444no—
118C2×C4C22⋊Dic1112yes—
119C2×C4C22⋊Dic1111yescharacteristic
120C2×C4C22×Dic1111yescharacteristic
121C22—22no—
122C22—21no—
123C22—42no—
124C22—41no—
125C22—44no—
126C22—42no—
127C22—84no—
128C22C2×C22⋊Dic1111yescharacteristic
129C4—22no—
130C4—21no—
131C4—42no—
132C4—884no—
133C4#6689812yes—
134C2—21no—
135C2—42no—
136C2—41no—
137C2—82no—
138C2C2×#6689811yescharacteristic
subgroupG/H
centerC2C2×#66898
commutatorC2×C4×C11C22×C4
FrattiniC2×D4C22×D11
Fitting, prime radicalC11×#535C2
socleC2×C11C2×#99
cosocleC2×D4×C11C23
hypercenter#535D11
hypocenterC11#2128
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
2. #10622853C2semidirect
3. #10622183C2semidirect
5. C22×D4×C11C4semidirect
7. C11×#124C4semidirect
10. C11×#117C4semidirect
13. #66898C22semidirect
69. C22×D4Dic11semidirect
71. #124Dic11semidirect
75. #117Dic11semidirect
101. C11#2128semidirect

Maximal subgroups

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

subgroupindex
C11×#5352
#106228532
#106221832
#212811