Finite Group Databasebeta

← #11761223

Subgroups — #11761223

Order 1056.

156 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 49 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
1C2×#63159C211yesmaximal, characteristic
2C2×C4×D33C211yesmaximal, characteristic, complemented
3C3×C11×C22⋊C4C211yesmaximal, characteristic, complemented
4#10587208C211yesmaximal, characteristic, complemented
5#10587203C211yesmaximal, characteristic, complemented
6C4⋊Dic33C211yesmaximal, characteristic, complemented
7#10587201C211yesmaximal, characteristic, complemented
8#66936—31nomaximal, Hall
9C23×C3×C11C2211yescharacteristic
10C22×D33C2211yescharacteristic
11C2×C3×C4×C11C2211yescharacteristic
12C2×C3×C4×C11C2211yescharacteristic
13#63159—22no—
14C2×Dic33C2211yescharacteristic
15C2×Dic33C2211yescharacteristic
16C2×Dic33C2211yescharacteristic
17C4×D33—22no—
18C2×C22⋊D11—31no—
19C2×C4×D11—31no—
20C11×C22⋊C4D311yescharacteristic, complemented
21C22⋊Dic11—31no—
22(C2×D11)⋊C4—31no—
23C4⋊Dic11—31no—
24Dic11⋊C4—31no—
25C22×C3×C11—21no—
26C22×C3×C11—21no—
27C22×C3×C11—21no—
28C22×C3×C11C2311yescharacteristic
29C2×D33—21no—
30C2×D33—21no—
31C2×D33D412yes—
32C3×C4×C11—21no—
33C3×C4×C11—21no—
34Dic33—21no—
35Dic33—21no—
36Dic33—21no—
37#883—111nomaximal, Hall
38C23×C11C2×D311yescharacteristic
39C22×D11—31no—
40C2×C4×C11C2×D311yescharacteristic
41C2×C4×C11C2×D311yescharacteristic
42C22⋊D11—62no—
43C2×Dic11—31no—
44C2×Dic11—31no—
45C2×Dic11—31no—
46C4×D11—62no—
47C2×C3×C11—41no—
48C2×C3×C11C2×D411yescharacteristic
49C2×C3×C11#4111yescharacteristic
50C2×C3×C11#4111yescharacteristic
51D33—22no—
52C2×#67—111no—
53C2×C4×D3—111no—
54C3×C22⋊C4D1111yescharacteristic, complemented
55#217—111no—
56(C2×D3)⋊C4—111no—
57C4⋊Dic3—111no—
58Dic3⋊C4—111no—
59C22×C11—21no—
60C22×C11—21no—
61C22×C11—21no—
62C22×C11C22×D311yescharacteristic
63C2×D11—32no—
64C2×D11—61no—
65C2×D11—61no—
66C4×C11—21no—
67C4×C11—21no—
68Dic11—61no—
69Dic11—61no—
70Dic11—61no—
71C3×C11#12311yescharacteristic, complemented, Hall
72#123—331noSylow
73C23×C3C2×D1111yescharacteristic
74C22×D3—111no—
75C2×C3×C4C2×D1111yescharacteristic
76C2×C3×C4C2×D1111yescharacteristic
77#67—222no—
78C2×Dic3—111no—
79C2×Dic3—111no—
80C2×Dic3—111no—
81C4×D3—222no—
82C2×C11—41no—
83C2×C11#23511yescharacteristic
84C2×C11D3×D411yescharacteristic
85C2×C11#23711yescharacteristic
86D11—62no—
87C2×D4—331no—
88C22×C4—331no—
89C4⋊C4—331no—
90C4⋊C4—331no—
91C22⋊C4—331no—
92C22⋊C4—331no—
93C22⋊C4D3311yescharacteristic, complemented
94C22×C3—21no—
95C22×C3—21no—
96C22×C3—21no—
97C22×C3C22×D1111yescharacteristic
98C2×D3—112no—
99C2×D3—221no—
100C2×D3—221no—
101C3×C4—21no—
102C3×C4—21no—
103Dic3—221no—
104Dic3—221no—
105Dic3—221no—
106C11#88311yescharacteristic, complemented, Sylow
107C23—331no—
108C23C2×D3311yescharacteristic
109D4—662no—
110C2×C4—331no—
111C2×C4—331no—
112C2×C4—331no—
113C2×C4—662no—
114C2×C4C2×D3311yescharacteristic
115C2×C4C2×D3311yescharacteristic
116C2×C3—41no—
117C2×C3#433911yescharacteristic
118C2×C3D4×D1111yescharacteristic
119C2×C3#434111yescharacteristic
120D3—222no—
121C22—21no—
122C22—21no—
123C22—21no—
124C22—332no—
125C22—661no—
126C22—661no—
127C22C22×D3311yescharacteristic
128C4—21no—
129C4—21no—
130C4—661no—
131C4—661no—
132C4—661no—
133C3#6693611yescharacteristic, complemented, Sylow
134C2—41no—
135C2—662no—
136C2#1058727911yescharacteristic
137C2D4×D3311yescharacteristic
138C2#1058728111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D33
commutator, socle, cosocleC22×C3×C11C23
FittingC3×C11×C22⋊C4C2
prime radicalC2×#63159C2
hypercenterC22⋊C4D33
hypocenterC3×C11#123
LCSG ▷ C22×C3×C11 ▷ C3×C11
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D33C2semidirect
3. C3×C11×C22⋊C4C2semidirect
4. #10587208C2semidirect
5. #10587203C2semidirect
6. C4⋊Dic33C2semidirect
7. #10587201C2semidirect
20. C11×C22⋊C4D3semidirect
54. C3×C22⋊C4D11semidirect
71. C3×C11#123semidirect
93. C22⋊C4D33semidirect
106. C11#883semidirect
133. C3#66936semidirect

Maximal subgroups

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

subgroupindex
C2×#631592
C2×C4×D332
C3×C11×C22⋊C42
#105872082
#105872032
C4⋊Dic332
#105872012
#669363
#88311