Finite Group Databasebeta

← #11760880

Subgroups — #11760880

Order 1056.

156 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 48 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×C3×C4×D11C211yesmaximal, characteristic, complemented
2C2×#63141C211yesmaximal, characteristic
3#10587203C211yesmaximal, characteristic, complemented
4C11×Dic3⋊C4C211yesmaximal, characteristic, complemented
5#10587158C211yesmaximal, characteristic, complemented
6#10587156C211yesmaximal, characteristic, complemented
7(C2×D11)⋊Dic3C211yesmaximal, characteristic, complemented
8#66947—31nomaximal, Hall
9C22×D33C2211yescharacteristic
10C22×C3×D11C2211yescharacteristic
11C2×C3×C4×C11C2211yescharacteristic
12C2×Dic33C2211yescharacteristic
13C2×C11×Dic3C2211yescharacteristic
14C2×C11×Dic3C2211yescharacteristic
15C2×C3×Dic11C2211yescharacteristic
16C3×C4×D11—22no—
17#63141—22no—
18C2×D44—31no—
19C2×C4×D11D311yescharacteristic, complemented
20C11×C4⋊C4—31no—
21(C2×D11)⋊C4—31no—
22(C2×D11)⋊C4—31no—
23(C2×D11)⋊C4—31no—
24Dic11⋊C4—31no—
25C22×C3×C11C2311yescharacteristic
26C2×D33—21no—
27C2×D33—21no—
28C2×D33—21no—
29C2×C3×D11—21no—
30C2×C3×D11—21no—
31C2×C3×D11D412yes—
32C3×C4×C11—21no—
33Dic33—21no—
34C3×Dic11—21no—
35C11×Dic3—21no—
36C11×Dic3—21no—
37#929—111nomaximal, Hall
38C22×D11—31no—
39C22×D11C2×D311yescharacteristic
40C2×C4×C11—31no—
41C2×C4×C11—31no—
42C2×C4×C11C2×D311yescharacteristic
43C2×Dic11—31no—
44C2×Dic11C2×D311yescharacteristic
45D44—62no—
46C4×D11—22no—
47C2×C3×C11C2×D411yescharacteristic
48C2×C3×C11#4111yescharacteristic
49C2×C3×C11#4111yescharacteristic
50D33—41no—
51C3×D11—22no—
52C22×C3×C4—111no—
53C2×#67—111no—
54#217—111no—
55(C2×D3)⋊C4—111no—
56(C2×D3)⋊C4—111no—
57Dic3⋊C4—111no—
58Dic3⋊C4D1111yescharacteristic, complemented
59C22×C11C22×D311yescharacteristic
60C2×D11—21no—
61C2×D11—21no—
62C2×D11—61no—
63C2×D11—61no—
64C2×D11—61no—
65C2×D11#6712yes—
66C4×C11—21no—
67C4×C11—61no—
68C4×C11—61no—
69Dic11—21no—
70Dic11—61no—
71C3×C11#12311yescharacteristic, complemented, Hall
72#123—331noSylow
73C23×C3—111no—
74C22×D3—111no—
75C2×C3×C4—111no—
76C2×C3×C4—222no—
77C2×C3×C4C2×D1111yescharacteristic
78#67—222no—
79C2×Dic3—111no—
80C2×Dic3C2×D1111yescharacteristic
81C2×Dic3C2×D1111yescharacteristic
82C2×C11#23511yescharacteristic
83C2×C11#23511yescharacteristic
84C2×C11C2×#6711yescharacteristic
85D11—22no—
86D11—121no—
87C2×D4—331no—
88C22×C4—111no—
89C4⋊C4—31no—
90C4⋊C4—331no—
91C22⋊C4—331no—
92C22⋊C4—331no—
93C22⋊C4—331no—
94C22×C3—112no—
95C22×C3—221no—
96C22×C3—221no—
97C22×C3C22×D1111yescharacteristic
98C2×D3—221no—
99C2×D3—221no—
100C2×D3—221no—
101C3×C4—21no—
102C3×C4—221no—
103Dic3—21no—
104Dic3—21no—
105Dic3—221no—
106C11#92911yescharacteristic, complemented, Sylow
107C23—111no—
108C23—331no—
109D4—662no—
110C2×C4—31no—
111C2×C4—31no—
112C2×C4—111no—
113C2×C4—222no—
114C2×C4—331no—
115C2×C4D3×D1111yescharacteristic
116C2×C3—222no—
117C2×C3#433911yescharacteristic
118C2×C3D4×D1111yescharacteristic
119C2×C3#434311yescharacteristic
120D3—441no—
121C22—112no—
122C22—221no—
123C22—221no—
124C22—661no—
125C22—661no—
126C22—661no—
127C22C2×D3×D1111yescharacteristic
128C4—21no—
129C4—61no—
130C4—61no—
131C4—221no—
132C4—661no—
133C3#6694711yescharacteristic, complemented, Sylow
134C2—222no—
135C2—1321no—
136C2#1058723311yescharacteristic
137C2#1058723511yescharacteristic
138C2D11×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D11
commutator, socle, cosocleC22×C3×C11C23
FittingC2×C3×C4×C11C22
prime radicalC2×#63141C2
hypercenterC2×C4D3×D11
hypocenterC3×C11#123
LCSG ▷ C22×C3×C11 ▷ C3×C11
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×D11C2semidirect
3. #10587203C2semidirect
4. C11×Dic3⋊C4C2semidirect
5. #10587158C2semidirect
6. #10587156C2semidirect
7. (C2×D11)⋊Dic3C2semidirect
19. C2×C4×D11D3semidirect
58. Dic3⋊C4D11semidirect
71. C3×C11#123semidirect
106. C11#929semidirect
133. C3#66947semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D112
C2×#631412
#105872032
C11×Dic3⋊C42
#105871582
#105871562
(C2×D11)⋊Dic32
#669473
#92911