Finite Group Databasebeta

← C3×#23779059 #44479194

Subgroups — C3×#23779059 #44479194

Order 30492.

296 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C32×C7×C11⋊D11C211yesmaximal, characteristic, complemented
2C3×C11×D231C212yesmaximal, complemented
3#23779059C311yesmaximal, characteristic, direct product factor
4C3×D77⋊D11—31nomaximal
5C32×C7×C112C2211yescharacteristic, complemented, Hall
6C11×D231C2×C312yescomplemented
7C3×C11×D77—32no—
8C3×C7×C11⋊D11—21no—
9C3×C7×C11⋊D11D311yescharacteristic, complemented
10C3×C7×C11⋊D11C2×C311yescharacteristic, complemented
11C3×D33⋊D11—71nomaximal, Hall
12D77⋊D11—31noHall
13C3×D11×D21—112nomaximal
14C3×C7×C112—21no—
15C3×C7×C112C2×D311yescharacteristic, complemented
16C3×C7×C112C22×C311yescharacteristic, complemented
17C3×C11×D33—72no—
18C32×C11⋊D11D711yescharacteristic, complemented
19C11×D77—32no—
20C7×C11⋊D11C3×D311yescharacteristic, complemented
21D33⋊D11—71no—
22C3×D112—211no—
23C3×D231D1112yescomplemented
24C3×C11×D21—112no—
25C32×C7×D11—112no—
26C32×C7×D11—225no—
27C32×C112C2×D711yescharacteristic, complemented, Hall
28D11×D21—112no—
29C3×D7×D11—332no—
30C7×C112C2×C3×D311yescharacteristic, complemented, Hall
31C11×D33—72no—
32C3×C11⋊D11—21no—
33C3×C11⋊D11C3×D711yescharacteristic, complemented
34C3×C11⋊D11D2111yescharacteristic, complemented
35C3×C11×D11—212no—
36C32×C7×C11—25no—
37C32×C7×C11C2×D1112yescomplemented
38D112—211noHall
39D231C3×D1112yescomplemented
40C11×D21—112no—
41C3×D77—32no—
42C3×C11×D7—332no—
43C3×C7×D11—112no—
44C3×C7×D11—112no—
45C3×C7×D11—222no—
46C3×C7×D11—225no—
47C3×C7×D11—225no—
48C3×C7×D11—2210no—
49C3×D3×D11—772no—
50C3×C112—21no—
51C3×C112C2×C3×D711yescharacteristic, complemented
52C3×C112C2×D2111yescharacteristic, complemented
53D7×D11—332no—
54C2×C3×D21—1211noHall
55C11⋊D11C3×D2111yescharacteristic, complemented
56C11×D11—212no—
57C3×C7×C11—210no—
58C3×C7×C11—22no—
59C3×C7×C11—25no—
60C3×C7×C11—25no—
61C3×C7×C11D3×D1112yescomplemented
62C3×C7×C11C2×C3×D1112yescomplemented
63C3×D33—72no—
64C3×D3×C11—772no—
65C32×D11—112no—
66C32×D11—225no—
67D77—32no—
68C7×D11—112no—
69C7×D11—225no—
70C11×D7—332no—
71C2×C3×D11—2312no—
72D3×D11—772no—
73C2×C32×C7—1211no—
74C3×D21—112no—
75C112C2×C3×D2111yescharacteristic, complemented, Sylow
76C32×C11—25no—
77C32×C11D7×D1112yescomplemented
78C2×D21—1211no—
79C2×C3×D7—3631no—
80C7×C11—25no—
81C7×C11C3×D3×D1112yescomplemented
82C2×C3×C11—2312no—
83D33—72no—
84C3×D11—112no—
85C3×D11—112no—
86C3×D11—212no—
87C3×D11—225no—
88C3×D11—225no—
89C3×D11—222no—
90C3×D11—2210no—
91D3×C11—772no—
92C32×C7D11211yescharacteristic, complemented, Hall
93C2×D11—2312no—
94C2×C3×C7—1211no—
95C2×C3×C7—1211no—
96C2×C3×C7—2421no—
97D21—112no—
98C3×D7—332no—
99C2×C3×D3—8471noHall
100C3×C11—210no—
101C3×C11—22no—
102C3×C11—25no—
103C3×C11—25no—
104C3×C11C3×D7×D1112yescomplemented
105C3×C11D11×D2112yescomplemented
106C2×D7—3631noHall
107C2×C11—2312no—
108D11—112no—
109D11—212no—
110D11—225no—
111C3×C7—21no—
112C3×C7C3×D11211yescharacteristic, complemented
113C3×C7D33⋊D1111yescharacteristic, complemented
114C2×C32—1211no—
115C3×D3—772no—
116C2×C7—1211no—
117D7—332no—
118C22×C3—25411no—
119C2×D3—8471no—
120C11—25no—
121C11C3×D11×D2112yescomplemented
122C32D77⋊D1111yescharacteristic, complemented, Sylow
123C7C3×D33⋊D1111yescharacteristic, complemented, Sylow
124C2×C3—1211no—
125C2×C3—1211no—
126C2×C3—2312no—
127C2×C3—2421no—
128D3—772no—
129C22—25411noSylow
130C3—21no—
131C3C3×D77⋊D1111yescharacteristic, complemented
132C3#2377905911yescharacteristic, direct product factor
133C2—1211no—
134C2—2312no—
subgroupG/H
center, hypercenterC3#23779059
commutator, cosocle, hypocenterC3×C7×C112C22×C3
FrattiniC1G
Fitting, socleC32×C7×C112C22
LCSG ▷ C3×C7×C112
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C7×C11⋊D11C2semidirect
2. C3×C11×D231C2semidirect
3. #23779059C3direct (N × H)
5. C32×C7×C112C22semidirect
6. C11×D231C2×C3semidirect
9. C3×C7×C11⋊D11D3semidirect
10. C3×C7×C11⋊D11C2×C3semidirect
15. C3×C7×C112C2×D3semidirect
16. C3×C7×C112C22×C3semidirect
18. C32×C11⋊D11D7semidirect
20. C7×C11⋊D11C3×D3semidirect
23. C3×D231D11semidirect
27. C32×C112C2×D7semidirect
30. C7×C112C2×C3×D3semidirect
33. C3×C11⋊D11C3×D7semidirect
34. C3×C11⋊D11D21semidirect
37. C32×C7×C11C2×D11semidirect
39. D231C3×D11semidirect
51. C3×C112C2×C3×D7semidirect
52. C3×C112C2×D21semidirect
55. C11⋊D11C3×D21semidirect
61. C3×C7×C11D3×D11semidirect
62. C3×C7×C11C2×C3×D11semidirect
75. C112C2×C3×D21semidirect
77. C32×C11D7×D11semidirect
81. C7×C11C3×D3×D11semidirect
92. C32×C7D112semidirect
104. C3×C11C3×D7×D11semidirect
105. C3×C11D11×D21semidirect
112. C3×C7C3×D112semidirect
113. C3×C7D33⋊D11semidirect
121. C11C3×D11×D21semidirect
122. C32D77⋊D11semidirect
123. C7C3×D33⋊D11semidirect
131. C3C3×D77⋊D11semidirect
132. C3#23779059direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7×C11⋊D112
C3×C11×D2312
#237790593
C3×D77⋊D113
C3×D33⋊D117
C3×D11×D2111