Finite Group Databasebeta

← #44479227

Subgroups — #44479227

Order 30492.

296 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 43 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
1C3×C11×D231C212yesmaximal, complemented
2C7×C3⋊(C3⋊(C11⋊D11))C211yesmaximal, characteristic, complemented
3D77⋊D33—32nomaximal
4C32×C7×C112C2211yescharacteristic, complemented, Hall
5C11×D231D312yescomplemented
6C7×C3⋊(C11⋊D11)—32no—
7C7×C3⋊(C11⋊D11)—61no—
8C3×C11×D77—32no—
9D332—71nomaximal, Hall
10D77⋊D11—91noHall
11D21⋊D33—112nomaximal
12C3×C7×C112—21no—
13C3×C7×C112C2×D312yescomplemented
14C3⋊(C3⋊(C11⋊D11))D711yescharacteristic, complemented
15C3×C11×D33—72no—
16C11×D77—32no—
17C7×C11⋊D11—91no—
18D11×D33—212no—
19C7×C3⋊D33—112no—
20C7×C3⋊D33—225no—
21C3×D231D1112yescomplemented
22C3×C11×D21—112no—
23C32×C112C2×D711yescharacteristic, complemented, Hall
24D21⋊D11—332no—
25D7×D33—332no—
26C7×C112D3211yescharacteristic, complemented, Hall
27C3⋊(C11⋊D11)—32no—
28C3⋊(C11⋊D11)—61no—
29C11×D33—72no—
30C3×C11×D11—212no—
31C32×C7×C11—25no—
32C32×C7×C11C2×D1112yescomplemented
33D112—631noHall
34D231D3312yescomplemented
35C11×D21—112no—
36C7×D33—332no—
37C7×D33—332no—
38C7×D33—662no—
39C7×D33—6610no—
40C7×D33—6610no—
41C3×D77—32no—
42C3×C11×D7—332no—
43D3×D33—772no—
44C3×C112—21no—
45C3×C112D3×D712yescomplemented
46D7×D11—992no—
47(C3⋊D3)⋊D7—1211noHall
48C11⋊D11—91no—
49C11×D11—212no—
50C3×C7×C11—210no—
51C3×C7×C11—22no—
52C3×C7×C11—210no—
53C3×C7×C11D3×D1112yescomplemented
54C3×C7×C11C2×D3312yescomplemented
55C3⋊D33—112no—
56C3⋊D33—225no—
57C3×D33—72no—
58C3×D3×C11—772no—
59D77—32no—
60C7×D11—992no—
61C7×D11—1985no—
62C11×D7—332no—
63C2×D33—2312no—
64D3×D11—2312no—
65C7×C3⋊D3—1211no—
66C3×D21—112no—
67C112(C3⋊D3)⋊D711yescharacteristic, complemented, Sylow
68C32×C11—25no—
69C32×C11D7×D1112yescomplemented
70D3×D7—3632no—
71C7×C11—25no—
72C7×C11D3×D3312yescomplemented
73C2×C3×C11—2312no—
74D33—72no—
75D33—332no—
76D33—332no—
77D33—6610no—
78D33—662no—
79D33—6610no—
80C3×D11—212no—
81D3×C11—772no—
82C32×C7D11211yescharacteristic, complemented, Hall
83C2×D11—6932no—
84D21—112no—
85C3×D7—332no—
86D3×C7—3632no—
87D3×C7—7261no—
88D32—8471noHall
89C3×C11—210no—
90C3×C11—22no—
91C3×C11—210no—
92C3×C11D7×D3312yescomplemented
93C3×C11D21⋊D1112yescomplemented
94C2×D7—10891noHall
95C2×C11—2312no—
96D11—212no—
97D11—992no—
98D11—1985no—
99C3×C7—21no—
100C3×C7D11×D3312yescomplemented
101C3⋊D3—1211no—
102C3×D3—772no—
103C2×C7—10891no—
104D7—332no—
105C2×D3—25412no—
106C11—25no—
107C11D21⋊D3312yescomplemented
108C32D77⋊D1111yescharacteristic, complemented, Sylow
109C7D33211yescharacteristic, complemented, Sylow
110C2×C3—2312no—
111D3—772no—
112D3—3632no—
113D3—7261no—
114C22—76231noSylow
115C3—21no—
116C3D77⋊D3312yescomplemented
117C2—10891no—
118C2—2312no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C7×C112C22
LCSG ▷ C32×C7×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C11×D231C2semidirect
2. C7×C3⋊(C3⋊(C11⋊D11))C2semidirect
4. C32×C7×C112C22semidirect
5. C11×D231D3semidirect
13. C3×C7×C112C2×D3semidirect
14. C3⋊(C3⋊(C11⋊D11))D7semidirect
21. C3×D231D11semidirect
23. C32×C112C2×D7semidirect
26. C7×C112D32semidirect
32. C32×C7×C11C2×D11semidirect
34. D231D33semidirect
45. C3×C112D3×D7semidirect
53. C3×C7×C11D3×D11semidirect
54. C3×C7×C11C2×D33semidirect
67. C112(C3⋊D3)⋊D7semidirect
69. C32×C11D7×D11semidirect
72. C7×C11D3×D33semidirect
82. C32×C7D112semidirect
92. C3×C11D7×D33semidirect
93. C3×C11D21⋊D11semidirect
100. C3×C7D11×D33semidirect
107. C11D21⋊D33semidirect
108. C32D77⋊D11semidirect
109. C7D332semidirect
116. C3D77⋊D33semidirect

Maximal subgroups

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

subgroupindex
C3×C11×D2312
C7×C3⋊(C3⋊(C11⋊D11))2
D77⋊D333
D3327
D21⋊D3311