Finite Group Databasebeta

← #49137553

Subgroups — #49137553

Order 36300.

180 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 20 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
1C52⋊C3×C11⋊D11C211yesmaximal, characteristic, complemented
2C11×C11⋊#3874C211yesmaximal, characteristic, complemented
3C11×C11⋊#3874C211yesmaximal, characteristic, complemented
4C5×D55⋊D11—31nomaximal, Hall
5C112×C52⋊C3C2211yescharacteristic, complemented, Hall
6C5×C11×D55—31no—
7C5×C11×D55—31no—
8C52×C11⋊D11D311yescharacteristic, complemented
9D11×#3874—111nomaximal
10D11×#3874—111nomaximal
11C52×C112C2×D311yescharacteristic, complemented, Hall
12D55⋊D11—31no—
13C5×D112—151no—
14D11×C52⋊C3—111no—
15D11×C52⋊C3—111no—
16D11×C52⋊C3—225no—
17C11⋊#3874D1111yescharacteristic, complemented
18C11⋊#3874D1111yescharacteristic, complemented
19C11×#3874—111no—
20C11×#3874—111no—
21D33⋊D11—251nomaximal, Hall
22C11×D55—31no—
23C11×D55—31no—
24C5×C11⋊D11—31no—
25C5×C11⋊D11—61no—
26C5×C11×D11—151no—
27C5×C11×D11—151no—
28C5×D5×D11—331no—
29C5×D5×D11—331no—
30C11×C52⋊C3—25no—
31C11×C52⋊C3C2×D1111yescharacteristic, complemented
32C11×C52⋊C3C2×D1111yescharacteristic, complemented
33C11×D33—251no—
34C11×D33—251no—
35C3×C11⋊D11—501no—
36C5×C112—31no—
37C5×C112—61no—
38C5×D55—31no—
39C5×D55—31no—
40C5×D5×C11—331no—
41C5×D5×C11—331no—
42C52×D11—111no—
43C52×D11—111no—
44C52×D11—225no—
45D112—151noHall
46C3×C112—501noHall
47C2×#3874—1211noHall
48C52×C11—25no—
49C52×C11D3×D1111yescharacteristic, complemented
50C52×C11D3×D1111yescharacteristic, complemented
51C11⋊D11#387411yescharacteristic, complemented
52C11×D11—151no—
53C11×D11—151no—
54C2×C5×D11—1651no—
55C2×C5×D11—1651no—
56D5×D11—331no—
57D5×D11—331no—
58C2×C52⋊C3—1211no—
59#3874—111no—
60#3874—111no—
61D3×D11—2751no—
62D3×D11—2751no—
63C112C2×#387411yescharacteristic, complemented, Sylow
64C2×C5×C11—1651no—
65C2×C5×C11—1651no—
66D55—31no—
67D55—31no—
68C5×D11—151no—
69C5×D11—151no—
70C5×D11—331no—
71C5×D11—661no—
72C5×D11—661no—
73C5×D11—661no—
74C5×D11—665no—
75C5×D11—665no—
76D5×C11—331no—
77D5×C11—331no—
78C2×C5×D5—3631noHall
79C52⋊C3D11211yescharacteristic, complemented, Hall
80D33—251no—
81D33—251no—
82C3×D11—2751no—
83C3×D11—5501no—
84C3×D11—5505no—
85D3×C11—2751no—
86D3×C11—2751no—
87C5×C11—31no—
88C5×C11—65no—
89C5×C11—65no—
90C5×C11—61no—
91C5×C11—61no—
92C5×C11—61no—
93C2×C52—1211no—
94C5×D5—331no—
95C5×D5—331no—
96C2×D11—1651no—
97C2×D11—1651no—
98C3×C11—251no—
99C3×C11—505no—
100C3×C11—501no—
101C52D33⋊D1111yescharacteristic, complemented, Sylow
102C2×C11—1651no—
103C2×C11—1651no—
104D11—111no—
105D11—111no—
106D11—151no—
107D11—151no—
108D11—225no—
109C22×C5—18151no—
110C2×D5—3631no—
111C2×D3—30251noHall
112C11—25no—
113C11D11×#387411yescharacteristic, complemented
114C11D11×#387411yescharacteristic, complemented
115C2×C5—1651no—
116C2×C5—1651no—
117C2×C5—7261no—
118C2×C5—7261no—
119D5—331no—
120D5—331no—
121C2×C3—60501no—
122D3—2751no—
123D3—2751no—
124C5—61no—
125C5—61no—
126C22—18151noSylow
127C3—501noSylow
128C2—1211no—
129C2—1651no—
130C2—1651no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocle, hypocenterC112×C52⋊C3C22
Fitting, socleC52×C112C2×D3
LCSG ▷ C112×C52⋊C3
UCSC1

Complements

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

NH ≅ G/Ntype
1. C52⋊C3×C11⋊D11C2semidirect
2. C11×C11⋊#3874C2semidirect
3. C11×C11⋊#3874C2semidirect
5. C112×C52⋊C3C22semidirect
8. C52×C11⋊D11D3semidirect
11. C52×C112C2×D3semidirect
17. C11⋊#3874D11semidirect
18. C11⋊#3874D11semidirect
31. C11×C52⋊C3C2×D11semidirect
32. C11×C52⋊C3C2×D11semidirect
49. C52×C11D3×D11semidirect
50. C52×C11D3×D11semidirect
51. C11⋊D11#3874semidirect
63. C112C2×#3874semidirect
79. C52⋊C3D112semidirect
101. C52D33⋊D11semidirect
113. C11D11×#3874semidirect
114. C11D11×#3874semidirect

Maximal subgroups

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

subgroupindex
C52⋊C3×C11⋊D112
C11×C11⋊#38742
C5×D55⋊D113
D11×#387411
D33⋊D1125