Finite Group Databasebeta

← #37541988

Subgroups — #37541988

Order 23168.

348 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 133 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
1#26041221C213yesmaximal
2#26041213C213yesmaximal
3#26041211C213yesmaximal
4#26041200C213yesmaximal
5#26041149C211yesmaximal, characteristic
6#26041147C211yesmaximal, characteristic
7#383×C181C211yesmaximal, characteristic
8C22×Dic362C2211yescharacteristic
9C2×C4⋊Dic181C2213yes—
10C2×C4⋊Dic181C2213yes—
11C2×C4⋊Dic181C2213yes—
12C2×#15668428C2213yes—
13C2×#15668428C2213yes—
14#19153723C2213yes—
15#19153723C2213yes—
16#19153723C2213yes—
17#19153723C2213yes—
18C2×C42×C181C2211yescharacteristic
19#95×C181C2213yes—
20#95×C181C2213yes—
21C2×Dic362—43no—
22C22×Dic181C2313yes—
23C22×Dic181C2311yescharacteristic
24C22×Dic181C2311yescharacteristic
25C22×Dic181C2313yes—
26C4⋊Dic181—43no—
27C4⋊Dic181—43no—
28C4⋊Dic181—43no—
29#15668428—43no—
30#15668428—43no—
31C22×C4×C181C2313yes—
32C22×C4×C181C2311yescharacteristic
33C22×C4×C181C2313yes—
34C42×C181Q814yescomplemented
35Dic362—44no—
36C2×Dic181—23no—
37C2×Dic181—23no—
38C2×Dic181—23no—
39C2×Dic181—23no—
40C2×Dic181—23no—
41C2×Dic181—23no—
42C2×Dic181—26no—
43C23×C181C2411yescharacteristic
44C2×C4×C181—23no—
45C2×C4×C181—23no—
46C2×C4×C181—23no—
47C2×C4×C181—23no—
48C2×C4×C181—26no—
49C2×C4×C181C2×Q816yes—
50C22×C181C22×Q811yescharacteristic
51C22×C181H(5,𝔽2)13yes—
52C22×C1812−1+413yes—
53C4×C181—26no—
54C4×C181—41no—
55C4×C181—43no—
56Dic181—43no—
57Dic181—41no—
58Dic181—41no—
59Dic181—43no—
60C2×C181#54413yes—
61C2×C181#56011yescharacteristic
62C2×C181#56313yes—
63C181#284311yescharacteristic, complemented, Sylow
64#2843—1811nomaximal, Sylow
65#400—1813no—
66#398—1813no—
67#398—1813no—
68#395—1813no—
69#384—1811no—
70#383—1811no—
71#383D18111yescharacteristic
72C22×Q8—1811no—
73C2×C4⋊C4—1813no—
74C2×C4⋊C4—1813no—
75C2×C4⋊C4—1813no—
76C2×C4⋊C4—1813no—
77C2×C4⋊C4—1813no—
78C2×C42C2×D18111yescharacteristic
79#95—1813no—
80#95—1813no—
81#95—1813no—
82#95—1813no—
83#95C2×D18113yes—
84#95C2×D18113yes—
85C2×Q8—7243no—
86C22×C4—1813no—
87C22×C4—1811no—
88C22×C4—1811no—
89C22×C4—1813no—
90C22×C4C22×D18113yes—
91C22×C4C22×D18111yescharacteristic
92C22×C4C22×D18113yes—
93C4⋊C4—7243no—
94C4⋊C4—7243no—
95C4⋊C4—7243no—
96C4⋊C4—7243no—
97C4⋊C4—7243no—
98C42Dic36214yescomplemented
99C23C23×D18111yescharacteristic
100Q8—7244no—
101C2×C4—23no—
102C2×C4—23no—
103C2×C4—23no—
104C2×C4—23no—
105C2×C4—26no—
106C2×C4—3623no—
107C2×C4—3623no—
108C2×C4—3623no—
109C2×C4—3623no—
110C2×C4—3623no—
111C2×C4—3623no—
112C2×C4—3626no—
113C2×C4C2×Dic36216yes—
114C22C22×Dic36211yescharacteristic
115C22#1915386213yes—
116C22#1915386313yes—
117C4—26no—
118C4—41no—
119C4—43no—
120C4—7241no—
121C4—7241no—
122C4—7243no—
123C4—7243no—
124C2#2604190713yes—
125C2#2604202011yescharacteristic
126C2#2604203113yes—
subgroupG/H
center, FrattiniC23C23×D181
commutator, socle, prime radical, cosocleC23×C181C24
Fitting#383×C181C2
hypercenter#383D181
hypocenterC181#2843
LCSG ▷ C23×C181 ▷ C181
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
34. C42×C181Q8semidirect
63. C181#2843semidirect
98. C42Dic362semidirect

Maximal subgroups

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

subgroupindex
#260412212
#260412132
#260412112
#260412002
#260411492
#260411472
#383×C1812
#2843181