Finite Group Databasebeta

← #92203⋊C4 #14515744

Subgroups — #92203⋊C4 #14515744

Order 1944.

145 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 145 conjugacy classes of subgroups — too many to draw. Only its 24 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×#92203C211yesmaximal, characteristic
2#11757289C211yesmaximal, characteristic, complemented
3#11757288C211yesmaximal, characteristic, complemented
4#4169⋊C4—31nomaximal
5#4169⋊C4—31nomaximal
6C2×#6861C2211yescharacteristic
7#92203C412yescomplemented
8C2×#4169—31no—
9C2×#4169—31no—
10C2×#4169—61no—
11#66328D311yescharacteristic
12#66328D311yescharacteristic
13(C3⋊Dic3)⋊C9—31no—
14(C3⋊Dic3)⋊C9—31no—
15#6861C2×C411yescharacteristic, complemented, Sylow
16#6294—91no—
17(C3⋊D9)⋊C4—91no—
18(C3⋊D9)⋊C4—91no—
19C2×C32⋊C9—21no—
20C2×C32⋊C9C2×D311yescharacteristic
21C2×C32⋊C9C2×D311yescharacteristic
22#4169—32no—
23#4169—32no—
24#4169—62no—
25C2×C3×C3⋊D3—91no—
26C3×C3⋊Dic3—31no—
27C3×C3⋊Dic3—31no—
28C2×C3⋊D9—31no—
29C2×C3⋊D9—31no—
30C2×C3⋊D9—61no—
31C9×Dic3—91no—
32C9×Dic3—91no—
33C3×Dic9—91no—
34C3×Dic9—91no—
35C32⋊C9—21no—
36C32⋊C9C4×D311yescharacteristic
37C32⋊C9C4×D311yescharacteristic
38#624—271no—
39D3×Dic3—271no—
40D3×Dic3—271no—
41C4×D9—271no—
42C4×D9—271no—
43C2×C33D3211yescharacteristic
44C3×C3⋊D3—92no—
45C2×C3×C9—31no—
46C2×C3×C9—31no—
47C2×C3×C9—61no—
48C3⋊D9—32no—
49C3⋊D9—32no—
50C3⋊D9—62no—
51C2×C3⋊D3—91no—
52C2×C3×D3—271no—
53C2×C3×D3—271no—
54C2×C3×D3—541no—
55C3⋊Dic3—31no—
56C3⋊Dic3—31no—
57C3×Dic3—91no—
58C3×Dic3—91no—
59C3×Dic3—271no—
60C3×Dic3—271no—
61C2×D9—271no—
62C2×D9—271no—
63C2×D9—541no—
64C4×C9—271no—
65C4×C9—271no—
66Dic9—91no—
67Dic9—91no—
68C33#62411yescharacteristic
69C3×C9—31no—
70C3×C9—31no—
71C3×C9—61no—
72C2×Dic3—811no—
73C4×D3—811no—
74C4×D3—811no—
75C2×C32—31no—
76C2×C32—31no—
77C2×C32—61no—
78C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
79C3⋊D3—92no—
80C3×D3—272no—
81C3×D3—272no—
82C3×D3—542no—
83C2×C9—91no—
84C2×C9—91no—
85C2×C9—181no—
86D9—272no—
87D9—272no—
88D9—542no—
89C22×C3—811no—
90C2×D3—271no—
91C2×D3—271no—
92C2×D3—541no—
93C3×C4—271no—
94C3×C4—271no—
95Dic3—91no—
96Dic3—91no—
97Dic3—271no—
98Dic3—271no—
99C32—31no—
100C32—31no—
101C32—61no—
102C32#619911yescharacteristic
103C9—91no—
104C9—91no—
105C9—181no—
106C2×C4—2431noSylow
107C2×C3—21no—
108C2×C3—91no—
109C2×C3—812no—
110C2×C3#4176⋊C211yescharacteristic
111C2×C3#4178⋊C211yescharacteristic
112D3—272no—
113D3—272no—
114D3—542no—
115C22—811no—
116C4—271no—
117C4—271no—
118C3—21no—
119C3—91no—
120C3#4184⋊C411yescharacteristic
121C3#4185⋊C411yescharacteristic
122C2—812no—
123C2#92165⋊C211yescharacteristic
subgroupG/H
center, hypercenterC2#92165⋊C2
commutator, hypocenter#6861C2×C4
FrattiniC2×C33D32
Fitting, cosocleC2×#6861C22
socleC2×C32((C3⋊D3)⋊C3)⋊C2
prime radicalC2×#92203C2
LCSG ▷ #6861
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #11757289C2semidirect
3. #11757288C2semidirect
7. #92203C4semidirect
15. #6861C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#922032
#117572892
#117572882
#4169⋊C43