Finite Group Databasebeta

← #92213⋊C4 #14515799

Subgroups — #92213⋊C4 #14515799

Order 1944.

138 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 27 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×#92213C211yesmaximal, characteristic
2#11757305C211yesmaximal, characteristic, complemented
3#11757304C211yesmaximal, characteristic, complemented
4#4207⋊C4—31nomaximal
5Dic3×D27—31nomaximal
6C2×#6872C2211yescharacteristic
7#92213C412yescomplemented
8C2×#4207—31no—
9#66410D311yescharacteristic
10#66409—31no—
11C2×D27⋊C3—61no—
12C2×C3×D27—31no—
13C3⋊Dic27D311yescharacteristic, complemented
14Dic3×C27—31no—
15#6872C2×C411yescharacteristic, complemented, Sylow
16((C3⋊D3)⋊C3)⋊C4—91no—
17(C3⋊D9)⋊C4—91no—
18Dic3×D9—91no—
19C4×D27—91no—
20C2×#737C2×D311yescharacteristic
21#4207—32no—
22C2×C27⋊C3—21no—
23C2×C3×C27C2×D311yescharacteristic
24D27⋊C3—62no—
25C3×D27—32no—
26C2×C3⋊D9—31no—
27C2×AGL(1,ℤ/9)—181no—
28C2×(C3⋊D3)⋊C3—91no—
29C2×C3×D9—91no—
30#1084D911yescharacteristic
31C3⋊Dic9—31no—
323−1+2⋊C4—181no—
33(C3⋊Dic3)⋊C3—91no—
34C9×Dic3—31no—
35C9×Dic3—91no—
36C3×Dic9—91no—
37C2×D27—31no—
38C2×D27—61no—
39C4×C27—91no—
40Dic27—91no—
41#737C4×D311yescharacteristic
42C27⋊C3—21no—
43C3×C27C4×D311yescharacteristic, complemented
44#624—271no—
45D3×Dic3—271no—
46C4×D9—271no—
47C2×3−1+2—21no—
48C2×3−1+2—61no—
49C2×H(3,𝔽3)C2×D911yescharacteristic
50C2×C3×C9—31no—
51C2×C3×C9D3211yescharacteristic
52C3⋊D9—32no—
53AGL(1,ℤ/9)—182no—
54(C3⋊D3)⋊C3—92no—
55C3×D9—92no—
56C2×C27—31no—
57C2×C27—61no—
58D27—32no—
59D27—62no—
60C2×C3⋊D3—91no—
61C2×C3×D3—271no—
62C3⋊Dic3—91no—
63C3×Dic3—31no—
64C3×Dic3—91no—
65C3×Dic3—271no—
66C2×D9—91no—
67C2×D9—181no—
68C4×C9—91no—
69Dic9—91no—
70Dic9—181no—
713−1+2—21no—
723−1+2—61no—
73H(3,𝔽3)C4×D911yescharacteristic
74C3×C9—31no—
75C3×C9#62411yescharacteristic
76C27—31no—
77C27—61no—
78C2×Dic3—811no—
79C4×D3—811no—
80C4×D3—811no—
81C2×C32—31no—
82C2×C32D3×D911yescharacteristic
83C3⋊D3—92no—
84C3×D3—272no—
85C2×C9—21no—
86C2×C9—61no—
87C2×C9((C3⋊D3)⋊C3)⋊C211yescharacteristic
88D9—92no—
89D9—182no—
90C22×C3—811no—
91C2×D3—271no—
92C2×D3—811no—
93C3×C4—91no—
94C3×C4—811no—
95Dic3—31no—
96Dic3—91no—
97Dic3—271no—
98Dic3—811no—
99C32—31no—
100C32(C3⋊D9)⋊C411yescharacteristic
101C9—21no—
102C9—61no—
103C9#619911yescharacteristic
104C2×C4—2431noSylow
105C2×C3—31no—
106C2×C3—91no—
107C2×C3—812no—
108C2×C3((C3⋊D3)⋊C9)⋊C211yescharacteristic
109D3—272no—
110D3—812no—
111C22—811no—
112C4—91no—
113C4—811no—
114C3—31no—
115C3—91no—
116C3#4181⋊C411yescharacteristic
117C2—812no—
118C2#92181⋊C211yescharacteristic
subgroupG/H
center, hypercenterC2#92181⋊C2
commutator, hypocenter#6872C2×C4
FrattiniC2×C3×C9D32
Fitting, cosocleC2×#6872C22
socleC2×C3((C3⋊D3)⋊C9)⋊C2
prime radicalC2×#92213C2
LCSG ▷ #6872
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #11757305C2semidirect
3. #11757304C2semidirect
7. #92213C4semidirect
13. C3⋊Dic27D3semidirect
15. #6872C2×C4semidirect
43. C3×C27C4×D3semidirect

Maximal subgroups

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

subgroupindex
C2×#922132
#117573052
#117573042
#4207⋊C43
Dic3×D273