Finite Group Databasebeta

← C4×#92213 #14516141

Subgroups — C4×#92213 #14516141

Order 1944.

182 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 44 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
2C4×#6872C211yesmaximal, characteristic, complemented
3#11757336C211yesmaximal, characteristic, complemented
4C4×#4207—31nomaximal
5C4×D27⋊C3—32nomaximal
6C3×C4×D27—31nomaximal
7C2×#6872C2211yescharacteristic
8#92213C412yesdirect product factor
9C2×#4207—31no—
10C4×#737D311yescharacteristic
11#66409—31no—
12C2×D27⋊C3—32no—
13C2×C3×D27—31no—
14C4×C27⋊C3D312yescomplemented
15C3×C4×C27D311yescharacteristic, complemented
16(C27⋊C3)⋊C4—32no—
17C3×Dic27—31no—
18#6872C2×C411yescharacteristic, complemented, Sylow
19C4×C3⋊D9—31no—
20C4×AGL(1,ℤ/9)—92no—
21C4×(C3⋊D3)⋊C3—91no—
22C3×C4×D9—91no—
23C4×D27—31no—
24C4×D27—32no—
25C2×#737C2×D311yescharacteristic
26#4207—32no—
27C2×C27⋊C3C2×D312yes—
28C2×C3×C27C2×D311yescharacteristic
29D27⋊C3—34no—
30C3×D27—32no—
31C2×C3⋊D9—31no—
32C2×AGL(1,ℤ/9)—92no—
33C2×(C3⋊D3)⋊C3—91no—
34C2×C3×D9—91no—
35C4×3−1+2—61no—
36C4×3−1+2D912yes—
37C4×H(3,𝔽3)D911yescharacteristic
38C3×C4×C9—31no—
39C3×C4×C9C3⋊D311yescharacteristic
40C3⋊Dic9—31no—
413−1+2⋊C4—92no—
42(C3⋊Dic3)⋊C3—91no—
43C3×Dic9—91no—
44C2×D27—31no—
45C2×D27—32no—
46C4×C27—31no—
47C4×C27—32no—
48Dic27—31no—
49Dic27—32no—
50#737C4×D311yescharacteristic
51C27⋊C3C4×D312yescomplemented
52C3×C27C4×D311yescharacteristic, complemented
53C4×C3⋊D3—91no—
54C3×C4×D3—271no—
55C4×D9—92no—
56C4×D9—91no—
57C2×3−1+2—61no—
58C2×3−1+2C2×D912yes—
59C2×H(3,𝔽3)C2×D911yescharacteristic
60C2×C3×C9—31no—
61C2×C3×C9C2×C3⋊D311yescharacteristic
62C3⋊D9—32no—
63AGL(1,ℤ/9)—94no—
64(C3⋊D3)⋊C3—92no—
65C3×D9—92no—
66C2×C27—31no—
67C2×C27—32no—
68D27—32no—
69D27—34no—
70C2×C3⋊D3—91no—
71C2×C3×D3—271no—
72C32×C4—31no—
73C32×C4C3⋊D911yescharacteristic
74C3⋊Dic3—91no—
75C3×Dic3—271no—
76C2×D9—92no—
77C2×D9—91no—
78C4×C9—21no—
79C4×C9—32no—
80C4×C9#27211yescharacteristic
81Dic9—92no—
82Dic9—91no—
833−1+2—61no—
843−1+2C4×D912yes—
85H(3,𝔽3)C4×D911yescharacteristic
86C3×C9—31no—
87C3×C9C4×C3⋊D311yescharacteristic
88C27—31no—
89C27—32no—
90C2×C3×C4—811no—
91C4×D3—271no—
92C4×D3—811no—
93C2×C32—31no—
94C2×C32C2×C3⋊D911yescharacteristic
95C3⋊D3—92no—
96C3×D3—272no—
97C2×C9—21no—
98C2×C9—32no—
99C2×C9C2×#27211yescharacteristic
100D9—94no—
101D9—92no—
102C22×C3—811no—
103C2×D3—271no—
104C2×D3—811no—
105C3×C4—31no—
106C3×C4—91no—
107C3×C4—811no—
108C3×C4#418111yescharacteristic
109Dic3—271no—
110Dic3—811no—
111C32—31no—
112C32C4×C3⋊D911yescharacteristic
113C9—21no—
114C9—32no—
115C9C4×#27211yescharacteristic
116C2×C4—811noSylow
117C2×C3—31no—
118C2×C3—91no—
119C2×C3—812no—
120C2×C3C2×#418111yescharacteristic
121D3—272no—
122D3—812no—
123C22—811no—
124C4—811no—
125C4#9221311yescharacteristic, direct product factor
126C3—31no—
127C3—91no—
128C3C4×#418111yescharacteristic
129C2—812no—
130C2C2×#9221311yescharacteristic
subgroupG/H
center, hypercenterC4#92213
commutator, hypocenter#6872C2×C4
FrattiniC2×C3×C9C2×C3⋊D3
FittingC4×#6872C2
socleC2×C3C2×#4181
prime radicalC2×#92213C2
cosocleC2×#6872C22
LCSG ▷ #6872
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C4×#6872C2semidirect
3. #11757336C2semidirect
8. #92213C4direct (N × H)
14. C4×C27⋊C3D3semidirect
15. C3×C4×C27D3semidirect
18. #6872C2×C4semidirect
51. C27⋊C3C4×D3semidirect
52. C3×C27C4×D3semidirect
125. C4#92213direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#922132
C4×#68722
#117573362
C4×#42073
C4×D27⋊C33
C3×C4×D273