Finite Group Databasebeta

← C2×#88940 #11724347

Subgroups — C2×#88940 #11724347

Order 864.

324 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C22×C3×#157C211yesmaximal, characteristic
2C2×#6294C212yesmaximal
3#88940C214yesmaximal, direct product factor
4C2×#3773—31nomaximal
5C22×C3×C3⋊D3C2211yescharacteristic
6C2×C3×#157C414yescomplemented
7C2×C3×#157C2212yes—
8C2×C3×C3⋊Dic3—22no—
9#6294—22no—
10#6294C2214yes—
11C22×#157D311yescharacteristic
12C2×#624—32no—
13C2×D3×Dic3—62no—
14#3773—34no—
15C22×C33D411yescharacteristic
16C2×C3×C3⋊D3C2×C412yes—
17C2×C3×C3⋊D3D411yescharacteristic
18C2×C3×C3⋊D3Q812yes—
19C2×C3×C3⋊D3C2311yescharacteristic
20C3×#157C2×C414yescomplemented
21C3×C3⋊Dic3—24no—
22C2×C4⋊Dic3—91nomaximal
23C22×C3⋊D3C2×D311yescharacteristic
24C22×C3×D3—62no—
25C2×#157Dic314yescomplemented
26C2×#157C2×D312yes—
27C2×C3⋊Dic3—22no—
28C2×C3×Dic3—62no—
29C2×C3×Dic3—62no—
30C2×C3×Dic3—122no—
31#624—34no—
32#624—62no—
33D3×Dic3—64no—
34D3×Dic3—64no—
35C2×C33C4⋊C412yescomplemented
36C2×C33C2×D411yescharacteristic
37C3×C3⋊D3C4⋊C412yescomplemented
38C3×C3⋊D3C22×C411yescharacteristic
39C3×C3⋊D3C2×Q811yescharacteristic
40C22×C3×C4—91no—
41C22×Dic3—92no—
42C2×C4×D3—182no—
43C4⋊Dic3—94no—
44C22×C32—22no—
45C22×C32—42no—
46C22×C32D1211yescharacteristic
47C2×C3⋊D3Dic612yes—
48C2×C3⋊D3D1211yescharacteristic
49C2×C3⋊D3C2×Dic312yes—
50C2×C3⋊D3C22×D311yescharacteristic
51C2×C3×D3—64no—
52C2×C3×D3—62no—
53C2×C3×D3—64no—
54C2×C3×D3—62no—
55#157C2×Dic314yescomplemented
56C3⋊Dic3—24no—
57C3×Dic3—64no—
58C3×Dic3—64no—
59C3×Dic3—124no—
60C2×C4⋊C4—271noSylow
61C33C2×C4⋊C411yescharacteristic, complemented, Sylow
62C23×C3—91no—
63C22×D3—62no—
64C2×C3×C4—94no—
65C2×C3×C4—92no—
66C2×C3×C4—182no—
67C2×Dic3—62no—
68C2×Dic3—62no—
69C2×Dic3—94no—
70C2×Dic3—122no—
71C2×Dic3—182no—
72C4×D3—184no—
73C4×D3—184no—
74C2×C32—22no—
75C2×C32—24no—
76C2×C32—44no—
77C2×C32—42no—
78C2×C32C4⋊Dic312yescomplemented
79C2×C32C2×D1211yescharacteristic
80C3⋊D3C4⋊Dic312yescomplemented
81C3⋊D3C2×Dic611yescharacteristic
82C3⋊D3C22×Dic311yescharacteristic
83C3×D3—64no—
84C3×D3—62no—
85C3×D3—62no—
86C22×C4—91no—
87C22×C4—272no—
88C4⋊C4—274no—
89C22×C3—22no—
90C22×C3—42no—
91C22×C3—91no—
92C22×C3—91no—
93C22×C3—92no—
94C22×C3—92no—
95C22×C3GO+(4,𝔽2)11yescharacteristic
96C2×D3—62no—
97C2×D3—62no—
98C2×D3—64no—
99C2×D3—64no—
100C3×C4—94no—
101C3×C4—184no—
102Dic3—64no—
103Dic3—64no—
104Dic3—124no—
105C32—22no—
106C32—42no—
107C32C2×C4⋊Dic311yescharacteristic, complemented
108C23—91no—
109C2×C4—92no—
110C2×C4—94no—
111C2×C4—182no—
112C2×C4—274no—
113C2×C4—542no—
114C2×C3—22no—
115C2×C3—24no—
116C2×C3—42no—
117C2×C3—44no—
118C2×C3—91no—
119C2×C3—91no—
120C2×C3—92no—
121C2×C3#377312yescomplemented
122C2×C3C2×GO+(4,𝔽2)11yescharacteristic
123D3—64no—
124D3—62no—
125D3—62no—
126C22—91no—
127C22—91no—
128C22—92no—
129C22—92no—
130C22#157⋊D311yescharacteristic
131C4—94no—
132C4—184no—
133C3—22no—
134C3—42no—
135C3C2×#377311yescharacteristic, complemented
136C2—91no—
137C2—91no—
138C2—92no—
139C2#8894012yesdirect product factor
140C2C2×#157⋊D311yescharacteristic
subgroupG/H
center, hypercenterC22#157⋊D3
commutatorC3×C3⋊D3C22×C4
FrattiniC2C2×#157⋊D3
Fitting, socleC22×C33D4
prime radicalC22×C3×C3⋊D3C22
cosocleC2×C3×C3⋊D3C23
hypocenterC33C2×C4⋊C4
LCSG ▷ C3×C3⋊D3 ▷ C33
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
3. #88940C2direct (N × H)
6. C2×C3×#157C4semidirect
20. C3×#157C2×C4semidirect
25. C2×#157Dic3semidirect
35. C2×C33C4⋊C4semidirect
37. C3×C3⋊D3C4⋊C4semidirect
55. #157C2×Dic3semidirect
61. C33C2×C4⋊C4semidirect
78. C2×C32C4⋊Dic3semidirect
80. C3⋊D3C4⋊Dic3semidirect
107. C32C2×C4⋊Dic3semidirect
121. C2×C3#3773semidirect
135. C3C2×#3773semidirect
139. C2#88940direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1572
C2×#62942
#889402
C2×#37733
C2×C4⋊Dic39