Finite Group Databasebeta

← C3×#63781 #11723081

Subgroups — C3×#63781 #11723081

Order 864.

292 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 64 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×#157C212yesmaximal
2C2×C3×C4×C3⋊D3C211yesmaximal, characteristic
3#63781C311yesmaximal, characteristic, direct product factor
4C22×C3×C3⋊D3C2211yescharacteristic
5C2×C3×#157—22no—
6C2×C3×#157—22no—
7C2×C3×#157C414yescomplemented
8C2×C33×C4C411yescharacteristic, complemented
9C2×C3×C3⋊Dic3C411yescharacteristic, complemented
10C3×C4×C3⋊D3—22no—
11C22×#157C2×C312yes—
12C2×C4×C3⋊D3C2×C311yescharacteristic
13C2×C3×C4×D3—62no—
14C22×C33C2×C411yescharacteristic
15C2×C3×C3⋊D3C2×C412yes—
16C2×C3×C3⋊D3D411yescharacteristic
17C2×C3×C3⋊D3D412yes—
18C2×C3×C3⋊D3Q811yescharacteristic
19C3×#157—24no—
20C33×C4—21no—
21C3×C3⋊Dic3—21no—
22C3×#95—91nomaximal
23C22×C3⋊D3C22×C311yescharacteristic
24C22×C3×D3—62no—
25C2×#157—22no—
26C2×#157—22no—
27C2×#157C3×C414yescomplemented
28C2×C32×C4—22no—
29C2×C32×C4—42no—
30C2×C32×C4C3×C411yescharacteristic, complemented
31C2×C3⋊Dic3C3×C411yescharacteristic, complemented
32C4×C3⋊D3—22no—
33C2×C3×Dic3—62no—
34C3×C4×D3—68no—
35C2×C33C4211yescharacteristic
36C2×C33C22⋊C411yescharacteristic
37C2×C33C4⋊C411yescharacteristic
38C3×C3⋊D3C22⋊C412yes—
39C3×C3⋊D3C4⋊C412yes—
40C22×C3×C4—92no—
41C22×C3×C4—91no—
42C2×C4×D3—62no—
43C22×C32—22no—
44C22×C32—42no—
45C22×C32C2×C3×C411yescharacteristic
46C2×C3⋊D3C2×C3×C412yes—
47C2×C3⋊D3C3×D411yescharacteristic
48C2×C3⋊D3C3×D412yes—
49C2×C3⋊D3C3×Q811yescharacteristic
50C2×C3×D3—64no—
51C2×C3×D3—64no—
52C2×C3×D3—62no—
53C2×C3×D3—62no—
54#157—24no—
55C32×C4—21no—
56C32×C4—24no—
57C32×C4—44no—
58C3⋊Dic3—21no—
59C3×Dic3—64no—
60#95—91noSylow
61C33#9511yescharacteristic, complemented, Sylow
62C23×C3—91no—
63C22×D3—62no—
64C2×C3×C4—22no—
65C2×C3×C4—42no—
66C2×C3×C4—94no—
67C2×C3×C4—91no—
68C2×C3×C4—182no—
69C2×C3×C4—182no—
70C2×C3×C4—182no—
71C2×C3×C4#15711yescharacteristic, complemented
72C2×Dic3—62no—
73C4×D3—68no—
74C2×C32—22no—
75C2×C32—22no—
76C2×C32—22no—
77C2×C32—42no—
78C2×C32—42no—
79C2×C32—42no—
80C2×C32C3×C4211yescharacteristic
81C2×C32C3×C22⋊C411yescharacteristic
82C2×C32C3×C4⋊C411yescharacteristic
83C3⋊D3C3×C22⋊C412yes—
84C3⋊D3C3×C4⋊C412yes—
85C3×D3—64no—
86C3×D3—64no—
87C22×C4—92no—
88C22×C4—91no—
89C22×C3—22no—
90C22×C3—42no—
91C22×C3—92no—
92C22×C3—91no—
93C22×C3—91no—
94C22×C3—92no—
95C22×C3C2×#15711yescharacteristic
96C2×D3—64no—
97C2×D3—64no—
98C2×D3—62no—
99C2×D3—62no—
100C3×C4—24no—
101C3×C4—21no—
102C3×C4—44no—
103C3×C4—184no—
104C3×C4—181no—
105Dic3—64no—
106C32—22no—
107C32—42no—
108C32C3×#9511yescharacteristic, complemented
109C23—91no—
110C2×C4—94no—
111C2×C4—91no—
112C2×C4—182no—
113C2×C4—182no—
114C2×C4—182no—
115C2×C4C3×#15711yescharacteristic, complemented
116C2×C3—22no—
117C2×C3—22no—
118C2×C3—22no—
119C2×C3—42no—
120C2×C3—42no—
121C2×C3—42no—
122C2×C3—92no—
123C2×C3—92no—
124C2×C3C4×#15711yescharacteristic
125C2×C3C4⋊#15711yescharacteristic
126C2×C3C22⋊#15711yescharacteristic
127D3—64no—
128D3—64no—
129C22—92no—
130C22—91no—
131C22—91no—
132C22—92no—
133C22C2×C3×#15711yescharacteristic
134C4—21no—
135C4—184no—
136C4—181no—
137C3—22no—
138C3—42no—
139C3#6378111yescharacteristic, direct product factor
140C2—92no—
141C2—92no—
142C2C3×C4×#15711yescharacteristic
143C2C3×C4⋊#15711yescharacteristic
144C2C3×C22⋊#15711yescharacteristic
subgroupG/H
centerC22×C3C2×#157
commutatorC2×C32C3×C42
FrattiniC22C2×C3×#157
FittingC2×C33×C4C4
socleC22×C33C2×C4
prime radicalC22×C3×C3⋊D3C22
cosocleC22×C3⋊D3C22×C3
hypercenterC2×C3×C4#157
hypocenterC32C3×#95
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
3. #63781C3direct (N × H)
7. C2×C3×#157C4semidirect
8. C2×C33×C4C4semidirect
9. C2×C3×C3⋊Dic3C4semidirect
27. C2×#157C3×C4semidirect
30. C2×C32×C4C3×C4semidirect
31. C2×C3⋊Dic3C3×C4semidirect
61. C33#95semidirect
71. C2×C3×C4#157semidirect
108. C32C3×#95semidirect
115. C2×C4C3×#157semidirect
139. C3#63781direct (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×C3×C4×C3⋊D32
#637813
C3×#959