Finite Group Databasebeta

← #88955

Subgroups — #88955

Order 432.

290 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 50 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×#1113C211yesmaximal, characteristic, complemented
2C2×D3×C3⋊D3C211yesmaximal, characteristic, complemented
3#6292C212yesmaximal, complemented
4C3×#626C212yesmaximal, complemented
5C3×#624C211yesmaximal, characteristic, complemented
6#3811—31nomaximal
7D3×D12—32nomaximal
8C2×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
9C2×C3×C3⋊D3C2211yescharacteristic
10C2×C3×C3⋊D3C2212yescomplemented
11C2×C32×D3C2211yescharacteristic, complemented
12#1113—22no—
13D3×C3⋊D3—22no—
14C32×Dic3C2212yescomplemented
15C22×C3⋊D3—31no—
16C2×D32—31no—
17C2×D32—32no—
18C2×D32—32no—
19C2×D32—61no—
20C4⋊(C3⋊D3)—32no—
21C3×#67—32no—
22C3×D12—32no—
23C3×C4×D3—32no—
24#626—32no—
25#626—32no—
26#626—62no—
27#626D312yescomplemented
28#624D311yescharacteristic, complemented
29C2×C33C2311yescharacteristic
30C3⋊(C3⋊D3)—21no—
31C3×C3⋊D3—22no—
32C3×C3⋊D3D412yescomplemented
33C32×D3—21no—
34D3×D4—92no—
35C2×D12—91no—
36C22×C32—31no—
37C2×C3⋊D3—31no—
38C2×C3⋊D3—32no—
39C2×C3⋊D3—61no—
40C2×C3⋊D3—62no—
41C2×C3⋊D3—62no—
42C2×C3⋊D3—121no—
43C2×C3⋊D3C2×D311yescharacteristic
44C2×C3⋊D3C2×D312yescomplemented
45C2×C3×D3—21no—
46C2×C3×D3—32no—
47C2×C3×D3—32no—
48C2×C3×D3—32no—
49C2×C3×D3—61no—
50C2×C3×D3—62no—
51C2×C3×D3C2×D312yescomplemented
52D32—64no—
53D32—64no—
54D32—64no—
55D32—62no—
56C32×C4—32no—
57C3×Dic3—22no—
58C3×Dic3C2×D312yescomplemented
59C3×Dic3C2×D312yescomplemented
60C33C2×D411yescharacteristic, complemented, Sylow
61C22×D3—91no—
62C22×D3—92no—
63C22×D3—92no—
64C22×D3—91no—
65C22×D3—181no—
66C3×D4—92no—
67C2×C3×C4—91no—
68#67—32no—
69#67—92no—
70D12—32no—
71D12—92no—
72D12—92no—
73D12—182no—
74C4×D3—32no—
75C2×C32—22no—
76C2×C32—21no—
77C2×C32—41no—
78C2×C32—61no—
79C2×C32C22×D311yescharacteristic
80C2×C32C22×D312yes—
81C3⋊D3—22no—
82C3⋊D3—61no—
83C3⋊D3—62no—
84C3⋊D3—62no—
85C3⋊D3—122no—
86C3⋊D3—122no—
87C3⋊D3D1212yescomplemented
88C3×D3—22no—
89C3×D3—22no—
90C3×D3—34no—
91C3×D3—62no—
92C3×D3—62no—
93C3×D3—62no—
94C3×D3—122no—
95C2×D4—271noSylow
96C22×C3—32no—
97C22×C3—61no—
98C22×C3—91no—
99C22×C3—92no—
100C2×D3—32no—
101C2×D3—32no—
102C2×D3—32no—
103C2×D3—61no—
104C2×D3—62no—
105C2×D3—91no—
106C2×D3—92no—
107C2×D3—181no—
108C2×D3—182no—
109C2×D3—182no—
110C2×D3—184no—
111C2×D3—184no—
112C2×D3—182no—
113C2×D3—184no—
114C2×D3—361no—
115C2×D3D3211yescharacteristic, complemented
116C3×C4—32no—
117C3×C4—32no—
118C3×C4—62no—
119Dic3D3212yescomplemented
120C32—22no—
121C32—21no—
122C32—41no—
123C32C2×D1211yescharacteristic, complemented
124C32D3×D412yescomplemented
125C23—271no—
126C23—271no—
127D4—92no—
128D4—272no—
129C2×C4—91no—
130C2×C3—22no—
131C2×C3—21no—
132C2×C3—41no—
133C2×C3—62no—
134C2×C3—62no—
135C2×C3—92no—
136C2×C3—182no—
137C2×C3C2×D3212yes—
138C2×C3C2×D3211yescharacteristic
139D3—21no—
140D3—34no—
141D3—62no—
142D3—62no—
143D3—62no—
144D3—122no—
145D3—182no—
146D3—182no—
147D3—181no—
148D3—362no—
149D3—362no—
150C22—31no—
151C22—91no—
152C22—92no—
153C22—271no—
154C22—542no—
155C22—542no—
156C4—32no—
157C3—21no—
158C3—22no—
159C3—41no—
160C3D3×D1212yescomplemented
161C3#381111yescharacteristic, complemented
162C2—61no—
163C2—92no—
164C2—182no—
165C2—541no—
166C2D3311yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D33
commutator, Fitting, socle, cosocleC2×C33C23
hypocenterC33C2×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#1113C2semidirect
2. C2×D3×C3⋊D3C2semidirect
3. #6292C2semidirect
4. C3×#626C2semidirect
5. C3×#624C2semidirect
8. C2×C3⋊(C3⋊D3)C22semidirect
10. C2×C3×C3⋊D3C22semidirect
11. C2×C32×D3C22semidirect
14. C32×Dic3C22semidirect
27. #626D3semidirect
28. #624D3semidirect
32. C3×C3⋊D3D4semidirect
44. C2×C3⋊D3C2×D3semidirect
51. C2×C3×D3C2×D3semidirect
58. C3×Dic3C2×D3semidirect
59. C3×Dic3C2×D3semidirect
60. C33C2×D4semidirect
87. C3⋊D3D12semidirect
115. C2×D3D32semidirect
119. Dic3D32semidirect
123. C32C2×D12semidirect
124. C32D3×D4semidirect
160. C3D3×D12semidirect
161. C3#3811semidirect

Maximal subgroups

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

subgroupindex
C2×#11132
C2×D3×C3⋊D32
#62922
C3×#6262
C3×#6242
#38113
D3×D123