Finite Group Databasebeta

← #11920954

Subgroups — #11920954

Order 1152.

298 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 29 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
1C3⋊#5930C212yesmaximal, complemented
2C3×#393⋊C3C211yesmaximal, characteristic
3#72998—33nomaximal
4#69701—31nomaximal
5C3×C22⋊SL(2,𝔽3)C2211yescharacteristic
6C2×C3⋊SL(2,ℤ/4)—41nomaximal
7#5930—36no—
8#5483—31no—
9C3×#393D311yescharacteristic
10#5228—32no—
11#393⋊C3D313yes—
12#4525—31no—
13#4452—32no—
14C22×C3×A4—41no—
15C3⋊SL(2,ℤ/4)—42no—
16C3⋊#226—82no—
17#1602—91noSylow
18C22×C3×Q8C2×D311yescharacteristic
19C22⋊SL(2,𝔽3)C2×D313yes—
20C2×SL(2,ℤ/4)—123no—
21C2×C3×C22⋊C4—31no—
22C2×#217—61no—
23C2×#216—62no—
24#924—32no—
25#924—61no—
26#878—62no—
27#878—62no—
28C3×#95—31no—
29#835—62no—
30#830—32no—
31C2×C3×A4—42no—
32C2×C3×A4—41no—
33C2×C3⋊Dic3—161no—
34C3×SL(2,𝔽3)—82no—
35#543—91no—
36#451—92no—
37#393C3⋊D311yescharacteristic
38#328—92no—
39#323—91no—
40C24×C3S411yescharacteristic
41C22×A4—43no—
42C2×C3×Q8—62no—
43C22×C3×C4—31no—
44C22×C3×C4—31no—
45C22×Dic3—61no—
46C22×Dic3—61no—
47C2×Dic6—32no—
48C2×Dic6—61no—
49SL(2,ℤ/4)—126no—
50#226—246no—
51C3×C22⋊C4—62no—
52#217—62no—
53#217—62no—
54#216—122no—
55#216—122no—
56C4⋊Dic3—32no—
57C4⋊Dic3—61no—
58Dic3⋊C4—62no—
59Dic3⋊C4—62no—
60C2×C3⋊C8—62no—
61C22×C32—161no—
62C3×A4—41no—
63C3⋊Dic3—162no—
64C22×Q8C2×C3⋊D311yescharacteristic
65C2×Q16—182no—
66C22⋊Q8—92no—
67C22⋊Q8—182no—
68C22⋊Q8—182no—
69C22⋊Q8—181no—
70C2×C22⋊C4—31no—
71C2×C22⋊C4—181no—
72#103—182no—
73C22⋊C8—92no—
74#95—31no—
75C23×C3—61no—
76C23×C3—61no—
77C23×C3#22612yescomplemented
78C23×C3C2×S411yescharacteristic
79C2×A4—43no—
80C2×A4—46no—
81C3×Q8—22no—
82C3×Q8—62no—
83C2×C3×C4—32no—
84C2×C3×C4—61no—
85C2×C3×C4—121no—
86C2×C3×C4—121no—
87C2×Dic3—62no—
88C2×Dic3—62no—
89C2×Dic3—241no—
90C2×Dic3—241no—
91C2×Dic3—483no—
92Dic6—122no—
93Dic6—241no—
94SL(2,𝔽3)—86no—
95C3⋊C8—122no—
96C2×C32—162no—
97C2×C32—161no—
98C24C3⋊S411yescharacteristic
99C2×Q8—62no—
100C2×Q8—92no—
101C2×Q8—181no—
102C22×C4—31no—
103C22×C4—31no—
104C22×C4—181no—
105C22×C4—181no—
106Q16—362no—
107Q16—362no—
108C2×C8—182no—
109C4⋊C4—92no—
110C4⋊C4—182no—
111C4⋊C4—182no—
112C4⋊C4—181no—
113C22⋊C4—62no—
114C22⋊C4—182no—
115C22⋊C4—182no—
116C22×C3—31no—
117C22×C3—31no—
118C22×C3—41no—
119C22×C3—62no—
120C22×C3—121no—
121C22×C3—163no—
122C22×C3C2×#22611yescharacteristic
123A4—43no—
124C3×C4—62no—
125C3×C4—121no—
126Dic3—122no—
127Dic3—122no—
128Dic3—486no—
129C32—161noSylow
130C23—61no—
131C23—61no—
132C23C3⋊#22612yescomplemented
133C23C2×C3⋊S411yescharacteristic
134Q8—22no—
135Q8—62no—
136Q8—362no—
137Q8—721no—
138C2×C4—32no—
139C2×C4—61no—
140C2×C4—121no—
141C2×C4—121no—
142C2×C4—182no—
143C2×C4—182no—
144C2×C4—721no—
145C2×C4—721no—
146C8—362no—
147C2×C3—31no—
148C2×C3—31no—
149C2×C3—42no—
150C2×C3—166no—
151C2×C3—163no—
152C2×C3#1020⋊C211yescharacteristic
153C22—31no—
154C22—31no—
155C22—41no—
156C22—62no—
157C22—121no—
158C22C2×C3⋊#22611yescharacteristic
159C4—62no—
160C4—121no—
161C4—362no—
162C4—362no—
163C3—163no—
164C3#7299811yescharacteristic, complemented
165C2—31no—
166C2—31no—
167C2—42no—
168C2#1059363011yescharacteristic
subgroupG/H
center, hypercenterC2#10593630
commutator, cosocle, hypocenterC3×C22⋊SL(2,𝔽3)C22
FrattiniC23C2×C3⋊S4
FittingC3×#393D3
socleC23×C3C2×S4
prime radicalC3×#393⋊C3C2
LCSG ▷ C3×C22⋊SL(2,𝔽3)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3⋊#5930C2semidirect
77. C23×C3#226semidirect
132. C23C3⋊#226semidirect
164. C3#72998semidirect

Maximal subgroups

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

subgroupindex
C3⋊#59302
C3×#393⋊C32
#729983
#697013
C2×C3⋊SL(2,ℤ/4)4