Finite Group Databasebeta

← #11920942

Subgroups — #11920942

Order 1152.

242 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 27 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×#376⋊C3C211yesmaximal, characteristic
2C3⋊#4621C212yesmaximal
3#72986—33nomaximal
4#69433—31nomaximal
5#64259—41nomaximal
6C3×#95⋊C3C2211yescharacteristic
7#5470—31no—
8C3×#376D311yescharacteristic
9#4926—31no—
10#376⋊C3D313yes—
11#4621—36no—
12#4452—32no—
13#4452—32no—
14C3×C4×A4—41no—
15C3⋊SL(2,ℤ/4)—42no—
16#1506—91noSylow
17A4⋊Q8—123no—
18C2×C3×C42—31no—
19#926—61no—
20#924—32no—
21#924—61no—
22#870—61no—
23#869—31no—
24#869—31no—
25C4×Dic6—32no—
26C4×Dic6—61no—
27C3×#95—31no—
28C3×#95C2×D311yescharacteristic
29#830—32no—
30C4⋊(C3⋊C8)—61no—
31#803—61no—
32#95⋊C3C2×D313yes—
33C2×C3×A4—41no—
34#634—161no—
35#533—91no—
36#432—91no—
37#376C3⋊D311yescharacteristic
38#328—92no—
39#328—92no—
40C22×C3×C4—31no—
41C22×C3×C4—31no—
42C22×C3×C4S411yescharacteristic
43C2×Dic6—32no—
44C2×Dic6—61no—
45C4×A4—43no—
46SL(2,ℤ/4)—126no—
47C3×C42—31no—
48C3×C42—31no—
49C3×C42—31no—
50C3×C42—31no—
51#217—62no—
52C4⋊Dic3—32no—
53C4⋊Dic3—61no—
54C4⋊Dic3—61no—
55C4⋊Dic3—61no—
56Dic3⋊C4—62no—
57Dic3⋊C4—62no—
58C4×Dic3—62no—
59C2×C3⋊C8—62no—
60C3×A4—41no—
61C32×C4—161no—
62C3⋊Dic3—162no—
63C4⋊Q8—91no—
64C4⋊Q8—91no—
65#125—181no—
66C22⋊Q8—92no—
67C22⋊Q8—181no—
68C4×Q8—92no—
69C4×Q8—181no—
70#117—181no—
71C2×C42—31no—
72C4⋊C8—181no—
73C22⋊C8—92no—
74#97—181no—
75#95—31no—
76#95C2×C3⋊D311yescharacteristic
77C23×C3C2×S411yescharacteristic
78C2×A4—43no—
79C2×C3×C4—31no—
80C2×C3×C4—31no—
81C2×C3×C4—31no—
82C2×C3×C4—31no—
83C2×C3×C4—31no—
84C2×C3×C4—31no—
85C2×C3×C4—61no—
86C2×C3×C4—61no—
87C2×C3×C4—121no—
88C2×Dic3—62no—
89C2×Dic3—62no—
90Dic6—121no—
91Dic6—121no—
92Dic6—122no—
93Dic6—483no—
94C3⋊C8—122no—
95C2×C32—161no—
96C2×Q8—92no—
97C2×Q8—181no—
98C22×C4—31no—
99C22×C4—31no—
100C22×C4C3⋊S411yescharacteristic
101C2×C8—182no—
102C4⋊C4—92no—
103C4⋊C4—181no—
104C4⋊C4—181no—
105C4⋊C4—182no—
106C4⋊C4—182no—
107C4⋊C4—181no—
108C22⋊C4—182no—
109C42—31no—
110C42—31no—
111C42—31no—
112C42—31no—
113C42—182no—
114C22×C3—31no—
115C22×C3—31no—
116C22×C3#98411yescharacteristic
117A4—43no—
118C3×C4—31no—
119C3×C4—61no—
120C3×C4—61no—
121C3×C4—61no—
122C3×C4—61no—
123C3×C4—163no—
124C3×C4#85711yescharacteristic
125Dic3—122no—
126Dic3—122no—
127Dic3—486no—
128C32—161noSylow
129C23C2×C3⋊S411yescharacteristic
130Q8—361no—
131Q8—362no—
132Q8—361no—
133C2×C4—31no—
134C2×C4—31no—
135C2×C4—31no—
136C2×C4—31no—
137C2×C4—31no—
138C2×C4—31no—
139C2×C4—61no—
140C2×C4—61no—
141C2×C4—121no—
142C2×C4—182no—
143C2×C4—182no—
144C8—362no—
145C2×C3—31no—
146C2×C3—31no—
147C2×C3—163no—
148C2×C3C2×#85711yescharacteristic
149C22—31no—
150C22—31no—
151C22#6426511yescharacteristic
152C4—31no—
153C4—61no—
154C4—61no—
155C4—61no—
156C4—61no—
157C4—362no—
158C4—362no—
159C4C3⋊#85711yescharacteristic
160C3—163no—
161C3#7298611yescharacteristic, complemented
162C2—31no—
163C2—31no—
164C2C2×C3⋊#85711yescharacteristic
subgroupG/H
centerC2C2×C3⋊#857
commutator, prime radical, cosocle, hypocenterC3×#95⋊C3C22
FrattiniC23C2×C3⋊S4
FittingC3×#376D3
socleC23×C3C2×S4
hypercenterC4C3⋊#857
LCSG ▷ C3×#95⋊C3
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
161. C3#72986semidirect

Maximal subgroups

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

subgroupindex
C3×#376⋊C32
C3⋊#46212
#729863
#694333
#642594