Finite Group Databasebeta

← #11920951

Subgroups — #11920951

Order 1152.

282 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 25 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×#392⋊C3C211yesmaximal, characteristic
2C3⋊#4621C212yesmaximal, complemented
3#72995—33nomaximal
4#69698—31nomaximal
5#64259—41nomaximal
6C3×#95⋊C3C2211yescharacteristic
7#5483—31no—
8C3×#392D311yescharacteristic
9#5218—32no—
10#392⋊C3D313yes—
11#4621—36no—
12#4525—31no—
13#4452—32no—
14C3×C4×A4—41no—
15C3⋊SL(2,ℤ/4)—42no—
16#1596—91noSylow
17C22×C3×D4—31no—
18A4⋊Q8—123no—
19C2×C3×C22⋊C4—31no—
20C2×#217—61no—
21C2×#214—62no—
22#924—32no—
23#924—61no—
24#878—62no—
25#878—62no—
26C3×#95C2×D311yescharacteristic
27#832—62no—
28#830—32no—
29#95⋊C3C2×D313yes—
30C2×C3×A4—41no—
31#634—161no—
32#543—91no—
33#450—92no—
34#392C3⋊D311yescharacteristic
35#328—92no—
36#323—91no—
37C24×C3—31no—
38C2×C3×D4—62no—
39C2×C3×D4—122no—
40C22×C3×C4—31no—
41C22×C3×C4S411yescharacteristic
42C22×Dic3—61no—
43C22×Dic3—61no—
44C2×Dic6—32no—
45C2×Dic6—61no—
46C4×A4—43no—
47SL(2,ℤ/4)—126no—
48C3×C22⋊C4—62no—
49#217—62no—
50#217—62no—
51#214—124no—
52C4⋊Dic3—32no—
53C4⋊Dic3—61no—
54Dic3⋊C4—62no—
55Dic3⋊C4—62no—
56C2×C3⋊C8—62no—
57C3×A4—41no—
58C32×C4—161no—
59C3⋊Dic3—162no—
60C22×D4—31no—
61C2×SD16—182no—
62C22⋊Q8—92no—
63C22⋊Q8—182no—
64C22⋊Q8—182no—
65C22⋊Q8—181no—
66C2×C22⋊C4—31no—
67C2×C22⋊C4—181no—
68#102—182no—
69C22⋊C8—92no—
70#95C2×C3⋊D311yescharacteristic
71C23×C3—32no—
72C23×C3—61no—
73C23×C3—61no—
74C23×C3—121no—
75C23×C3—121no—
76C23×C3C2×S411yescharacteristic
77C2×A4—43no—
78C3×D4—64no—
79C3×D4—122no—
80C2×C3×C4—32no—
81C2×C3×C4—61no—
82C2×C3×C4—121no—
83C2×Dic3—62no—
84C2×Dic3—62no—
85C2×Dic3—241no—
86C2×Dic3—241no—
87Dic6—122no—
88Dic6—241no—
89Dic6—483no—
90C3⋊C8—122no—
91C2×C32—161no—
92C24—31no—
93C2×Q8—92no—
94C2×Q8—181no—
95C2×D4—62no—
96C2×D4—122no—
97C22×C4—31no—
98C22×C4—181no—
99C22×C4—181no—
100C22×C4C3⋊S411yescharacteristic
101SD16—364no—
102C2×C8—182no—
103C4⋊C4—92no—
104C4⋊C4—182no—
105C4⋊C4—182no—
106C4⋊C4—181no—
107C22⋊C4—62no—
108C22⋊C4—182no—
109C22⋊C4—182no—
110C22×C3—31no—
111C22×C3—31no—
112C22×C3—62no—
113C22×C3—122no—
114C22×C3—121no—
115C22×C3—121no—
116C22×C3—241no—
117C22×C3#98411yescharacteristic
118A4—43no—
119C3×C4—41no—
120C3×C4—62no—
121C3×C4—163no—
122Dic3—122no—
123Dic3—122no—
124Dic3—486no—
125C32—161noSylow
126C23—32no—
127C23—61no—
128C23—61no—
129C23—121no—
130C23—121no—
131C23C2×C3⋊S411yescharacteristic
132Q8—362no—
133Q8—721no—
134D4—64no—
135D4—122no—
136C2×C4—32no—
137C2×C4—61no—
138C2×C4—121no—
139C2×C4—182no—
140C2×C4—182no—
141C2×C4—721no—
142C2×C4—721no—
143C8—362no—
144C2×C3—31no—
145C2×C3—31no—
146C2×C3—122no—
147C2×C3—163no—
148C2×C3#857⋊C211yescharacteristic
149C22—31no—
150C22—31no—
151C22—62no—
152C22—122no—
153C22—121no—
154C22—121no—
155C22—241no—
156C22#6426511yescharacteristic
157C4—41no—
158C4—62no—
159C4—362no—
160C4—362no—
161C3—163no—
162C3#7299511yescharacteristic, complemented
163C2—31no—
164C2—31no—
165C2—122no—
166C2#1059363111yescharacteristic
subgroupG/H
center, hypercenterC2#10593631
commutator, cosocle, hypocenterC3×#95⋊C3C22
FrattiniC23C2×C3⋊S4
FittingC3×#392D3
socleC23×C3C2×S4
prime radicalC3×#392⋊C3C2
LCSG ▷ C3×#95⋊C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊#4621C2semidirect
162. C3#72995semidirect

Maximal subgroups

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

subgroupindex
C3×#392⋊C32
C3⋊#46212
#729953
#696983
#642594