Finite Group Databasebeta

← #11920960

Subgroups — #11920960

Order 1152.

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

normal subgroups only

This group has 266 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×#399⋊C3C211yesmaximal, characteristic
2C3⋊#4621C212yesmaximal, complemented
3#73004—33nomaximal
4#69716—31nomaximal
5C2×C3⋊SL(2,ℤ/4)—41nomaximal
6C3×#95⋊C3C2211yescharacteristic
7#5483—31no—
8C3×#399D311yescharacteristic
9#4970—32no—
10#399⋊C3D313yes—
11#4621—36no—
12#4525—31no—
13#4452—32no—
14C22×C3×A4—41no—
15C3⋊SL(2,ℤ/4)—42no—
16#1614—91noSylow
17C2×SL(2,ℤ/4)—123no—
18C2×C3×C4⋊C4—31no—
19C2×C3×C22⋊C4—31no—
20C2×#217—61no—
21#924—32no—
22#924—61no—
23#878—62no—
24#878—62no—
25C3×#95C2×D311yescharacteristic
26#830—32no—
27#810—62no—
28#807—62no—
29#95⋊C3C2×D313yes—
30C2×C3×A4—42no—
31C2×C3×A4—41no—
32C2×C3⋊Dic3—161no—
33#543—91no—
34#484—92no—
35#399C3⋊D311yescharacteristic
36#328—92no—
37#323—91no—
38C24×C3S411yescharacteristic
39C22×A4—43no—
40C22×C3×C4—31no—
41C22×C3×C4—31no—
42C22×Dic3—61no—
43C22×Dic3—61no—
44C2×Dic6—32no—
45C2×Dic6—61no—
46SL(2,ℤ/4)—126no—
47C3×C4⋊C4—62no—
48C3×C22⋊C4—62no—
49#217—62no—
50#217—62no—
51C4⋊Dic3—32no—
52C4⋊Dic3—61no—
53Dic3⋊C4—62no—
54Dic3⋊C4—62no—
55C2×C3⋊C8—62no—
56C22×C32—161no—
57C3×A4—41no—
58C3⋊Dic3—162no—
59C22⋊Q8—92no—
60C22⋊Q8—182no—
61C22⋊Q8—182no—
62C22⋊Q8—181no—
63C2×C4⋊C4—31no—
64C2×C22⋊C4—31no—
65C2×C22⋊C4—181no—
66#107—182no—
67#103—182no—
68C22⋊C8—92no—
69#95C2×C3⋊D311yescharacteristic
70C23×C3—61no—
71C23×C3—61no—
72C23×C3#22612yes—
73C23×C3C2×S411yescharacteristic
74C2×A4—43no—
75C2×A4—46no—
76C2×C3×C4—32no—
77C2×C3×C4—61no—
78C2×C3×C4—121no—
79C2×C3×C4—121no—
80C2×Dic3—62no—
81C2×Dic3—62no—
82C2×Dic3—241no—
83C2×Dic3—241no—
84C2×Dic3—483no—
85Dic6—122no—
86Dic6—241no—
87C3⋊C8—122no—
88C2×C32—162no—
89C2×C32—161no—
90C24C3⋊S411yescharacteristic
91C2×Q8—92no—
92C2×Q8—181no—
93C22×C4—31no—
94C22×C4—31no—
95C22×C4—181no—
96C22×C4—181no—
97C2×C8—182no—
98C4⋊C4—62no—
99C4⋊C4—92no—
100C4⋊C4—182no—
101C4⋊C4—182no—
102C4⋊C4—181no—
103C22⋊C4—62no—
104C22⋊C4—182no—
105C22⋊C4—182no—
106C22×C3—31no—
107C22×C3—31no—
108C22×C3—41no—
109C22×C3—62no—
110C22×C3—121no—
111C22×C3—163no—
112C22×C3C2×#22611yescharacteristic
113A4—43no—
114C3×C4—62no—
115C3×C4—121no—
116Dic3—122no—
117Dic3—122no—
118Dic3—486no—
119C32—161noSylow
120C23—61no—
121C23—61no—
122C23C3⋊#22612yes—
123C23C2×C3⋊S411yescharacteristic
124Q8—362no—
125Q8—721no—
126C2×C4—32no—
127C2×C4—61no—
128C2×C4—121no—
129C2×C4—121no—
130C2×C4—182no—
131C2×C4—182no—
132C2×C4—721no—
133C2×C4—721no—
134C8—362no—
135C2×C3—31no—
136C2×C3—31no—
137C2×C3—42no—
138C2×C3—166no—
139C2×C3—163no—
140C2×C3#857⋊C211yescharacteristic
141C22—31no—
142C22—31no—
143C22—41no—
144C22—62no—
145C22—121no—
146C22C2×C3⋊#22611yescharacteristic
147C4—62no—
148C4—121no—
149C4—362no—
150C4—362no—
151C3—163no—
152C3#7300411yescharacteristic, complemented
153C2—31no—
154C2—31no—
155C2—42no—
156C2#1059363111yescharacteristic
subgroupG/H
center, hypercenterC2#10593631
commutator, cosocle, hypocenterC3×#95⋊C3C22
FrattiniC23C2×C3⋊S4
FittingC3×#399D3
socleC23×C3C2×S4
prime radicalC3×#399⋊C3C2
LCSG ▷ C3×#95⋊C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊#4621C2semidirect
152. C3#73004semidirect

Maximal subgroups

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

subgroupindex
C3×#399⋊C32
C3⋊#46212
#730043
#697163
C2×C3⋊SL(2,ℤ/4)4