Finite Group Databasebeta

← #11920953

Subgroups — #11920953

Order 1152.

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

normal subgroups only

This group has 350 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, complemented
2C3⋊#4622C212yesmaximal, complemented
3#72997—33nomaximal
4#69696—31nomaximal
5C4⋊(C3⋊S4)—41nomaximal
6C3×#95⋊C3C2211yescharacteristic, complemented
7#5493—31no—
8C3×#392D311yescharacteristic, complemented
9#5217—32no—
10#392⋊C3D313yescomplemented
11#4622—36no—
12#4525—31no—
13#4451—32no—
14C2×C3⋊S4—42no—
15C3×C4×A4—41no—
16#1595—91noSylow
17C22×C3×D4—31no—
18C22×#67—61no—
19C4⋊S4—123no—
20C2×C3×C22⋊C4—31no—
21C2×#213—62no—
22#930—32no—
23#930—61no—
24#886—62no—
25#882—62no—
26C3×#95C2×D311yescharacteristic
27#832—62no—
28#830—32no—
29#95⋊C3C2×D313yescomplemented
30C2×C3×A4—41no—
31C3⋊S4—82no—
32C4⋊(C3⋊D3)—161no—
33#534—91no—
34#447—92no—
35#392C3⋊D311yescharacteristic, complemented
36#327—92no—
37#323—91no—
38C24×C3—31no—
39C23×D3—61no—
40C2×S4—126no—
41C2×C3×D4—62no—
42C2×C3×D4—122no—
43C22×C3×C4—31no—
44C22×C3×C4S411yescharacteristic
45C2×#67—62no—
46C2×#67—62no—
47C2×#67—122no—
48C2×#67—122no—
49C22×Dic3—61no—
50C2×D12—32no—
51C2×D12—61no—
52C4×A4—43no—
53C3×C22⋊C4—62no—
54#213—124no—
55(C2×D3)⋊C4—62no—
56(C2×D3)⋊C4—62no—
57C4⋊Dic3—32no—
58C4⋊Dic3—61no—
59C2×C3⋊C8—62no—
60C2×C3⋊D3—162no—
61C3×A4—41no—
62C32×C4—161no—
63C22×D4—31no—
64C22×D4—181no—
65C2×D8—182no—
66#123—182no—
67#121—92no—
68#121—181no—
69#120—182no—
70C2×C22⋊C4—31no—
71#102—182no—
72C22⋊C8—92no—
73#95C2×C3⋊D311yescharacteristic
74C23×C3—32no—
75C23×C3—61no—
76C23×C3—61no—
77C23×C3—121no—
78C23×C3—121no—
79C23×C3C2×S411yescharacteristic
80C22×D3—62no—
81C22×D3—122no—
82C22×D3—241no—
83C22×D3—241no—
84C2×A4—43no—
85S4—246no—
86C3×D4—64no—
87C3×D4—122no—
88C2×C3×C4—32no—
89C2×C3×C4—61no—
90C2×C3×C4—121no—
91#67—122no—
92#67—124no—
93#67—122no—
94C2×Dic3—62no—
95C2×Dic3—122no—
96D12—122no—
97D12—241no—
98D12—483no—
99C3⋊C8—122no—
100C2×C32—161no—
101C3⋊D3—322no—
102C24—31no—
103C24—181no—
104C2×D4—62no—
105C2×D4—92no—
106C2×D4—122no—
107C2×D4—181no—
108C2×D4—182no—
109C2×D4—182no—
110C2×D4—362no—
111C2×D4—362no—
112C22×C4—31no—
113C22×C4—181no—
114C22×C4C3⋊S411yescharacteristic
115D8—364no—
116C2×C8—182no—
117C4⋊C4—92no—
118C4⋊C4—181no—
119C22⋊C4—62no—
120C22⋊C4—182no—
121C22⋊C4—182no—
122C22×C3—31no—
123C22×C3—31no—
124C22×C3—62no—
125C22×C3—122no—
126C22×C3—121no—
127C22×C3—121no—
128C22×C3—241no—
129C22×C3#98611yescharacteristic
130C2×D3—122no—
131C2×D3—122no—
132C2×D3—122no—
133C2×D3—244no—
134C2×D3—486no—
135A4—43no—
136C3×C4—41no—
137C3×C4—62no—
138C3×C4—163no—
139Dic3—122no—
140C32—161noSylow
141C23—32no—
142C23—61no—
143C23—61no—
144C23—121no—
145C23—121no—
146C23—182no—
147C23—362no—
148C23—721no—
149C23—721no—
150C23C2×C3⋊S411yescharacteristic
151D4—64no—
152D4—122no—
153D4—362no—
154D4—362no—
155D4—364no—
156D4—362no—
157D4—721no—
158C2×C4—32no—
159C2×C4—61no—
160C2×C4—121no—
161C2×C4—182no—
162C2×C4—362no—
163C8—362no—
164C2×C3—31no—
165C2×C3—31no—
166C2×C3—122no—
167C2×C3—163no—
168C2×C3#857⋊C211yescharacteristic
169D3—242no—
170D3—966no—
171C22—31no—
172C22—31no—
173C22—62no—
174C22—122no—
175C22—121no—
176C22—121no—
177C22—241no—
178C22—362no—
179C22—362no—
180C22—362no—
181C22—724no—
182C22#6426711yescharacteristic
183C4—41no—
184C4—62no—
185C4—362no—
186C3—163no—
187C3#7299711yescharacteristic, complemented
188C2—31no—
189C2—31no—
190C2—122no—
191C2—722no—
192C2#1059363111yescharacteristic
subgroupG/H
center, hypercenterC2#10593631
commutator, cosocle, hypocenterC3×#95⋊C3C22
FrattiniC23C2×C3⋊S4
FittingC3×#392D3
socleC23×C3C2×S4
LCSG ▷ C3×#95⋊C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3×#392⋊C3C2semidirect
2. C3⋊#4622C2semidirect
6. C3×#95⋊C3C22semidirect
8. C3×#392D3semidirect
10. #392⋊C3D3semidirect
29. #95⋊C3C2×D3semidirect
35. #392C3⋊D3semidirect
187. C3#72997semidirect

Maximal subgroups

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

subgroupindex
C3×#392⋊C32
C3⋊#46222
#729973
#696963
C4⋊(C3⋊S4)4