Finite Group Databasebeta

← #11920961

Subgroups — #11920961

Order 1152.

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

normal subgroups only

This group has 382 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, complemented
2C3⋊#4622C212yesmaximal, complemented
3#73005—33nomaximal
4#69714—31nomaximal
5C22×C3⋊S4—41nomaximal
6C3×#95⋊C3C2211yescharacteristic, complemented
7#5493—31no—
8C3×#399D311yescharacteristic, complemented
9#4968—32no—
10#399⋊C3D313yescomplemented
11#4622—36no—
12#4525—31no—
13#4451—32no—
14C22×C3×A4—41no—
15C2×C3⋊S4—42no—
16C2×C3⋊S4—44no—
17#1613—91noSylow
18C22×S4—123no—
19C22×#67—61no—
20C2×C3×C4⋊C4—31no—
21C2×C3×C22⋊C4—31no—
22#930—32no—
23#930—61no—
24#886—62no—
25#882—62no—
26C3×#95C2×D311yescharacteristic, complemented
27#830—32no—
28#809—62no—
29#808—62no—
30#95⋊C3C2×D313yescomplemented
31C22×C3⋊D3—161no—
32C2×C3×A4—42no—
33C2×C3×A4—41no—
34C3⋊S4—44no—
35#534—91no—
36#481—92no—
37#399C3⋊D311yescharacteristic, complemented
38#327—92no—
39#323—91no—
40C24×C3S411yescharacteristic
41C23×D3—61no—
42C22×A4—43no—
43C2×S4—126no—
44C2×S4—1212no—
45C22×C3×C4—31no—
46C22×C3×C4—31no—
47C2×#67—62no—
48C2×#67—62no—
49C2×#67—122no—
50C2×#67—122no—
51C22×Dic3—61no—
52C2×D12—32no—
53C2×D12—61no—
54C3×C4⋊C4—62no—
55C3×C22⋊C4—62no—
56(C2×D3)⋊C4—62no—
57(C2×D3)⋊C4—62no—
58C4⋊Dic3—32no—
59C4⋊Dic3—61no—
60C2×C3⋊C8—62no—
61C22×C32—161no—
62C2×C3⋊D3—162no—
63C2×C3⋊D3—164no—
64C3×A4—41no—
65C22×D4—181no—
66#123—182no—
67#121—92no—
68#121—181no—
69#120—182no—
70C2×C4⋊C4—31no—
71C2×C22⋊C4—31no—
72#106—182no—
73#102—182no—
74C22⋊C8—92no—
75#95C2×C3⋊D311yescharacteristic, complemented
76C23×C3—61no—
77C23×C3—61no—
78C23×C3GL(2,𝔽3)12yes—
79C23×C3C2×S411yescharacteristic
80C22×D3—62no—
81C22×D3—122no—
82C22×D3—241no—
83C22×D3—241no—
84C22×D3—483no—
85C2×A4—43no—
86C2×A4—46no—
87S4—1212no—
88C2×C3×C4—32no—
89C2×C3×C4—61no—
90C2×C3×C4—121no—
91C2×C3×C4—121no—
92#67—122no—
93#67—124no—
94#67—122no—
95C2×Dic3—62no—
96C2×Dic3—122no—
97D12—122no—
98D12—241no—
99C3⋊C8—122no—
100C2×C32—162no—
101C2×C32—161no—
102C3⋊D3—164no—
103C24—181no—
104C24C3⋊S411yescharacteristic
105C2×D4—92no—
106C2×D4—181no—
107C2×D4—182no—
108C2×D4—182no—
109C2×D4—362no—
110C2×D4—362no—
111C22×C4—31no—
112C22×C4—31no—
113C22×C4—181no—
114C2×C8—182no—
115C4⋊C4—62no—
116C4⋊C4—92no—
117C4⋊C4—181no—
118C22⋊C4—62no—
119C22⋊C4—182no—
120C22⋊C4—182no—
121C22×C3—31no—
122C22×C3—31no—
123C22×C3—41no—
124C22×C3—62no—
125C22×C3—121no—
126C22×C3—163no—
127C22×C3C2×GL(2,𝔽3)11yescharacteristic
128C2×D3—122no—
129C2×D3—122no—
130C2×D3—122no—
131C2×D3—244no—
132C2×D3—486no—
133C2×D3—4812no—
134A4—43no—
135C3×C4—62no—
136C3×C4—121no—
137Dic3—122no—
138C32—161noSylow
139C23—61no—
140C23—61no—
141C23—182no—
142C23—362no—
143C23—721no—
144C23—721no—
145C23C3⋊GL(2,𝔽3)12yes—
146C23C2×C3⋊S411yescharacteristic
147D4—362no—
148D4—362no—
149D4—364no—
150D4—362no—
151D4—721no—
152C2×C4—32no—
153C2×C4—61no—
154C2×C4—121no—
155C2×C4—121no—
156C2×C4—182no—
157C2×C4—362no—
158C8—362no—
159C2×C3—31no—
160C2×C3—31no—
161C2×C3—42no—
162C2×C3—166no—
163C2×C3—163no—
164C2×C3#857⋊C211yescharacteristic
165D3—242no—
166D3—4812no—
167C22—31no—
168C22—31no—
169C22—41no—
170C22—62no—
171C22—121no—
172C22—362no—
173C22—362no—
174C22—362no—
175C22—724no—
176C22C2×C3⋊GL(2,𝔽3)11yescharacteristic
177C4—62no—
178C4—121no—
179C4—362no—
180C3—163no—
181C3#7300511yescharacteristic, complemented
182C2—31no—
183C2—31no—
184C2—42no—
185C2—722no—
186C2#1059363111yescharacteristic
subgroupG/H
center, hypercenterC2#10593631
commutator, cosocle, hypocenterC3×#95⋊C3C22
FrattiniC23C2×C3⋊S4
FittingC3×#399D3
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×#399⋊C3C2semidirect
2. C3⋊#4622C2semidirect
6. C3×#95⋊C3C22semidirect
8. C3×#399D3semidirect
10. #399⋊C3D3semidirect
26. C3×#95C2×D3semidirect
30. #95⋊C3C2×D3semidirect
37. #399C3⋊D3semidirect
75. #95C2×C3⋊D3semidirect
181. C3#73005semidirect

Maximal subgroups

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

subgroupindex
C3×#399⋊C32
C3⋊#46222
#730053
#697143
C22×C3⋊S44