Finite Group Databasebeta

← #11920959

Subgroups — #11920959

Order 1152.

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

normal subgroups only

This group has 328 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⋊#5931C212yesmaximal, complemented
2C3×#395⋊C3C211yesmaximal, characteristic, complemented
3#73003—33nomaximal
4#69706—31nomaximal
5C3×C22⋊SL(2,𝔽3)C2211yescharacteristic
6C4⋊(C3⋊S4)—41nomaximal
7#5931—36no—
8#5510—31no—
9C3×#395D311yescharacteristic, complemented
10#5227—32no—
11#395⋊C3D313yescomplemented
12#4528—31no—
13#4451—32no—
14C2×C3⋊S4—42no—
15C3×C4×A4—41no—
16C3⋊GL(2,𝔽3)—82no—
17#1604—91noSylow
18C22×C3×Q8C2×D311yescharacteristic
19C2×#235—61no—
20C22⋊SL(2,𝔽3)C2×D313yes—
21C4⋊S4—123no—
22C2×C3×C4⋊C4—31no—
23C2×#215—62no—
24#930—32no—
25#930—61no—
26#897—62no—
27#895—62no—
28C3×#95—31no—
29#835—62no—
30#830—32no—
31C2×C3×A4—41no—
32C3⋊S4—82no—
33C4⋊(C3⋊D3)—161no—
34C3×SL(2,𝔽3)—82no—
35#537—91no—
36#448—92no—
37#395C3⋊D311yescharacteristic, complemented
38#327—92no—
39#324—91no—
40C2×S4—126no—
41C2×C3×Q8—62no—
42C22×C3×C4—31no—
43C22×C3×C4—31no—
44C22×C3×C4S411yescharacteristic
45C2×#67—62no—
46#235—122no—
47#235—122no—
48C2×D12—32no—
49C2×D12—61no—
50C2×D12—61no—
51C2×C4×D3—62no—
52C2×Dic6—61no—
53C4×A4—43no—
54GL(2,𝔽3)—246no—
55C3×C4⋊C4—62no—
56#215—122no—
57#215—122no—
58(C2×D3)⋊C4—62no—
59(C2×D3)⋊C4—62no—
60C4⋊Dic3—32no—
61C4⋊Dic3—61no—
62C2×C3⋊C8—62no—
63C2×C3⋊D3—162no—
64C3×A4—41no—
65C32×C4—161no—
66C2×#41—181no—
67C22×Q8C2×C3⋊D311yescharacteristic
68C2×SD16—182no—
69C22⋊Q8—182no—
70#121—92no—
71#121—182no—
72#121—181no—
73C2×C4⋊C4—31no—
74#103—182no—
75C22⋊C8—92no—
76#95—31no—
77C23×C3C2×S411yescharacteristic
78C22×D3—62no—
79C2×A4—43no—
80S4—246no—
81C3×Q8—22no—
82C3×Q8—62no—
83C2×C3×C4—32no—
84C2×C3×C4—32no—
85C2×C3×C4—61no—
86C2×C3×C4—61no—
87C2×C3×C4—61no—
88C2×C3×C4—121no—
89#67—122no—
90#67—122no—
91C2×Dic3—62no—
92D12—122no—
93D12—122no—
94D12—241no—
95D12—483no—
96C4×D3—124no—
97Dic6—122no—
98SL(2,𝔽3)—86no—
99C3⋊C8—122no—
100C2×C32—161no—
101C3⋊D3—322no—
102#41—362no—
103#41—362no—
104C2×Q8—62no—
105C2×Q8—181no—
106C2×D4—92no—
107C2×D4—181no—
108C2×D4—181no—
109C2×D4—182no—
110C22×C4—31no—
111C22×C4—31no—
112C22×C4—182no—
113C22×C4C3⋊S411yescharacteristic
114SD16—362no—
115SD16—362no—
116C2×C8—182no—
117C4⋊C4—62no—
118C4⋊C4—92no—
119C4⋊C4—181no—
120C22⋊C4—182no—
121C22⋊C4—182no—
122C22×C3—31no—
123C22×C3—31no—
124C22×C3#98611yescharacteristic
125C2×D3—122no—
126C2×D3—122no—
127C2×D3—122no—
128C2×D3—486no—
129A4—43no—
130C3×C4—41no—
131C3×C4—62no—
132C3×C4—62no—
133C3×C4—163no—
134Dic3—122no—
135C32—161noSylow
136C23—182no—
137C23C2×C3⋊S411yescharacteristic
138Q8—22no—
139Q8—62no—
140Q8—362no—
141D4—362no—
142D4—362no—
143D4—362no—
144D4—362no—
145D4—721no—
146C2×C4—32no—
147C2×C4—32no—
148C2×C4—61no—
149C2×C4—61no—
150C2×C4—61no—
151C2×C4—121no—
152C2×C4—182no—
153C2×C4—364no—
154C8—362no—
155C2×C3—31no—
156C2×C3—31no—
157C2×C3—163no—
158C2×C3#1020⋊C211yescharacteristic
159D3—242no—
160D3—966no—
161C22—31no—
162C22—31no—
163C22—362no—
164C22—362no—
165C22—362no—
166C22#6426711yescharacteristic
167C4—41no—
168C4—62no—
169C4—62no—
170C4—362no—
171C3—163no—
172C3#7300311yescharacteristic, complemented
173C2—31no—
174C2—31no—
175C2—722no—
176C2#1059363011yescharacteristic
subgroupG/H
center, hypercenterC2#10593630
commutator, cosocle, hypocenterC3×C22⋊SL(2,𝔽3)C22
FrattiniC23C2×C3⋊S4
FittingC3×#395D3
socleC23×C3C2×S4
LCSG ▷ C3×C22⋊SL(2,𝔽3)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3⋊#5931C2semidirect
2. C3×#395⋊C3C2semidirect
9. C3×#395D3semidirect
11. #395⋊C3D3semidirect
37. #395C3⋊D3semidirect
172. C3#73003semidirect

Maximal subgroups

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

subgroupindex
C3⋊#59312
C3×#395⋊C32
#730033
#697063
C4⋊(C3⋊S4)4