Finite Group Databasebeta

← #78094⋊C3 #11921193

Subgroups — #78094⋊C3 #11921193

Order 1152.

206 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 31 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⋊(#401⋊C3)C212yesmaximal, complemented
3#78094C311yesmaximal, characteristic, complemented
4#2834⋊C3—31nomaximal
5C2×Dic3×A4—41nomaximal
6C3×#95⋊C3C2211yescharacteristic
7C3×#399C2×C311yescharacteristic
8#4982—32no—
9#4953—31no—
10#4946—31no—
11C3⋊#401C2×C312yescomplemented
12#401⋊C3—32no—
13#399⋊C3—21no—
14#399⋊C3D311yescharacteristic
15C22×C3×A4—41no—
16Dic3×A4—42no—
17#2834—31noSylow
18C23×Dic3A411yescharacteristic
19C2×C4×A4—121no—
20C2×C3×C4⋊C4—31no—
21C2×C3×C22⋊C4—31no—
22C2×#217—31no—
23C2×C4⋊Dic3—31no—
24C2×Dic3⋊C4—32no—
25C3×#95C22×C311yescharacteristic
26C3⋊#95—31no—
27C3⋊#95—32no—
28C3⋊#95—32no—
29#95⋊C3—21no—
30#95⋊C3C2×D311yescharacteristic
31C2×C3×A4—42no—
32C2×C3×A4—41no—
33C2×C3×Dic3—161no—
34#401—32no—
35#399C3×D311yescharacteristic
36#398—92no—
37#397—91no—
38#385—91no—
39C24×C3C2×A411yescharacteristic
40C22×A4—41no—
41C22×A4—81no—
42C22×C3×C4—31no—
43C22×C3×C4—31no—
44C22×Dic3—32no—
45C22×Dic3—121no—
46C22×Dic3C2×A412yes—
47C4×A4—122no—
48C3×C4⋊C4—121no—
49C3×C22⋊C4—121no—
50#217—62no—
51C4⋊Dic3—121no—
52Dic3⋊C4—122no—
53C22×C32—161no—
54C3×A4—41no—
55C3×Dic3—162no—
56C23×C4—31no—
57C2×C4⋊C4—31no—
58C2×C4⋊C4—92no—
59C2×C4⋊C4—91no—
60C2×C22⋊C4—31no—
61C2×C22⋊C4—91no—
62#95—92no—
63#95—92no—
64#95—91no—
65#95C2×C3×D311yescharacteristic
66C23×C3—61no—
67C23×C3—61no—
68C23×C3#41⋊C312yes—
69C23×C3C22×A411yescharacteristic
70C2×A4—41no—
71C2×A4—42no—
72C2×A4—81no—
73C2×A4—82no—
74C2×C3×C4—62no—
75C2×C3×C4—61no—
76C2×C3×C4—61no—
77C2×C3×C4—62no—
78C2×C3×C4—481no—
79C2×Dic3—41no—
80C2×Dic3—62no—
81C2×Dic3—62no—
82C2×Dic3—62no—
83C2×Dic3—62no—
84C2×Dic3—121no—
85C2×C32—162no—
86C2×C32—161no—
87C24D3×A411yescharacteristic
88C22×C4—31no—
89C22×C4—31no—
90C22×C4—32no—
91C22×C4—92no—
92C22×C4—361no—
93C4⋊C4—121no—
94C4⋊C4—362no—
95C4⋊C4—361no—
96C22⋊C4—121no—
97C22⋊C4—182no—
98C22×C3—31no—
99C22×C3—31no—
100C22×C3—41no—
101C22×C3—62no—
102C22×C3—121no—
103C22×C3—161no—
104C22×C3—321no—
105C22×C3C2×#41⋊C311yescharacteristic
106A4—41no—
107A4—81no—
108C3×C4—121no—
109C3×C4—121no—
110C3×C4—482no—
111Dic3—42no—
112Dic3—122no—
113C32—161noSylow
114C23—61no—
115C23—61no—
116C23C3⋊(#41⋊C3)12yes—
117C23C2×D3×A411yescharacteristic
118C2×C4—61no—
119C2×C4—61no—
120C2×C4—62no—
121C2×C4—62no—
122C2×C4—121no—
123C2×C4—182no—
124C2×C4—182no—
125C2×C4—182no—
126C2×C4—182no—
127C2×C4—361no—
128C2×C3—31no—
129C2×C3—31no—
130C2×C3—42no—
131C2×C3—162no—
132C2×C3—161no—
133C2×C3—322no—
134C2×C3—321no—
135C2×C3#560⋊C311yescharacteristic
136C22—31no—
137C22—31no—
138C22—41no—
139C22—62no—
140C22—121no—
141C22C2×C3⋊(#41⋊C3)11yescharacteristic
142C4—121no—
143C4—121no—
144C4—122no—
145C4—362no—
146C3—161no—
147C3—321no—
148C3#2834⋊C311yescharacteristic, complemented
149C2—31no—
150C2—31no—
151C2—42no—
152C2#5720⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2#5720⋊C3
commutator, cosocle, hypocenterC3×#95C22×C3
FrattiniC23C2×D3×A4
FittingC3×#399C2×C3
socleC23×C3C22×A4
prime radicalC3×#399⋊C3C2
LCSG ▷ C3×#95
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊(#401⋊C3)C2semidirect
3. #78094C3semidirect
11. C3⋊#401C2×C3semidirect
148. C3#2834⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#399⋊C32
C3⋊(#401⋊C3)2
#780943
#2834⋊C33
C2×Dic3×A44