Finite Group Databasebeta

← #11771214

Subgroups — #11771214

Order 1152.

230 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 48 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
1#10596484C211yesmaximal, characteristic
2#10593539C211yesmaximal, characteristic
3C4×#3773C211yesmaximal, characteristic
4C2×C4×#157C2211yescharacteristic
5#64283—21no—
6C2×#3773—21no—
7C22⋊AGL(1,𝔽9)—21no—
8C4⋊AGL(1,𝔽9)C412yescomplemented
9C4×AGL(1,𝔽9)—21no—
10C4×#624—21no—
11#63744—21no—
12#63744C412yescomplemented
13#63737C412yes—
14C22×#157C2×C411yescharacteristic
15C22×#157D411yescharacteristic
16C2×AGL(1,𝔽9)—22no—
17C2×C4×C3⋊D3D411yescharacteristic
18C2×#624—22no—
19#3792—41no—
20C4×#157C2×C411yescharacteristic
21C4×#157C2×C411yescharacteristic
22C4×#157D411yescharacteristic
23C4×#157Q811yescharacteristic
24#3788—41no—
25#3787—22no—
26#3773—24no—
27C3×C4×Dic3—41no—
28Dic32—41no—
29#1303—91nomaximal, Sylow
30C42×D3—121no—
31C22×C3⋊D3C22⋊C411yescharacteristic
32C2×#157—22no—
33C2×#157—41no—
34C2×#157C4211yescharacteristic
35C2×#157C22⋊C411yescharacteristic
36C2×#157C4⋊C411yescharacteristic
37C2×#157C4⋊C411yescharacteristic
38AGL(1,𝔽9)—42no—
39C2×C32×C4SD1611yescharacteristic
40C2×C3⋊Dic3D811yescharacteristic
41C4×C3⋊D3C22⋊C411yescharacteristic
42C4×C3⋊D3C4⋊C411yescharacteristic
43C4×C3⋊D3SD1611yescharacteristic
44C4×C3⋊D3Q1611yescharacteristic
45C2×C3×Dic3—42no—
46#624—24no—
47#624—42no—
48#622—42no—
49#431—91no—
50#423—91no—
51C4×C4⋊C4—91no—
52C2×C4×D3—121no—
53C2×C4×D3—122no—
54C3×C42—121no—
55C4×Dic3—41no—
56C4×Dic3—122no—
57C22×C32#10211yescharacteristic
58C2×C3⋊D3—21no—
59C2×C3⋊D3—21no—
60C2×C3⋊D3#9511yescharacteristic
61C2×C3⋊D3#10311yescharacteristic
62#157—21no—
63#157—21no—
64#157—21no—
65#157#10412yes—
66C32×C4#10311yescharacteristic
67C32×C4#10611yescharacteristic
68C3⋊Dic3#10211yescharacteristic
69C3⋊Dic3#10711yescharacteristic
70C3×Dic3—44no—
71C2×M16—181no—
72C2×C4⋊C4—181no—
73C2×C42—91no—
74C2×C42—181no—
75C4⋊C8—92no—
76C4⋊C8—92no—
77C4⋊C8—181no—
78C22⋊C8—181no—
79C4×C8—181no—
80#95—92no—
81C22×D3—121no—
82C2×C3×C4—41no—
83C2×C3×C4—122no—
84C2×Dic3—42no—
85C2×Dic3—121no—
86C4×D3—121no—
87C4×D3—121no—
88C4×D3—121no—
89C4×D3—121no—
90C4×D3—124no—
91C4×D3—124no—
92C2×C32—21no—
93C2×C32#34011yescharacteristic
94C3⋊D3—21no—
95C3⋊D3#33911yescharacteristic
96C3⋊D3#34411yescharacteristic
97C22×C4—91no—
98C22×C4—91no—
99C22×C4—91no—
100C22×C4—182no—
101M16—361no—
102M16—361no—
103C2×C8—182no—
104C2×C8—182no—
105C4⋊C4—184no—
106C42—91no—
107C42—91no—
108C42—91no—
109C42—91no—
110C42—121no—
111C42—361no—
112C22×C3—41no—
113C2×D3—121no—
114C2×D3—121no—
115C2×D3—122no—
116C2×D3—122no—
117C3×C4—41no—
118C3×C4—41no—
119C3×C4—124no—
120Dic3—44no—
121Dic3—121no—
122Dic3—121no—
123C32#130311yescharacteristic, complemented, Sylow
124C23—91no—
125C2×C4—91no—
126C2×C4—91no—
127C2×C4—91no—
128C2×C4—91no—
129C2×C4—91no—
130C2×C4—91no—
131C2×C4—91no—
132C2×C4—91no—
133C2×C4—91no—
134C2×C4—122no—
135C2×C4—182no—
136C2×C4—184no—
137C2×C4—362no—
138C2×C4—361no—
139C2×C4AΓL(1,𝔽9)11yescharacteristic
140C8—362no—
141C8—362no—
142C2×C3—42no—
143C2×C3—41no—
144D3—121no—
145D3—121no—
146D3—122no—
147C22—91no—
148C22—91no—
149C22—181no—
150C22—181no—
151C22GO+(4,𝔽2)⋊C411yescharacteristic
152C4—92no—
153C4—91no—
154C4—91no—
155C4—124no—
156C4—181no—
157C4—181no—
158C4—181no—
159C4PSU(3,𝔽2)⋊C411yescharacteristic
160C4AGL(1,𝔽9)⋊C411yescharacteristic
161C3—41no—
162C2—21no—
163C2—91no—
164C2—91no—
165C2—181no—
166C2#1059316611yescharacteristic
subgroupG/H
centerC4PSU(3,𝔽2)⋊C4
commutatorC2×#157C42
Frattini, hypercenterC2×C4AΓL(1,𝔽9)
FittingC2×C32×C4SD16
socleC2×C32#340
prime radicalC22×C3⋊D3C22⋊C4
cosocleC2×C4×#157C22
hypocenterC32#1303
LCSG ▷ C2×#157 ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
8. C4⋊AGL(1,𝔽9)C4semidirect
12. #63744C4semidirect
123. C32#1303semidirect

Maximal subgroups

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

subgroupindex
#105964842
#105935392
C4×#37732
#13039