Finite Group Databasebeta

← #11772479

Subgroups — #11772479

Order 1152.

242 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C2×#63768C211yesmaximal, characteristic
2#10590712C211yesmaximal, characteristic
3C2×#63544C211yesmaximal, characteristic
4C2×C4⋊#157—21no—
5C2×C8×C3⋊D3C2211yescharacteristic
6#63849—21no—
7#63768—21no—
8#63768C412yescomplemented
9C3×#817—21no—
10C2×C3×C3⋊C16—21no—
11#63576C412yescomplemented
12#63544—21no—
13#63544C412yescomplemented
14C2×#798—61no—
15#4860—61no—
16C22×#157—41no—
17C2×C4×C3⋊D3D411yescharacteristic
18C4⋊#157—22no—
19C4⋊#157—41no—
20C2×C32×C8D411yescharacteristic
21C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
22C8×C3⋊D3C2×C411yescharacteristic
23C8×C3⋊D3C2×C411yescharacteristic
24C8×C3⋊D3D411yescharacteristic
25C8×C3⋊D3Q811yescharacteristic
26C3×C4⋊Dic3—22no—
27#3722—41no—
28Dic32—41no—
29C3×C3⋊C16—22no—
30#1386—91nomaximal, Sylow
31C2×D3×C8—61no—
32C2×D3×C8—61no—
33#892—62no—
34C2×C3×C16—61no—
35C3×#106—61no—
36#817—21no—
37C2×C3⋊C16—21no—
38#807—62no—
39#798—62no—
40#798—62no—
41C22×C3⋊D3D811yescharacteristic
42C2×#157—42no—
43C2×#157—82no—
44C2×C32×C4C22⋊C411yescharacteristic
45C2×C3⋊Dic3SD1611yescharacteristic
46C4×C3⋊D3C22⋊C411yescharacteristic
47C4×C3⋊D3C4⋊C411yescharacteristic
48C4×C3⋊D3SD1611yescharacteristic
49C4×C3⋊D3Q1611yescharacteristic
50C2×C3×Dic3—42no—
51C32×C8C22⋊C411yescharacteristic
52C32×C8C4⋊C411yescharacteristic
53C3⋊(C3⋊C8)C4211yescharacteristic
54C3⋊(C3⋊C8)C4⋊C411yescharacteristic
55C2×M32—91no—
56#427—91no—
57C2×#106—91no—
58C2×C4×D3—61no—
59C2×C4×D3—61no—
60C2×C3×C8—21no—
61C2×C3×C8—21no—
62C3×C4⋊C4—62no—
63(C2×D3)⋊C4—122no—
64C4⋊Dic3—22no—
65C4×Dic3—122no—
66C2×C3⋊C8—61no—
67C2×C3⋊C8—61no—
68D3×C8—61no—
69D3×C8—61no—
70D3×C8—61no—
71D3×C8—61no—
72D3×C8—61no—
73D3×C8—61no—
74D3×C8—61no—
75D3×C8—61no—
76C3×C16—62no—
77C3⋊C16—22no—
78C22×C32#10211yescharacteristic
79C2×C3⋊D3—22no—
80C2×C3⋊D3#10211yescharacteristic
81C2×C3⋊D3#10711yescharacteristic
82#157—82no—
83C32×C4#9511yescharacteristic
84C32×C4#10311yescharacteristic
85C3⋊Dic3#10311yescharacteristic
86C3⋊Dic3#10611yescharacteristic
87C3×Dic3—82no—
88C22×C8—91no—
89#117—181no—
90C2×C4⋊C4—181no—
91M32—92no—
92M32—181no—
93C2×C16—61no—
94#107—92no—
95#106—61no—
96#106—92no—
97#106—181no—
98C22×D3—61no—
99C22×D3—61no—
100C2×C3×C4—21no—
101C2×C3×C4—21no—
102C2×C3×C4—122no—
103C2×Dic3—42no—
104C2×Dic3—61no—
105C2×Dic3—61no—
106C4×D3—61no—
107C4×D3—61no—
108C4×D3—61no—
109C4×D3—61no—
110C4×D3—61no—
111C4×D3—61no—
112C4×D3—61no—
113C4×D3—61no—
114C3×C8—21no—
115C3×C8—21no—
116C3×C8—21no—
117C3×C8—21no—
118C3⋊C8—61no—
119C3⋊C8—61no—
120C3⋊C8—61no—
121C3⋊C8—61no—
122C2×C32#34011yescharacteristic
123C2×C32#36012yes—
124C3⋊D3—21no—
125C3⋊D3—21no—
126C22×C4—91no—
127C22×C4—361no—
128C2×C8—91no—
129C2×C8—91no—
130C2×C8—91no—
131C2×C8—91no—
132C2×C8—91no—
133C2×C8GO+(4,𝔽2)11yescharacteristic
134C4⋊C4—62no—
135C4⋊C4—182no—
136C4⋊C4—361no—
137C22⋊C4—361no—
138C42—361no—
139C16—62no—
140C22×C3—21no—
141C22×C3—21no—
142C2×D3—61no—
143C2×D3—61no—
144C2×D3—61no—
145C2×D3—61no—
146C2×D3—122no—
147C2×D3—122no—
148C3×C4—21no—
149C3×C4—21no—
150C3×C4—21no—
151C3×C4—21no—
152C3×C4—242no—
153Dic3—61no—
154Dic3—61no—
155Dic3—61no—
156Dic3—61no—
157Dic3—82no—
158C32#138611yescharacteristic, complemented, Sylow
159C23—91no—
160C2×C4—91no—
161C2×C4—91no—
162C2×C4—91no—
163C2×C4—91no—
164C2×C4—91no—
165C2×C4—122no—
166C2×C4—362no—
167C2×C4—722no—
168C2×C4D32⋊C411yescharacteristic
169C8—91no—
170C8—91no—
171C8D32⋊C411yescharacteristic
172C8#377311yescharacteristic
173C2×C3—22no—
174C2×C3—22no—
175C2×C3—21no—
176C2×C3—21no—
177D3—121no—
178D3—121no—
179D3—121no—
180D3—121no—
181C22—91no—
182C22—91no—
183C22—182no—
184C22#6372911yescharacteristic
185C4—91no—
186C4—91no—
187C4—242no—
188C4—722no—
189C4#6373011yescharacteristic
190C4#6373711yescharacteristic
191C3—21no—
192C3—21no—
193C2—181no—
194C2—181no—
195C2#1059001912yes—
196C2#1059004911yescharacteristic
subgroupG/H
centerC22#63729
commutatorC3⋊(C3⋊C8)C42
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#102
prime radicalC22×C3⋊D3D8
cosocleC2×C8×C3⋊D3C22
hypocenterC32#1386
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
8. #63768C4semidirect
11. #63576C4semidirect
13. #63544C4semidirect
158. C32#1386semidirect

Maximal subgroups

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

subgroupindex
C2×#637682
#105907122
C2×#635442
#13869