Finite Group Databasebeta

← #11772409

Subgroups — #11772409

Order 1152.

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

normal subgroups only

This group has 238 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×#63770C211yesmaximal, characteristic
2#10590712C211yesmaximal, characteristic
3C2×#63542C211yesmaximal, characteristic
4C2×#3788—21no—
5C2×C8×C3⋊D3C2211yescharacteristic
6#63849—21no—
7#63770—21no—
8#63770C412yescomplemented
9C3×#817—21no—
10C2×C3×C3⋊C16—21no—
11#63576C412yes—
12#63542—21no—
13#63542C412yescomplemented
14C2×D3×C16—61no—
15#4860—61no—
16C2×C4×C3⋊D3D411yescharacteristic
17C2×#622—41no—
18#3788—22no—
19#3788—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#1382—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—
39D3×C16—62no—
40D3×C16—62no—
41C22×C3⋊D3SD1611yescharacteristic
42C2×C32×C4C22⋊C411yescharacteristic
43C2×C3⋊Dic3D811yescharacteristic
44C4×C3⋊D3C22⋊C411yescharacteristic
45C4×C3⋊D3C4⋊C411yescharacteristic
46C4×C3⋊D3SD1611yescharacteristic
47C4×C3⋊D3Q1611yescharacteristic
48C2×C3×Dic3—42no—
49#622—42no—
50C32×C8C22⋊C411yescharacteristic
51C32×C8C4⋊C411yescharacteristic
52C3⋊(C3⋊C8)C4211yescharacteristic
53C3⋊(C3⋊C8)C4⋊C411yescharacteristic
54C22×C16—91no—
55C2×#108—91no—
56#427—91no—
57C2×C4×D3—61no—
58C2×C4×D3—61no—
59C2×C3×C8—21no—
60C2×C3×C8—21no—
61C3×C4⋊C4—62no—
62(C2×D3)⋊C4—122no—
63C4⋊Dic3—22no—
64C4×Dic3—122no—
65C2×C3⋊C8—61no—
66C2×C3⋊C8—61no—
67D3×C8—61no—
68D3×C8—61no—
69D3×C8—61no—
70D3×C8—61no—
71D3×C8—61no—
72D3×C8—61no—
73D3×C8—61no—
74D3×C8—61no—
75C3×C16—62no—
76C3⋊C16—22no—
77C22×C32#10211yescharacteristic
78C2×C3⋊D3—22no—
79C2×C3⋊D3#10311yescharacteristic
80C2×C3⋊D3#10611yescharacteristic
81C32×C4#9511yescharacteristic
82C32×C4#10311yescharacteristic
83C3⋊Dic3#10211yescharacteristic
84C3⋊Dic3#10711yescharacteristic
85C3×Dic3—82no—
86C2×M16—181no—
87C22×C8—91no—
88#117—181no—
89C2×C16—61no—
90C2×C16—92no—
91C2×C16—181no—
92#108—92no—
93#108—181no—
94#107—92no—
95#106—61no—
96C22×D3—61no—
97C22×D3—61no—
98C2×C3×C4—21no—
99C2×C3×C4—21no—
100C2×C3×C4—122no—
101C2×Dic3—42no—
102C2×Dic3—61no—
103C2×Dic3—61no—
104C4×D3—61no—
105C4×D3—61no—
106C4×D3—61no—
107C4×D3—61no—
108C4×D3—61no—
109C4×D3—61no—
110C4×D3—61no—
111C4×D3—61no—
112C3×C8—21no—
113C3×C8—21no—
114C3×C8—21no—
115C3×C8—21no—
116C3⋊C8—61no—
117C3⋊C8—61no—
118C3⋊C8—61no—
119C3⋊C8—61no—
120C2×C32#34011yescharacteristic
121C2×C32#35912yes—
122C3⋊D3—21no—
123C3⋊D3—21no—
124C22×C4—91no—
125M16—182no—
126M16—361no—
127C2×C8—91no—
128C2×C8—91no—
129C2×C8—91no—
130C2×C8—91no—
131C2×C8—91no—
132C2×C8—361no—
133C2×C8GO+(4,𝔽2)11yescharacteristic
134C4⋊C4—62no—
135C22⋊C4—361no—
136C42—361no—
137C16—62no—
138C22×C3—21no—
139C22×C3—21no—
140C2×D3—61no—
141C2×D3—61no—
142C2×D3—61no—
143C2×D3—61no—
144C2×D3—64no—
145C2×D3—122no—
146C3×C4—21no—
147C3×C4—21no—
148C3×C4—21no—
149C3×C4—21no—
150C3×C4—242no—
151Dic3—61no—
152Dic3—61no—
153Dic3—61no—
154Dic3—61no—
155Dic3—82no—
156C32#138211yescharacteristic, complemented, Sylow
157C23—91no—
158C2×C4—91no—
159C2×C4—91no—
160C2×C4—91no—
161C2×C4—91no—
162C2×C4—91no—
163C2×C4—122no—
164C2×C4D32⋊C411yescharacteristic
165C8—91no—
166C8—91no—
167C8—362no—
168C8D32⋊C411yescharacteristic
169C8#377311yescharacteristic
170C2×C3—22no—
171C2×C3—22no—
172C2×C3—21no—
173C2×C3—21no—
174D3—62no—
175D3—62no—
176D3—121no—
177D3—121no—
178C22—91no—
179C22—91no—
180C22—182no—
181C22#6372911yescharacteristic
182C4—91no—
183C4—91no—
184C4—242no—
185C4#6373011yescharacteristic
186C4#6373711yescharacteristic
187C3—21no—
188C3—21no—
189C2—181no—
190C2—181no—
191C2#1059001812yes—
192C2#1059004911yescharacteristic
subgroupG/H
centerC22#63729
commutatorC3⋊(C3⋊C8)C42
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#102
prime radicalC22×C3⋊D3SD16
cosocleC2×C8×C3⋊D3C22
hypocenterC32#1382
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. #63770C4semidirect
13. #63542C4semidirect
156. C32#1382semidirect

Maximal subgroups

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

subgroupindex
C2×#637702
#105907122
C2×#635422
#13829