Finite Group Databasebeta

← #11771240

Subgroups — #11771240

Order 1152.

318 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 43 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#10593812C211yesmaximal, characteristic
2#10593803C211yesmaximal, characteristic
3#10593802C211yesmaximal, characteristic
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×C22⋊#157C412yes—
6C2×#3792—21no—
7C2×C4⋊#157—21no—
8C2×#3788C412yescomplemented
9C22⋊#622—21no—
10#63781—21no—
11#63778—21no—
12#63778—21no—
13#63778C412yescomplemented
14C23×C3⋊D3C2×C411yescharacteristic
15C22×#157—22no—
16C22×C32×C4Q811yescharacteristic
17C22×C3⋊Dic3D411yescharacteristic
18C2×C4×C3⋊D3—42no—
19C2×C4×C3⋊D3C2×C411yescharacteristic
20C2×C4×C3⋊D3C2×C411yescharacteristic
21C2×C4×C3⋊D3D411yescharacteristic
22C2×C4×C3⋊D3D411yescharacteristic
23C22⋊#157—42no—
24#3792—42no—
25C2×#622—22no—
26C2×#622—22no—
27C4⋊#157—42no—
28#3788—42no—
29#1305—91nomaximal, Sylow
30C22×C4×D3—121no—
31C23×C32C4⋊C411yescharacteristic
32C22×C3⋊D3—21no—
33C22×C3⋊D3—21no—
34C22×C3⋊D3—41no—
35C22×C3⋊D3—41no—
36C22×C3⋊D3C4211yescharacteristic
37C22×C3⋊D3C22⋊C411yescharacteristic
38C2×#157—42no—
39C2×#157—42no—
40C2×#157—42no—
41C2×C32×C4—41no—
42C2×C32×C4C4⋊C411yescharacteristic
43C2×C32×C4C4⋊C411yescharacteristic
44C2×C3⋊Dic3—22no—
45C2×C3⋊Dic3C22⋊C411yescharacteristic
46C2×C3⋊Dic3C22⋊C411yescharacteristic
47C4×C3⋊D3—22no—
48C4×C3⋊D3—22no—
49C4×C3⋊D3—41no—
50C4×C3⋊D3—41no—
51#622—42no—
52#622—42no—
53#407—91no—
54#407—91no—
55#380—91no—
56C23×D3—121no—
57C22×C3×C4—41no—
58C22×Dic3—121no—
59C2×C4×D3—121no—
60C2×C4×D3—121no—
61C2×C4×D3—121no—
62C2×C4×D3—121no—
63C2×C4×D3—128no—
64C22×C32—21no—
65C22×C32—21no—
66C22×C32—21no—
67C22×C32#9511yescharacteristic
68C2×C3⋊D3—21no—
69C2×C3⋊D3—21no—
70C2×C3⋊D3—21no—
71C2×C3⋊D3—21no—
72C2×C3⋊D3—21no—
73C2×C3⋊D3—42no—
74C2×C3⋊D3—42no—
75C2×C3⋊D3#10011yescharacteristic
76C2×C3⋊D3#10111yescharacteristic
77#157—82no—
78C32×C4—21no—
79C32×C4—21no—
80C3⋊Dic3—21no—
81C3⋊Dic3#9912yes—
82C23×C4—91no—
83C2×M16—92no—
84C2×M16—181no—
85C2×C4⋊C4—181no—
86C2×C22⋊C4—92no—
87C22⋊C8—92no—
88C22⋊C8—181no—
89C22⋊C8—181no—
90C22⋊C8—181no—
91#95—181no—
92C23×C3—41no—
93C22×D3—121no—
94C22×D3—121no—
95C22×D3—122no—
96C22×D3—122no—
97C22×D3—124no—
98C22×D3—124no—
99C2×C3×C4—44no—
100C2×C3×C4—41no—
101C2×C3×C4—41no—
102C2×Dic3—121no—
103C2×Dic3—121no—
104C2×Dic3—124no—
105C4×D3—124no—
106C4×D3—124no—
107C4×D3—124no—
108C4×D3—124no—
109C2×C32—41no—
110C2×C32#34211yescharacteristic
111C2×C32#34311yescharacteristic
112C2×C32#34411yescharacteristic
113C3⋊D3—21no—
114C3⋊D3—21no—
115C3⋊D3—41no—
116C24—91no—
117C22×C4—91no—
118C22×C4—91no—
119C22×C4—91no—
120C22×C4—91no—
121C22×C4—91no—
122C22×C4—182no—
123C22×C4—362no—
124C22×C4PSU(3,𝔽2)11yescharacteristic
125M16—362no—
126M16—362no—
127C2×C8—182no—
128C2×C8—182no—
129C4⋊C4—362no—
130C22⋊C4—362no—
131C22×C3—42no—
132C22×C3—42no—
133C22×C3—42no—
134C22×C3—41no—
135C2×D3—121no—
136C2×D3—121no—
137C2×D3—122no—
138C2×D3—122no—
139C2×D3—122no—
140C2×D3—122no—
141C2×D3—122no—
142C2×D3—128no—
143C2×D3—128no—
144C3×C4—42no—
145C3×C4—42no—
146Dic3—122no—
147Dic3—122no—
148C32#130511yescharacteristic, complemented, Sylow
149C23—91no—
150C23—91no—
151C23—181no—
152C23—181no—
153C23—361no—
154C23—361no—
155C23#377711yescharacteristic
156C2×C4—41no—
157C2×C4—91no—
158C2×C4—91no—
159C2×C4—182no—
160C2×C4—182no—
161C2×C4—182no—
162C2×C4—361no—
163C2×C4—361no—
164C2×C4—362no—
165C2×C4—362no—
166C2×C4—362no—
167C2×C4#377711yescharacteristic
168C2×C4#377711yescharacteristic
169C8—362no—
170C8—362no—
171C2×C3—44no—
172C2×C3—41no—
173C2×C3—41no—
174C2×C3—41no—
175D3—122no—
176D3—122no—
177D3—124no—
178C22—21no—
179C22—21no—
180C22—21no—
181C22—91no—
182C22—91no—
183C22—181no—
184C22—181no—
185C22—181no—
186C22—181no—
187C22—181no—
188C22—362no—
189C22—362no—
190C22#6374711yescharacteristic
191C4—21no—
192C4—21no—
193C4—92no—
194C4—181no—
195C4—722no—
196C3—41no—
197C2—41no—
198C2—181no—
199C2—181no—
200C2—361no—
201C2#1059009411yescharacteristic
202C2#1059009511yescharacteristic
203C2#1059009811yescharacteristic
subgroupG/H
centerC22#63747
commutatorC22×C3⋊D3C42
Frattini, hypercenterC22×C4PSU(3,𝔽2)
FittingC22×C32×C4Q8
socleC22×C32#95
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C4×C3⋊D3C22
hypocenterC32#1305
LCSG ▷ C22×C3⋊D3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. C2×#3788C4semidirect
13. #63778C4semidirect
148. C32#1305semidirect

Maximal subgroups

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

subgroupindex
#105938122
#105938032
#105938022
#13059