Finite Group Databasebeta

← #11771233

Subgroups — #11771233

Order 1152.

390 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 44 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#10593802C211yesmaximal, characteristic
3#10592425C211yesmaximal, characteristic
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×C22⋊#157C412yes—
6C2×#3792C412yescomplemented
7C2×C4⋊#157—21no—
8C2×#3743—21no—
9#63781—21no—
10#63778—21no—
11#63778—21no—
12C32×C22⋊C8C411yescharacteristic, complemented
13#63657C411yescharacteristic, complemented
14#63647—21no—
15#4726—62no—
16C23×C3⋊D3C2×C411yescharacteristic
17C22×#157—22no—
18C22×C32×C4C2×C411yescharacteristic
19C22×C3⋊Dic3C2×C411yescharacteristic
20C2×C4×C3⋊D3—42no—
21C2×C4×C3⋊D3D411yescharacteristic
22C2×C4×C3⋊D3D411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3Q811yescharacteristic
25C22⋊#157—42no—
26#3792—42no—
27C2×#622—22no—
28C4⋊#157—42no—
29C2×C32×C8—21no—
30C2×C3⋊(C3⋊C8)—21no—
31#3743—42no—
32#1305—91nomaximal, Sylow
33C22×C4×D3—62no—
34C2×ΓL(1,𝔽25)—64no—
35C3×C22⋊C8—22no—
36#830—62no—
37(C2×D3)⋊C8—64no—
38C23×C32C4211yescharacteristic
39C22×C3⋊D3—21no—
40C22×C3⋊D3—21no—
41C22×C3⋊D3—41no—
42C22×C3⋊D3—41no—
43C22×C3⋊D3C22⋊C411yescharacteristic
44C22×C3⋊D3C4⋊C411yescharacteristic
45C2×#157—42no—
46C2×#157—42no—
47C2×#157—42no—
48C2×C32×C4—41no—
49C2×C32×C4C22⋊C411yescharacteristic
50C2×C32×C4C4⋊C411yescharacteristic
51C2×C3⋊Dic3—22no—
52C2×C3⋊Dic3C22⋊C411yescharacteristic
53C2×C3⋊Dic3C4⋊C411yescharacteristic
54C4×C3⋊D3—22no—
55C4×C3⋊D3—22no—
56C4×C3⋊D3—41no—
57C4×C3⋊D3—41no—
58#622—42no—
59C32×C8—41no—
60C3⋊(C3⋊C8)—41no—
61#407—91no—
62#407—91no—
63#380—91no—
64C23×D3—62no—
65C22×C3×C4—22no—
66C22×Dic3—62no—
67C2×C4×D3—62no—
68C2×C4×D3—62no—
69C2×C4×D3—62no—
70C2×C4×D3—62no—
71C2×C4×D3—128no—
72C2×C3×C8—24no—
73C2×C3⋊C8—64no—
74ΓL(1,𝔽25)—128no—
75C22×C32—21no—
76C22×C32—21no—
77C22×C32—21no—
78C22×C32#9511yescharacteristic
79C2×C3⋊D3—21no—
80C2×C3⋊D3—21no—
81C2×C3⋊D3—21no—
82C2×C3⋊D3—21no—
83C2×C3⋊D3—21no—
84C2×C3⋊D3—42no—
85C2×C3⋊D3—42no—
86C2×C3⋊D3#10011yescharacteristic
87C2×C3⋊D3#10111yescharacteristic
88#157—82no—
89C32×C4—21no—
90C32×C4—21no—
91C3⋊Dic3—21no—
92C3⋊Dic3#9912yes—
93C23×C4—91no—
94C2×M16—92no—
95C2×M16—181no—
96C2×C4⋊C4—181no—
97C2×C22⋊C4—92no—
98C22⋊C8—91no—
99C22⋊C8—181no—
100C22⋊C8—181no—
101C22⋊C8—181no—
102C22⋊C8#15711yescharacteristic, complemented
103#95—181no—
104C23×C3—22no—
105C22×D3—62no—
106C22×D3—62no—
107C22×D3—122no—
108C22×D3—122no—
109C22×D3—124no—
110C22×D3—124no—
111C2×C3×C4—22no—
112C2×C3×C4—22no—
113C2×C3×C4—44no—
114C2×Dic3—62no—
115C2×Dic3—62no—
116C2×Dic3—124no—
117C4×D3—68no—
118C4×D3—124no—
119C4×D3—124no—
120C4×D3—124no—
121C3×C8—44no—
122C3⋊C8—124no—
123C2×C32—41no—
124C2×C32#34211yescharacteristic
125C2×C32#34311yescharacteristic
126C2×C32#34411yescharacteristic
127C3⋊D3—21no—
128C3⋊D3—21no—
129C3⋊D3—41no—
130C24—91no—
131C22×C4—91no—
132C22×C4—91no—
133C22×C4—91no—
134C22×C4—91no—
135C22×C4—91no—
136C22×C4—182no—
137C22×C4—362no—
138C22×C4C2×#15711yescharacteristic
139M16—362no—
140M16—362no—
141C2×C8—21no—
142C2×C8—182no—
143C2×C8—181no—
144C4⋊C4—362no—
145C22⋊C4—362no—
146C22×C3—24no—
147C22×C3—22no—
148C22×C3—42no—
149C22×C3—42no—
150C2×D3—62no—
151C2×D3—62no—
152C2×D3—64no—
153C2×D3—122no—
154C2×D3—122no—
155C2×D3—122no—
156C2×D3—122no—
157C2×D3—128no—
158C2×D3—128no—
159C3×C4—24no—
160C3×C4—42no—
161Dic3—64no—
162Dic3—122no—
163C32#130511yescharacteristic, complemented, Sylow
164C23—91no—
165C23—91no—
166C23—181no—
167C23—181no—
168C23—361no—
169C23—361no—
170C23C4×#15711yescharacteristic
171C2×C4—41no—
172C2×C4—91no—
173C2×C4—91no—
174C2×C4—182no—
175C2×C4—182no—
176C2×C4—182no—
177C2×C4—361no—
178C2×C4—361no—
179C2×C4—362no—
180C2×C4—362no—
181C2×C4—362no—
182C2×C4C4⋊#15711yescharacteristic
183C2×C4C22⋊#15711yescharacteristic
184C8—41no—
185C8—361no—
186C8—362no—
187C2×C3—22no—
188C2×C3—22no—
189C2×C3—22no—
190C2×C3—44no—
191D3—122no—
192D3—122no—
193D3—124no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—91no—
198C22—91no—
199C22—181no—
200C22—181no—
201C22—181no—
202C22—181no—
203C22—181no—
204C22—362no—
205C22—362no—
206C22#6378111yescharacteristic
207C4—21no—
208C4—21no—
209C4—92no—
210C4—181no—
211C4—722no—
212C3—22no—
213C2—41no—
214C2—181no—
215C2—181no—
216C2—361no—
217C2#1059015511yescharacteristic
218C2#1059018311yescharacteristic
219C2#1059018811yescharacteristic
subgroupG/H
centerC22#63781
commutatorC23×C32C42
FrattiniC22×C4C2×#157
FittingC32×C22⋊C8C4
socleC22×C32#95
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C4×C3⋊D3C22
hypercenterC22⋊C8#157
hypocenterC32#1305
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
6. C2×#3792C4semidirect
12. C32×C22⋊C8C4semidirect
13. #63657C4semidirect
102. C22⋊C8#157semidirect
163. C32#1305semidirect

Maximal subgroups

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

subgroupindex
#105938122
#105938022
#105924252
#13059