Finite Group Databasebeta

← #11771248

Subgroups — #11771248

Order 1152.

382 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 42 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#10593811C211yesmaximal, characteristic
2#10593803C211yesmaximal, characteristic
3#10592425C211yesmaximal, characteristic
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×C22⋊#157C412yes—
6C2×#3788—21no—
7C2×#3743—21no—
8C22⋊#622C412yescomplemented
9#63781—21no—
10#63781—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—
26C2×#622—22no—
27#3788—42no—
28C2×C32×C8—21no—
29C2×C3⋊(C3⋊C8)—21no—
30#3743—42no—
31#1306—91nomaximal, Sylow
32C22×C4×D3—62no—
33C2×ΓL(1,𝔽25)—64no—
34C3×C22⋊C8—22no—
35#830—62no—
36(C2×D3)⋊C8—64no—
37C23×C32C4211yescharacteristic
38C22×C3⋊D3—22no—
39C22×C3⋊D3—41no—
40C22×C3⋊D3—41no—
41C22×C3⋊D3C22⋊C411yescharacteristic
42C22×C3⋊D3C4⋊C411yescharacteristic
43C2×#157—42no—
44C2×#157—42no—
45C2×#157—42no—
46C2×C32×C4—41no—
47C2×C32×C4C22⋊C411yescharacteristic
48C2×C32×C4C4⋊C411yescharacteristic
49C2×C3⋊Dic3—41no—
50C2×C3⋊Dic3C22⋊C411yescharacteristic
51C2×C3⋊Dic3C4⋊C411yescharacteristic
52C4×C3⋊D3—22no—
53C4×C3⋊D3—22no—
54C4×C3⋊D3—41no—
55C4×C3⋊D3—41no—
56#622—42no—
57C32×C8—41no—
58C3⋊(C3⋊C8)—41no—
59#407—91no—
60#407—91no—
61#381—91no—
62C23×D3—62no—
63C22×C3×C4—22no—
64C22×Dic3—62no—
65C2×C4×D3—62no—
66C2×C4×D3—62no—
67C2×C4×D3—62no—
68C2×C4×D3—62no—
69C2×C4×D3—128no—
70C2×C3×C8—24no—
71C2×C3⋊C8—64no—
72ΓL(1,𝔽25)—128no—
73C22×C32—21no—
74C22×C32—21no—
75C22×C32—21no—
76C22×C32#9511yescharacteristic
77C2×C3⋊D3—21no—
78C2×C3⋊D3—21no—
79C2×C3⋊D3—21no—
80C2×C3⋊D3—21no—
81C2×C3⋊D3—21no—
82C2×C3⋊D3—44no—
83C2×C3⋊D3#9912yes—
84#157—82no—
85C32×C4—21no—
86C32×C4—21no—
87C3⋊Dic3—21no—
88C3⋊Dic3—21no—
89C23×C4—91no—
90C2×M16—181no—
91C2×M16—181no—
92C2×C22⋊C4—92no—
93C22⋊C8—92no—
94C22⋊C8—91no—
95C22⋊C8—181no—
96C22⋊C8—181no—
97C22⋊C8#15711yescharacteristic, complemented
98#95—181no—
99#95—181no—
100C23×C3—22no—
101C22×D3—62no—
102C22×D3—62no—
103C22×D3—124no—
104C22×D3—124no—
105C22×D3—124no—
106C2×C3×C4—22no—
107C2×C3×C4—22no—
108C2×C3×C4—44no—
109C2×Dic3—62no—
110C2×Dic3—62no—
111C2×Dic3—124no—
112C4×D3—68no—
113C4×D3—124no—
114C4×D3—124no—
115C4×D3—124no—
116C3×C8—44no—
117C3⋊C8—124no—
118C2×C32—41no—
119C2×C32#34211yescharacteristic
120C2×C32#34411yescharacteristic
121C2×C32#34411yescharacteristic
122C3⋊D3—22no—
123C3⋊D3—41no—
124C24—91no—
125C22×C4—91no—
126C22×C4—91no—
127C22×C4—91no—
128C22×C4—91no—
129C22×C4—91no—
130C22×C4—182no—
131C22×C4—362no—
132C22×C4C2×#15711yescharacteristic
133M16—362no—
134M16—362no—
135C2×C8—21no—
136C2×C8—182no—
137C2×C8—181no—
138C22⋊C4—362no—
139C22×C3—24no—
140C22×C3—22no—
141C22×C3—42no—
142C22×C3—42no—
143C2×D3—64no—
144C2×D3—64no—
145C2×D3—122no—
146C2×D3—122no—
147C2×D3—122no—
148C2×D3—122no—
149C2×D3—1216no—
150C3×C4—24no—
151C3×C4—42no—
152Dic3—64no—
153Dic3—122no—
154C32#130611yescharacteristic, complemented, Sylow
155C23—91no—
156C23—91no—
157C23—182no—
158C23—361no—
159C23—361no—
160C23C4×#15711yescharacteristic
161C2×C4—41no—
162C2×C4—91no—
163C2×C4—91no—
164C2×C4—182no—
165C2×C4—182no—
166C2×C4—361no—
167C2×C4—361no—
168C2×C4—361no—
169C2×C4—362no—
170C2×C4—362no—
171C2×C4—362no—
172C2×C4C4⋊#15711yescharacteristic
173C2×C4C22⋊#15711yescharacteristic
174C8—41no—
175C8—361no—
176C8—362no—
177C2×C3—22no—
178C2×C3—22no—
179C2×C3—22no—
180C2×C3—44no—
181D3—124no—
182D3—124no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—92no—
187C22—181no—
188C22—181no—
189C22—181no—
190C22—181no—
191C22—181no—
192C22—364no—
193C22#6378111yescharacteristic
194C4—21no—
195C4—21no—
196C4—181no—
197C4—181no—
198C4—722no—
199C3—22no—
200C2—41no—
201C2—182no—
202C2—361no—
203C2#1059015511yescharacteristic
204C2#1059018311yescharacteristic
205C2#1059019111yescharacteristic
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#1306
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
8. C22⋊#622C4semidirect
12. C32×C22⋊C8C4semidirect
13. #63657C4semidirect
97. C22⋊C8#157semidirect
154. C32#1306semidirect

Maximal subgroups

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

subgroupindex
#105938112
#105938032
#105924252
#13069