Finite Group Databasebeta

← #11771205

Subgroups — #11771205

Order 1152.

370 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 54 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#10593805C211yesmaximal, characteristic
2#10593801C211yesmaximal, characteristic
3#10592348C211yesmaximal, characteristic
4C2×#3792—21no—
5C2×#3750—21no—
6C2×C4×C3⋊Dic3—21no—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C22⋊#622—21no—
9#63779—21no—
10#63779C412yescomplemented
11C4⋊#622C412yescomplemented
12C4×#622—21no—
13C32×#95C411yescharacteristic
14#63658C411yescharacteristic
15#4649—62no—
16C22×C32×C4—21no—
17C22×C32×C4C2×C411yescharacteristic
18C22×C3⋊Dic3—21no—
19C22×C3⋊Dic3D411yescharacteristic
20C22×C3⋊Dic3D411yescharacteristic
21#3792—41no—
22#3792—41no—
23C2×#622—22no—
24C2×#622—22no—
25#3750—24no—
26C4×C3⋊Dic3—41no—
27C4×C3⋊Dic3—41no—
28C4×C3⋊Dic3C2×C411yescharacteristic
29C4×C3⋊Dic3C2×C411yescharacteristic
30C4×C3⋊Dic3D411yescharacteristic
31C4×C3⋊Dic3Q811yescharacteristic
32#1303—91nomaximal, Sylow
33C2×Dic3⋊C4—64no—
34C2×C4×Dic3—62no—
35C2×C4×Dic3—64no—
36C3×#95—22no—
37C3⋊#95—62no—
38C23×C32C22⋊C411yescharacteristic
39C2×C32×C4—22no—
40C2×C32×C4—41no—
41C2×C32×C4—41no—
42C2×C32×C4—41no—
43C2×C32×C4C4211yescharacteristic
44C2×C32×C4C4⋊C411yescharacteristic
45C2×C3⋊Dic3—22no—
46C2×C3⋊Dic3—22no—
47C2×C3⋊Dic3—41no—
48C2×C3⋊Dic3—41no—
49C2×C3⋊Dic3C22⋊C411yescharacteristic
50C2×C3⋊Dic3C22⋊C411yescharacteristic
51C2×C3⋊Dic3C4⋊C411yescharacteristic
52C2×C3⋊Dic3C4⋊C411yescharacteristic
53C2×C3⋊Dic3D811yescharacteristic
54C2×C3⋊Dic3SD1611yescharacteristic
55C2×C3⋊Dic3SD1611yescharacteristic
56C2×C3⋊Dic3Q1611yescharacteristic
57#622—42no—
58#622—42no—
59#431—91no—
60#423—91no—
61C4×C4⋊C4—91no—
62C22×C3×C4—24no—
63C22×C3×C4—22no—
64C22×Dic3—62no—
65C22×Dic3—62no—
66C22×Dic3—64no—
67Dic3⋊C4—616no—
68C4×Dic3—62no—
69C4×Dic3—62no—
70C4×Dic3—62no—
71C4×Dic3—62no—
72C4×Dic3—124no—
73C4×Dic3—124no—
74C22×C32—21no—
75C22×C32—21no—
76C22×C32#9511yescharacteristic
77C22×C32#10211yescharacteristic
78C22×C32#10311yescharacteristic
79C32×C4—21no—
80C32×C4—21no—
81C32×C4—42no—
82C3⋊Dic3—21no—
83C3⋊Dic3—42no—
84C3⋊Dic3#10211yescharacteristic
85C3⋊Dic3#10311yescharacteristic
86C3⋊Dic3#10412yes—
87C3⋊Dic3#10611yescharacteristic
88C3⋊Dic3#10711yescharacteristic
89C2×M16—181no—
90C2×C4⋊C4—181no—
91C2×C42—91no—
92C2×C42—181no—
93C4⋊C8—92no—
94C4⋊C8—92no—
95C4⋊C8—181no—
96C22⋊C8—181no—
97C4×C8—181no—
98#95—91no—
99#95#15711yescharacteristic
100C23×C3—22no—
101C2×C3×C4—28no—
102C2×C3×C4—22no—
103C2×C3×C4—22no—
104C2×C3×C4—44no—
105C2×C3×C4—44no—
106C2×C3×C4—44no—
107C2×Dic3—62no—
108C2×Dic3—62no—
109C2×Dic3—62no—
110C2×Dic3—62no—
111C2×Dic3—62no—
112C2×Dic3—62no—
113C2×Dic3—62no—
114C2×Dic3—62no—
115C2×Dic3—68no—
116C2×Dic3—68no—
117C2×Dic3—124no—
118C2×Dic3—124no—
119C2×C32—21no—
120C2×C32—21no—
121C2×C32#33911yescharacteristic
122C2×C32#34011yescharacteristic
123C2×C32#34411yescharacteristic
124C22×C4—21no—
125C22×C4—91no—
126C22×C4—91no—
127C22×C4—181no—
128C22×C4C2×#15711yescharacteristic
129M16—361no—
130M16—361no—
131C2×C8—182no—
132C2×C8—182no—
133C4⋊C4—184no—
134C42—91no—
135C42—91no—
136C42—91no—
137C42—91no—
138C42—361no—
139C42—361no—
140C22×C3—24no—
141C22×C3—24no—
142C22×C3—22no—
143C22×C3—22no—
144C22×C3—22no—
145C3×C4—42no—
146C3×C4—42no—
147C3×C4—48no—
148Dic3—62no—
149Dic3—62no—
150Dic3—64no—
151Dic3—62no—
152Dic3—62no—
153Dic3—64no—
154Dic3—128no—
155C32#130311yescharacteristic, complemented, Sylow
156C23C22⋊#15711yescharacteristic
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—91no—
162C2×C4—91no—
163C2×C4—91no—
164C2×C4—91no—
165C2×C4—91no—
166C2×C4—91no—
167C2×C4—91no—
168C2×C4—91no—
169C2×C4—182no—
170C2×C4—182no—
171C2×C4—361no—
172C2×C4—361no—
173C2×C4C4×#15711yescharacteristic
174C2×C4C4⋊#15711yescharacteristic
175C8—362no—
176C8—362no—
177C2×C3—24no—
178C2×C3—24no—
179C2×C3—22no—
180C2×C3—22no—
181C2×C3—22no—
182C22—21no—
183C22—21no—
184C22#6378111yescharacteristic
185C22#6378211yescharacteristic
186C22#6378411yescharacteristic
187C4—21no—
188C4—21no—
189C4—42no—
190C4—92no—
191C4—91no—
192C4—91no—
193C4—91no—
194C4—91no—
195C4—181no—
196C4—362no—
197C3—22no—
198C2—21no—
199C2—21no—
200C2#1059015111yescharacteristic
201C2#1059015611yescharacteristic
202C2#1059016311yescharacteristic
subgroupG/H
centerC22#63781
commutatorC2×C32×C4C42
FrattiniC22×C4C2×#157
FittingC32×#95C4
socleC22×C32#95
prime radicalC23×C32C22⋊C4
cosocleC2×C4×C3⋊Dic3C22
hypercenter#95#157
hypocenterC32#1303
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
10. #63779C4semidirect
11. C4⋊#622C4semidirect
155. C32#1303semidirect

Maximal subgroups

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

subgroupindex
#105938052
#105938012
#105923482
#13039