Finite Group Databasebeta

← #11771164

Subgroups — #11771164

Order 1152.

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

normal subgroups only

This group has 266 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
2C2×#63779C211yesmaximal, characteristic
3#10592417C211yesmaximal, characteristic
4C2×#3792—21no—
5C22×#622—21no—
6C2×C4×C3⋊Dic3C2211yescharacteristic
7#63779—21no—
8#63779—21no—
9#63779C412yes—
10C4⋊#622C412yes—
11C32×C22⋊C8C411yescharacteristic
12#63657C411yescharacteristic
13#63641—21no—
14C8×C3⋊Dic3—21no—
15#4718—62no—
16C22×C32×C4C2×C411yescharacteristic
17C22×C3⋊Dic3D411yescharacteristic
18C22×C3⋊Dic3Q811yescharacteristic
19#3792—41no—
20#3792—41no—
21C2×#622—22no—
22C2×#622—22no—
23C2×#622—41no—
24C2×#622—41no—
25C2×C32×C8—21no—
26C4×C3⋊Dic3C2×C411yescharacteristic
27C4×C3⋊Dic3C2×C411yescharacteristic
28C4×C3⋊Dic3D411yescharacteristic
29C4×C3⋊Dic3D411yescharacteristic
30C2×C3⋊(C3⋊C8)—21no—
31#1301—91nomaximal, Sylow
32C2×C4×Dic3—62no—
33C3×C22⋊C8—22no—
34#830—62no—
35Dic3⋊C8—64no—
36C8×Dic3—64no—
37C23×C32C4⋊C411yescharacteristic
38C2×C32×C4—41no—
39C2×C32×C4C4211yescharacteristic
40C2×C32×C4C22⋊C411yescharacteristic
41C2×C3⋊Dic3—22no—
42C2×C3⋊Dic3C22⋊C411yescharacteristic
43C2×C3⋊Dic3C22⋊C411yescharacteristic
44C2×C3⋊Dic3C4⋊C411yescharacteristic
45C2×C3⋊Dic3C4⋊C411yescharacteristic
46C2×C3⋊Dic3D811yescharacteristic
47C2×C3⋊Dic3SD1611yescharacteristic
48C2×C3⋊Dic3SD1611yescharacteristic
49C2×C3⋊Dic3Q1611yescharacteristic
50#622—42no—
51#622—42no—
52C32×C8—41no—
53C3⋊(C3⋊C8)—41no—
54#431—91no—
55#423—91no—
56C2×C4⋊C8—91no—
57C22×C3×C4—22no—
58C22×Dic3—62no—
59C22×Dic3—62no—
60C2×C3×C8—24no—
61C4×Dic3—62no—
62C4×Dic3—62no—
63C4×Dic3—62no—
64C4×Dic3—62no—
65C2×C3⋊C8—64no—
66C22×C32—21no—
67C22×C32—21no—
68C22×C32#9511yescharacteristic
69C22×C32#10611yescharacteristic
70C22×C32#10711yescharacteristic
71C32×C4—21no—
72C32×C4—21no—
73C3⋊Dic3—21no—
74C3⋊Dic3#10211yescharacteristic
75C3⋊Dic3#10211yescharacteristic
76C3⋊Dic3#10311yescharacteristic
77C3⋊Dic3#10311yescharacteristic
78C3⋊Dic3#10812yes—
79C2×M16—181no—
80C22×C8—181no—
81C2×C42—91no—
82C4⋊C8—92no—
83C4⋊C8—92no—
84C4⋊C8—181no—
85C4⋊C8—181no—
86C4⋊C8—181no—
87C22⋊C8—91no—
88C22⋊C8#15711yescharacteristic
89C4×C8—181no—
90C23×C3—22no—
91C2×C3×C4—22no—
92C2×C3×C4—22no—
93C2×C3×C4—44no—
94C2×Dic3—62no—
95C2×Dic3—62no—
96C2×Dic3—62no—
97C2×Dic3—62no—
98C2×Dic3—62no—
99C2×Dic3—62no—
100C2×Dic3—62no—
101C2×Dic3—62no—
102C2×Dic3—124no—
103C3×C8—44no—
104C3⋊C8—124no—
105C2×C32—21no—
106C2×C32—21no—
107C2×C32#34011yescharacteristic
108C2×C32#34111yescharacteristic
109C2×C32#34411yescharacteristic
110C22×C4—91no—
111C22×C4—91no—
112C22×C4C2×#15711yescharacteristic
113M16—361no—
114M16—361no—
115C2×C8—21no—
116C2×C8—182no—
117C2×C8—182no—
118C2×C8—181no—
119C2×C8—361no—
120C2×C8—361no—
121C42—91no—
122C42—91no—
123C42—91no—
124C42—91no—
125C22×C3—22no—
126C22×C3—22no—
127C22×C3—22no—
128C22×C3—42no—
129C22×C3—42no—
130C3×C4—24no—
131C3×C4—42no—
132Dic3—62no—
133Dic3—62no—
134Dic3—62no—
135Dic3—62no—
136Dic3—64no—
137Dic3—122no—
138C32#130111yescharacteristic, complemented, Sylow
139C23C4⋊#15711yescharacteristic
140C2×C4—41no—
141C2×C4—91no—
142C2×C4—91no—
143C2×C4—91no—
144C2×C4—91no—
145C2×C4—91no—
146C2×C4—91no—
147C2×C4—91no—
148C2×C4—91no—
149C2×C4—182no—
150C2×C4C4×#15711yescharacteristic
151C2×C4C22⋊#15711yescharacteristic
152C8—41no—
153C8—361no—
154C8—362no—
155C8—362no—
156C2×C3—22no—
157C2×C3—22no—
158C2×C3—22no—
159C2×C3—42no—
160C2×C3—42no—
161C22—21no—
162C22—21no—
163C22#6376811yescharacteristic
164C22#6376911yescharacteristic
165C22#6378111yescharacteristic
166C4—21no—
167C4—21no—
168C4—91no—
169C4—91no—
170C4—91no—
171C4—91no—
172C4—92no—
173C4—181no—
174C3—22no—
175C2—21no—
176C2—21no—
177C2#1059015611yescharacteristic
178C2#1059018211yescharacteristic
179C2#1059019011yescharacteristic
subgroupG/H
centerC22#63781
commutatorC2×C32×C4C42
FrattiniC22×C4C2×#157
FittingC32×C22⋊C8C4
socleC22×C32#95
prime radicalC23×C32C4⋊C4
cosocleC2×C4×C3⋊Dic3C22
hypercenterC22⋊C8#157
hypocenterC32#1301
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
138. C32#1301semidirect

Maximal subgroups

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

subgroupindex
#105938052
C2×#637792
#105924172
#13019