Finite Group Databasebeta

← #11771163

Subgroups — #11771163

Order 1152.

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

normal subgroups only

This group has 274 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#10593726C211yesmaximal, characteristic
2#10593725C211yesmaximal, characteristic
3#10592536C211yesmaximal, characteristic
4C2×#3787—21no—
5C2×#3743—21no—
6C42×C3⋊D3C2211yescharacteristic
7#63779—21no—
8#63779C412yes—
9#63778C412yes—
10C4⋊#622—21no—
11C4×#622—21no—
12C32×C4⋊C8C411yescharacteristic
13#63641—21no—
14C4⋊(C3⋊(C3⋊C8))C411yescharacteristic
15#4837—62no—
16C2×C4×C3⋊D3C2×C411yescharacteristic
17C2×C4×C3⋊D3D411yescharacteristic
18C2×C4×C3⋊D3Q811yescharacteristic
19C2×#622—22no—
20C2×#622—22no—
21#3787—41no—
22#3787—41no—
23C2×C32×C8—21no—
24C32×C42C2×C411yescharacteristic
25C4×C3⋊Dic3C2×C411yescharacteristic
26C4×C3⋊Dic3D411yescharacteristic
27C4×C3⋊Dic3D411yescharacteristic
28C2×C3⋊(C3⋊C8)—21no—
29#3743—41no—
30#3743—41no—
31#1301—91nomaximal, Sylow
32C2×ΓL(1,𝔽25)—64no—
33C42×D3—62no—
34C3×C4⋊C8—22no—
35Dic3⋊C8—64no—
36C4⋊(C3⋊C8)—62no—
37C22×C3⋊D3C4⋊C411yescharacteristic
38C2×C32×C4C4211yescharacteristic
39C2×C32×C4C22⋊C411yescharacteristic
40C2×C32×C4C4⋊C411yescharacteristic
41C2×C3⋊Dic3C22⋊C411yescharacteristic
42C2×C3⋊Dic3C22⋊C411yescharacteristic
43C2×C3⋊Dic3C4⋊C411yescharacteristic
44C4×C3⋊D3—22no—
45C4×C3⋊D3—41no—
46C4×C3⋊D3D811yescharacteristic
47C4×C3⋊D3SD1611yescharacteristic
48C4×C3⋊D3SD1611yescharacteristic
49C4×C3⋊D3Q1611yescharacteristic
50#622—42no—
51#622—42no—
52C32×C8—41no—
53C3⋊(C3⋊C8)—41no—
54#431—91no—
55#423—91no—
56C2×C4⋊C8—91no—
57C2×C4×D3—62no—
58C2×C4×D3—62no—
59C2×C4×D3—62no—
60C2×C3×C8—24no—
61C3×C42—22no—
62C4×Dic3—62no—
63C4×Dic3—62no—
64C4×Dic3—62no—
65C2×C3⋊C8—64no—
66ΓL(1,𝔽25)—124no—
67ΓL(1,𝔽25)—124no—
68C22×C32#9511yescharacteristic
69C2×C3⋊D3—21no—
70C2×C3⋊D3—21no—
71C2×C3⋊D3#10611yescharacteristic
72C2×C3⋊D3#10711yescharacteristic
73C32×C4—21no—
74C32×C4—21no—
75C32×C4#10211yescharacteristic
76C32×C4#10311yescharacteristic
77C3⋊Dic3—21no—
78C3⋊Dic3#10211yescharacteristic
79C3⋊Dic3#10311yescharacteristic
80C3⋊Dic3#10812yes—
81C2×M16—181no—
82C22×C8—181no—
83C2×C42—91no—
84C4⋊C8—92no—
85C4⋊C8—91no—
86C4⋊C8—181no—
87C4⋊C8—181no—
88C4⋊C8—181no—
89C4⋊C8#15711yescharacteristic
90C22⋊C8—92no—
91C4×C8—181no—
92C22×D3—62no—
93C2×C3×C4—22no—
94C2×C3×C4—22no—
95C2×C3×C4—22no—
96C2×Dic3—62no—
97C2×Dic3—62no—
98C2×Dic3—62no—
99C4×D3—62no—
100C4×D3—62no—
101C4×D3—62no—
102C4×D3—62no—
103C4×D3—124no—
104C4×D3—124no—
105C3×C8—44no—
106C3⋊C8—124no—
107C2×C32#34011yescharacteristic
108C2×C32#34111yescharacteristic
109C2×C32#34411yescharacteristic
110C3⋊D3—21no—
111C3⋊D3—21no—
112C22×C4—91no—
113C22×C4—91no—
114C22×C4—91no—
115M16—361no—
116M16—361no—
117C2×C8—21no—
118C2×C8—182no—
119C2×C8—182no—
120C2×C8—181no—
121C2×C8—361no—
122C2×C8—361no—
123C42—91no—
124C42—91no—
125C42—91no—
126C42C2×#15711yescharacteristic
127C22×C3—22no—
128C2×D3—62no—
129C2×D3—62no—
130C2×D3—122no—
131C2×D3—122no—
132C3×C4—24no—
133C3×C4—22no—
134C3×C4—22no—
135C3×C4—42no—
136Dic3—62no—
137Dic3—62no—
138Dic3—64no—
139Dic3—122no—
140C32#130111yescharacteristic, complemented, Sylow
141C23—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×C4—361no—
151C2×C4C4×#15711yescharacteristic
152C2×C4C4⋊#15711yescharacteristic
153C2×C4C22⋊#15711yescharacteristic
154C8—41no—
155C8—362no—
156C8—362no—
157C8—361no—
158C2×C3—22no—
159C2×C3—22no—
160C2×C3—22no—
161D3—122no—
162D3—122no—
163C22—91no—
164C22—91no—
165C22—181no—
166C22—181no—
167C22#6378111yescharacteristic
168C4—21no—
169C4—21no—
170C4—91no—
171C4—91no—
172C4—92no—
173C4—181no—
174C4#6378211yescharacteristic
175C4#6378411yescharacteristic
176C3—22no—
177C2—181no—
178C2—181no—
179C2#1059016311yescharacteristic
180C2#1059018311yescharacteristic
181C2#1059019011yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC2×C32×C4C42
FrattiniC42C2×#157
FittingC32×C4⋊C8C4
socleC22×C32#95
prime radicalC22×C3⋊D3C4⋊C4
cosocleC42×C3⋊D3C22
hypercenterC4⋊C8#157
hypocenterC32#1301
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
140. C32#1301semidirect

Maximal subgroups

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

subgroupindex
#105937262
#105937252
#105925362
#13019