Finite Group Databasebeta

← #11771146

Subgroups — #11771146

Order 1152.

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

normal subgroups only

This group has 314 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#10593733C211yesmaximal, characteristic
2#10593730C211yesmaximal, characteristic
3#10592406C211yesmaximal, characteristic
4C2×C4×#157—21no—
5C2×#3743—21no—
6C42×C3⋊D3C2211yescharacteristic
7#63781—21no—
8#63781C412yes—
9#63778—21no—
10#63777—21no—
11C4⋊#622C412yescomplemented
12C32×#97C411yescharacteristic, complemented
13C8×C3⋊Dic3—21no—
14#63630C411yescharacteristic, complemented
15#4707—62no—
16C22×#157—22no—
17C2×C4×C3⋊D3C2×C411yescharacteristic
18C2×C4×C3⋊D3D411yescharacteristic
19C2×C4×C3⋊D3D411yescharacteristic
20C2×#622—22no—
21C4×#157—24no—
22C2×C32×C8—21no—
23C32×C42C2×C411yescharacteristic
24C4×C3⋊Dic3C2×C411yescharacteristic
25C4×C3⋊Dic3D411yescharacteristic
26C4×C3⋊Dic3Q811yescharacteristic
27C2×C3⋊(C3⋊C8)—21no—
28#3743—24no—
29#1300—91nomaximal, Sylow
30C2×ΓL(1,𝔽25)—64no—
31C42×D3—62no—
32C3×#97—22no—
33C8×Dic3—64no—
34#803—62no—
35C22×C3⋊D3C22⋊C411yescharacteristic
36C2×#157—24no—
37C2×#157—42no—
38C2×#157—42no—
39C2×C32×C4C4211yescharacteristic
40C2×C32×C4C22⋊C411yescharacteristic
41C2×C32×C4C4⋊C411yescharacteristic
42C2×C3⋊Dic3C22⋊C411yescharacteristic
43C2×C3⋊Dic3C4⋊C411yescharacteristic
44C2×C3⋊Dic3C4⋊C411yescharacteristic
45C4×C3⋊D3—22no—
46C4×C3⋊D3—22no—
47C4×C3⋊D3—41no—
48#622—42no—
49C32×C8—22no—
50C3⋊(C3⋊C8)—22no—
51#432—91no—
52C4×M16—91no—
53#376—91no—
54C2×C4×D3—62no—
55C2×C4×D3—62no—
56C2×C4×D3—62no—
57C2×C3×C8—24no—
58C3×C42—22no—
59C4×Dic3—62no—
60C4×Dic3—62no—
61C4×Dic3—62no—
62C2×C3⋊C8—64no—
63ΓL(1,𝔽25)—616no—
64C22×C32#9511yescharacteristic
65C2×C3⋊D3—21no—
66C2×C3⋊D3—21no—
67C2×C3⋊D3#10412yes—
68#157—44no—
69C32×C4—21no—
70C32×C4—21no—
71C32×C4—21no—
72C3⋊Dic3—21no—
73C3⋊Dic3—21no—
74C3⋊Dic3#10412yes—
75C2×M16—181no—
76C2×C42—91no—
77C2×C42—181no—
78C4⋊C8—92no—
79C22⋊C8—181no—
80#97—91no—
81#97—181no—
82#97#15711yescharacteristic, complemented
83C4×C8—181no—
84#95—92no—
85#95—181no—
86C22×D3—62no—
87C2×C3×C4—22no—
88C2×C3×C4—22no—
89C2×C3×C4—22no—
90C2×Dic3—62no—
91C2×Dic3—62no—
92C2×Dic3—62no—
93C4×D3—68no—
94C4×D3—124no—
95C4×D3—124no—
96C3×C8—28no—
97C3⋊C8—68no—
98C2×C32#33911yescharacteristic
99C2×C32#33911yescharacteristic
100C2×C32#34411yescharacteristic
101C3⋊D3—22no—
102C22×C4—91no—
103C22×C4—91no—
104C22×C4—91no—
105C22×C4—182no—
106M16—184no—
107C2×C8—21no—
108C2×C8—181no—
109C2×C8—182no—
110C42—91no—
111C42—91no—
112C42—91no—
113C42—184no—
114C42C2×#15711yescharacteristic
115C22×C3—22no—
116C2×D3—64no—
117C2×D3—122no—
118C2×D3—122no—
119C3×C4—24no—
120C3×C4—42no—
121C3×C4—42no—
122Dic3—64no—
123Dic3—64no—
124Dic3—64no—
125C32#130011yescharacteristic, complemented, Sylow
126C23—91no—
127C2×C4—91no—
128C2×C4—91no—
129C2×C4—91no—
130C2×C4—182no—
131C2×C4—182no—
132C2×C4—184no—
133C2×C4—361no—
134C2×C4—362no—
135C2×C4—362no—
136C2×C4C4×#15711yescharacteristic
137C2×C4C4⋊#15711yescharacteristic
138C2×C4C22⋊#15711yescharacteristic
139C8—22no—
140C8—182no—
141C8—362no—
142C2×C3—22no—
143C2×C3—22no—
144C2×C3—22no—
145D3—124no—
146C22—92no—
147C22—181no—
148C22—181no—
149C22#6378111yescharacteristic
150C4—21no—
151C4—21no—
152C4—21no—
153C4—92no—
154C4—181no—
155C4—181no—
156C4—364no—
157C3—22no—
158C2—182no—
159C2#1059015111yescharacteristic
160C2#1059018911yescharacteristic
161C2#1059019111yescharacteristic
subgroupG/H
centerC22#63781
commutatorC2×C32×C4C42
FrattiniC42C2×#157
FittingC32×#97C4
socleC22×C32#95
prime radicalC22×C3⋊D3C22⋊C4
cosocleC42×C3⋊D3C22
hypercenter#97#157
hypocenterC32#1300
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
11. C4⋊#622C4semidirect
12. C32×#97C4semidirect
14. #63630C4semidirect
82. #97#157semidirect
125. C32#1300semidirect

Maximal subgroups

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

subgroupindex
#105937332
#105937302
#105924062
#13009