Finite Group Databasebeta

← #11771683

Subgroups — #11771683

Order 1152.

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

normal subgroups only

This group has 196 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#10592529C211yesmaximal, characteristic
2C4⋊#3708C211yesmaximal, characteristic
3C4×#3708C211yesmaximal, characteristic
4C4×#634C411yescharacteristic
5C2×#3708—21no—
6C2×#3708—21no—
7C32×C4⋊C8C411yescharacteristic
8#63641—21no—
9C8×C3⋊Dic3—21no—
10C4×C3⋊(C3⋊C8)C2211yescharacteristic
11#4830—62no—
12C2×#634C811yescharacteristic
13C2×C32×C8—21no—
14C32×C42C2×C411yescharacteristic
15C4⋊(C3⋊Dic3)C811yescharacteristic
16#3750—21no—
17C4×C3⋊Dic3—21no—
18C2×C3⋊(C3⋊C8)D411yescharacteristic
19C2×C3⋊(C3⋊C8)D411yescharacteristic
20#3708—22no—
21#3708—41no—
22Q8⋊C16—91nomaximal, Sylow
23C4×Dic6—62no—
24C3×C4⋊C8—22no—
25Dic3⋊C8—64no—
26C8×Dic3—64no—
27C4×C3⋊C8—62no—
28C2×C32×C4C22⋊C411yescharacteristic
29C2×C32×C4C2×C811yescharacteristic
30C2×C32×C4M1611yescharacteristic
31C2×C3⋊Dic3—21no—
32C2×C3⋊Dic3—21no—
33#634—21no—
34#634C1612yescomplemented
35C32×C8—41no—
36C3⋊(C3⋊C8)—21no—
37C3⋊(C3⋊C8)SD1611yescharacteristic
38C3⋊(C3⋊C8)Q1611yescharacteristic
39C8×Q8—91no—
40C4⋊C16—91no—
41C4×C16—91no—
42C2×Dic6—62no—
43C2×C3×C8—24no—
44C3×C42—22no—
45C4⋊Dic3—62no—
46Dic3⋊C4—64no—
47C4×Dic3—64no—
48C2×C3⋊C8—62no—
49C2×C3⋊C8—62no—
50C22×C32C22⋊C811yescharacteristic
51C32×C4—21no—
52C32×C4#10311yescharacteristic
53C32×C4#10411yescharacteristic
54C32×C4C2×C1611yescharacteristic
55C32×C4M3211yescharacteristic
56C3⋊Dic3—22no—
57C3⋊Dic3—41no—
58C4×Q8—91no—
59C2×C16—181no—
60C2×C16—181no—
61C4⋊C8—181no—
62C4⋊C8#15711yescharacteristic
63C4×C8—91no—
64C4×C8—181no—
65C2×C3×C4—22no—
66C2×C3×C4—22no—
67C2×C3×C4—22no—
68C2×Dic3—64no—
69C2×Dic3—64no—
70Dic6—64no—
71Dic6—64no—
72C3×C8—44no—
73C3⋊C8—62no—
74C3⋊C8—62no—
75C3⋊C8—122no—
76C2×C32Q8⋊C811yescharacteristic
77C2×C32C22⋊C1611yescharacteristic
78C2×C32#35011yescharacteristic
79C2×Q8—91no—
80C2×C8—21no—
81C2×C8—91no—
82C2×C8—91no—
83C4⋊C4—91no—
84C4⋊C4—181no—
85C42—181no—
86C42C2×#15711yescharacteristic
87C16—182no—
88C16—361no—
89C22×C3—22no—
90C3×C4—22no—
91C3×C4—22no—
92C3×C4—22no—
93C3×C4—22no—
94C3×C4—42no—
95Dic3—68no—
96Dic3—124no—
97C32Q8⋊C1611yescharacteristic, complemented, Sylow
98Q8—92no—
99Q8—181no—
100C2×C4—181no—
101C2×C4—181no—
102C2×C4#378711yescharacteristic
103C2×C4#378811yescharacteristic
104C2×C4C22⋊#15711yescharacteristic
105C8—41no—
106C8—91no—
107C8—91no—
108C8—181no—
109C2×C3—22no—
110C2×C3—22no—
111C2×C3—22no—
112C22#6377811yescharacteristic
113C4—21no—
114C4—182no—
115C4—361no—
116C4#6376411yescharacteristic
117C4#6376511yescharacteristic
118C4#6378311yescharacteristic
119C4#6378411yescharacteristic
120C3—22no—
121C2#1059016111yescharacteristic
122C2#1059017611yescharacteristic
123C2#1059018711yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC32×C4C2×C16
FrattiniC42C2×#157
FittingC32×C4⋊C8C4
socle, prime radicalC22×C32C22⋊C8
cosocleC4×C3⋊(C3⋊C8)C22
hypercenterC4⋊C8#157
hypocenterC32Q8⋊C16
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
34. #634C16semidirect
97. C32Q8⋊C16semidirect

Maximal subgroups

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

subgroupindex
#105925292
C4⋊#37082
C4×#37082
Q8⋊C169