Finite Group Databasebeta

← #11772270

Subgroups — #11772270

Order 1152.

258 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C2×C8×#157C211yesmaximal, characteristic
2C2×#63542C212yesmaximal
3C2×C4×#157C411yescharacteristic
4C2×#3787C411yescharacteristic
5C2×C8×C3⋊D3C2211yescharacteristic
6C8×#157—22no—
7C2×C3×C3⋊C16—22no—
8#63542—22no—
9#63542C414yescomplemented
10C2×D3×C16—62no—
11C22×#157C812yes—
12C2×C4×C3⋊D3C2×C411yescharacteristic
13C2×#622—21no—
14C4×#157—21no—
15C4×#157—21no—
16#3787—21no—
17#3787C812yes—
18C2×C32×C8D411yescharacteristic
19C2×C3⋊(C3⋊C8)Q811yescharacteristic
20C8×C3⋊D3C2×C412yes—
21C8×C3⋊D3D412yes—
22C3×C3⋊C16—24no—
23#1374—91nomaximal, Sylow
24C2×D3×C8—62no—
25C2×C3×C16—62no—
26C2×C3⋊C16—22no—
27D3×C16—64no—
28D3×C16—64no—
29C22×C3⋊D3C2×C811yescharacteristic
30C2×#157—22no—
31C2×#157—22no—
32C2×#157C1614yescomplemented
33C2×C32×C4C4⋊C411yescharacteristic
34C2×C3⋊Dic3M1611yescharacteristic
35C4×C3⋊D3C4211yescharacteristic
36C4×C3⋊D3C22⋊C411yescharacteristic
37C4×C3⋊D3C2×C811yescharacteristic
38C4×C3⋊D3M1611yescharacteristic
39#622—22no—
40C32×C8C22⋊C412yes—
41C3⋊(C3⋊C8)C4⋊C412yes—
42C22×C16—92no—
43C2×C4×C8—91no—
44C2×C4×D3—62no—
45C2×C3×C8—22no—
46C2×C3⋊C8—62no—
47D3×C8—62no—
48D3×C8—62no—
49D3×C8—62no—
50D3×C8—62no—
51C3×C16—64no—
52C3⋊C16—24no—
53C22×C32C4⋊C811yescharacteristic
54C2×C3⋊D3C4×C811yescharacteristic
55C2×C3⋊D3C22⋊C811yescharacteristic
56C2×C3⋊D3C2×C1612yes—
57C2×C3⋊D3M3212yes—
58#157—24no—
59C32×C4#9511yescharacteristic
60C32×C4C4⋊C811yescharacteristic
61C3⋊Dic3#9711yescharacteristic
62C3⋊Dic3C22⋊C811yescharacteristic
63C22×C8—91no—
64C22×C8—91no—
65C2×C42—91no—
66C2×C16—62no—
67C2×C16—94no—
68C2×C16—182no—
69C4×C8—182no—
70C22×D3—62no—
71C2×C3×C4—22no—
72C2×Dic3—62no—
73C4×D3—62no—
74C4×D3—62no—
75C4×D3—62no—
76C4×D3—62no—
77C3×C8—22no—
78C3×C8—22no—
79C3⋊C8—62no—
80C3⋊C8—62no—
81C2×C32#33611yescharacteristic
82C2×C32C4⋊C1612yes—
83C3⋊D3C4×C1611yescharacteristic
84C3⋊D3#34611yescharacteristic
85C3⋊D3C22⋊C1612yes—
86C22×C4—91no—
87C22×C4—92no—
88C2×C8—91no—
89C2×C8—92no—
90C2×C8—92no—
91C2×C8—92no—
92C2×C8—181no—
93C2×C8—181no—
94C2×C8GO+(4,𝔽2)11yescharacteristic
95C42—181no—
96C42—181no—
97C16—64no—
98C22×C3—22no—
99C2×D3—62no—
100C2×D3—62no—
101C2×D3—64no—
102C2×D3—64no—
103C3×C4—22no—
104C3×C4—22no—
105Dic3—62no—
106Dic3—62no—
107C32#137411yescharacteristic, complemented, Sylow
108C23—91no—
109C2×C4—91no—
110C2×C4—91no—
111C2×C4—91no—
112C2×C4—91no—
113C2×C4—91no—
114C2×C4—94no—
115C2×C4—182no—
116C2×C4—182no—
117C2×C4#377311yescharacteristic
118C8—92no—
119C8—182no—
120C8D32⋊C412yes—
121C2×C3—24no—
122C2×C3—22no—
123D3—62no—
124D3—62no—
125D3—64no—
126C22—92no—
127C22—92no—
128C22—91no—
129C22—91no—
130C22#6373211yescharacteristic
131C4—91no—
132C4—91no—
133C4—184no—
134C4#6373211yescharacteristic
135C4#6373711yescharacteristic
136C3—22no—
137C2—92no—
138C2—91no—
139C2—91no—
140C2#1059002212yes—
141C2#1059004411yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2×C8GO+(4,𝔽2)
commutatorC3⋊D3C4×C16
FittingC2×C32×C8D4
socleC22×C32C4⋊C8
prime radicalC22×C3⋊D3C2×C8
cosocleC2×C8×C3⋊D3C22
hypocenterC32#1374
LCSG ▷ C3⋊D3 ▷ C32
UCSC1 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
9. #63542C4semidirect
32. C2×#157C16semidirect
107. C32#1374semidirect

Maximal subgroups

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

subgroupindex
C2×C8×#1572
C2×#635422
#13749