Finite Group Databasebeta

← #11797387

Subgroups — #11797387

Order 1152.

270 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C4×#3748C211yesmaximal, characteristic
2#10590201C212yesmaximal
3#10590150C212yesmaximal, complemented
4#10590149C212yesmaximal, complemented
5C2×C32×C42C411yescharacteristic
6C2×#3748C411yescharacteristic
7C2×#3748C2211yescharacteristic
8#63773C2214yes—
9#63630C411yescharacteristic
10#63630C2211yescharacteristic
11C4×C3⋊(C3⋊C8)C411yescharacteristic
12C4×C3⋊(C3⋊C8)C2211yescharacteristic
13C4×#208—62no—
14C22×C32×C4—21no—
15C22×C32×C4C2×C411yescharacteristic
16C32×C42—21no—
17C32×C42C2×C411yescharacteristic
18C32×C42C2×C411yescharacteristic
19#3748—22no—
20#3748—22no—
21C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
22C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
23C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
24C2×C3⋊(C3⋊C8)C2311yescharacteristic
25#3708—24no—
26#2165—91nomaximal, Sylow
27C2×C3×C42—22no—
28C2×#208—62no—
29C2×#208—62no—
30#803—62no—
31#803—62no—
32C4×C3⋊C8—62no—
33C4×C3⋊C8—62no—
34C23×C32M1611yescharacteristic
35C2×C32×C4—21no—
36C2×C32×C4—21no—
37C2×C32×C4—21no—
38C2×C32×C4—21no—
39C2×C32×C4—42no—
40C2×C32×C4M1611yescharacteristic
41C2×C32×C4C22×C411yescharacteristic
42C3⋊(C3⋊C8)—21no—
43C3⋊(C3⋊C8)—21no—
44C3⋊(C3⋊C8)M1612yes—
45C3⋊(C3⋊C8)#4112yes—
46C4×M16—91no—
47#364—92no—
48#349—92no—
49#347—92no—
50C22×C3×C4—24no—
51C22×C3×C4—22no—
52C3×C42—24no—
53C3×C42—22no—
54C3×C42—22no—
55#208—68no—
56#208—68no—
57C2×C3⋊C8—62no—
58C2×C3⋊C8—62no—
59C2×C3⋊C8—62no—
60C2×C3⋊C8—62no—
61C22×C32—21no—
62C22×C32—41no—
63C22×C32C2×M1611yescharacteristic
64C32×C4—22no—
65C32×C4—21no—
66C32×C4—41no—
67C32×C4#11711yescharacteristic
68C32×C4C2×M1611yescharacteristic
69C2×M16—91no—
70C2×M16—91no—
71C2×C42#15711yescharacteristic
72M32—94no—
73#97—91no—
74#97—91no—
75C4×C8—91no—
76C4×C8—91no—
77C23×C3—22no—
78C2×C3×C4—24no—
79C2×C3×C4—24no—
80C2×C3×C4—24no—
81C2×C3×C4—24no—
82C2×C3×C4—22no—
83C2×C3×C4—22no—
84C2×C3×C4—48no—
85C3⋊C8—64no—
86C3⋊C8—64no—
87C3⋊C8—64no—
88C3⋊C8—64no—
89C2×C32—21no—
90C2×C32—41no—
91C2×C32#43211yescharacteristic
92C22×C4—21no—
93C22×C4C2×#15711yescharacteristic
94M16—182no—
95M16—182no—
96C2×C8—91no—
97C2×C8—91no—
98C2×C8—91no—
99C2×C8—91no—
100C42—21no—
101C42C2×#15711yescharacteristic
102C42C2×#15711yescharacteristic
103C16—184no—
104C22×C3—24no—
105C22×C3—22no—
106C22×C3—44no—
107C3×C4—24no—
108C3×C4—28no—
109C3×C4—22no—
110C3×C4—22no—
111C3×C4—44no—
112C32#216511yescharacteristic, complemented, Sylow
113C23#379211yescharacteristic
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—42no—
119C2×C4#379211yescharacteristic
120C2×C4C22×#15711yescharacteristic
121C8—92no—
122C8—92no—
123C8—181no—
124C8—181no—
125C2×C3—24no—
126C2×C3—22no—
127C2×C3—44no—
128C22—21no—
129C22—41no—
130C22C2×#379211yescharacteristic
131C4—22no—
132C4—21no—
133C4—41no—
134C4#6428311yescharacteristic
135C4#6428611yescharacteristic
136C3—22no—
137C2—21no—
138C2—41no—
139C2#1059380411yescharacteristic
subgroupG/H
centerC4#64286
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC2×C32×C42C4
socleC2×C32#432
prime radicalC23×C32M16
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC2×C42#157
hypocenterC32#2165
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C42 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. #10590150C2semidirect
4. #10590149C2semidirect
112. C32#2165semidirect

Maximal subgroups

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

subgroupindex
C4×#37482
#105902012
#105901502
#105901492
#21659