Finite Group Databasebeta

← #11771414

Subgroups — #11771414

Order 1152.

318 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 32 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#10592906C211yesmaximal, characteristic
2#10590201C212yesmaximal, complemented
3C23×C32×C4C411yescharacteristic
4C2×#3748C411yescharacteristic
5C2×#3748C2211yescharacteristic
6#63773—22no—
7#63657—22no—
8#5207—62no—
9C24×C32C811yescharacteristic
10C22×C32×C4—21no—
11C22×C32×C4—21no—
12C22×C32×C4—41no—
13C22×C32×C4—41no—
14C22×C32×C4C811yescharacteristic
15C22×C32×C4C2×C411yescharacteristic
16#3748—41no—
17#3748—41no—
18C2×C3⋊(C3⋊C8)—21no—
19C2×C3⋊(C3⋊C8)D412yes—
20#3708—42no—
21#1320—91nomaximal, Sylow
22C23×C3×C4—22no—
23C2×#208—62no—
24C2×#208—62no—
25#830—68no—
26C23×C32—21no—
27C23×C32—42no—
28C23×C32—41no—
29C23×C32C2×C811yescharacteristic
30C2×C32×C4—21no—
31C2×C32×C4—21no—
32C2×C32×C4—21no—
33C2×C32×C4—42no—
34C2×C32×C4—41no—
35C2×C32×C4—41no—
36C2×C32×C4—41no—
37C2×C32×C4C22⋊C411yescharacteristic
38C2×C32×C4M1611yescharacteristic
39C3⋊(C3⋊C8)—22no—
40C3⋊(C3⋊C8)—41no—
41#407—91no—
42#349—92no—
43C24×C3—22no—
44C22×C3×C4—24no—
45C22×C3×C4—24no—
46C22×C3×C4—22no—
47C22×C3×C4—22no—
48C22×C3×C4—44no—
49C22×C3×C4—44no—
50#208—124no—
51#208—124no—
52C2×C3⋊C8—64no—
53C2×C3⋊C8—64no—
54C22×C32—22no—
55C22×C32—21no—
56C22×C32—41no—
57C22×C32—41no—
58C22×C32—42no—
59C22×C32—42no—
60C22×C32—41no—
61C22×C32C22⋊C811yescharacteristic
62C32×C4—21no—
63C32×C4—41no—
64C32×C4#9911yescharacteristic
65C32×C4#10011yescharacteristic
66C23×C4#15711yescharacteristic
67C2×M16—91no—
68C2×M16—91no—
69M32—182no—
70C22⋊C8—182no—
71C23×C3—24no—
72C23×C3—22no—
73C23×C3—44no—
74C23×C3—48no—
75C2×C3×C4—24no—
76C2×C3×C4—24no—
77C2×C3×C4—24no—
78C2×C3×C4—22no—
79C2×C3×C4—22no—
80C2×C3×C4—48no—
81C2×C3×C4—44no—
82C2×C3×C4—44no—
83C2×C3×C4—44no—
84C3⋊C8—124no—
85C3⋊C8—124no—
86C2×C32—21no—
87C2×C32—42no—
88C2×C32—41no—
89C2×C32#32311yescharacteristic
90C24#62211yescharacteristic
91C22×C4—21no—
92C22×C4—21no—
93C22×C4—41no—
94C22×C4—41no—
95C22×C4#62211yescharacteristic
96C22×C4C2×#15711yescharacteristic
97M16—361no—
98M16—361no—
99C2×C8—92no—
100C2×C8—181no—
101C16—362no—
102C22×C3—24no—
103C22×C3—28no—
104C22×C3—22no—
105C22×C3—44no—
106C22×C3—44no—
107C22×C3—44no—
108C22×C3—48no—
109C22×C3—48no—
110C3×C4—24no—
111C3×C4—22no—
112C3×C4—22no—
113C3×C4—44no—
114C32#132011yescharacteristic, complemented, Sylow
115C23—21no—
116C23—41no—
117C23—42no—
118C23C2×#62211yescharacteristic
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—42no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4#379211yescharacteristic
127C2×C4C22⋊#15711yescharacteristic
128C8—182no—
129C8—361no—
130C2×C3—24no—
131C2×C3—22no—
132C2×C3—44no—
133C2×C3—48no—
134C22—22no—
135C22—21no—
136C22—41no—
137C22—41no—
138C22—42no—
139C22—42no—
140C22—41no—
141C22C22⋊#62211yescharacteristic
142C4—21no—
143C4—41no—
144C4#6378611yescharacteristic
145C4#6378811yescharacteristic
146C3—22no—
147C2—21no—
148C2—42no—
149C2—41no—
150C2#1059022211yescharacteristic
subgroupG/H
centerC4#63786
commutatorC23×C32C2×C8
FrattiniC22×C4C2×#157
FittingC23×C32×C4C4
socleC2×C32#323
prime radicalC24×C32C8
cosocleC2×#3748C22
hypercenterC23×C4#157
hypocenterC32#1320
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #10590201C2semidirect
114. C32#1320semidirect

Maximal subgroups

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

subgroupindex
#105929062
#105902012
#13209