Finite Group Databasebeta

← #11771415

Subgroups — #11771415

Order 1152.

318 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 30 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#10592825C211yesmaximal, characteristic
2#10590201C212yesmaximal, complemented
3C22×C4×C3⋊D3C411yescharacteristic
4C2×C32×M16C411yescharacteristic
5C2×#3748C2211yescharacteristic
6#63773—22no—
7#63647—22no—
8#5126—62no—
9C23×C3⋊D3C811yescharacteristic
10C22×C32×C4C2×C411yescharacteristic
11C22×C3⋊Dic3C811yescharacteristic
12C2×C4×C3⋊D3—21no—
13C2×C4×C3⋊D3—21no—
14C2×C4×C3⋊D3—41no—
15C2×C4×C3⋊D3—41no—
16C32×M16—41no—
17C2×C32×C8—21no—
18#3748—41no—
19C2×C3⋊(C3⋊C8)D412yes—
20#3708—42no—
21#1320—91nomaximal, Sylow
22C22×C4×D3—62no—
23C2×C3×M16—22no—
24C2×#208—62no—
25(C2×D3)⋊C8—68no—
26C23×C32C2×C811yescharacteristic
27C22×C3⋊D3—21no—
28C22×C3⋊D3—42no—
29C22×C3⋊D3—41no—
30C2×C32×C4—21no—
31C2×C32×C4—21no—
32C2×C32×C4C22⋊C411yescharacteristic
33C2×C32×C4M1611yescharacteristic
34C2×C3⋊Dic3—21no—
35C2×C3⋊Dic3—41no—
36C4×C3⋊D3—42no—
37C4×C3⋊D3—41no—
38C4×C3⋊D3—41no—
39C32×C8—41no—
40C3⋊(C3⋊C8)—22no—
41#407—91no—
42#349—92no—
43C23×D3—62no—
44C22×C3×C4—22no—
45C22×Dic3—62no—
46C2×C4×D3—64no—
47C2×C4×D3—64no—
48C2×C4×D3—124no—
49C2×C4×D3—124no—
50C3×M16—44no—
51C2×C3×C8—24no—
52#208—124no—
53C2×C3⋊C8—64no—
54C22×C32—21no—
55C22×C32—41no—
56C22×C32C22⋊C811yescharacteristic
57C2×C3⋊D3—22no—
58C2×C3⋊D3—41no—
59C2×C3⋊D3—42no—
60C2×C3⋊D3—41no—
61C2×C3⋊D3—42no—
62C32×C4—21no—
63C32×C4#9911yescharacteristic
64C32×C4#10011yescharacteristic
65C3⋊Dic3—41no—
66C23×C4—91no—
67C2×M16—91no—
68C2×M16#15711yescharacteristic
69M32—182no—
70C22⋊C8—182no—
71C23×C3—22no—
72C22×D3—64no—
73C22×D3—128no—
74C22×D3—124no—
75C2×C3×C4—24no—
76C2×C3×C4—24no—
77C2×C3×C4—22no—
78C2×C3×C4—22no—
79C2×Dic3—64no—
80C2×Dic3—124no—
81C4×D3—128no—
82C4×D3—124no—
83C4×D3—124no—
84C3×C8—44no—
85C3⋊C8—124no—
86C2×C32—21no—
87C2×C32—41no—
88C2×C32#32311yescharacteristic
89C3⋊D3—42no—
90C24—91no—
91C22×C4—91no—
92C22×C4—181no—
93C22×C4—181no—
94C22×C4—361no—
95C22×C4—361no—
96C22×C4C2×#15711yescharacteristic
97M16—41no—
98M16—361no—
99C2×C8—21no—
100C2×C8—92no—
101C16—362no—
102C22×C3—24no—
103C22×C3—22no—
104C22×C3—44no—
105C2×D3—68no—
106C2×D3—124no—
107C2×D3—124no—
108C2×D3—128no—
109C2×D3—128no—
110C3×C4—24no—
111C3×C4—22no—
112C3×C4—22no—
113Dic3—124no—
114C32#132011yescharacteristic, complemented, Sylow
115C23—181no—
116C23—361no—
117C23—362no—
118C23#378711yescharacteristic
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—181no—
122C2×C4—362no—
123C2×C4—361no—
124C2×C4—361no—
125C2×C4—361no—
126C2×C4#378811yescharacteristic
127C2×C4C22⋊#15711yescharacteristic
128C8—41no—
129C8—182no—
130C2×C3—24no—
131C2×C3—22no—
132C2×C3—44no—
133D3—128no—
134C22—21no—
135C22—41no—
136C22—182no—
137C22—361no—
138C22—362no—
139C22—362no—
140C22—361no—
141C22#6377811yescharacteristic
142C4—21no—
143C4—361no—
144C4#6377411yescharacteristic
145C4#6378811yescharacteristic
146C3—22no—
147C2—21no—
148C2—41no—
149C2—362no—
150C2#1059020411yescharacteristic
subgroupG/H
centerC4#63774
commutatorC23×C32C2×C8
FrattiniC22×C4C2×#157
FittingC2×C32×M16C4
socleC2×C32#323
prime radicalC23×C3⋊D3C8
cosocleC2×#3748C22
hypercenterC2×M16#157
hypocenterC32#1320
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

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
#105928252
#105902012
#13209