Finite Group Databasebeta

← #11771507

Subgroups — #11771507

Order 1152.

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

normal subgroups only

This group has 222 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#10592817C211yesmaximal, characteristic
2#10590201C212yesmaximal
3C2×C32×M16C411yescharacteristic
4C2×C4×C3⋊Dic3C411yescharacteristic
5C2×#3748C2211yescharacteristic
6#63773—22no—
7#63641—22no—
8#5118—62no—
9C22×C32×C4C2×C411yescharacteristic
10C22×C3⋊Dic3—21no—
11C32×M16—41no—
12C2×C32×C8—21no—
13C4×C3⋊Dic3—21no—
14C4×C3⋊Dic3C811yescharacteristic
15C4×C3⋊Dic3C811yescharacteristic
16#3748—41no—
17C2×C3⋊(C3⋊C8)D412yes—
18#3708—42no—
19#1327—91nomaximal, Sylow
20C2×C3×M16—22no—
21C2×C4×Dic3—62no—
22C2×#208—62no—
23Dic3⋊C8—68no—
24C23×C32M1611yescharacteristic
25C2×C32×C4—21no—
26C2×C32×C4—21no—
27C2×C32×C4C22⋊C411yescharacteristic
28C2×C32×C4C2×C811yescharacteristic
29C2×C3⋊Dic3—21no—
30C2×C3⋊Dic3—21no—
31C2×C3⋊Dic3—42no—
32C32×C8—41no—
33C3⋊(C3⋊C8)—22no—
34#423—91no—
35#349—92no—
36C22×C3×C4—22no—
37C22×Dic3—64no—
38C3×M16—44no—
39C2×C3×C8—24no—
40C4×Dic3—62no—
41C4×Dic3—62no—
42C4×Dic3—64no—
43#208—124no—
44C2×C3⋊C8—64no—
45C22×C32—21no—
46C22×C32—41no—
47C22×C32C22⋊C811yescharacteristic
48C32×C4—21no—
49C32×C4#9911yescharacteristic
50C32×C4#10111yescharacteristic
51C3⋊Dic3—22no—
52C3⋊Dic3—41no—
53C2×M16—91no—
54C2×M16#15711yescharacteristic
55C2×C42—91no—
56M32—182no—
57C4⋊C8—182no—
58C23×C3—22no—
59C2×C3×C4—24no—
60C2×C3×C4—24no—
61C2×C3×C4—22no—
62C2×C3×C4—22no—
63C2×Dic3—64no—
64C2×Dic3—64no—
65C2×Dic3—128no—
66C3×C8—44no—
67C3⋊C8—124no—
68C2×C32—21no—
69C2×C32—41no—
70C2×C32#32411yescharacteristic
71C22×C4—181no—
72C22×C4C2×#15711yescharacteristic
73M16—41no—
74M16—361no—
75C2×C8—21no—
76C2×C8—92no—
77C42—91no—
78C42—91no—
79C42—181no—
80C16—362no—
81C22×C3—24no—
82C22×C3—22no—
83C22×C3—44no—
84C3×C4—24no—
85C3×C4—22no—
86C3×C4—22no—
87Dic3—68no—
88Dic3—124no—
89C32#132711yescharacteristic, complemented, Sylow
90C23#378811yescharacteristic
91C2×C4—21no—
92C2×C4—21no—
93C2×C4—181no—
94C2×C4—181no—
95C2×C4—362no—
96C2×C4#378711yescharacteristic
97C2×C4C22⋊#15711yescharacteristic
98C8—41no—
99C8—182no—
100C2×C3—24no—
101C2×C3—22no—
102C2×C3—44no—
103C22—21no—
104C22—41no—
105C22#6377811yescharacteristic
106C4—21no—
107C4—182no—
108C4—361no—
109C4#6378011yescharacteristic
110C4#6378611yescharacteristic
111C3—22no—
112C2—21no—
113C2—41no—
114C2#1059020311yescharacteristic
subgroupG/H
centerC4#63786
commutatorC2×C32×C4C2×C8
FrattiniC22×C4C2×#157
FittingC2×C32×M16C4
socleC2×C32#324
prime radicalC23×C32M16
cosocleC2×#3748C22
hypercenterC2×M16#157
hypocenterC32#1327
LCSG ▷ C2×C32×C4 ▷ 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
89. C32#1327semidirect

Maximal subgroups

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

subgroupindex
#105928172
#105902012
#13279