Finite Group Databasebeta

← #11771506

Subgroups — #11771506

Order 1152.

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

normal subgroups only

This group has 222 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#10592623C211yesmaximal, characteristic
2#10590201C212yesmaximal
3C2×C32×C42C411yescharacteristic
4C2×#3748C411yescharacteristic
5C2×#3748C2211yescharacteristic
6#63773—22no—
7C4⋊(C3⋊(C3⋊C8))—22no—
8#4924—62no—
9C22×C32×C4—21no—
10C22×C32×C4C2×C411yescharacteristic
11C32×C42—21no—
12C32×C42C811yescharacteristic
13C32×C42C811yescharacteristic
14#3748—41no—
15#3748—41no—
16C2×C3⋊(C3⋊C8)—21no—
17C2×C3⋊(C3⋊C8)D412yes—
18#3708—42no—
19#1327—91nomaximal, Sylow
20C2×C3×C42—22no—
21C2×#208—62no—
22C2×#208—62no—
23C4⋊(C3⋊C8)—68no—
24C23×C32M1611yescharacteristic
25C2×C32×C4—21no—
26C2×C32×C4—21no—
27C2×C32×C4—21no—
28C2×C32×C4—21no—
29C2×C32×C4—42no—
30C2×C32×C4C22⋊C411yescharacteristic
31C2×C32×C4C2×C811yescharacteristic
32C3⋊(C3⋊C8)—22no—
33C3⋊(C3⋊C8)—41no—
34#423—91no—
35#349—92no—
36C22×C3×C4—24no—
37C22×C3×C4—22no—
38C3×C42—24no—
39C3×C42—22no—
40C3×C42—22no—
41#208—124no—
42#208—124no—
43C2×C3⋊C8—64no—
44C2×C3⋊C8—64no—
45C22×C32—21no—
46C22×C32—41no—
47C22×C32C22⋊C811yescharacteristic
48C32×C4—22no—
49C32×C4—21no—
50C32×C4—41no—
51C32×C4#9911yescharacteristic
52C32×C4#10111yescharacteristic
53C2×M16—91no—
54C2×M16—91no—
55C2×C42#15711yescharacteristic
56M32—182no—
57C4⋊C8—182no—
58C23×C3—22no—
59C2×C3×C4—24no—
60C2×C3×C4—24no—
61C2×C3×C4—24no—
62C2×C3×C4—24no—
63C2×C3×C4—22no—
64C2×C3×C4—22no—
65C2×C3×C4—48no—
66C3⋊C8—124no—
67C3⋊C8—124no—
68C2×C32—21no—
69C2×C32—41no—
70C2×C32#32411yescharacteristic
71C22×C4—21no—
72C22×C4C2×#15711yescharacteristic
73M16—361no—
74M16—361no—
75C2×C8—92no—
76C2×C8—181no—
77C42—21no—
78C42#62211yescharacteristic
79C42#62211yescharacteristic
80C16—362no—
81C22×C3—24no—
82C22×C3—22no—
83C22×C3—44no—
84C3×C4—24no—
85C3×C4—28no—
86C3×C4—22no—
87C3×C4—22no—
88C3×C4—44no—
89C32#132711yescharacteristic, complemented, Sylow
90C23#379211yescharacteristic
91C2×C4—21no—
92C2×C4—21no—
93C2×C4—21no—
94C2×C4—21no—
95C2×C4—42no—
96C2×C4C2×#62211yescharacteristic
97C2×C4C22⋊#15711yescharacteristic
98C8—182no—
99C8—361no—
100C2×C3—24no—
101C2×C3—22no—
102C2×C3—44no—
103C22—21no—
104C22—41no—
105C22C22⋊#62211yescharacteristic
106C4—22no—
107C4—21no—
108C4—41no—
109C4#6377411yescharacteristic
110C4#6378011yescharacteristic
111C3—22no—
112C2—21no—
113C2—41no—
114C2#1059020211yescharacteristic
subgroupG/H
centerC4#63774
commutatorC2×C32×C4C2×C8
FrattiniC22×C4C2×#157
FittingC2×C32×C42C4
socleC2×C32#324
prime radicalC23×C32M16
cosocleC2×#3748C22
hypercenterC2×C42#157
hypocenterC32#1327
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

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
#105926232
#105902012
#13279