Finite Group Databasebeta

← #11771477

Subgroups — #11771477

Order 1152.

320 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 36 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#10592634C211yesmaximal, characteristic
2#10590202C212yesmaximal
3C2×C32×C42C411yescharacteristic
4C2×C4⋊(C3⋊Dic3)—22no—
5C2×C4⋊(C3⋊Dic3)C411yescharacteristic
6C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
7C22⋊#622—22no—
8#4935—62no—
9C22×C32×C4—21no—
10C22×C32×C4C2×C411yescharacteristic
11C22×C3⋊Dic3—21no—
12C22×C3⋊Dic3D412yes—
13C2×#622—42no—
14C32×C42—21no—
15C32×C42C812yescomplemented
16C4⋊(C3⋊Dic3)—41no—
17C4⋊(C3⋊Dic3)—44no—
18C4⋊(C3⋊Dic3)—41no—
19#1325—91nomaximal, Sylow
20C2×C3×C42—22no—
21C2×C4⋊Dic3—62no—
22C2×C4⋊Dic3—62no—
23C2×C4⋊Dic3—68no—
24C23×C32C22⋊C411yescharacteristic
25C2×C32×C4—22no—
26C2×C32×C4—22no—
27C2×C32×C4—22no—
28C2×C32×C4—21no—
29C2×C32×C4—21no—
30C2×C32×C4C2×C811yescharacteristic
31C2×C32×C4M1611yescharacteristic
32C2×C3⋊Dic3—22no—
33C2×C3⋊Dic3—42no—
34C2×C3⋊Dic3—42no—
35C2×C3⋊Dic3—41no—
36#622—82no—
37#384—91no—
38#324—92no—
39C22×C3×C4—24no—
40C22×C3×C4—22no—
41C22×Dic3—64no—
42C22×Dic3—64no—
43C3×C42—24no—
44C3×C42—24no—
45C4⋊Dic3—124no—
46C4⋊Dic3—124no—
47C4⋊Dic3—1216no—
48C22×C32—21no—
49C22×C32—21no—
50C22×C32C22⋊C811yescharacteristic
51C22×C32#9911yescharacteristic
52C22×C32#10111yescharacteristic
53C32×C4—24no—
54C32×C4—21no—
55C32×C4—21no—
56C3⋊Dic3—42no—
57C3⋊Dic3—81no—
58C2×C4⋊C4—91no—
59C2×C4⋊C4—91no—
60C2×C4⋊C4—182no—
61C2×C42#15711yescharacteristic
62C22⋊C8—182no—
63C23×C3—22no—
64C2×C3×C4—28no—
65C2×C3×C4—24no—
66C2×C3×C4—28no—
67C2×C3×C4—28no—
68C2×C3×C4—24no—
69C2×C3×C4—22no—
70C2×C3×C4—22no—
71C2×Dic3—124no—
72C2×Dic3—128no—
73C2×Dic3—128no—
74C2×Dic3—124no—
75C2×C32—21no—
76C2×C32—21no—
77C2×C32#32411yescharacteristic
78C2×C32#35311yescharacteristic
79C2×C32#35611yescharacteristic
80C22×C4—21no—
81C22×C4—92no—
82C22×C4—181no—
83C22×C4C2×#15711yescharacteristic
84C2×C8—362no—
85C4⋊C4—361no—
86C4⋊C4—361no—
87C4⋊C4—364no—
88C42—21no—
89C42#62212yescomplemented
90C22×C3—24no—
91C22×C3—24no—
92C22×C3—22no—
93C22×C3—22no—
94C22×C3—22no—
95C3×C4—216no—
96C3×C4—24no—
97C3×C4—24no—
98Dic3—244no—
99Dic3—244no—
100C32#132511yescharacteristic, complemented, Sylow
101C23C22⋊#15711yescharacteristic
102C2×C4—22no—
103C2×C4—22no—
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—22no—
107C2×C4—182no—
108C2×C4—362no—
109C2×C4—362no—
110C2×C4—361no—
111C2×C4C2×#62211yescharacteristic
112C2×C4#379211yescharacteristic
113C8—722no—
114C2×C3—24no—
115C2×C3—24no—
116C2×C3—22no—
117C2×C3—22no—
118C2×C3—22no—
119C22—21no—
120C22—21no—
121C22#6377411yescharacteristic
122C22#6378011yescharacteristic
123C22C22⋊#62211yescharacteristic
124C4—24no—
125C4—21no—
126C4—21no—
127C4—362no—
128C4—721no—
129C3—22no—
130C2—21no—
131C2—21no—
132C2#1059014211yescharacteristic
133C2#1059014411yescharacteristic
134C2#1059020211yescharacteristic
subgroupG/H
centerC22#63774
commutatorC2×C32×C4C2×C8
FrattiniC22×C4C2×#157
FittingC2×C32×C42C4
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC2×C4⋊(C3⋊Dic3)C22
hypercenterC2×C42#157
hypocenterC32#1325
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
15. C32×C42C8semidirect
89. C42#622semidirect
100. C32#1325semidirect

Maximal subgroups

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

subgroupindex
#105926342
#105902022
#13259