Finite Group Databasebeta

← #11771465

Subgroups — #11771465

Order 1152.

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

normal subgroups only

This group has 272 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#10592635C211yesmaximal, characteristic
2#10590202C212yesmaximal
3C2×C32×C42C411yescharacteristic
4C2×C4⋊(C3⋊Dic3)C411yescharacteristic
5C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
6C22⋊#622—22no—
7#63658—22no—
8#4936—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)—41no—
18#1324—91nomaximal, Sylow
19C2×C3×C42—22no—
20C2×C4⋊Dic3—62no—
21C2×C4⋊Dic3—62no—
22C3⋊#95—68no—
23C23×C32C22⋊C411yescharacteristic
24C2×C32×C4—21no—
25C2×C32×C4—21no—
26C2×C32×C4—22no—
27C2×C32×C4—41no—
28C2×C32×C4—41no—
29C2×C32×C4C2×C811yescharacteristic
30C2×C32×C4M1611yescharacteristic
31C2×C3⋊Dic3—22no—
32C2×C3⋊Dic3—42no—
33C2×C3⋊Dic3—42no—
34C2×C3⋊Dic3—41no—
35#622—82no—
36#382—91no—
37#324—92no—
38C22×C3×C4—24no—
39C22×C3×C4—22no—
40C22×Dic3—64no—
41C22×Dic3—64no—
42C3×C42—24no—
43C3×C42—24no—
44C4⋊Dic3—124no—
45C4⋊Dic3—124no—
46C22×C32—21no—
47C22×C32—21no—
48C22×C32C22⋊C811yescharacteristic
49C22×C32#9911yescharacteristic
50C22×C32#10111yescharacteristic
51C32×C4—21no—
52C32×C4—21no—
53C32×C4—42no—
54C3⋊Dic3—42no—
55C3⋊Dic3—81no—
56C2×C4⋊C4—91no—
57C2×C4⋊C4—91no—
58C2×C42#15711yescharacteristic
59C22⋊C8—182no—
60#95—182no—
61C23×C3—22no—
62C2×C3×C4—24no—
63C2×C3×C4—24no—
64C2×C3×C4—28no—
65C2×C3×C4—22no—
66C2×C3×C4—22no—
67C2×C3×C4—44no—
68C2×C3×C4—44no—
69C2×Dic3—124no—
70C2×Dic3—124no—
71C2×Dic3—128no—
72C2×Dic3—128no—
73C2×C32—21no—
74C2×C32—21no—
75C2×C32#32411yescharacteristic
76C2×C32#35411yescharacteristic
77C2×C32#35511yescharacteristic
78C22×C4—21no—
79C22×C4—92no—
80C22×C4—181no—
81C22×C4C2×#15711yescharacteristic
82C2×C8—362no—
83C4⋊C4—361no—
84C4⋊C4—361no—
85C42—21no—
86C42#62212yescomplemented
87C22×C3—24no—
88C22×C3—24no—
89C22×C3—22no—
90C22×C3—22no—
91C22×C3—22no—
92C3×C4—24no—
93C3×C4—24no—
94C3×C4—48no—
95Dic3—244no—
96Dic3—244no—
97C32#132411yescharacteristic, complemented, Sylow
98C23C22⋊#15711yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—22no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4—182no—
105C2×C4—362no—
106C2×C4—362no—
107C2×C4—361no—
108C2×C4C2×#62211yescharacteristic
109C2×C4#379211yescharacteristic
110C8—722no—
111C2×C3—24no—
112C2×C3—24no—
113C2×C3—22no—
114C2×C3—22no—
115C2×C3—22no—
116C22—21no—
117C22—21no—
118C22#6377411yescharacteristic
119C22#6378011yescharacteristic
120C22C22⋊#62211yescharacteristic
121C4—21no—
122C4—21no—
123C4—42no—
124C4—362no—
125C4—721no—
126C3—22no—
127C2—21no—
128C2—21no—
129C2#1059014311yescharacteristic
130C2#1059014511yescharacteristic
131C2#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#1324
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
86. C42#622semidirect
97. C32#1324semidirect

Maximal subgroups

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

subgroupindex
#105926352
#105902022
#13249