Finite Group Databasebeta

← #11770939

Subgroups — #11770939

Order 1152.

236 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 42 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#10593731C211yesmaximal, characteristic
2#10593727C211yesmaximal, characteristic
3#10592404C211yesmaximal, characteristic
4C42×C3⋊D3C2211yescharacteristic
5#63779—21no—
6#63778—21no—
7#63778C412yes—
8#63777—21no—
9C4⋊#622—21no—
10C4×#622C412yes—
11C32×#97C411yescharacteristic
12#63647—21no—
13#63641—21no—
14#63630C411yescharacteristic
15#4705—62no—
16C2×C4×C3⋊D3C2×C411yescharacteristic
17C2×C4×C3⋊D3D411yescharacteristic
18C2×C4×C3⋊D3Q811yescharacteristic
19C2×#622—22no—
20C2×#622—22no—
21C2×C32×C8—21no—
22C32×C42C2×C411yescharacteristic
23C4×C3⋊Dic3C2×C411yescharacteristic
24C4×C3⋊Dic3D411yescharacteristic
25C4×C3⋊Dic3D411yescharacteristic
26C2×C3⋊(C3⋊C8)—21no—
27#1287—91nomaximal, Sylow
28C42×D3—62no—
29C3×#97—22no—
30(C2×D3)⋊C8—64no—
31Dic3⋊C8—64no—
32#803—62no—
33C22×C3⋊D3C4⋊C411yescharacteristic
34C2×C32×C4C4211yescharacteristic
35C2×C32×C4C22⋊C411yescharacteristic
36C2×C32×C4C4⋊C411yescharacteristic
37C2×C3⋊Dic3C22⋊C411yescharacteristic
38C2×C3⋊Dic3C22⋊C411yescharacteristic
39C2×C3⋊Dic3C4⋊C411yescharacteristic
40C4×C3⋊D3—22no—
41C4×C3⋊D3—41no—
42C4×C3⋊D3—41no—
43#622—42no—
44#622—42no—
45C32×C8—41no—
46C3⋊(C3⋊C8)—41no—
47#432—91no—
48#432—91no—
49#431—91no—
50C2×C4×D3—62no—
51C2×C4×D3—62no—
52C2×C4×D3—62no—
53C2×C3×C8—24no—
54C3×C42—22no—
55C4×Dic3—62no—
56C4×Dic3—62no—
57C4×Dic3—62no—
58C2×C3⋊C8—64no—
59C22×C32#9511yescharacteristic
60C2×C3⋊D3—21no—
61C2×C3⋊D3—21no—
62C2×C3⋊D3—21no—
63C32×C4—21no—
64C32×C4—21no—
65C32×C4—21no—
66C3⋊Dic3—21no—
67C3⋊Dic3—21no—
68C3⋊Dic3#10812yes—
69C2×C42—91no—
70C4⋊C8—181no—
71C4⋊C8—181no—
72C4⋊C8—181no—
73C22⋊C8—92no—
74C22⋊C8—181no—
75C22⋊C8—181no—
76#97—91no—
77#97—181no—
78#97#15711yescharacteristic
79C4×C8—92no—
80C22×D3—62no—
81C2×C3×C4—22no—
82C2×C3×C4—22no—
83C2×C3×C4—22no—
84C2×Dic3—62no—
85C2×Dic3—62no—
86C2×Dic3—62no—
87C4×D3—124no—
88C4×D3—124no—
89C4×D3—124no—
90C3×C8—44no—
91C3⋊C8—124no—
92C2×C32H(3,ℤ/4)11yescharacteristic
93C2×C32#34111yescharacteristic
94C2×C32#34411yescharacteristic
95C3⋊D3—41no—
96C22×C4—91no—
97C22×C4—91no—
98C22×C4—91no—
99C2×C8—21no—
100C2×C8—182no—
101C2×C8—182no—
102C2×C8—181no—
103C42—91no—
104C42—91no—
105C42—91no—
106C42C2×#15711yescharacteristic
107C22×C3—22no—
108C2×D3—64no—
109C2×D3—122no—
110C2×D3—122no—
111C3×C4—24no—
112C3×C4—42no—
113C3×C4—42no—
114Dic3—64no—
115Dic3—122no—
116Dic3—122no—
117C32#128711yescharacteristic, complemented, Sylow
118C23—91no—
119C2×C4—91no—
120C2×C4—91no—
121C2×C4—91no—
122C2×C4—182no—
123C2×C4—361no—
124C2×C4—361no—
125C2×C4C4×#15711yescharacteristic
126C2×C4C4⋊#15711yescharacteristic
127C2×C4C22⋊#15711yescharacteristic
128C8—41no—
129C8—361no—
130C8—362no—
131C8—362no—
132C2×C3—22no—
133C2×C3—22no—
134C2×C3—22no—
135D3—124no—
136C22—181no—
137C22—181no—
138C22—181no—
139C22#6378111yescharacteristic
140C4—21no—
141C4—21no—
142C4—21no—
143C4—92no—
144C4—181no—
145C4—181no—
146C3—22no—
147C2—361no—
148C2#1059015211yescharacteristic
149C2#1059019011yescharacteristic
150C2#1059019111yescharacteristic
subgroupG/H
centerC22#63781
commutatorC2×C32×C4C42
FrattiniC42C2×#157
FittingC32×#97C4
socleC22×C32#95
prime radicalC22×C3⋊D3C4⋊C4
cosocleC42×C3⋊D3C22
hypercenter#97#157
hypocenterC32#1287
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
117. C32#1287semidirect

Maximal subgroups

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

subgroupindex
#105937312
#105937272
#105924042
#12879