Finite Group Databasebeta

← #11771153

Subgroups — #11771153

Order 1152.

226 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 43 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#10593733C211yesmaximal, characteristic
2#10593731C211yesmaximal, characteristic
3C4×#3788C211yesmaximal, characteristic
4C2×C4×#157—21no—
5C2×#3788—21no—
6C42×C3⋊D3C2211yescharacteristic
7#63781—21no—
8#63781C412yes—
9#63779C412yescomplemented
10#63778—21no—
11#63777—21no—
12#63777C412yescomplemented
13C4×#622—21no—
14C22×#157—22no—
15C2×C4×C3⋊D3C2×C411yescharacteristic
16C2×C4×C3⋊D3D411yescharacteristic
17C2×C4×C3⋊D3D411yescharacteristic
18C2×#622—22no—
19C2×#622—22no—
20C4×#157—24no—
21#3788—24no—
22C32×C42Q811yescharacteristic
23C4×C3⋊Dic3C2×C411yescharacteristic
24C4×C3⋊Dic3C2×C411yescharacteristic
25C4×C3⋊Dic3D411yescharacteristic
26#1300—91nomaximal, Sylow
27C42×D3—121no—
28C22×C3⋊D3C22⋊C411yescharacteristic
29C2×#157—24no—
30C2×#157—42no—
31C2×#157—42no—
32C2×C32×C4C4⋊C411yescharacteristic
33C2×C32×C4C4⋊C411yescharacteristic
34C2×C32×C4C4⋊C411yescharacteristic
35C2×C3⋊Dic3C4211yescharacteristic
36C2×C3⋊Dic3C22⋊C411yescharacteristic
37C2×C3⋊Dic3C22⋊C411yescharacteristic
38C4×C3⋊D3—22no—
39C4×C3⋊D3—22no—
40C4×C3⋊D3—41no—
41#622—24no—
42#622—42no—
43#432—91no—
44C4×M16—91no—
45#376—91no—
46C2×C4×D3—121no—
47C2×C4×D3—121no—
48C2×C4×D3—121no—
49C3×C42—41no—
50C4×Dic3—121no—
51C4×Dic3—121no—
52C4×Dic3—121no—
53C22×C32#9511yescharacteristic
54C2×C3⋊D3—21no—
55C2×C3⋊D3—21no—
56C2×C3⋊D3#10412yes—
57#157—44no—
58C32×C4—21no—
59C32×C4—21no—
60C32×C4—21no—
61C3⋊Dic3—21no—
62C3⋊Dic3—21no—
63C3⋊Dic3#10412yes—
64C2×M16—181no—
65C2×C42—91no—
66C2×C42—181no—
67C4⋊C8—92no—
68C22⋊C8—181no—
69#97—92no—
70#97—181no—
71C4×C8—181no—
72#95—92no—
73#95—181no—
74C22×D3—121no—
75C2×C3×C4—41no—
76C2×C3×C4—41no—
77C2×C3×C4—41no—
78C2×Dic3—121no—
79C2×Dic3—121no—
80C2×Dic3—121no—
81C4×D3—124no—
82C4×D3—124no—
83C4×D3—124no—
84C2×C32#33911yescharacteristic
85C2×C32#33911yescharacteristic
86C2×C32#34411yescharacteristic
87C3⋊D3—22no—
88C22×C4—91no—
89C22×C4—91no—
90C22×C4—91no—
91C22×C4—182no—
92M16—184no—
93C2×C8—182no—
94C2×C8—182no—
95C42—91no—
96C42—91no—
97C42—91no—
98C42—184no—
99C42PSU(3,𝔽2)11yescharacteristic
100C22×C3—41no—
101C2×D3—122no—
102C2×D3—122no—
103C2×D3—122no—
104C3×C4—42no—
105C3×C4—42no—
106C3×C4—42no—
107Dic3—122no—
108Dic3—122no—
109Dic3—122no—
110C32#130011yescharacteristic, complemented, Sylow
111C23—91no—
112C2×C4—91no—
113C2×C4—91no—
114C2×C4—91no—
115C2×C4—182no—
116C2×C4—182no—
117C2×C4—184no—
118C2×C4—361no—
119C2×C4—362no—
120C2×C4—362no—
121C2×C4#377711yescharacteristic
122C2×C4#377711yescharacteristic
123C2×C4#377711yescharacteristic
124C8—184no—
125C8—362no—
126C2×C3—41no—
127C2×C3—41no—
128C2×C3—41no—
129D3—124no—
130C22—92no—
131C22—181no—
132C22—181no—
133C22#6374711yescharacteristic
134C4—21no—
135C4—21no—
136C4—21no—
137C4—92no—
138C4—181no—
139C4—181no—
140C4—364no—
141C3—41no—
142C2—182no—
143C2#1059009211yescharacteristic
144C2#1059009211yescharacteristic
145C2#1059009511yescharacteristic
subgroupG/H
centerC22#63747
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC42PSU(3,𝔽2)
FittingC32×C42Q8
socleC22×C32#95
prime radicalC22×C3⋊D3C22⋊C4
cosocleC42×C3⋊D3C22
hypocenterC32#1300
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
9. #63779C4semidirect
12. #63777C4semidirect
110. C32#1300semidirect

Maximal subgroups

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

subgroupindex
#105937332
#105937312
C4×#37882
#13009