Finite Group Databasebeta

← #11772523

Subgroups — #11772523

Order 1152.

162 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 47 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#10593771C211yesmaximal, characteristic
2C2×#63771C211yesmaximal, characteristic
3#10593762C211yesmaximal, characteristic
4#64283—21no—
5C2×#3788—21no—
6C2×C8×C3⋊D3C2211yescharacteristic
7#63773C412yes—
8#63771—21no—
9#63771—21no—
10#63771C412yes—
11#63770C412yes—
12#63765—21no—
13#63764—21no—
14C2×C4×C3⋊D3D411yescharacteristic
15#3792—41no—
16C2×#622—41no—
17#3788—22no—
18#3788—22no—
19#3788—41no—
20#3787—41no—
21C2×C32×C8Q811yescharacteristic
22C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
23C8×C3⋊D3C2×C411yescharacteristic
24C8×C3⋊D3C2×C411yescharacteristic
25C8×C3⋊D3D411yescharacteristic
26C8×C3⋊D3D411yescharacteristic
27#3708—22no—
28#1388—91nomaximal, Sylow
29C2×D3×C8—121no—
30C22×C3⋊D3Q1611yescharacteristic
31C2×C32×C4C4⋊C411yescharacteristic
32C2×C3⋊Dic3D811yescharacteristic
33C4×C3⋊D3C22⋊C411yescharacteristic
34C4×C3⋊D3C22⋊C411yescharacteristic
35C4×C3⋊D3SD1611yescharacteristic
36C4×C3⋊D3SD1611yescharacteristic
37#622—42no—
38#622—42no—
39C32×C8C4⋊C411yescharacteristic
40C32×C8C4⋊C411yescharacteristic
41C3⋊(C3⋊C8)C4211yescharacteristic
42C3⋊(C3⋊C8)C22⋊C411yescharacteristic
43C2×M32—91no—
44C2×#108—91no—
45C2×#108—91no—
46C2×C4×D3—121no—
47C2×C3×C8—41no—
48C2×C3⋊C8—121no—
49D3×C8—121no—
50D3×C8—121no—
51D3×C8—121no—
52D3×C8—121no—
53C22×C32#10711yescharacteristic
54C2×C3⋊D3—41no—
55C2×C3⋊D3#10311yescharacteristic
56C2×C3⋊D3#10311yescharacteristic
57C32×C4#9511yescharacteristic
58C32×C4#10611yescharacteristic
59C3⋊Dic3#10211yescharacteristic
60C3⋊Dic3#10211yescharacteristic
61C2×M16—181no—
62C2×M16—181no—
63C22×C8—91no—
64M32—92no—
65M32—181no—
66C2×C16—181no—
67#108—92no—
68#108—92no—
69#108—181no—
70#108—181no—
71C22×D3—121no—
72C2×C3×C4—41no—
73C2×Dic3—121no—
74C4×D3—121no—
75C4×D3—121no—
76C4×D3—121no—
77C4×D3—121no—
78C3×C8—41no—
79C3×C8—41no—
80C3⋊C8—121no—
81C3⋊C8—121no—
82C2×C32—21no—
83C2×C32#34011yescharacteristic
84C3⋊D3—21no—
85C3⋊D3—21no—
86C22×C4—91no—
87M16—182no—
88M16—182no—
89M16—361no—
90M16—361no—
91C2×C8—91no—
92C2×C8—91no—
93C2×C8—91no—
94C2×C8—91no—
95C2×C8—91no—
96C2×C8—361no—
97C2×C8—361no—
98C2×C8PSU(3,𝔽2)11yescharacteristic
99C16—182no—
100C22×C3—41no—
101C2×D3—121no—
102C2×D3—121no—
103C2×D3—124no—
104C3×C4—41no—
105C3×C4—41no—
106Dic3—121no—
107Dic3—121no—
108C32#138811yescharacteristic, complemented, Sylow
109C23—91no—
110C2×C4—91no—
111C2×C4—91no—
112C2×C4—91no—
113C2×C4—91no—
114C2×C4—91no—
115C2×C4#377711yescharacteristic
116C8—91no—
117C8—91no—
118C8—362no—
119C8—362no—
120C8#377711yescharacteristic
121C8#377711yescharacteristic
122C2×C3—42no—
123C2×C3—41no—
124D3—122no—
125D3—122no—
126C22—91no—
127C22—91no—
128C22—361no—
129C22#6374611yescharacteristic
130C4—91no—
131C4—91no—
132C4#6374511yescharacteristic
133C4#6374711yescharacteristic
134C3—41no—
135C2—21no—
136C2—181no—
137C2—181no—
138C2#1059009311yescharacteristic
subgroupG/H
centerC2#10590093
commutatorC3⋊(C3⋊C8)C42
Frattini, hypercenterC2×C8PSU(3,𝔽2)
FittingC2×C32×C8Q8
socleC2×C32#340
prime radicalC22×C3⋊D3Q16
cosocleC2×C8×C3⋊D3C22
hypocenterC32#1388
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
108. C32#1388semidirect

Maximal subgroups

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

subgroupindex
#105937712
C2×#637712
#105937622
#13889