Finite Group Databasebeta

← #11772411

Subgroups — #11772411

Order 1152.

170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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
2#10593768C211yesmaximal, characteristic
3C2×#63764C211yesmaximal, characteristic
4#64286—21no—
5#64283—21no—
6C2×C8×C3⋊D3C2211yescharacteristic
7C2×#3708C412yescomplemented
8#63771—21no—
9#63770C412yescomplemented
10#63769C412yes—
11#63768—21no—
12#63764—21no—
13#63764—21no—
14C2×C4×C3⋊D3D411yescharacteristic
15C22⋊#157—41no—
16#3792—41no—
17C4⋊#157—22no—
18C4×#157—41no—
19#3788—22no—
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#1382—91nomaximal, Sylow
29C2×D3×C8—121no—
30C22×C3⋊D3SD1611yescharacteristic
31C2×#157—42no—
32C2×C32×C4C4⋊C411yescharacteristic
33C2×C3⋊Dic3SD1611yescharacteristic
34C4×C3⋊D3C22⋊C411yescharacteristic
35C4×C3⋊D3C22⋊C411yescharacteristic
36C4×C3⋊D3D811yescharacteristic
37C4×C3⋊D3Q1611yescharacteristic
38#622—42no—
39C32×C8C4⋊C411yescharacteristic
40C32×C8C4⋊C411yescharacteristic
41C3⋊(C3⋊C8)C4211yescharacteristic
42C3⋊(C3⋊C8)C22⋊C411yescharacteristic
43C22×C16—91no—
44C2×#108—91no—
45#427—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#10611yescharacteristic
54C2×C3⋊D3—22no—
55C2×C3⋊D3#10211yescharacteristic
56C2×C3⋊D3#10311yescharacteristic
57#157—82no—
58C32×C4#9511yescharacteristic
59C32×C4#10711yescharacteristic
60C3⋊Dic3#10211yescharacteristic
61C3⋊Dic3#10311yescharacteristic
62C2×M16—181no—
63C22×C8—91no—
64#117—181no—
65C2×C16—92no—
66C2×C16—181no—
67C2×C16—181no—
68#108—92no—
69#108—181no—
70#107—92no—
71#106—181no—
72C22×D3—121no—
73C2×C3×C4—41no—
74C2×Dic3—121no—
75C4×D3—121no—
76C4×D3—121no—
77C4×D3—121no—
78C4×D3—121no—
79C3×C8—41no—
80C3×C8—41no—
81C3⋊C8—121no—
82C3⋊C8—121no—
83C2×C32—21no—
84C2×C32#34011yescharacteristic
85C3⋊D3—21no—
86C3⋊D3#35912yes—
87C22×C4—91no—
88M16—182no—
89M16—361no—
90C2×C8—91no—
91C2×C8—91no—
92C2×C8—91no—
93C2×C8—91no—
94C2×C8—91no—
95C2×C8—361no—
96C2×C8PSU(3,𝔽2)11yescharacteristic
97C4⋊C4—182no—
98C22⋊C4—361no—
99C42—361no—
100C16—182no—
101C22×C3—41no—
102C2×D3—121no—
103C2×D3—121no—
104C2×D3—124no—
105C3×C4—41no—
106C3×C4—41no—
107Dic3—121no—
108Dic3—121no—
109C32#138211yescharacteristic, complemented, Sylow
110C23—91no—
111C2×C4—91no—
112C2×C4—91no—
113C2×C4—91no—
114C2×C4—91no—
115C2×C4—91no—
116C2×C4—362no—
117C2×C4#377711yescharacteristic
118C8—91no—
119C8—91no—
120C8—362no—
121C8#377711yescharacteristic
122C8#377711yescharacteristic
123C2×C3—42no—
124C2×C3—41no—
125D3—122no—
126D3—122no—
127C22—91no—
128C22—91no—
129C22—182no—
130C22#6374511yescharacteristic
131C4—91no—
132C4—91no—
133C4—722no—
134C4#6374611yescharacteristic
135C4#6374711yescharacteristic
136C3—41no—
137C2—21no—
138C2—92no—
139C2—181no—
140C2#1059009311yescharacteristic
subgroupG/H
centerC4#63746
commutatorC3⋊(C3⋊C8)C42
Frattini, hypercenterC2×C8PSU(3,𝔽2)
FittingC2×C32×C8Q8
socleC2×C32#340
prime radicalC22×C3⋊D3SD16
cosocleC2×C8×C3⋊D3C22
hypocenterC32#1382
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
7. C2×#3708C4semidirect
9. #63770C4semidirect
109. C32#1382semidirect

Maximal subgroups

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

subgroupindex
#105937712
#105937682
C2×#637642
#13829