Finite Group Databasebeta

← #11772025

Subgroups — #11772025

Order 1152.

176 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 29 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#10590905C211yesmaximal, characteristic
2#10590178C211yesmaximal, characteristic
3#10589135C211yesmaximal, characteristic
4C2×C3×Dic12—21no—
5#63873C412yes—
6C2×#3718—21no—
7#63773—21no—
8C8×C3⋊Dic3C2211yescharacteristic
9C3×#812—21no—
10#5183—61no—
11#4511—61no—
12C2×C3×Dic6—22no—
13C2×C32×C8D411yescharacteristic
14C4×C3⋊Dic3C2×C411yescharacteristic
15C2×C3⋊(C3⋊C8)D411yescharacteristic
16C3×Dic12—41no—
17C3×Dic12—41no—
18#3724—42no—
19#3718—41no—
20#3718—41no—
21#3708—41no—
22C3×C3⋊C16—41no—
23#1358—91nomaximal, Sylow
24C2×C3×Q16—61no—
25#944—62no—
26C2×#216—62no—
27C2×Dic12—21no—
28C3×M32—61no—
29C8×Dic3—61no—
30C8×Dic3—61no—
31#812—21no—
32C2×C32×C4C22⋊C411yescharacteristic
33C2×C3⋊Dic3—21no—
34C2×C3×Dic3—42no—
35C3×Dic6—42no—
36C3×Dic6—42no—
37C32×C8D811yescharacteristic
38C32×C8SD1611yescharacteristic
39C3⋊(C3⋊C8)D811yescharacteristic
40C3⋊(C3⋊C8)SD1611yescharacteristic
41#494—91no—
42#364—91no—
43#364—91no—
44C2×C3×Q8—62no—
45C2×Dic6—22no—
46C3×Q16—121no—
47C3×Q16—121no—
48C2×C3×C8—21no—
49C2×C3×C8—21no—
50#216—122no—
51#216—122no—
52Dic3⋊C4—124no—
53C4×Dic3—61no—
54C4×Dic3—61no—
55C2×C3⋊C8—61no—
56C2×C3⋊C8—61no—
57Dic12—41no—
58Dic12—41no—
59C3×C16—121no—
60C3⋊C16—41no—
61C22×C32#10011yescharacteristic
62C32×C4#10211yescharacteristic
63C32×C4#10211yescharacteristic
64C3⋊Dic3—22no—
65C3×Dic3—82no—
66C2×Q16—61no—
67C2×Q16—181no—
68C4⋊Q8—92no—
69M32—61no—
70M32—181no—
71C4×C8—91no—
72C3×Q8—122no—
73C3×Q8—122no—
74C2×C3×C4—21no—
75C2×C3×C4—21no—
76C2×C3×C4—122no—
77C2×Dic3—42no—
78C2×Dic3—62no—
79C2×Dic3—121no—
80Dic6—42no—
81Dic6—42no—
82C3×C8—21no—
83C3×C8—21no—
84C3×C8—21no—
85C3×C8—21no—
86C3⋊C8—61no—
87C3⋊C8—61no—
88C3⋊C8—61no—
89C3⋊C8—61no—
90C2×C32—21no—
91C2×C32#33111yescharacteristic
92C2×Q8—62no—
93Q16—121no—
94Q16—121no—
95Q16—361no—
96Q16—361no—
97C2×C8—91no—
98C2×C8GO+(4,𝔽2)11yescharacteristic
99C4⋊C4—362no—
100C42—91no—
101C16—121no—
102C16—361no—
103C22×C3—21no—
104C22×C3—21no—
105C3×C4—21no—
106C3×C4—21no—
107C3×C4—21no—
108C3×C4—21no—
109C3×C4—242no—
110Dic3—64no—
111Dic3—82no—
112Dic3—122no—
113C32#135811yescharacteristic, complemented, Sylow
114Q8—122no—
115Q8—122no—
116C2×C4—122no—
117C2×C4—181no—
118C2×C4D32⋊C411yescharacteristic
119C8—91no—
120C8—91no—
121C8#377411yescharacteristic
122C8#377511yescharacteristic
123C2×C3—22no—
124C2×C3—21no—
125C2×C3—21no—
126C2×C3—41no—
127C22#6372711yescharacteristic
128C4—182no—
129C4—242no—
130C4#6372911yescharacteristic
131C4#6373911yescharacteristic
132C3—21no—
133C3—21no—
134C2—21no—
135C2#1059003711yescharacteristic
subgroupG/H
centerC2#10590037
commutatorC4×C3⋊Dic3C2×C4
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#331
prime radicalC22×C32#100
cosocleC8×C3⋊Dic3C22
hypocenterC32#1358
LCSG ▷ C4×C3⋊Dic3 ▷ C2×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
113. C32#1358semidirect

Maximal subgroups

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

subgroupindex
#105909052
#105901782
#105891352
#13589