Finite Group Databasebeta

← #11771633

Subgroups — #11771633

Order 1152.

178 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 33 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#10590790C211yesmaximal, characteristic
2#10590172C211yesmaximal, characteristic
3#10589104C211yesmaximal, characteristic
4#63843—21no—
5C2×#3718C411yescharacteristic
6C4⋊#622—21no—
7C8×C3⋊Dic3C2211yescharacteristic
8C3×#816—21no—
9C2×C3×C3⋊C16—21no—
10#63576C411yescharacteristic
11#4790—61no—
12#4502—61no—
13C2×C3×Dic6—21no—
14C2×#622—41no—
15C2×C32×C8D411yescharacteristic
16C4×C3⋊Dic3D411yescharacteristic
17C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
18C3×C4⋊Dic3—21no—
19Dic3⋊Dic3—41no—
20Dic32—41no—
21#3718—21no—
22#3718C812yescomplemented
23C3×C3⋊C16—22no—
24#1334—91nomaximal, Sylow
25Q8×Dic3—61no—
26C2×#216—61no—
27#887—61no—
28C2×C3×C16—61no—
29C3×#103—61no—
30#816—21no—
31C8×Dic3—61no—
32C8×Dic3—61no—
33C2×C3⋊C16—21no—
34#807—61no—
35C2×C32×C4C22⋊C411yescharacteristic
36C2×C3⋊Dic3D811yescharacteristic
37C2×C3⋊Dic3SD1611yescharacteristic
38C2×C3×Dic3—41no—
39C2×C3×Dic3—41no—
40C3×Dic6—22no—
41C3×Dic6—41no—
42#622—81no—
43C32×C8—21no—
44C3⋊(C3⋊C8)C2×C811yescharacteristic
45C3⋊(C3⋊C8)M1611yescharacteristic
46C4×Q16—91no—
47#346—91no—
48#334—91no—
49C2×C3×Q8—61no—
50C2×Dic6—21no—
51C2×C3×C8—21no—
52C2×C3×C8—21no—
53C3×C4⋊C4—61no—
54#216—62no—
55#216—62no—
56C4⋊Dic3—21no—
57C4⋊Dic3—121no—
58Dic3⋊C4—121no—
59C4×Dic3—61no—
60C4×Dic3—61no—
61C4×Dic3—121no—
62C4×Dic3—121no—
63C2×C3⋊C8—61no—
64C2×C3⋊C8—61no—
65C3×C16—62no—
66C3⋊C16—22no—
67C22×C32#10211yescharacteristic
68C32×C4C22⋊C811yescharacteristic
69C32×C4#10411yescharacteristic
70C3⋊Dic3—21no—
71C3⋊Dic3—21no—
72C3×Dic3—42no—
73C3×Dic3—81no—
74C2×Q16—91no—
75C4×Q8—181no—
76C2×C16—61no—
77#107—91no—
78C4⋊C8—181no—
79#103—61no—
80C4×C8—91no—
81C3×Q8—62no—
82C3×Q8—121no—
83C2×C3×C4—21no—
84C2×C3×C4—21no—
85C2×C3×C4—121no—
86C2×C3×C4—121no—
87C2×Dic3—41no—
88C2×Dic3—41no—
89C2×Dic3—61no—
90C2×Dic3—61no—
91C2×Dic3—61no—
92C2×Dic3—61no—
93Dic6—22no—
94Dic6—41no—
95C3×C8—21no—
96C3×C8—21no—
97C3×C8—41no—
98C3⋊C8—61no—
99C3⋊C8—61no—
100C3⋊C8—61no—
101C3⋊C8—61no—
102C2×C32D4⋊C811yescharacteristic
103C2×C32#36011yescharacteristic
104C2×C32#36211yescharacteristic
105C2×Q8—61no—
106Q16—92no—
107Q16—181no—
108C2×C8—91no—
109C2×C8—361no—
110C2×C8GO+(4,𝔽2)11yescharacteristic
111C4⋊C4—61no—
112C4⋊C4—361no—
113C42—91no—
114C42—361no—
115C16—62no—
116C22×C3—21no—
117C22×C3—21no—
118C3×C4—21no—
119C3×C4—21no—
120C3×C4—21no—
121C3×C4—21no—
122C3×C4—122no—
123C3×C4—241no—
124Dic3—42no—
125Dic3—62no—
126Dic3—81no—
127Dic3—121no—
128Dic3—121no—
129Dic3—121no—
130C32#133411yescharacteristic, complemented, Sylow
131Q8—62no—
132Q8—121no—
133C2×C4—91no—
134C2×C4—91no—
135C2×C4—121no—
136C2×C4—121no—
137C2×C4D32⋊C411yescharacteristic
138C8—21no—
139C8—91no—
140C8—91no—
141C8—721no—
142C2×C3—21no—
143C2×C3—21no—
144C2×C3—21no—
145C2×C3—21no—
146C2×C3—21no—
147C2×C3—21no—
148C22#6372911yescharacteristic
149C4—122no—
150C4—181no—
151C4—181no—
152C4—241no—
153C4D32⋊C811yescharacteristic
154C4#6374111yescharacteristic
155C3—21no—
156C3—21no—
157C2#1059001911yescharacteristic
158C2#1059002111yescharacteristic
159C2#1059003011yescharacteristic
subgroupG/H
centerC22#63729
commutatorC3⋊(C3⋊C8)C2×C8
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socle, prime radicalC22×C32#102
cosocleC8×C3⋊Dic3C22
hypocenterC32#1334
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
22. #3718C8semidirect
130. C32#1334semidirect

Maximal subgroups

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

subgroupindex
#105907902
#105901722
#105891042
#13349