Finite Group Databasebeta

← #11781979

Subgroups — #11781979

Order 1152.

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

normal subgroups only

This group has 260 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#10593835C211yesmaximal, characteristic
2#10593388C211yesmaximal, characteristic
3#10591633C212yesmaximal
4#10590041C211yesmaximal, characteristic
5#10590038C212yesmaximal
6Q8×C3⋊Dic3C2211yescharacteristic
7C2×C3×#216—22no—
8#63873C2212yes—
9#63779—21no—
10#63777—21no—
11C4⋊#622C2211yescharacteristic
12C4×#622C2211yescharacteristic
13#63743—21no—
14#63743—21no—
15#63572C2212yes—
16#63566—22no—
17#5182—62no—
18C2×C32×Q8D411yescharacteristic
19C2×C3×Dic6—22no—
20C2×#622—21no—
21C2×#622D411yescharacteristic
22C2×#622D411yescharacteristic
23C4⋊(C3⋊Dic3)—21no—
24C4⋊(C3⋊Dic3)D411yescharacteristic
25C4×C3⋊Dic3—21no—
26C4×C3⋊Dic3C2311yescharacteristic
27C3×#216—44no—
28C2×C3×C3⋊C8—22no—
29#3724—22no—
30#3724—22no—
31#1694—91nomaximal, Sylow
32C2×C3×Q16—62no—
33Q8×Dic3—62no—
34#944—62no—
35C2×#216—22no—
36#835—62no—
37#816—62no—
38Dic3⋊C8—62no—
39C32×Q8—22no—
40C2×C32×C4—21no—
41C2×C32×C4C2×D411yescharacteristic
42C2×C3⋊Dic3—21no—
43C2×C3⋊Dic3C2×D411yescharacteristic
44C2×C3⋊Dic3#4111yescharacteristic
45C2×C3×Dic3—42no—
46C3×Dic6—42no—
47C3×Dic6—42no—
48#622—21no—
49#622—41no—
50#622Q1612yescomplemented
51C3×C3⋊C8—42no—
52#500—91no—
53#462—92no—
54#446—91no—
55#334—91no—
56#332—92no—
57C2×C3×Q8—22no—
58C2×C3×Q8—62no—
59C2×Dic6—22no—
60C3×Q16—124no—
61C2×C3×C8—62no—
62#216—44no—
63C4⋊Dic3—62no—
64C4⋊Dic3—122no—
65Dic3⋊C4—122no—
66Dic3⋊C4—122no—
67C4×Dic3—62no—
68C4×Dic3—122no—
69C2×C3⋊C8—22no—
70C22×C32#12111yescharacteristic
71C32×C4—41no—
72C32×C4AGL(1,ℤ/8)12yes—
73C3⋊Dic3—21no—
74C3⋊Dic3—41no—
75C3⋊Dic3C2×Q1611yescharacteristic
76C3⋊Dic3#13711yescharacteristic
77C3×Dic3—82no—
78C2×Q16—62no—
79C4⋊Q8—92no—
80C4×Q8—91no—
81#107—181no—
82#107—181no—
83C4⋊C8—92no—
84C4⋊C8—91no—
85C4⋊C8—181no—
86#103—182no—
87#97—181no—
88C4×C8—91no—
89C3×Q8—24no—
90C3×Q8—42no—
91C3×Q8—122no—
92C3×Q8—122no—
93C2×C3×C4—22no—
94C2×C3×C4—42no—
95C2×C3×C4—122no—
96C2×Dic3—42no—
97C2×Dic3—62no—
98C2×Dic3—62no—
99C2×Dic3—122no—
100Dic6—42no—
101Dic6—42no—
102C3×C8—122no—
103C3⋊C8—42no—
104C2×C32#46211yescharacteristic
105C2×C32#46911yescharacteristic
106C2×C32#47311yescharacteristic
107C2×Q8—62no—
108C2×Q8GO+(4,𝔽2)11yescharacteristic
109Q16—124no—
110C2×C8—62no—
111C2×C8—91no—
112C2×C8—91no—
113C2×C8—181no—
114C4⋊C4—91no—
115C4⋊C4—181no—
116C4⋊C4—182no—
117C4⋊C4—182no—
118C42—91no—
119C42—181no—
120C22×C3—22no—
121C3×C4—22no—
122C3×C4—22no—
123C3×C4—44no—
124C3×C4—242no—
125Dic3—62no—
126Dic3—62no—
127Dic3—82no—
128Dic3—122no—
129Dic3—242no—
130C32#169411yescharacteristic, complemented, Sylow
131Q8—22no—
132Q8—122no—
133Q8—122no—
134C2×C4—21no—
135C2×C4—91no—
136C2×C4—91no—
137C2×C4—122no—
138C2×C4—181no—
139C2×C4C2×GO+(4,𝔽2)11yescharacteristic
140C8—92no—
141C8—122no—
142C8—181no—
143C8—361no—
144C2×C3—22no—
145C2×C3—22no—
146C2×C3—22no—
147C22#6424211yescharacteristic
148C4—41no—
149C4—91no—
150C4—91no—
151C4—181no—
152C4—242no—
153C4—361no—
154C4#6423612yes—
155C3—22no—
156C2#1059347711yescharacteristic
157C2#1059348211yescharacteristic
158C2#1059352211yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×Q8D4
socle, prime radicalC22×C32#121
hypercenterC2×Q8GO+(4,𝔽2)
hypocenterC32#1694
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
50. #622Q16semidirect
130. C32#1694semidirect

Maximal subgroups

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

subgroupindex
#105938352
#105933882
#105916332
#105900412
#105900382
#16949