Finite Group Databasebeta

← #11797799

Subgroups — #11797799

Order 1152.

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

normal subgroups only

This group has 258 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
1C2×#63736C211yesmaximal, characteristic
2#10590790C212yesmaximal
3#10590175C211yesmaximal, characteristic
4#10590069C211yesmaximal, characteristic
5#10590062C212yesmaximal
6#63843—22no—
7C2×#3718C2212yes—
8C2×#3708C2211yescharacteristic
9C2×#3708C2211yescharacteristic
10#63736C414yescomplemented
11C8×C3⋊Dic3C2211yescharacteristic
12C3×#816—22no—
13#63576C2212yes—
14#4790—62no—
15C2×C3×Dic6—22no—
16C2×C32×C8D411yescharacteristic
17C4×C3⋊Dic3D411yescharacteristic
18C2×C3⋊(C3⋊C8)C2311yescharacteristic
19C3×C4⋊Dic3—22no—
20Dic3⋊Dic3—42no—
21Dic32—42no—
22#3718—22no—
23#3718C2×C414yes—
24#3708—21no—
25#3708C2×C412yes—
26#2176—91nomaximal, Sylow
27Q8×Dic3—62no—
28C2×#216—62no—
29#887—62no—
30C3×#103—62no—
31#816—22no—
32C8×Dic3—62no—
33#807—62no—
34C2×C32×C4C2×D411yescharacteristic
35C2×C3⋊Dic3D812yes—
36C2×C3×Dic3—42no—
37C2×C3×Dic3—42no—
38C3×Dic6—24no—
39C3×Dic6—42no—
40C32×C8—21no—
41C3⋊(C3⋊C8)C22×C411yescharacteristic
42C3⋊(C3⋊C8)#4111yescharacteristic
43C2×Q32—91no—
44C4×Q16—92no—
45#367—91no—
46#358—92no—
47#346—91no—
48C2×C3×Q8—62no—
49C2×Dic6—22no—
50C2×C3×C8—22no—
51C3×C4⋊C4—62no—
52#216—64no—
53#216—64no—
54C4⋊Dic3—22no—
55C4⋊Dic3—122no—
56Dic3⋊C4—122no—
57C4×Dic3—62no—
58C4×Dic3—122no—
59C4×Dic3—122no—
60C2×C3⋊C8—62no—
61C22×C32C2×D811yescharacteristic
62C32×C4C4×D411yescharacteristic
63C32×C4#13511yescharacteristic
64C3⋊Dic3—22no—
65C3×Dic3—44no—
66C3×Dic3—82no—
67C2×Q16—92no—
68C4×Q8—182no—
69Q32—94no—
70C2×C16—91no—
71C2×C16—91no—
72#107—92no—
73#103—62no—
74C4×C8—91no—
75C3×Q8—64no—
76C3×Q8—122no—
77C2×C3×C4—22no—
78C2×C3×C4—122no—
79C2×C3×C4—122no—
80C2×Dic3—42no—
81C2×Dic3—42no—
82C2×Dic3—62no—
83C2×Dic3—62no—
84Dic6—24no—
85Dic6—42no—
86C3×C8—42no—
87C3⋊C8—62no—
88C3⋊C8—62no—
89C2×C32C4×D811yescharacteristic
90C2×C32#51012yes—
91C2×Q8—62no—
92Q16—94no—
93Q16—182no—
94C2×C8—91no—
95C2×C8GO+(4,𝔽2)11yescharacteristic
96C4⋊C4—62no—
97C4⋊C4—362no—
98C42—91no—
99C42—362no—
100C16—92no—
101C16—181no—
102C22×C3—22no—
103C3×C4—22no—
104C3×C4—22no—
105C3×C4—124no—
106C3×C4—242no—
107Dic3—44no—
108Dic3—64no—
109Dic3—82no—
110Dic3—122no—
111C32#217611yescharacteristic, complemented, Sylow
112Q8—64no—
113Q8—122no—
114C2×C4—92no—
115C2×C4—122no—
116C2×C4—122no—
117C2×C4C2×GO+(4,𝔽2)11yescharacteristic
118C8—21no—
119C8—91no—
120C8—91no—
121C2×C3—22no—
122C2×C3—22no—
123C2×C3—22no—
124C22#6422511yescharacteristic
125C4—124no—
126C4—182no—
127C4—242no—
128C4C4×GO+(4,𝔽2)11yescharacteristic
129C4#6423711yescharacteristic
130C3—22no—
131C2#1059327912yes—
132C2#1059342011yescharacteristic
subgroupG/H
centerC22#64225
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socle, prime radicalC22×C32C2×D8
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2176
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
10. #63736C4semidirect
111. C32#2176semidirect

Maximal subgroups

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

subgroupindex
C2×#637362
#105907902
#105901752
#105900692
#105900622
#21769