Finite Group Databasebeta

← #11797798

Subgroups — #11797798

Order 1152.

258 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 51 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
2C4×#3718C212yesmaximal
3#10590148C211yesmaximal, characteristic
4#10590069C211yesmaximal, characteristic
5#10590062C212yesmaximal
6C3×C4×Dic6—22no—
7C2×#3718C2212yes—
8C2×#3708C2211yescharacteristic
9C2×#3708C2211yescharacteristic
10#63736C414yescomplemented
11C4×C3⋊(C3⋊C8)C2211yescharacteristic
12#63576C2212yes—
13#63565—22no—
14C4×#216—62no—
15C2×C3×Dic6—22no—
16C32×C42D411yescharacteristic
17C2×C3⋊(C3⋊C8)D411yescharacteristic
18C2×C3⋊(C3⋊C8)C2311yescharacteristic
19C3×C4⋊Dic3—22no—
20C3×Dic3⋊C4—42no—
21C3×C4×Dic3—42no—
22#3718—22no—
23#3718C2×C414yes—
24#3708—21no—
25#3708C2×C412yes—
26#2176—91nomaximal, Sylow
27C3×C4×Q8—62no—
28C2×#216—62no—
29C4×Dic6—22no—
30#835—62no—
31#810—62no—
32#807—62no—
33C4×C3⋊C8—62no—
34C2×C32×C4D812yes—
35C2×C32×C4C2×D411yescharacteristic
36C2×C3×Dic3—42no—
37C2×C3×Dic3—42no—
38C3×Dic6—24no—
39C3×Dic6—42no—
40C3⋊(C3⋊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—
50C3×C4⋊C4—62no—
51C3×C4⋊C4—122no—
52C3×C42—22no—
53C3×C42—122no—
54#216—64no—
55#216—64no—
56C4⋊Dic3—22no—
57Dic3⋊C4—42no—
58C4×Dic3—42no—
59C2×C3⋊C8—62no—
60C2×C3⋊C8—62no—
61C22×C32C2×D811yescharacteristic
62C32×C4—22no—
63C32×C4C4×D411yescharacteristic
64C32×C4#13511yescharacteristic
65C3×Dic3—44no—
66C3×Dic3—82no—
67C2×Q16—92no—
68C4×Q8—62no—
69Q32—94no—
70C2×C16—91no—
71C2×C16—91no—
72#107—92no—
73#103—182no—
74C4×C8—91no—
75C3×Q8—64no—
76C3×Q8—122no—
77C2×C3×C4—22no—
78C2×C3×C4—22no—
79C2×C3×C4—22no—
80C2×C3×C4—122no—
81C2×C3×C4—122no—
82C2×Dic3—42no—
83C2×Dic3—42no—
84Dic6—24no—
85Dic6—42no—
86C3⋊C8—62no—
87C3⋊C8—62no—
88C3⋊C8—122no—
89C2×C32C4×D811yescharacteristic
90C2×C32#51012yes—
91C2×Q8—62no—
92Q16—94no—
93Q16—182no—
94C2×C8—91no—
95C2×C8—91no—
96C4⋊C4—62no—
97C4⋊C4—122no—
98C42—122no—
99C42GO+(4,𝔽2)11yescharacteristic
100C16—92no—
101C16—181no—
102C22×C3—22no—
103C3×C4—24no—
104C3×C4—22no—
105C3×C4—22no—
106C3×C4—42no—
107C3×C4—124no—
108C3×C4—242no—
109Dic3—44no—
110Dic3—82no—
111C32#217611yescharacteristic, complemented, Sylow
112Q8—64no—
113Q8—122no—
114C2×C4—122no—
115C2×C4—122no—
116C2×C4#377412yes—
117C2×C4C2×GO+(4,𝔽2)11yescharacteristic
118C8—91no—
119C8—91no—
120C8—181no—
121C2×C3—22no—
122C2×C3—22no—
123C2×C3—22no—
124C22C2×#377411yescharacteristic
125C4—22no—
126C4—124no—
127C4—242no—
128C4#6422311yescharacteristic
129C4C4×GO+(4,𝔽2)11yescharacteristic
130C3—22no—
131C2#1059333612yes—
132C2C4×#377411yescharacteristic
subgroupG/H
centerC22C2×#3774
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socle, prime radicalC22×C32C2×D8
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#2176
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

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
C4×#37182
#105901482
#105900692
#105900622
#21769