Finite Group Databasebeta

← #11797599

Subgroups — #11797599

Order 1152.

250 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 58 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#10593772C212yesmaximal, complemented
2#10592594C211yesmaximal, characteristic
3#10590187C212yesmaximal, complemented
4#10590178C211yesmaximal, characteristic, complemented
5#10590175C211yesmaximal, characteristic, complemented
6#64116C2212yes—
7#64113C411yescharacteristic
8#63773C2212yes—
9C2×#3708C2211yescharacteristic
10C2×#3708C2211yescharacteristic
11#63765—22no—
12#63764—22no—
13C32×#108C411yescharacteristic
14#63652C412yes—
15C8×C3⋊Dic3C2211yescharacteristic
16#4895—62no—
17#3828C2×C412yes—
18C32×M16C2×C412yes—
19C2×C32×C8C2×C411yescharacteristic
20C4×C3⋊Dic3C2×C411yescharacteristic
21C2×C3⋊(C3⋊C8)C2311yescharacteristic
22#3746C811yescharacteristic
23#3745C811yescharacteristic
24#3744C812yes—
25#3743—22no—
26C8×C3⋊D3—22no—
27#3708—22no—
28#3708—21no—
29#3708D412yes—
30#2171—91nomaximal, Sylow
31#907—64no—
32#904—62no—
33C3×#108—22no—
34#825—64no—
35C8×Dic3—62no—
36C2×C32×C4C22×C411yescharacteristic
37#638—22no—
38C2×C3⋊Dic3—21no—
39C4⋊(C3⋊D3)C2×C812yes—
40C4×C3⋊D3—22no—
41#634C2×C812yes—
42C32×C8—22no—
43C32×C8C2×C811yescharacteristic
44C32×C8C2×C811yescharacteristic
45C3⋊(C3⋊C8)C2×D411yescharacteristic
46C3⋊(C3⋊C8)#4111yescharacteristic
47#504—92no—
48#443—91no—
49#364—91no—
50#350—92no—
51#346—91no—
52#235—64no—
53C3×M16—24no—
54C2×C3×C8—22no—
55C4×Dic3—62no—
56C2×C3⋊C8—62no—
57Dic12—62no—
58D24—62no—
59#204—64no—
60ΓL(1,𝔽25)—124no—
61D3×C8—124no—
62C22×C32#13111yescharacteristic
63C2×C3⋊D3—22no—
64C32×C4C4×D411yescharacteristic
65C32×C4C22×C811yescharacteristic
66C3⋊Dic3—22no—
67C3⋊Dic3—41no—
68#135—91no—
69#131—92no—
70M32—92no—
71M32—182no—
72C2×C16—91no—
73C2×C16—91no—
74C2×C16—182no—
75#108#15711yescharacteristic
76#104—92no—
77C4×C8—91no—
78C2×C3×C4—22no—
79#67—124no—
80C2×Dic3—122no—
81D12—64no—
82C4×D3—124no—
83Dic6—64no—
84C3×C8—22no—
85C3×C8—22no—
86C3×C8—44no—
87C3⋊C8—62no—
88C3⋊C8—62no—
89C2×C32—21no—
90C2×C32C8×D411yescharacteristic
91C3⋊D3—42no—
92#41—92no—
93Q16—91no—
94SD16—92no—
95D8—91no—
96M16—182no—
97M16C2×#15712yes—
98C2×C8—91no—
99C2×C8—182no—
100C2×C8C2×#15711yescharacteristic
101C42—91no—
102C16—92no—
103C16—181no—
104C16—182no—
105C22×C3—22no—
106C2×D3—124no—
107C3×C4—22no—
108C3×C4—22no—
109Dic3—124no—
110Dic3—124no—
111C32#217111yescharacteristic, complemented, Sylow
112Q8—92no—
113D4—92no—
114D4—182no—
115C2×C4—182no—
116C2×C4—181no—
117C2×C4C22×#15711yescharacteristic
118C8—22no—
119C8—91no—
120C8—91no—
121C8#378711yescharacteristic
122C8#378711yescharacteristic
123C2×C3—22no—
124C2×C3—42no—
125D3—244no—
126C22—182no—
127C22#6428911yescharacteristic
128C4—182no—
129C4—361no—
130C4C2×#378711yescharacteristic
131C4D4×#15711yescharacteristic
132C3—22no—
133C2—21no—
134C2—362no—
135C2#1059374911yescharacteristic
subgroupG/H
centerC4D4×#157
commutatorC32×C4C22×C8
FrattiniC2×C4C22×#157
FittingC32×#108C4
socleC2×C32C8×D4
prime radical#64113C4
cosocleC2×C3⋊(C3⋊C8)C23
hypercenter#108#157
hypocenterC32#2171
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

Complements

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

NH ≅ G/Ntype
1. #10593772C2semidirect
3. #10590187C2semidirect
4. #10590178C2semidirect
5. #10590175C2semidirect
111. C32#2171semidirect

Maximal subgroups

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

subgroupindex
#105937722
#105925942
#105901872
#105901782
#105901752
#21719