Finite Group Databasebeta

← #11797598

Subgroups — #11797598

Order 1152.

250 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 66 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#10593838C212yesmaximal, complemented
2#10592895C211yesmaximal, characteristic
3#10590221C212yesmaximal, complemented
4#10590178C211yesmaximal, characteristic, complemented
5#10590175C211yesmaximal, characteristic, complemented
6C32×#135C411yescharacteristic
7#64157C2212yes—
8#63773—22no—
9#63773C2212yes—
10C2×#3708—22no—
11C2×#3708C2211yescharacteristic
12C2×#3708C2211yescharacteristic
13#63664C412yes—
14#63646C411yescharacteristic
15C8×C3⋊Dic3C2211yescharacteristic
16#5196—62no—
17C32×#41C2×C412yes—
18C32×Q16C811yescharacteristic
19C32×SD16C812yes—
20C32×D8C811yescharacteristic
21C2×C32×C8C2×C411yescharacteristic
22C4×C3⋊Dic3C2×C411yescharacteristic
23#3748—22no—
24#3748C2×C412yes—
25C2×C3⋊(C3⋊C8)—22no—
26C2×C3⋊(C3⋊C8)C2311yescharacteristic
27#3708—22no—
28#3708—21no—
29#3708D412yes—
30#2171—91nomaximal, Sylow
31C3×#135—22no—
32#948—64no—
33#837—64no—
34#819—62no—
35C8×Dic3—62no—
36C32×Q8C2×C812yes—
37C32×D4—22no—
38C32×D4C2×C812yes—
39C2×C32×C4—22no—
40C2×C32×C4C22×C411yescharacteristic
41C2×C3⋊Dic3—21no—
42C32×C8C2×C811yescharacteristic
43C32×C8C2×C811yescharacteristic
44C3⋊(C3⋊C8)—22no—
45C3⋊(C3⋊C8)C2×D411yescharacteristic
46C3⋊(C3⋊C8)#4111yescharacteristic
47#504—92no—
48#443—91no—
49#364—91no—
50#350—92no—
51#346—91no—
52C3×#41—24no—
53C3×Q16—22no—
54C3×SD16—24no—
55C3×D8—22no—
56C2×C3×C8—22no—
57C4×Dic3—62no—
58#208—64no—
59#208—124no—
60C2×C3⋊C8—62no—
61C2×C3⋊C8—124no—
62C22×C32—22no—
63C22×C32#13111yescharacteristic
64C32×C4—22no—
65C32×C4C4×D411yescharacteristic
66C32×C4C22×C811yescharacteristic
67C3⋊Dic3—41no—
68#135#15711yescharacteristic
69#131—92no—
70M32—92no—
71M32—182no—
72C2×C16—91no—
73C2×C16—91no—
74C2×C16—182no—
75#108—91no—
76#104—92no—
77C4×C8—91no—
78C3×Q8—24no—
79C3×D4—24no—
80C3×D4—44no—
81C2×C3×C4—22no—
82C2×C3×C4—44no—
83C2×Dic3—122no—
84C3×C8—22no—
85C3×C8—22no—
86C3⋊C8—62no—
87C3⋊C8—62no—
88C3⋊C8—124no—
89C2×C32—21no—
90C2×C32—42no—
91C2×C32C8×D411yescharacteristic
92#41C2×#15712yes—
93Q16#62211yescharacteristic
94SD16#62212yes—
95D8#62211yescharacteristic
96M16—92no—
97M16—182no—
98C2×C8—91no—
99C2×C8—182no—
100C2×C8C2×#15711yescharacteristic
101C42—91no—
102C16—92no—
103C16—181no—
104C16—182no—
105C22×C3—22no—
106C22×C3—44no—
107C3×C4—22no—
108C3×C4—22no—
109C3×C4—44no—
110Dic3—124no—
111C32#217111yescharacteristic, complemented, Sylow
112Q8C2×#62212yes—
113D4—22no—
114D4C2×#62212yes—
115C2×C4—22no—
116C2×C4—181no—
117C2×C4C22×#15711yescharacteristic
118C8—91no—
119C8—91no—
120C8—182no—
121C8C2×#62211yescharacteristic
122C8C2×#62211yescharacteristic
123C2×C3—22no—
124C2×C3—42no—
125C2×C3—84no—
126C22—22no—
127C22#6428711yescharacteristic
128C4—22no—
129C4—361no—
130C4D4×#15711yescharacteristic
131C4C22×#62211yescharacteristic
132C3—22no—
133C2—21no—
134C2—42no—
135C2D4×#62211yescharacteristic
subgroupG/H
centerC4D4×#157
commutatorC32×C4C22×C8
FrattiniC2×C4C22×#157
Fitting, prime radicalC32×#135C4
socleC2×C32C8×D4
cosocleC2×C3⋊(C3⋊C8)C23
hypercenter#135#157
hypocenterC32#2171
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #10593838C2semidirect
3. #10590221C2semidirect
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
#105938382
#105928952
#105902212
#105901782
#105901752
#21719