Finite Group Databasebeta

← #11797562

Subgroups — #11797562

Order 1152.

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

normal subgroups only

This group has 252 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#10590174C211yesmaximal, 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#3708D411yescharacteristic
30#3708D411yescharacteristic
31#2170—91nomaximal, Sylow
32C3×#135—22no—
33#948—64no—
34#837—64no—
35#819—62no—
36C8×Dic3—62no—
37C32×Q8C2×C812yes—
38C32×D4—22no—
39C32×D4C2×C812yes—
40C2×C32×C4—22no—
41C2×C32×C4C22×C411yescharacteristic
42C2×C3⋊Dic3—21no—
43C32×C8C2×C811yescharacteristic
44C32×C8C2×C811yescharacteristic
45C3⋊(C3⋊C8)—22no—
46C3⋊(C3⋊C8)C2×D411yescharacteristic
47C3⋊(C3⋊C8)#4111yescharacteristic
48#504—92no—
49#443—91no—
50#364—91no—
51#350—92no—
52C4×C16—91no—
53C3×#41—24no—
54C3×Q16—22no—
55C3×SD16—24no—
56C3×D8—22no—
57C2×C3×C8—22no—
58C4×Dic3—62no—
59#208—64no—
60#208—124no—
61C2×C3⋊C8—62no—
62C2×C3⋊C8—124no—
63C22×C32—22no—
64C22×C32#13111yescharacteristic
65C32×C4—22no—
66C32×C4C4×D411yescharacteristic
67C32×C4C22×C811yescharacteristic
68C3⋊Dic3—22no—
69#135#15711yescharacteristic
70#131—92no—
71M32—92no—
72M32—182no—
73C2×C16—91no—
74C2×C16—91no—
75C2×C16—182no—
76#108—91no—
77#104—92no—
78C4×C8—91no—
79C3×Q8—24no—
80C3×D4—24no—
81C3×D4—44no—
82C2×C3×C4—22no—
83C2×C3×C4—44no—
84C2×Dic3—122no—
85C3×C8—22no—
86C3×C8—22no—
87C3⋊C8—62no—
88C3⋊C8—62no—
89C3⋊C8—124no—
90C2×C32—21no—
91C2×C32—42no—
92C2×C32C8×D411yescharacteristic
93#41C2×#15712yes—
94Q16#62211yescharacteristic
95SD16#62212yes—
96D8#62211yescharacteristic
97M16—92no—
98M16—182no—
99C2×C8—91no—
100C2×C8—182no—
101C2×C8C2×#15711yescharacteristic
102C42—91no—
103C16—91no—
104C16—91no—
105C16—181no—
106C16—182no—
107C22×C3—22no—
108C22×C3—44no—
109C3×C4—22no—
110C3×C4—22no—
111C3×C4—44no—
112Dic3—124no—
113C32#217011yescharacteristic, complemented, Sylow
114Q8C2×#62212yes—
115D4—22no—
116D4C2×#62212yes—
117C2×C4—22no—
118C2×C4—181no—
119C2×C4C22×#15711yescharacteristic
120C8—91no—
121C8—91no—
122C8—182no—
123C8C2×#62211yescharacteristic
124C8C2×#62211yescharacteristic
125C2×C3—22no—
126C2×C3—42no—
127C2×C3—84no—
128C22—22no—
129C22#6428711yescharacteristic
130C4—22no—
131C4—182no—
132C4D4×#15711yescharacteristic
133C4C22×#62211yescharacteristic
134C3—22no—
135C2—21no—
136C2—42no—
137C2D4×#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#2170
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. #10590174C2semidirect
113. C32#2170semidirect

Maximal subgroups

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

subgroupindex
#105938382
#105928952
#105902212
#105901782
#105901742
#21709