Finite Group Databasebeta

← #11797848

Subgroups — #11797848

Order 1152.

230 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 46 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#10593787C212yesmaximal, complemented
2#10592618C211yesmaximal, characteristic
3#10590198C212yesmaximal, complemented
4#10590140C211yesmaximal, characteristic, complemented
5C16×#157C211yesmaximal, characteristic, complemented
6#64289—22no—
7#64128C2212yes—
8#63785—22no—
9#63771C2212yes—
10C8×#157C2211yescharacteristic
11#63764C2211yescharacteristic
12C32×Q32C411yescharacteristic, complemented
13#63655C412yescomplemented
14#63626C411yescharacteristic, complemented
15C16×C3⋊D3C2211yescharacteristic
16#4919—62no—
17#3832—22no—
18C4×#157D411yescharacteristic
19#3788—22no—
20#3788—42no—
21#3787—42no—
22#3787D411yescharacteristic
23C32×Q16C2×C412yes—
24#3755—22no—
25#3745C2×C412yes—
26C8×C3⋊D3C2311yescharacteristic
27#3708—21no—
28C32×C16C2×C411yescharacteristic
29C3⋊(C3⋊C16)C2×C411yescharacteristic
30#2178—91nomaximal, Sylow
31#919—64no—
32C3×Q32—22no—
33#828—64no—
34D48—62no—
35D3×C16—62no—
36C2×#157—21no—
37C32×Q8—22no—
38C4⋊(C3⋊D3)—22no—
39C4⋊(C3⋊D3)—42no—
40C4×C3⋊D3—42no—
41C4×C3⋊D3C2×D411yescharacteristic
42#622—42no—
43#622D811yescharacteristic
44#622D811yescharacteristic
45C32×C8C22×C411yescharacteristic
46C3⋊(C3⋊C8)#4111yescharacteristic
47#508—91no—
48#443—92no—
49#368—91no—
50#359—92no—
51C4×C16—91no—
52#239—124no—
53C3×Q16—24no—
54#215—124no—
55D24—64no—
56D3×C8—62no—
57C3×C16—22no—
58C3⋊C16—62no—
59C2×C3⋊D3—42no—
60C2×C3⋊D3#13511yescharacteristic
61#157—22no—
62C32×C4—42no—
63C32×C4C4×D411yescharacteristic
64C3⋊Dic3C2×D811yescharacteristic
65#135—92no—
66#131—182no—
67Q32#15711yescharacteristic, complemented
68SD32—92no—
69D16—91no—
70C2×C16—91no—
71C2×C16—91no—
72#108—92no—
73#104—182no—
74C4×C8—91no—
75C3×Q8—44no—
76D12—124no—
77D12—244no—
78C4×D3—62no—
79C4×D3—244no—
80C3×C8—22no—
81C3⋊C8—62no—
82C2×C32C4×D811yescharacteristic
83C3⋊D3—21no—
84C3⋊D3—82no—
85#41—182no—
86Q16C2×#15712yes—
87SD16—182no—
88D8—92no—
89M16—182no—
90M16—362no—
91C2×C8—91no—
92C2×C8—91no—
93C2×C8—362no—
94C42—91no—
95C16—91no—
96C16—181no—
97C16C2×#15711yescharacteristic
98C2×D3—62no—
99C2×D3—244no—
100C3×C4—22no—
101C3×C4—84no—
102Dic3—62no—
103C32#217811yescharacteristic, complemented, Sylow
104Q8—22no—
105D4—182no—
106D4—362no—
107C2×C4—91no—
108C2×C4—181no—
109C2×C4—362no—
110C8—91no—
111C8—91no—
112C8—91no—
113C8—362no—
114C8C22×#15711yescharacteristic
115C2×C3—22no—
116D3—122no—
117D3—484no—
118C22—91no—
119C22—362no—
120C4—42no—
121C4—91no—
122C4—182no—
123C4D4×#15711yescharacteristic
124C3—22no—
125C2—181no—
126C2—722no—
127C2D8×#15711yescharacteristic
subgroupG/H
centerC2D8×#157
commutatorC32×C8C22×C4
FrattiniC8C22×#157
FittingC32×Q32C4
socleC2×C32C4×D8
prime radical#10592618C2
cosocleC8×C3⋊D3C23
hypercenterQ32#157
hypocenterC32#2178
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32

Complements

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

NH ≅ G/Ntype
1. #10593787C2semidirect
3. #10590198C2semidirect
4. #10590140C2semidirect
5. C16×#157C2semidirect
12. C32×Q32C4semidirect
13. #63655C4semidirect
14. #63626C4semidirect
67. Q32#157semidirect
103. C32#2178semidirect

Maximal subgroups

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

subgroupindex
#105937872
#105926182
#105901982
#105901402
C16×#1572
#21789