Finite Group Databasebeta

← #11771609

Subgroups — #11771609

Order 1152.

242 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 36 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#10592571C211yesmaximal, characteristic
2#10590175C211yesmaximal, characteristic, complemented
3#10590170C211yesmaximal, characteristic, complemented
4C2×#3745C411yescharacteristic
5#64102—21no—
6C4⋊#622—21no—
7C2×#3708—21no—
8C32×#107C411yescharacteristic
9C8×C3⋊Dic3C2211yescharacteristic
10#63636—21no—
11#4872—62no—
12C2×C4⋊(C3⋊D3)—21no—
13C2×C4×C3⋊D3—41no—
14C2×#622—41no—
15C2×C32×C8C2×C411yescharacteristic
16C32×C4⋊C4—21no—
17#3752—41no—
18C4×C3⋊Dic3D411yescharacteristic
19C2×C3⋊(C3⋊C8)D411yescharacteristic
20#3745—21no—
21#3745C812yescomplemented
22#3708—22no—
23#1333—91nomaximal, Sylow
24C2×D24—62no—
25#893—64no—
26C3×#107—22no—
27C8×Dic3—62no—
28#809—64no—
29C22×C3⋊D3—41no—
30C2×C32×C4—41no—
31C2×C32×C4C22⋊C411yescharacteristic
32C2×C3⋊Dic3D811yescharacteristic
33C2×C3⋊Dic3SD1611yescharacteristic
34C4⋊(C3⋊D3)—22no—
35C4⋊(C3⋊D3)—41no—
36C4×C3⋊D3—82no—
37#622—81no—
38C32×C8C2×C811yescharacteristic
39C32×C8M1611yescharacteristic
40C3⋊(C3⋊C8)—21no—
41C4×D8—91no—
42#346—91no—
43#334—91no—
44C2×D12—64no—
45C2×C4×D3—124no—
46C2×C3×C8—22no—
47C3×C4⋊C4—24no—
48(C2×D3)⋊C4—124no—
49C4×Dic3—62no—
50C2×C3⋊C8—62no—
51D24—64no—
52D24—64no—
53C22×C32#10211yescharacteristic
54C2×C3⋊D3—42no—
55C2×C3⋊D3—81no—
56C2×C3⋊D3—81no—
57C32×C4—81no—
58C32×C4C22⋊C811yescharacteristic
59C32×C4#10411yescharacteristic
60C3⋊Dic3—21no—
61C3⋊Dic3—21no—
62C2×D8—91no—
63C4×D4—181no—
64C2×C16—181no—
65#107#15711yescharacteristic
66C4⋊C8—181no—
67#102—181no—
68C4×C8—91no—
69C22×D3—124no—
70C2×C3×C4—22no—
71C2×C3×C4—44no—
72C2×Dic3—62no—
73C2×Dic3—62no—
74D12—68no—
75D12—124no—
76C4×D3—248no—
77C3×C8—22no—
78C3×C8—22no—
79C3⋊C8—122no—
80C2×C32D4⋊C811yescharacteristic
81C2×C32#36011yescharacteristic
82C2×C32#36111yescharacteristic
83C3⋊D3—82no—
84C2×D4—181no—
85C22×C4—361no—
86D8—92no—
87D8—181no—
88C2×C8—91no—
89C2×C8—361no—
90C2×C8C2×#15711yescharacteristic
91C4⋊C4—21no—
92C22⋊C4—361no—
93C42—91no—
94C16—182no—
95C22×C3—22no—
96C2×D3—128no—
97C2×D3—244no—
98C2×D3—244no—
99C3×C4—22no—
100C3×C4—22no—
101C3×C4—84no—
102Dic3—64no—
103Dic3—122no—
104C32#133311yescharacteristic, complemented, Sylow
105C23—361no—
106D4—182no—
107D4—361no—
108C2×C4—41no—
109C2×C4—91no—
110C2×C4—91no—
111C2×C4—722no—
112C2×C4C22⋊#15711yescharacteristic
113C8—181no—
114C8—721no—
115C8#378711yescharacteristic
116C8#378811yescharacteristic
117C2×C3—22no—
118C2×C3—22no—
119C2×C3—22no—
120D3—248no—
121C22—362no—
122C22—721no—
123C22—721no—
124C22#6378211yescharacteristic
125C4—81no—
126C4—181no—
127C4—181no—
128C4#6377811yescharacteristic
129C4#6378511yescharacteristic
130C3—22no—
131C2—722no—
132C2#1059016011yescharacteristic
133C2#1059019511yescharacteristic
134C2#1059019611yescharacteristic
subgroupG/H
centerC22#63782
commutatorC32×C8C2×C8
FrattiniC2×C8C2×#157
FittingC32×#107C4
socleC22×C32#102
prime radicalC2×#3745C4
cosocleC8×C3⋊Dic3C22
hypercenter#107#157
hypocenterC32#1333
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10590175C2semidirect
3. #10590170C2semidirect
21. #3745C8semidirect
104. C32#1333semidirect

Maximal subgroups

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

subgroupindex
#105925712
#105901752
#105901702
#13339