Finite Group Databasebeta

← #11771573

Subgroups — #11771573

Order 1152.

244 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 38 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#10590174C211yesmaximal, characteristic, complemented
3#10590171C211yesmaximal, 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#1331—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—81no—
37C4×C3⋊D3—81no—
38#622—81no—
39C32×C8C2×C811yescharacteristic
40C32×C8M1611yescharacteristic
41C3⋊(C3⋊C8)—21no—
42C4×D8—91no—
43C4×C16—91no—
44#335—91no—
45C2×D12—64no—
46C2×C4×D3—124no—
47C2×C3×C8—22no—
48C3×C4⋊C4—24no—
49(C2×D3)⋊C4—124no—
50C4×Dic3—62no—
51C2×C3⋊C8—62no—
52D24—64no—
53D24—64no—
54C22×C32#10211yescharacteristic
55C2×C3⋊D3—42no—
56C2×C3⋊D3—81no—
57C2×C3⋊D3—81no—
58C32×C4—81no—
59C32×C4C22⋊C811yescharacteristic
60C32×C4#10411yescharacteristic
61C3⋊Dic3—21no—
62C3⋊Dic3D1611yescharacteristic
63C3⋊Dic3SD3211yescharacteristic
64C2×D8—91no—
65C4×D4—181no—
66C2×C16—181no—
67#107#15711yescharacteristic
68C4⋊C8—181no—
69#102—181no—
70C4×C8—91no—
71C22×D3—124no—
72C2×C3×C4—22no—
73C2×C3×C4—44no—
74C2×Dic3—62no—
75C2×Dic3—62no—
76D12—68no—
77D12—124no—
78C4×D3—244no—
79C4×D3—244no—
80C3×C8—22no—
81C3×C8—22no—
82C3⋊C8—122no—
83C2×C32D4⋊C811yescharacteristic
84C2×C32#35711yescharacteristic
85C2×C32#35911yescharacteristic
86C3⋊D3—82no—
87C2×D4—181no—
88C22×C4—361no—
89D8—92no—
90D8—181no—
91C2×C8—91no—
92C2×C8—361no—
93C2×C8C2×#15711yescharacteristic
94C4⋊C4—21no—
95C22⋊C4—361no—
96C42—91no—
97C16—182no—
98C22×C3—22no—
99C2×D3—128no—
100C2×D3—244no—
101C2×D3—244no—
102C3×C4—22no—
103C3×C4—22no—
104C3×C4—84no—
105Dic3—62no—
106Dic3—62no—
107Dic3—122no—
108C32#133111yescharacteristic, complemented, Sylow
109C23—361no—
110D4—182no—
111D4—361no—
112C2×C4—41no—
113C2×C4—91no—
114C2×C4—91no—
115C2×C4—721no—
116C2×C4—721no—
117C2×C4C22⋊#15711yescharacteristic
118C8—181no—
119C8—721no—
120C8#378711yescharacteristic
121C8#378811yescharacteristic
122C2×C3—22no—
123C2×C3—22no—
124C2×C3—22no—
125D3—248no—
126C22—362no—
127C22—721no—
128C22—721no—
129C22#6378211yescharacteristic
130C4—81no—
131C4—91no—
132C4—91no—
133C4—181no—
134C4#6377811yescharacteristic
135C4#6378511yescharacteristic
136C3—22no—
137C2—722no—
138C2#1059016011yescharacteristic
139C2#1059019311yescharacteristic
140C2#1059019811yescharacteristic
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#1331
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. #10590174C2semidirect
3. #10590171C2semidirect
21. #3745C8semidirect
108. C32#1331semidirect

Maximal subgroups

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

subgroupindex
#105925712
#105901742
#105901712
#13319