Finite Group Databasebeta

← #11772049

Subgroups — #11772049

Order 1152.

232 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 32 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#10592890C211yesmaximal, characteristic
2#10590177C211yesmaximal, characteristic, complemented
3#10590172C211yesmaximal, characteristic, complemented
4C2×C32×Q16C411yescharacteristic
5#64156—21no—
6C2×#3755—21no—
7C2×#3745C411yescharacteristic
8C4⋊#622—21no—
9C2×#3708—21no—
10C8×C3⋊Dic3C2211yescharacteristic
11#5191—62no—
12C2×C32×Q8—21no—
13C2×C4⋊(C3⋊D3)—21no—
14C2×#622—41no—
15C32×Q16—41no—
16C2×C32×C8C2×C411yescharacteristic
17#3755—41no—
18#3755—41no—
19#3752—41no—
20#3752—41no—
21C4×C3⋊Dic3D411yescharacteristic
22C2×C3⋊(C3⋊C8)D411yescharacteristic
23#3745—41no—
24#3708—41no—
25#1360—91nomaximal, Sylow
26C2×C3×Q16—22no—
27#947—64no—
28C2×#215—64no—
29C2×D24—62no—
30C8×Dic3—62no—
31C22×C3⋊D3—41no—
32C32×Q8—41no—
33C32×Q8—41no—
34C2×C32×C4—41no—
35C2×C32×C4C22⋊C411yescharacteristic
36C2×C3⋊Dic3D811yescharacteristic
37C2×C3⋊Dic3SD1611yescharacteristic
38C4⋊(C3⋊D3)—41no—
39C4⋊(C3⋊D3)—41no—
40#622—81no—
41C32×C8—21no—
42C3⋊(C3⋊C8)D811yescharacteristic
43C3⋊(C3⋊C8)SD1611yescharacteristic
44#495—91no—
45C4⋊C16—91no—
46#334—91no—
47C2×C3×Q8—24no—
48C2×D12—64no—
49C3×Q16—44no—
50C2×C3×C8—22no—
51#215—124no—
52#215—124no—
53(C2×D3)⋊C4—124no—
54(C2×D3)⋊C4—124no—
55C4×Dic3—62no—
56C2×C3⋊C8—62no—
57D24—124no—
58C22×C32#10211yescharacteristic
59C2×C3⋊D3—81no—
60C2×C3⋊D3—81no—
61C2×C3⋊D3—81no—
62C32×C4—81no—
63C32×C4#10011yescharacteristic
64C32×C4#10211yescharacteristic
65C3⋊Dic3—21no—
66C3⋊Dic3—21no—
67C2×Q16#15711yescharacteristic
68C2×SD16—181no—
69C2×D8—91no—
70#124—181no—
71C2×C16—181no—
72C4⋊C8—181no—
73C4×C8—91no—
74C22×D3—124no—
75C3×Q8—44no—
76C3×Q8—44no—
77C2×C3×C4—22no—
78C2×C3×C4—44no—
79C2×Dic3—62no—
80C2×Dic3—62no—
81D12—124no—
82D12—124no—
83C3×C8—24no—
84C3⋊C8—62no—
85C3⋊C8—62no—
86C2×C32#33111yescharacteristic
87C2×C32#35911yescharacteristic
88C2×C32#36011yescharacteristic
89C3⋊D3—161no—
90C2×Q8—21no—
91C2×D4—181no—
92Q16—41no—
93SD16—361no—
94SD16—361no—
95D8—361no—
96C2×C8—91no—
97C2×C8—361no—
98C2×C8C2×#15711yescharacteristic
99C22⋊C4—361no—
100C22⋊C4—361no—
101C42—91no—
102C16—361no—
103C22×C3—22no—
104C2×D3—244no—
105C2×D3—244no—
106C2×D3—244no—
107C3×C4—22no—
108C3×C4—22no—
109C3×C4—84no—
110Dic3—122no—
111Dic3—122no—
112C32#136011yescharacteristic, complemented, Sylow
113C23—361no—
114Q8—41no—
115Q8—41no—
116D4—361no—
117D4—361no—
118C2×C4—41no—
119C2×C4—91no—
120C2×C4—91no—
121C2×C4C22⋊#15711yescharacteristic
122C8—21no—
123C8—91no—
124C8—91no—
125C8—721no—
126C2×C3—22no—
127C2×C3—22no—
128C2×C3—22no—
129D3—484no—
130C22—721no—
131C22—721no—
132C22—721no—
133C22#6378211yescharacteristic
134C4—81no—
135C4—181no—
136C4—181no—
137C4#6378211yescharacteristic
138C4#6378811yescharacteristic
139C3—22no—
140C2—1441no—
141C2#1059019611yescharacteristic
142C2#1059019811yescharacteristic
143C2#1059021411yescharacteristic
subgroupG/H
centerC22#63782
commutatorC2×C32×C8C2×C4
FrattiniC2×C8C2×#157
FittingC2×C32×Q16C4
socleC22×C32#102
prime radicalC2×#3745C4
cosocleC8×C3⋊Dic3C22
hypercenterC2×Q16#157
hypocenterC32#1360
LCSG ▷ C2×C32×C8 ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. #10590177C2semidirect
3. #10590172C2semidirect
112. C32#1360semidirect

Maximal subgroups

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

subgroupindex
#105928902
#105901772
#105901722
#13609