Finite Group Databasebeta

← #11772066

Subgroups — #11772066

Order 1152.

280 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 34 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#10592850C211yesmaximal, characteristic
2#10590177C211yesmaximal, characteristic, complemented
3#10590173C211yesmaximal, characteristic, complemented
4C2×C32×D8C411yescharacteristic
5#64149—21no—
6C2×#3753—21no—
7C2×#3745C411yescharacteristic
8C4⋊#622—21no—
9C2×#3708—21no—
10C8×C3⋊Dic3C2211yescharacteristic
11#5151—62no—
12C2×C32×D4—21no—
13C2×#638—41no—
14C2×#638—41no—
15C2×C4⋊(C3⋊D3)—21no—
16C2×#622—41no—
17C32×D8—41no—
18C2×C32×C8C2×C411yescharacteristic
19#3753—41no—
20#3753—41no—
21C4×C3⋊Dic3D411yescharacteristic
22C2×C3⋊(C3⋊C8)D411yescharacteristic
23#3745—41no—
24#3708—41no—
25#1361—91nomaximal, Sylow
26C2×C3×D8—22no—
27#940—64no—
28C2×#213—64no—
29C2×D24—62no—
30C8×Dic3—62no—
31C23×C32—41no—
32C22×C3⋊D3—41no—
33C32×D4—41no—
34C32×D4—41no—
35C2×C32×C4C22⋊C411yescharacteristic
36#638—82no—
37#638—81no—
38#638—81no—
39C2×C3⋊Dic3D811yescharacteristic
40C2×C3⋊Dic3SD1611yescharacteristic
41C4⋊(C3⋊D3)—41no—
42C4⋊(C3⋊D3)—41no—
43#622—81no—
44C32×C8—21no—
45C3⋊(C3⋊C8)D811yescharacteristic
46C3⋊(C3⋊C8)SD1611yescharacteristic
47#493—91no—
48C4⋊C16—91no—
49#335—91no—
50C2×C3×D4—24no—
51C2×#67—124no—
52C2×#67—124no—
53C2×D12—64no—
54C3×D8—44no—
55C2×C3×C8—22no—
56#213—124no—
57#213—124no—
58C4×Dic3—62no—
59C2×C3⋊C8—62no—
60D24—124no—
61C22×C32—81no—
62C22×C32—81no—
63C22×C32—81no—
64C22×C32#10211yescharacteristic
65C2×C3⋊D3—81no—
66C2×C3⋊D3—81no—
67C2×C3⋊D3—81no—
68C32×C4#10011yescharacteristic
69C32×C4#10211yescharacteristic
70C3⋊Dic3—21no—
71C3⋊Dic3D1611yescharacteristic
72C3⋊Dic3SD3211yescharacteristic
73C2×D8—91no—
74C2×D8—181no—
75C2×D8#15711yescharacteristic
76#127—181no—
77C2×C16—181no—
78C4⋊C8—181no—
79C4×C8—91no—
80C23×C3—44no—
81C22×D3—124no—
82C3×D4—44no—
83C3×D4—44no—
84C2×C3×C4—22no—
85#67—244no—
86#67—244no—
87#67—248no—
88C2×Dic3—62no—
89C2×Dic3—62no—
90D12—124no—
91D12—124no—
92C3×C8—24no—
93C3⋊C8—62no—
94C3⋊C8—62no—
95C2×C32—161no—
96C2×C32#33111yescharacteristic
97C2×C32#35711yescharacteristic
98C2×C32#36111yescharacteristic
99C3⋊D3—161no—
100C2×D4—21no—
101C2×D4—181no—
102C2×D4—361no—
103C2×D4—361no—
104D8—41no—
105D8—361no—
106D8—361no—
107D8—361no—
108C2×C8—91no—
109C2×C8—361no—
110C2×C8C2×#15711yescharacteristic
111C42—91no—
112C16—361no—
113C22×C3—22no—
114C22×C3—84no—
115C22×C3—84no—
116C22×C3—84no—
117C2×D3—244no—
118C2×D3—244no—
119C2×D3—244no—
120C3×C4—22no—
121C3×C4—22no—
122Dic3—62no—
123Dic3—62no—
124Dic3—64no—
125C32#136111yescharacteristic, complemented, Sylow
126C23—41no—
127C23—361no—
128D4—41no—
129D4—41no—
130D4—361no—
131D4—361no—
132D4—721no—
133D4—721no—
134D4—722no—
135C2×C4—91no—
136C2×C4—91no—
137C2×C4C22⋊#15711yescharacteristic
138C8—21no—
139C8—91no—
140C8—91no—
141C8—721no—
142C2×C3—22no—
143C2×C3—22no—
144C2×C3—22no—
145C2×C3—164no—
146D3—484no—
147C22—81no—
148C22—81no—
149C22—81no—
150C22—721no—
151C22—721no—
152C22—721no—
153C22#6378211yescharacteristic
154C4—91no—
155C4—91no—
156C4—181no—
157C4#6378211yescharacteristic
158C4#6378811yescharacteristic
159C3—22no—
160C2—161no—
161C2—1441no—
162C2#1059019311yescharacteristic
163C2#1059019511yescharacteristic
164C2#1059021411yescharacteristic
subgroupG/H
centerC22#63782
commutatorC2×C32×C8C2×C4
FrattiniC2×C8C2×#157
FittingC2×C32×D8C4
socleC22×C32#102
prime radical#10592850C2
cosocleC8×C3⋊Dic3C22
hypercenterC2×D8#157
hypocenterC32#1361
LCSG ▷ C2×C32×C8 ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #10590177C2semidirect
3. #10590173C2semidirect
125. C32#1361semidirect

Maximal subgroups

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

subgroupindex
#105928502
#105901772
#105901732
#13619