Finite Group Databasebeta

← #11776860

Subgroups — #11776860

Order 1152.

234 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 73 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#10593726C211yesmaximal, characteristic
2#10593725C211yesmaximal, characteristic
3C4×#3788C211yesmaximal, characteristic
4#10590089C212yesmaximal, complemented
5#10590088C212yesmaximal, complemented
6C2×#3788C411yescharacteristic
7C2×#3788C411yescharacteristic
8C2×#3787—21no—
9C42×C3⋊D3C2211yescharacteristic
10#63779C2211yescharacteristic
11#63779C2212yes—
12#63779C2211yescharacteristic
13#63778—21no—
14#63777C412yes—
15C4⋊#622—21no—
16C4×#622—21no—
17C4×#622C2212yes—
18C2×C4×C3⋊D3C2×C411yescharacteristic
19C2×C4×C3⋊D3D411yescharacteristic
20C2×C4×C3⋊D3Q811yescharacteristic
21C2×#622—22no—
22C2×#622—21no—
23C2×#622—21no—
24C2×#622C2×C412yes—
25C2×#622C2×C412yes—
26#3788—22no—
27#3788C814yescomplemented
28#3787—42no—
29C32×C42Q811yescharacteristic
30C4×C3⋊Dic3C2×C411yescharacteristic
31C4×C3⋊Dic3D411yescharacteristic
32C4×C3⋊Dic3C2311yescharacteristic
33#1565—91nomaximal, Sylow
34C42×D3—121no—
35C22×C3⋊D3C4⋊C411yescharacteristic
36C2×C32×C4C4⋊C411yescharacteristic
37C2×C32×C4C4⋊C411yescharacteristic
38C2×C32×C4C2×Q811yescharacteristic
39C2×C3⋊Dic3C4⋊C411yescharacteristic
40C2×C3⋊Dic3C22×C411yescharacteristic
41C2×C3⋊Dic3C2×D411yescharacteristic
42C4×C3⋊D3—21no—
43C4×C3⋊D3—21no—
44C4×C3⋊D3—41no—
45C4×C3⋊D3C2×C812yes—
46C4×C3⋊D3M1612yes—
47#622—22no—
48#622—42no—
49#622—41no—
50#622—41no—
51#622C2×C814yescomplemented
52#431—91no—
53C2×C4⋊C8—91no—
54C4×M16—91no—
55#335—92no—
56#334—92no—
57C2×C4×D3—121no—
58C2×C4×D3—121no—
59C2×C4×D3—121no—
60C3×C42—41no—
61C4×Dic3—121no—
62C4×Dic3—121no—
63C4×Dic3—121no—
64C22×C32C2×C4⋊C411yescharacteristic
65C2×C3⋊D3—21no—
66C2×C3⋊D3—21no—
67C2×C3⋊D3C4⋊C812yes—
68C32×C4—21no—
69C32×C4—21no—
70C32×C4C4⋊C812yes—
71C3⋊Dic3—21no—
72C3⋊Dic3C22×C811yescharacteristic
73C3⋊Dic3C2×M1611yescharacteristic
74C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
75C3⋊Dic3#13711yescharacteristic
76C2×M16—91no—
77C2×M16—91no—
78C22×C8—181no—
79C2×C42—91no—
80C4⋊C8—91no—
81C4⋊C8—92no—
82C4⋊C8—91no—
83C4⋊C8—181no—
84C22⋊C8—181no—
85#97—92no—
86C4×C8—92no—
87C4×C8—181no—
88C22×D3—121no—
89C2×C3×C4—41no—
90C2×C3×C4—41no—
91C2×C3×C4—41no—
92C2×Dic3—121no—
93C2×Dic3—121no—
94C2×Dic3—121no—
95C4×D3—122no—
96C4×D3—122no—
97C4×D3—122no—
98C4×D3—122no—
99C4×D3—124no—
100C2×C32C2×C4⋊C811yescharacteristic
101C2×C32#42811yescharacteristic
102C2×C32#43011yescharacteristic
103C3⋊D3—22no—
104C22×C4—91no—
105C22×C4—91no—
106C22×C4—91no—
107M16—94no—
108M16—182no—
109C2×C8—92no—
110C2×C8—92no—
111C2×C8—181no—
112C2×C8—181no—
113C2×C8—182no—
114C2×C8—362no—
115C42—91no—
116C42—91no—
117C42—91no—
118C42PSU(3,𝔽2)11yescharacteristic
119C22×C3—41no—
120C2×D3—122no—
121C2×D3—122no—
122C2×D3—122no—
123C3×C4—42no—
124C3×C4—42no—
125C3×C4—42no—
126Dic3—121no—
127Dic3—121no—
128Dic3—121no—
129Dic3—121no—
130Dic3—122no—
131C32#156511yescharacteristic, complemented, Sylow
132C23—91no—
133C2×C4—91no—
134C2×C4—91no—
135C2×C4—92no—
136C2×C4—92no—
137C2×C4—91no—
138C2×C4—181no—
139C2×C4—181no—
140C2×C4—361no—
141C2×C4#377711yescharacteristic
142C2×C4#377711yescharacteristic
143C2×C4C2×PSU(3,𝔽2)11yescharacteristic
144C8—94no—
145C8—182no—
146C8—362no—
147C8—361no—
148C8—361no—
149C2×C3—41no—
150C2×C3—41no—
151C2×C3—41no—
152D3—124no—
153C22—92no—
154C22—181no—
155C22—181no—
156C22C2×#377711yescharacteristic
157C4—21no—
158C4—21no—
159C4—91no—
160C4—91no—
161C4—91no—
162C4—91no—
163C4—181no—
164C4#6374412yes—
165C3—41no—
166C2—182no—
167C2C2×#6374411yescharacteristic
168C2#1059354411yescharacteristic
169C2#1059354711yescharacteristic
subgroupG/H
centerC22C2×#3777
commutatorC3⋊Dic3C22×C8
FrattiniC2×C4C2×PSU(3,𝔽2)
FittingC32×C42Q8
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC42PSU(3,𝔽2)
hypocenterC32#1565
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10590089C2semidirect
5. #10590088C2semidirect
27. #3788C8semidirect
51. #622C2×C8semidirect
131. C32#1565semidirect

Maximal subgroups

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

subgroupindex
#105937262
#105937252
C4×#37882
#105900892
#105900882
#15659