Finite Group Databasebeta

← #11776996

Subgroups — #11776996

Order 1152.

222 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 65 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#10593729C211yesmaximal, characteristic
2#10593727C211yesmaximal, characteristic
3#10593726C211yesmaximal, characteristic
4#10590088C214yesmaximal, complemented
5C2×#3788—21no—
6C2×#3787—21no—
7C42×C3⋊D3C2211yescharacteristic
8#63779—21no—
9#63779C2212yes—
10#63779C2212yes—
11#63778C412yes—
12C4⋊#622—21no—
13C4⋊#622C412yes—
14C4×#622C2212yes—
15C2×C4×C3⋊D3C2×C411yescharacteristic
16C2×C4×C3⋊D3D411yescharacteristic
17C2×C4×C3⋊D3Q811yescharacteristic
18C2×#622—22no—
19C2×#622—22no—
20C2×#622C2×C414yes—
21#3788—42no—
22#3787—42no—
23C32×C42Q811yescharacteristic
24C4×C3⋊Dic3C2×C411yescharacteristic
25C4×C3⋊Dic3D411yescharacteristic
26C4×C3⋊Dic3C2311yescharacteristic
27#1570—91nomaximal, Sylow
28C42×D3—121no—
29C22×C3⋊D3C4⋊C411yescharacteristic
30C2×C32×C4C4⋊C411yescharacteristic
31C2×C32×C4C4⋊C411yescharacteristic
32C2×C32×C4C2×Q811yescharacteristic
33C2×C3⋊Dic3C4⋊C411yescharacteristic
34C2×C3⋊Dic3C22×C411yescharacteristic
35C2×C3⋊Dic3C2×D411yescharacteristic
36C4×C3⋊D3—22no—
37C4×C3⋊D3—41no—
38C4×C3⋊D3SD1612yes—
39C4×C3⋊D3SD1612yes—
40#622—24no—
41#622—42no—
42#622—42no—
43#431—91no—
44#423—91no—
45C2×C4⋊C8—91no—
46#334—94no—
47C2×C4×D3—121no—
48C2×C4×D3—121no—
49C2×C4×D3—121no—
50C3×C42—41no—
51C4×Dic3—121no—
52C4×Dic3—121no—
53C4×Dic3—121no—
54C22×C32C2×C4⋊C411yescharacteristic
55C2×C3⋊D3—21no—
56C2×C3⋊D3—21no—
57C2×C3⋊D3#10612yes—
58C32×C4—21no—
59C32×C4—21no—
60C32×C4#10612yes—
61C3⋊Dic3—21no—
62C3⋊Dic3#13112yes—
63C3⋊Dic3C2×SD1611yescharacteristic
64C3⋊Dic3C2×SD1611yescharacteristic
65C2×M16—181no—
66C22×C8—181no—
67C2×C42—91no—
68C4⋊C8—92no—
69C4⋊C8—92no—
70C4⋊C8—92no—
71C4⋊C8—181no—
72C4⋊C8—181no—
73C22⋊C8—92no—
74C4×C8—92no—
75C22×D3—121no—
76C2×C3×C4—41no—
77C2×C3×C4—41no—
78C2×C3×C4—41no—
79C2×Dic3—121no—
80C2×Dic3—121no—
81C2×Dic3—121no—
82C4×D3—122no—
83C4×D3—122no—
84C4×D3—124no—
85C4×D3—124no—
86C2×C32#42411yescharacteristic
87C2×C32C2×#10611yescharacteristic
88C2×C32#43011yescharacteristic
89C3⋊D3—22no—
90C22×C4—91no—
91C22×C4—91no—
92C22×C4—91no—
93M16—362no—
94C2×C8—94no—
95C2×C8—182no—
96C2×C8—182no—
97C2×C8—362no—
98C42—91no—
99C42—91no—
100C42—91no—
101C42PSU(3,𝔽2)11yescharacteristic
102C22×C3—41no—
103C2×D3—122no—
104C2×D3—122no—
105C2×D3—122no—
106C3×C4—42no—
107C3×C4—42no—
108C3×C4—42no—
109Dic3—122no—
110Dic3—121no—
111Dic3—121no—
112Dic3—122no—
113C32#157011yescharacteristic, complemented, Sylow
114C23—91no—
115C2×C4—91no—
116C2×C4—91no—
117C2×C4—92no—
118C2×C4—92no—
119C2×C4—91no—
120C2×C4—182no—
121C2×C4—361no—
122C2×C4#377711yescharacteristic
123C2×C4#377711yescharacteristic
124C2×C4C2×PSU(3,𝔽2)11yescharacteristic
125C8—184no—
126C8—362no—
127C8—362no—
128C2×C3—41no—
129C2×C3—41no—
130C2×C3—41no—
131D3—124no—
132C22—92no—
133C22—181no—
134C22—181no—
135C22C2×#377711yescharacteristic
136C4—21no—
137C4—21no—
138C4—92no—
139C4—91no—
140C4—91no—
141C4—181no—
142C4#6374512yes—
143C3—41no—
144C2—182no—
145C2#1059354011yescharacteristic
146C2C2×#6374511yescharacteristic
147C2#1059354711yescharacteristic
subgroupG/H
centerC22C2×#3777
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×PSU(3,𝔽2)
FittingC32×C42Q8
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC42PSU(3,𝔽2)
hypocenterC32#1570
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10590088C2semidirect
113. C32#1570semidirect

Maximal subgroups

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

subgroupindex
#105937292
#105937272
#105937262
#105900882
#15709