Finite Group Databasebeta

← #11776995

Subgroups — #11776995

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#10593805C211yesmaximal, characteristic
2#10593801C211yesmaximal, characteristic
3C2×#63779C211yesmaximal, characteristic
4#10590088C214yesmaximal, complemented
5C2×#3792—21no—
6C22×#622—21no—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C22⋊#622C412yes—
9#63779—21no—
10#63779C412yes—
11#63779C2212yes—
12#63779C2212yes—
13C4⋊#622—21no—
14C4×#622C2212yes—
15C22×C32×C4Q811yescharacteristic
16C22×C3⋊Dic3C2×C411yescharacteristic
17C22×C3⋊Dic3D411yescharacteristic
18#3792—42no—
19C2×#622—22no—
20C2×#622—22no—
21C2×#622—42no—
22C2×#622C2×C414yes—
23C4×C3⋊Dic3C2×C411yescharacteristic
24C4×C3⋊Dic3D411yescharacteristic
25C4×C3⋊Dic3Q811yescharacteristic
26C4×C3⋊Dic3C2311yescharacteristic
27#1570—91nomaximal, Sylow
28C2×C4×Dic3—121no—
29C23×C32C4⋊C411yescharacteristic
30C2×C32×C4—41no—
31C2×C32×C4C4⋊C411yescharacteristic
32C2×C32×C4C2×Q811yescharacteristic
33C2×C3⋊Dic3—22no—
34C2×C3⋊Dic3C4⋊C411yescharacteristic
35C2×C3⋊Dic3C4⋊C411yescharacteristic
36C2×C3⋊Dic3SD1612yes—
37C2×C3⋊Dic3SD1612yes—
38C2×C3⋊Dic3C22×C411yescharacteristic
39C2×C3⋊Dic3C2×D411yescharacteristic
40#622—24no—
41#622—42no—
42#622—42no—
43#431—91no—
44#423—91no—
45C2×C4⋊C8—91no—
46#334—94no—
47C22×C3×C4—41no—
48C22×Dic3—121no—
49C22×Dic3—121no—
50C4×Dic3—121no—
51C4×Dic3—121no—
52C4×Dic3—121no—
53C4×Dic3—121no—
54C22×C32—21no—
55C22×C32—21no—
56C22×C32#10612yes—
57C22×C32C2×C4⋊C411yescharacteristic
58C32×C4—21no—
59C32×C4—21no—
60C3⋊Dic3—21no—
61C3⋊Dic3#10612yes—
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—
75C23×C3—41no—
76C2×C3×C4—44no—
77C2×C3×C4—41no—
78C2×C3×C4—41no—
79C2×Dic3—121no—
80C2×Dic3—121no—
81C2×Dic3—122no—
82C2×Dic3—122no—
83C2×Dic3—121no—
84C2×Dic3—121no—
85C2×Dic3—124no—
86C2×C32—22no—
87C2×C32#42411yescharacteristic
88C2×C32C2×#10611yescharacteristic
89C2×C32#43011yescharacteristic
90C22×C4—91no—
91C22×C4—91no—
92C22×C4PSU(3,𝔽2)11yescharacteristic
93M16—362no—
94C2×C8—94no—
95C2×C8—182no—
96C2×C8—182no—
97C2×C8—362no—
98C42—91no—
99C42—91no—
100C42—91no—
101C42—91no—
102C22×C3—42no—
103C22×C3—42no—
104C22×C3—42no—
105C22×C3—41no—
106C3×C4—42no—
107C3×C4—42no—
108Dic3—122no—
109Dic3—122no—
110Dic3—121no—
111Dic3—121no—
112Dic3—122no—
113C32#157011yescharacteristic, complemented, Sylow
114C23#377711yescharacteristic
115C2×C4—41no—
116C2×C4—92no—
117C2×C4—92no—
118C2×C4—91no—
119C2×C4—91no—
120C2×C4—91no—
121C2×C4—91no—
122C2×C4—182no—
123C2×C4#377711yescharacteristic
124C2×C4C2×PSU(3,𝔽2)11yescharacteristic
125C8—184no—
126C8—362no—
127C8—362no—
128C2×C3—44no—
129C2×C3—41no—
130C2×C3—41no—
131C2×C3—41no—
132C22—21no—
133C22—21no—
134C22#6374512yes—
135C22C2×#377711yescharacteristic
136C4—21no—
137C4—21no—
138C4—92no—
139C4—91no—
140C4—91no—
141C4—92no—
142C4—181no—
143C3—41no—
144C2—22no—
145C2#1059354011yescharacteristic
146C2C2×#6374511yescharacteristic
147C2#1059356511yescharacteristic
subgroupG/H
centerC22C2×#3777
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×PSU(3,𝔽2)
FittingC22×C32×C4Q8
socleC22×C32C2×C4⋊C4
prime radicalC23×C32C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4PSU(3,𝔽2)
hypocenterC32#1570
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

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
#105938052
#105938012
C2×#637792
#105900882
#15709