Finite Group Databasebeta

← #11771102

Subgroups — #11771102

Order 1152.

364 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C4×C22⋊#157C212yesmaximal
2#10593802C211yesmaximal, characteristic
3C22×C4×C3⋊D3C2211yescharacteristic
4C2×C22⋊#157—22no—
5C2×#3792C412yescomplemented
6C2×C4×#157—22no—
7#63781C414yescomplemented
8#63778—22no—
9C23×C3⋊D3D411yescharacteristic
10C22×#157—24no—
11C22×C32×C4Q811yescharacteristic
12C22×C3⋊Dic3C2×C411yescharacteristic
13C2×C4×C3⋊D3—42no—
14C2×C4×C3⋊D3C2×C412yes—
15C2×C4×C3⋊D3D412yes—
16C22⋊#157—28no—
17#3792—42no—
18C2×#622—22no—
19C4×#157—44no—
20#1297—91nomaximal, Sylow
21C22×C4×D3—121no—
22C23×C32C4⋊C411yescharacteristic
23C22×C3⋊D3—24no—
24C22×C3⋊D3—41no—
25C22×C3⋊D3C22⋊C412yes—
26C2×#157—28no—
27C2×#157—44no—
28C2×#157—44no—
29C2×C32×C4—41no—
30C2×C32×C4C4⋊C412yes—
31C2×C3⋊Dic3—22no—
32C2×C3⋊Dic3C4211yescharacteristic
33C2×C3⋊Dic3C22⋊C411yescharacteristic
34C4×C3⋊D3—24no—
35C4×C3⋊D3—42no—
36#622—42no—
37#407—91no—
38C4×C22⋊C4—92no—
39C23×D3—121no—
40C22×C3×C4—41no—
41C22×Dic3—121no—
42C2×C4×D3—122no—
43C2×C4×D3—122no—
44C2×C4×D3—128no—
45C22×C32—22no—
46C22×C32—21no—
47C22×C32#9511yescharacteristic
48C2×C3⋊D3—22no—
49C2×C3⋊D3—22no—
50C2×C3⋊D3—44no—
51C2×C3⋊D3#10414yes—
52#157—48no—
53C32×C4—22no—
54C3⋊Dic3—21no—
55C3⋊Dic3#9912yes—
56C23×C4—91no—
57C2×M16—92no—
58C2×C22⋊C4—182no—
59C2×C42—182no—
60C22⋊C8—182no—
61#95—94no—
62C23×C3—41no—
63C22×D3—122no—
64C22×D3—128no—
65C22×D3—124no—
66C2×C3×C4—44no—
67C2×C3×C4—42no—
68C2×Dic3—121no—
69C2×Dic3—121no—
70C2×Dic3—124no—
71C4×D3—128no—
72C4×D3—128no—
73C2×C32—41no—
74C2×C32#33912yes—
75C2×C32#34211yescharacteristic
76C3⋊D3—24no—
77C24—91no—
78C22×C4—91no—
79C22×C4—92no—
80C22×C4—92no—
81C22×C4—184no—
82C22×C4—362no—
83C22×C4PSU(3,𝔽2)11yescharacteristic
84M16—362no—
85C2×C8—182no—
86C22⋊C4—188no—
87C42—364no—
88C22×C3—42no—
89C22×C3—44no—
90C22×C3—41no—
91C2×D3—124no—
92C2×D3—124no—
93C2×D3—124no—
94C2×D3—1216no—
95C3×C4—44no—
96Dic3—122no—
97Dic3—122no—
98C32#129711yescharacteristic, complemented, Sylow
99C23—92no—
100C23—184no—
101C23—361no—
102C23#377711yescharacteristic
103C2×C4—41no—
104C2×C4—91no—
105C2×C4—91no—
106C2×C4—184no—
107C2×C4—182no—
108C2×C4—188no—
109C2×C4—362no—
110C2×C4—364no—
111C2×C4—364no—
112C2×C4#377712yes—
113C8—362no—
114C2×C3—44no—
115C2×C3—42no—
116C2×C3—41no—
117D3—128no—
118C22—22no—
119C22—21no—
120C22—94no—
121C22—182no—
122C22—182no—
123C22—364no—
124C22#6374711yescharacteristic
125C4—22no—
126C4—92no—
127C4—181no—
128C4—368no—
129C3—41no—
130C2—41no—
131C2—184no—
132C2#1059009212yes—
133C2#1059009811yescharacteristic
subgroupG/H
centerC22#63747
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC22×C4PSU(3,𝔽2)
FittingC22×C32×C4Q8
socleC22×C32#95
prime radicalC23×C3⋊D3D4
cosocleC22×C4×C3⋊D3C22
hypocenterC32#1297
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
5. C2×#3792C4semidirect
7. #63781C4semidirect
98. C32#1297semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊#1572
#105938022
#12979