Finite Group Databasebeta

← #11771469

Subgroups — #11771469

Order 1152.

172 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 27 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#10593736C211yesmaximal, characteristic
2#10593260C212yesmaximal
3C2×C4⋊#157C411yescharacteristic
4C2×C4⋊#157C2211yescharacteristic
5C22⋊AGL(1,𝔽9)—22no—
6C42×C3⋊D3C411yescharacteristic
7#63781—22no—
8C22×#157—21no—
9C22×#157D412yes—
10C2×AGL(1,𝔽9)—42no—
11C2×C4×C3⋊D3—21no—
12C2×C4×C3⋊D3C2×C411yescharacteristic
13C4⋊#157—41no—
14C4⋊#157—41no—
15C32×C42C811yescharacteristic, complemented
16C4×C3⋊Dic3—21no—
17C4×C3⋊Dic3C811yescharacteristic, complemented
18#1324—91nomaximal, Sylow
19C42×D3—121no—
20C22×C3⋊D3C22⋊C411yescharacteristic
21C2×#157—22no—
22C2×#157—42no—
23C2×#157—42no—
24C2×#157—41no—
25AGL(1,𝔽9)—82no—
26C2×C32×C4—21no—
27C2×C32×C4C2×C811yescharacteristic
28C2×C3⋊Dic3—21no—
29C2×C3⋊Dic3M1611yescharacteristic
30C4×C3⋊D3—21no—
31C4×C3⋊D3—21no—
32C4×C3⋊D3—41no—
33C4×C3⋊D3—41no—
34#382—91no—
35#324—92no—
36C2×C4×D3—121no—
37C2×C4×D3—122no—
38C3×C42—41no—
39C4×Dic3—121no—
40C4×Dic3—122no—
41C22×C32C22⋊C811yescharacteristic
42C2×C3⋊D3—21no—
43C2×C3⋊D3—21no—
44C2×C3⋊D3#9911yescharacteristic
45C2×C3⋊D3#10111yescharacteristic
46#157—42no—
47#157—81no—
48C32×C4—21no—
49C32×C4—41no—
50C3⋊Dic3—21no—
51C3⋊Dic3—41no—
52C2×C4⋊C4—91no—
53C2×C4⋊C4—91no—
54C2×C42—91no—
55C22⋊C8—182no—
56#95—182no—
57C22×D3—121no—
58C2×C3×C4—42no—
59C2×C3×C4—41no—
60C2×Dic3—121no—
61C2×Dic3—122no—
62C4×D3—122no—
63C4×D3—122no—
64C4×D3—124no—
65C4×D3—124no—
66C2×C32—21no—
67C2×C32#32411yescharacteristic
68C3⋊D3—21no—
69C3⋊D3#35411yescharacteristic
70C3⋊D3#35511yescharacteristic
71C22×C4—91no—
72C22×C4—92no—
73C22×C4—181no—
74C22×C4—181no—
75C2×C8—362no—
76C4⋊C4—361no—
77C4⋊C4—361no—
78C42—91no—
79C42—181no—
80C42AGL(1,𝔽9)11yescharacteristic, complemented
81C22×C3—41no—
82C2×D3—121no—
83C2×D3—121no—
84C2×D3—122no—
85C2×D3—122no—
86C3×C4—42no—
87C3×C4—44no—
88Dic3—122no—
89Dic3—124no—
90C32#132411yescharacteristic, complemented, Sylow
91C23—91no—
92C2×C4—21no—
93C2×C4—91no—
94C2×C4—181no—
95C2×C4—181no—
96C2×C4—182no—
97C2×C4—181no—
98C2×C4—361no—
99C2×C4—361no—
100C2×C4—362no—
101C2×C4—361no—
102C2×C4—362no—
103C2×C4C2×AGL(1,𝔽9)11yescharacteristic
104C8—722no—
105C2×C3—42no—
106C2×C3—41no—
107D3—121no—
108D3—121no—
109D3—122no—
110C22—91no—
111C22—91no—
112C22—181no—
113C22—181no—
114C22C22⋊AGL(1,𝔽9)11yescharacteristic
115C4—21no—
116C4—41no—
117C4—181no—
118C4—361no—
119C4—362no—
120C4—721no—
121C3—41no—
122C2—21no—
123C2—91no—
124C2—91no—
125C2—181no—
126C2#1059326011yescharacteristic
subgroupG/H
centerC2#10593260
commutatorC2×C32×C4C2×C8
FrattiniC2×C4C2×AGL(1,𝔽9)
FittingC32×C42C8
socleC2×C32#324
prime radicalC22×C3⋊D3C22⋊C4
cosocleC2×C4⋊#157C22
hypercenterC42AGL(1,𝔽9)
hypocenterC32#1324
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
15. C32×C42C8semidirect
17. C4×C3⋊Dic3C8semidirect
80. C42AGL(1,𝔽9)semidirect
90. C32#1324semidirect

Maximal subgroups

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

subgroupindex
#105937362
#105932602
#13249