Finite Group Databasebeta

← #11771846

Subgroups — #11771846

Order 1152.

170 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 24 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#10593340C211yesmaximal, characteristic
2#10593260C211yesmaximal, characteristic
3#10590094C211yesmaximal, characteristic
4C2×C4⋊#157C2211yescharacteristic
5#64283—21no—
6C2×#3773C411yescharacteristic
7C22⋊AGL(1,𝔽9)—21no—
8#63883—21no—
9#63737—21no—
10#63737C411yescharacteristic
11C22×#157C2×C411yescharacteristic
12C22×#157D411yescharacteristic
13C2×AGL(1,𝔽9)—41no—
14C2×C4×C3⋊D3D411yescharacteristic
15C2×#624—21no—
16C2×#624—21no—
17#3792—41no—
18C4⋊#157—41no—
19#3788—22no—
20#3787—41no—
21#3773—41no—
22C3×Dic3⋊C4—41no—
23Dic3⋊Dic3—41no—
24#1346—91nomaximal, Sylow
25D3×C4⋊C4—121no—
26C22×C3⋊D3C22⋊C411yescharacteristic
27C2×#157—21no—
28C2×#157—21no—
29C2×#157—41no—
30C2×#157—41no—
31AGL(1,𝔽9)—81no—
32C2×C32×C4SD1611yescharacteristic
33C2×C3⋊Dic3D811yescharacteristic
34C4×C3⋊D3—21no—
35C4×C3⋊D3—21no—
36C2×C3×Dic3—41no—
37C2×C3×Dic3—41no—
38#624—22no—
39#624—41no—
40#624—41no—
41#624—41no—
42#622—42no—
43#398—91no—
44#343—91no—
45#324—91no—
46C2×C4×D3—121no—
47C2×C4×D3—121no—
48C2×C4×D3—121no—
49C3×C4⋊C4—121no—
50C4⋊Dic3—121no—
51Dic3⋊C4—41no—
52Dic3⋊C4—121no—
53C22×C32#10211yescharacteristic
54C2×C3⋊D3—21no—
55C2×C3⋊D3—21no—
56C2×C3⋊D3#9911yescharacteristic
57C2×C3⋊D3#10411yescharacteristic
58#157—41no—
59#157—41no—
60C32×C4—21no—
61C3⋊Dic3—21no—
62C3×Dic3—42no—
63C3×Dic3—81no—
64C2×M16—181no—
65C2×C4⋊C4—91no—
66C2×C4⋊C4—91no—
67C2×C4⋊C4—181no—
68C22⋊C8—181no—
69#95—91no—
70#95—181no—
71C22×D3—121no—
72C2×C3×C4—41no—
73C2×C3×C4—121no—
74C2×C3×C4—121no—
75C2×Dic3—41no—
76C2×Dic3—41no—
77C2×Dic3—121no—
78C4×D3—122no—
79C4×D3—122no—
80C4×D3—241no—
81C4×D3—241no—
82C4×D3—241no—
83C4×D3—241no—
84C2×C32—21no—
85C2×C32#32711yescharacteristic
86C3⋊D3—21no—
87C3⋊D3#35211yescharacteristic
88C3⋊D3#35611yescharacteristic
89C22×C4—91no—
90C22×C4—91no—
91C22×C4—91no—
92C22×C4—181no—
93C22×C4—181no—
94M16—182no—
95M16—361no—
96C2×C8—361no—
97C2×C8—361no—
98C4⋊C4—121no—
99C4⋊C4—361no—
100C4⋊C4—361no—
101C4⋊C4—361no—
102C22×C3—41no—
103C2×D3—121no—
104C2×D3—121no—
105C2×D3—121no—
106C2×D3—121no—
107C2×D3—121no—
108C2×D3—121no—
109C3×C4—81no—
110C3×C4—122no—
111C3×C4—241no—
112Dic3—42no—
113Dic3—81no—
114Dic3—241no—
115C32#134611yescharacteristic, complemented, Sylow
116C23—91no—
117C2×C4—91no—
118C2×C4—121no—
119C2×C4—121no—
120C2×C4—181no—
121C2×C4—181no—
122C2×C4—182no—
123C2×C4—181no—
124C2×C4—181no—
125C2×C4—361no—
126C2×C4—361no—
127C2×C4—361no—
128C2×C4—361no—
129C2×C4—361no—
130C2×C4AΓL(1,𝔽9)11yescharacteristic
131C8—362no—
132C8—721no—
133C2×C3—41no—
134C2×C3—41no—
135C2×C3—41no—
136D3—121no—
137D3—121no—
138D3—121no—
139D3—121no—
140C22—91no—
141C22—91no—
142C22—181no—
143C22—181no—
144C22GO+(4,𝔽2)⋊C411yescharacteristic
145C4—21no—
146C4—122no—
147C4—181no—
148C4—241no—
149C4—361no—
150C4—361no—
151C3—41no—
152C2—21no—
153C2—91no—
154C2—91no—
155C2—181no—
156C2#1059316411yescharacteristic
subgroupG/H
centerC2#10593164
commutatorC22×#157C2×C4
Frattini, hypercenterC2×C4AΓL(1,𝔽9)
FittingC2×C32×C4SD16
socleC2×C32#327
prime radicalC22×C3⋊D3C22⋊C4
cosocleC2×C4⋊#157C22
hypocenterC32#1346
LCSG ▷ C22×#157 ▷ C22×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
115. C32#1346semidirect

Maximal subgroups

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

subgroupindex
#105933402
#105932602
#105900942
#13469