Finite Group Databasebeta

← #10591167

Subgroups — #10591167

Order 576.

294 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C2×#3748C211yesmaximal, characteristic, complemented
2C3×#930C212yesmaximal, complemented
3C2×#3713C211yesmaximal, characteristic, complemented
4#63574C211yesmaximal, characteristic, complemented
5#63562C212yesmaximal, complemented
6#5039—32nomaximal
7C22×C32×C4C2211yescharacteristic
8C2×C3×#67—22no—
9C2×C3×D12C2212yes—
10#3748—22no—
11C2×C3⋊(C3⋊C8)C2211yescharacteristic
12C2×C3⋊(C3⋊C8)C2211yescharacteristic
13C3×(C2×D3)⋊C4—22no—
14C3×C4⋊Dic3C2212yes—
15#3713—22no—
16C3×#121—32no—
17C2×#213—32no—
18#930D312yescomplemented
19C2×#208—32no—
20C2×#208—61no—
21#832—32no—
22#809—32no—
23#808—32no—
24C23×C32D411yescharacteristic
25C22×C3×D3—22no—
26C2×C32×C4—21no—
27C2×C32×C4—21no—
28C2×C32×C4D411yescharacteristic
29C2×C32×C4C2311yescharacteristic
30C3×#67—44no—
31C2×C3×Dic3—22no—
32C3×D12—22no—
33C3×D12—22no—
34C3⋊(C3⋊C8)—21no—
35C3⋊(C3⋊C8)D412yescomplemented
36#469—91noSylow
37C2×C3×D4—32no—
38C2×C3×D4—62no—
39C22×C3×C4—21no—
40C22×C3×C4C2×D312yes—
41C2×#67—22no—
42C2×D12C2×D312yes—
43C3×C4⋊C4—32no—
44C3×C22⋊C4—62no—
45#213—64no—
46(C2×D3)⋊C4—22no—
47C4⋊Dic3C2×D312yes—
48#208—64no—
49#208—64no—
50C2×C3⋊C8—32no—
51C2×C3⋊C8—32no—
52C2×C3⋊C8—61no—
53C2×C3⋊C8—61no—
54C22×C32—21no—
55C22×C32—22no—
56C22×C32C2×D411yescharacteristic
57C2×C3×D3—42no—
58C2×C3×D3—42no—
59C2×C3×D3—42no—
60C32×C4—21no—
61C32×C4C2×D411yescharacteristic
62C32×C4#4111yescharacteristic
63C3×Dic3—42no—
64C2×D8—91no—
65C2×M16—91no—
66#121—32no—
67#106—91no—
68#102—92no—
69C23×C3—21no—
70C23×C3—62no—
71C23×C3#6712yes—
72C22×D3—22no—
73C3×D4—62no—
74C3×D4—62no—
75C3×D4—124no—
76C2×C3×C4—22no—
77C2×C3×C4—22no—
78C2×C3×C4—22no—
79C2×C3×C4—22no—
80C2×C3×C4—21no—
81C2×C3×C4—21no—
82C2×C3×C4—62no—
83C2×C3×C4#6712yes—
84C2×C3×C4C22×D312yes—
85#67—44no—
86C2×Dic3—22no—
87D12—22no—
88D12—22no—
89C3⋊C8—34no—
90C3⋊C8—62no—
91C3⋊C8—62no—
92C3⋊C8—62no—
93C2×C32—41no—
94C2×C32#12111yescharacteristic
95C2×C32AGL(1,ℤ/8)12yes—
96C3×D3—82no—
97C2×D4—32no—
98C2×D4—62no—
99C22×C4D3211yescharacteristic
100D8—182no—
101M16—182no—
102C2×C8—91no—
103C2×C8—91no—
104C4⋊C4—32no—
105C22⋊C4—62no—
106C22×C3—22no—
107C22×C3—22no—
108C22×C3—22no—
109C22×C3—22no—
110C22×C3—21no—
111C22×C3—42no—
112C22×C3—122no—
113C22×C3—122no—
114C22×C3—122no—
115C22×C3C2×#6712yes—
116C2×D3—42no—
117C2×D3—42no—
118C2×D3—42no—
119C3×C4—22no—
120C3×C4—22no—
121C3×C4—21no—
122C3×C4—21no—
123C3×C4—122no—
124C3×C4D3×D412yes—
125C3×C4#23712yes—
126Dic3—42no—
127C32#46911yescharacteristic, complemented, Sylow
128C23—62no—
129C23#62511yescharacteristic
130D4—62no—
131D4—62no—
132D4—124no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—62no—
136C2×C4#62511yescharacteristic
137C2×C4C2×D3211yescharacteristic
138C8—92no—
139C8—181no—
140C2×C3—22no—
141C2×C3—21no—
142C2×C3—42no—
143C2×C3—42no—
144C2×C3—242no—
145C2×C3#93212yes—
146C2×C3#93912yes—
147C2×C3#94912yes—
148D3—82no—
149C22—22no—
150C22—21no—
151C22—122no—
152C22—122no—
153C22—122no—
154C22C2×#62511yescharacteristic
155C4—21no—
156C4—122no—
157C4#380511yescharacteristic
158C4#381111yescharacteristic
159C3—21no—
160C3#503912yescomplemented
161C2—41no—
162C2—242no—
163C2#6382312yes—
164C2#6398011yescharacteristic
subgroupG/H
centerC22C2×#625
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC22×C32×C4C22
socleC22×C32C2×D4
hypercenterC22×C4D32
hypocenterC32#469
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#3748C2semidirect
2. C3×#930C2semidirect
3. C2×#3713C2semidirect
4. #63574C2semidirect
5. #63562C2semidirect
18. #930D3semidirect
35. C3⋊(C3⋊C8)D4semidirect
127. C32#469semidirect
160. C3#5039semidirect

Maximal subgroups

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

subgroupindex
C2×#37482
C3×#9302
C2×#37132
#635742
#635622
#50393