Finite Group Databasebeta

← C3×#10593276 #13166646

Subgroups — C3×#10593276 #13166646

Order 1728.

392 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 58 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
1C3×#63797C212yesmaximal, complemented
2C3×#63764C211yesmaximal, characteristic, complemented
3C3×#63734C214yesmaximal, complemented
4#10593276C311yesmaximal, characteristic, direct product factor
5C3×#3802—22no—
6C3×C8×C3⋊D3C2211yescharacteristic
7C32×D24—22no—
8C3×#3713C2214yescomplemented
9C3×#3708C2212yescomplemented
10C3×D3×D8—62no—
11#63797C2×C312yescomplemented
12#63764C2×C311yescharacteristic, complemented
13#63734C2×C314yescomplemented
14C2×C3×D32—42no—
15C3×C4×C3⋊D3D411yescharacteristic
16C32×D12—24no—
17C3×#625—42no—
18C33×C8D411yescharacteristic
19C3×C3⋊(C3⋊C8)C2311yescharacteristic
20C2×C3×D16—91nomaximal
21C3×D3×D4—64no—
22#3802—22no—
23C32×D8—62no—
24C8×C3⋊D3C22×C311yescharacteristic
25C3×#213—64no—
26C3×D24—22no—
27C3×D24—22no—
28C3×D24—42no—
29C3×D3×C8—62no—
30#3713C22×C314yescomplemented
31#3708C22×C312yescomplemented
32C2×C3×C3⋊D3D811yescharacteristic
33C2×C32×D3—44no—
34C3×D32—84no—
35C33×C4C2×D411yescharacteristic
36C3×C3⋊Dic3D811yescharacteristic
37C2×C3×D8—92no—
38D3×D8—62no—
39C3×D16—94no—
40C2×C3×C16—91no—
41C22×C3×D3—124no—
42C2×D32—42no—
43C32×D4—64no—
44C4×C3⋊D3C3×D411yescharacteristic
45C3×#67—124no—
46C3×D12—24no—
47C3×D12—24no—
48C3×D12—44no—
49C3×C4×D3—62no—
50#625—42no—
51C32×C8—22no—
52C32×C8—42no—
53C32×C8C3×D411yescharacteristic
54C3⋊(C3⋊C8)C23×C311yescharacteristic
55C3×C3⋊C8—62no—
56C2×D16—91noSylow
57C2×C33C2×D811yescharacteristic
58C3×C3⋊D3D1612yescomplemented
59C32×D3—84no—
60C2×C3×D4—182no—
61D3×D4—64no—
62C3×D8—62no—
63C3×D8—62no—
64C3×D8—94no—
65C3×D8—122no—
66C2×C3×C8—91no—
67#213—64no—
68D24—22no—
69D3×C8—62no—
70C3×C16—92no—
71C22×C32—124no—
72C2×C3⋊D3C3×D811yescharacteristic
73C2×C3×D3—44no—
74C2×C3×D3—44no—
75C2×C3×D3—62no—
76C2×C3×D3—84no—
77C2×C3×D3—248no—
78D32—84no—
79C32×C4—22no—
80C32×C4—42no—
81C32×C4C2×C3×D411yescharacteristic
82C3⋊Dic3C3×D811yescharacteristic
83C3×Dic3—62no—
84C2×D8—92no—
85D16—94no—
86C2×C16—91no—
87C33C2×D1611yescharacteristic, complemented, Sylow
88C23×C3—362no—
89C22×D3—124no—
90C3×D4—64no—
91C3×D4—64no—
92C3×D4—124no—
93C3×D4—362no—
94C2×C3×C4—91no—
95#67—124no—
96D12—24no—
97C4×D3—62no—
98C3×C8—22no—
99C3×C8—42no—
100C3×C8—91no—
101C3×C8GO+(4,𝔽2)11yescharacteristic
102C3⋊C8—62no—
103C2×C32—22no—
104C2×C32—42no—
105C2×C32—244no—
106C2×C32C2×C3×D811yescharacteristic
107C3⋊D3C3×D1612yescomplemented
108C3×D3—64no—
109C3×D3—84no—
110C3×D3—84no—
111C3×D3—164no—
112C2×D4—182no—
113D8—62no—
114D8—94no—
115C2×C8—91no—
116C16—92no—
117C22×C3—91no—
118C22×C3—124no—
119C22×C3—124no—
120C22×C3—244no—
121C22×C3—724no—
122C2×D3—44no—
123C2×D3—62no—
124C2×D3—248no—
125C3×C4—22no—
126C3×C4—42no—
127C3×C4—91no—
128C3×C4C2×GO+(4,𝔽2)11yescharacteristic
129Dic3—62no—
130C32—22no—
131C32—42no—
132C32C2×C3×D1611yescharacteristic, complemented
133C23—362no—
134D4—64no—
135D4—362no—
136C2×C4—91no—
137C8—91no—
138C8C3×GO+(4,𝔽2)11yescharacteristic
139C2×C3—22no—
140C2×C3—42no—
141C2×C3—92no—
142C2×C3—244no—
143C2×C3—244no—
144C2×C3—484no—
145C2×C3#6422511yescharacteristic
146D3—64no—
147D3—84no—
148C22—91no—
149C22—124no—
150C22—724no—
151C4—91no—
152C4C2×C3×GO+(4,𝔽2)11yescharacteristic
153C3—22no—
154C3—42no—
155C3#1059327611yescharacteristic, direct product factor
156C2—92no—
157C2—244no—
158C2C3×#6422511yescharacteristic
subgroupG/H
centerC2×C3#64225
commutator, cosocleC3⋊(C3⋊C8)C23×C3
FrattiniC4C2×C3×GO+(4,𝔽2)
FittingC33×C8D4
socleC2×C33C2×D8
hypercenterC3×C8GO+(4,𝔽2)
hypocenterC32C2×C3×D16
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8

Complements

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

NH ≅ G/Ntype
1. C3×#63797C2semidirect
2. C3×#63764C2semidirect
3. C3×#63734C2semidirect
4. #10593276C3direct (N × H)
8. C3×#3713C22semidirect
9. C3×#3708C22semidirect
11. #63797C2×C3semidirect
12. #63764C2×C3semidirect
13. #63734C2×C3semidirect
30. #3713C22×C3semidirect
31. #3708C22×C3semidirect
58. C3×C3⋊D3D16semidirect
87. C33C2×D16semidirect
107. C3⋊D3C3×D16semidirect
132. C32C2×C3×D16semidirect
155. C3#10593276direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#637972
C3×#637642
C3×#637342
#105932763
C2×C3×D169