Finite Group Databasebeta

← C3⋊(#392⋊C9) #13136823

Subgroups — C3⋊(#392⋊C9) #13136823

Order 1728.

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

normal subgroups only

This group has 273 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
1C3×#95⋊C9C211yesmaximal, characteristic, complemented
2C3×#4671C311yesmaximal, characteristic
3#392⋊C9—31nomaximal
4Dic3×C22⋊C9—41nomaximal
5C22×C3×D12—31no—
6C2×C3×(C2×D3)⋊C4—31no—
7C32×#95C2×C311yescharacteristic
8#95⋊C9—21no—
9#95⋊C9D311yescharacteristic, complemented
10C2×C3×C22⋊C9—41no—
11C3×#392—31no—
12#4671C911yescharacteristic, complemented
13C23×C3×D3—31no—
14C22×C32×C4—31no—
15C22×C3×Dic3A411yescharacteristic
16C2×C3×D12—62no—
17C2×C3×D12—64no—
18C3×(C2×D3)⋊C4—62no—
19C4×C22⋊C9—121no—
20C3×C22⋊C9—41no—
21C9×Dic3—161no—
22C22×C3×D4—91no—
23C22×D12—31no—
24C2×C3×C22⋊C4—91no—
25C2×(C2×D3)⋊C4—31no—
26C3×#95—21no—
27C3×#95C2×C911yescharacteristic
28C3×#95C3×D311yescharacteristic
29C23×C32C2×A411yescharacteristic
30C22×C3×D3—32no—
31C22×C3×D3—61no—
32C22×C3×D3—62no—
33C22×C3×D3—62no—
34C22×C3×D3—61no—
35C2×C32×C4—32no—
36C2×C32×C4—62no—
37C2×C3×Dic3—61no—
38C3×D12—68no—
39C2×C22⋊C9—41no—
40C2×C22⋊C9—81no—
41#392—31noSylow
42C2×C3×C9—161no—
43C24×C3—91no—
44C23×D3—31no—
45C2×C3×D4—182no—
46C2×C3×D4—184no—
47C22×C3×C4—31no—
48C22×C3×C4—31no—
49C22×C3×C4—31no—
50C22×C3×C4—61no—
51C22×Dic3C22⋊C911yescharacteristic
52C2×D12—62no—
53C2×D12—64no—
54C3×C22⋊C4—182no—
55(C2×D3)⋊C4—62no—
56C22×C32—31no—
57C22×C32—31no—
58C22×C32#41⋊C311yescharacteristic
59C2×C3×D3—64no—
60C2×C3×D3—62no—
61C2×C3×D3—121no—
62C2×C3×D3—122no—
63C2×C3×D3—121no—
64C32×C4—62no—
65C3×Dic3—41no—
66C22⋊C9—41no—
67C22⋊C9—81no—
68C4×C9—481no—
69C22×D4—91no—
70C2×C22⋊C4—91no—
71#95D3×C911yescharacteristic
72C3×C9—161noSylow
73C23×C3—21no—
74C23×C3—92no—
75C23×C3—181no—
76C23×C3—182no—
77C23×C3—182no—
78C23×C3—181no—
79C23×C3C2×C22⋊C911yescharacteristic
80C23×C3D3×A411yescharacteristic
81C22×D3—32no—
82C22×D3—61no—
83C22×D3—62no—
84C22×D3—62no—
85C22×D3—61no—
86C3×D4—188no—
87C2×C3×C4—32no—
88C2×C3×C4—32no—
89C2×C3×C4—62no—
90C2×C3×C4—62no—
91C2×C3×C4—62no—
92C2×C3×C4—122no—
93C2×C3×C4—181no—
94C2×Dic3—61no—
95D12—68no—
96C2×C32—31no—
97C2×C32—31no—
98C2×C32#127⋊C311yescharacteristic
99C3×D3—122no—
100C2×C9—161no—
101C2×C9—321no—
102C24—91no—
103C2×D4—182no—
104C2×D4—184no—
105C22×C4—31no—
106C22×C4—31no—
107C22⋊C4—182no—
108C22×C3—21no—
109C22×C3—31no—
110C22×C3—31no—
111C22×C3—31no—
112C22×C3—31no—
113C22×C3—61no—
114C22×C3—61no—
115C22×C3—184no—
116C22×C3—182no—
117C22×C3—361no—
118C22×C3—362no—
119C22×C3—361no—
120C22×C3#41⋊C911yescharacteristic
121C22×C3C3⋊(#41⋊C3)11yescharacteristic
122C2×D3—64no—
123C2×D3—62no—
124C2×D3—121no—
125C2×D3—122no—
126C2×D3—121no—
127C3×C4—62no—
128C3×C4—62no—
129C3×C4—122no—
130C3×C4—121no—
131Dic3—41no—
132C32#392⋊C311yescharacteristic
133C9—161no—
134C9—321no—
135C23—92no—
136C23—181no—
137C23—182no—
138C23—182no—
139C23—181no—
140C23D3×C22⋊C911yescharacteristic
141D4—188no—
142C2×C4—32no—
143C2×C4—62no—
144C2×C4—181no—
145C2×C3—21no—
146C2×C3—31no—
147C2×C3—31no—
148C2×C3—31no—
149C2×C3—31no—
150C2×C3—61no—
151C2×C3—61no—
152C2×C3—362no—
153C2×C3#127⋊C911yescharacteristic
154C2×C3C3⋊(#127⋊C3)11yescharacteristic
155D3—122no—
156C22—31no—
157C22—31no—
158C22—184no—
159C22—182no—
160C22—361no—
161C22—362no—
162C22—361no—
163C22C3⋊(#41⋊C9)11yescharacteristic
164C4—62no—
165C4—121no—
166C3—21no—
167C3#392⋊C911yescharacteristic, complemented
168C3C3⋊(#392⋊C3)11yescharacteristic
169C2—31no—
170C2—31no—
171C2—362no—
172C2C3⋊(#127⋊C9)11yescharacteristic
subgroupG/H
center, hypercenterC2×C3C3⋊(#127⋊C3)
commutator, hypocenterC3×#95C2×C9
FrattiniC23×C3D3×A4
Fitting, cosocleC32×#95C2×C3
socleC23×C32C2×A4
prime radicalC3×#4671C3
LCSG ▷ C3×#95
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C3×#95⋊C9C2semidirect
9. #95⋊C9D3semidirect
12. #4671C9semidirect
167. C3#392⋊C9semidirect

Maximal subgroups

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

subgroupindex
C3×#95⋊C92
C3×#46713
#392⋊C93
Dic3×C22⋊C94