Finite Group Databasebeta

← C3×C3⋊(#392⋊C3) #13157024

Subgroups — C3×C3⋊(#392⋊C3) #13157024

Order 1728.

351 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 351 conjugacy classes of subgroups — too many to draw. Only its 36 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
1C32×#95⋊C3C211yesmaximal, characteristic, complemented
2C3×#4671C311yesmaximal, characteristic, complemented
3C3×#392⋊C3—31nomaximal
4C3⋊(#392⋊C3)C313yesmaximal, direct product factor
5C3×Dic3×A4—41nomaximal
6C22×C3×D12—31no—
7C2×C3×(C2×D3)⋊C4—31no—
8C32×#95C2×C311yescharacteristic
9C3×#95⋊C3—21no—
10C3×#95⋊C3—23no—
11C3×#95⋊C3D311yescharacteristic, complemented
12C3×#95⋊C3C2×C313yescomplemented
13C2×C32×A4—41no—
14C3×#392—31no—
15#4671C3211yescharacteristic, complemented
16#392⋊C3—33no—
17C23×C3×D3—31no—
18C22×C32×C4—31no—
19C22×C3×Dic3A411yescharacteristic
20C2×C3×D12—62no—
21C2×C3×D12—64no—
22C3×C4×A4—121no—
23Dic3×A4—43no—
24C3×(C2×D3)⋊C4—62no—
25C32×A4—41no—
26C32×Dic3—161no—
27C22×C3×D4—91no—
28C22×D12—31no—
29C2×C3×C22⋊C4—91no—
30C2×(C2×D3)⋊C4—31no—
31C3×#95—21no—
32C3×#95C3×D311yescharacteristic
33C3×#95C2×C3211yescharacteristic
34#95⋊C3—23no—
35#95⋊C3C3×D313yescomplemented
36C23×C32C2×A411yescharacteristic
37C22×C3×D3—32no—
38C22×C3×D3—61no—
39C22×C3×D3—62no—
40C22×C3×D3—62no—
41C22×C3×D3—61no—
42C2×C3×A4—41no—
43C2×C3×A4—43no—
44C2×C3×A4—83no—
45C2×C3×A4—81no—
46C2×C32×C4—32no—
47C2×C32×C4—62no—
48C2×C3×Dic3—61no—
49C3×D12—68no—
50#392—31noSylow
51C2×C33—161no—
52C24×C3—91no—
53C23×D3—31no—
54C2×C3×D4—182no—
55C2×C3×D4—184no—
56C22×C3×C4—31no—
57C22×C3×C4—31no—
58C22×C3×C4—31no—
59C22×C3×C4—61no—
60C22×Dic3C3×A411yescharacteristic
61C2×D12—62no—
62C2×D12—64no—
63C4×A4—123no—
64C3×C22⋊C4—182no—
65(C2×D3)⋊C4—62no—
66C22×C32—31no—
67C22×C32—31no—
68C22×C32#41⋊C311yescharacteristic
69C2×C3×D3—64no—
70C2×C3×D3—62no—
71C2×C3×D3—121no—
72C2×C3×D3—122no—
73C2×C3×D3—121no—
74C3×A4—41no—
75C3×A4—43no—
76C3×A4—83no—
77C3×A4—81no—
78C32×C4—62no—
79C32×C4—481no—
80C3×Dic3—41no—
81C3×Dic3—163no—
82C22×D4—91no—
83C2×C22⋊C4—91no—
84#95C32×D311yescharacteristic
85C33—161noSylow
86C23×C3—21no—
87C23×C3—92no—
88C23×C3—181no—
89C23×C3—182no—
90C23×C3—182no—
91C23×C3—181no—
92C23×C3D3×A411yescharacteristic
93C23×C3C2×C3×A411yescharacteristic
94C22×D3—32no—
95C22×D3—61no—
96C22×D3—62no—
97C22×D3—62no—
98C22×D3—61no—
99C2×A4—43no—
100C2×A4—83no—
101C3×D4—188no—
102C2×C3×C4—32no—
103C2×C3×C4—32no—
104C2×C3×C4—62no—
105C2×C3×C4—62no—
106C2×C3×C4—62no—
107C2×C3×C4—122no—
108C2×C3×C4—181no—
109C2×Dic3—61no—
110D12—68no—
111C2×C32—31no—
112C2×C32—31no—
113C2×C32—161no—
114C2×C32—163no—
115C2×C32—323no—
116C2×C32—321no—
117C2×C32#127⋊C311yescharacteristic
118C3×D3—122no—
119C24—91no—
120C2×D4—182no—
121C2×D4—184no—
122C22×C4—31no—
123C22×C4—31no—
124C22⋊C4—182no—
125C22×C3—21no—
126C22×C3—31no—
127C22×C3—31no—
128C22×C3—31no—
129C22×C3—31no—
130C22×C3—61no—
131C22×C3—61no—
132C22×C3—184no—
133C22×C3—182no—
134C22×C3—361no—
135C22×C3—362no—
136C22×C3—361no—
137C22×C3C3⋊(#41⋊C3)11yescharacteristic
138C22×C3C3×#41⋊C311yescharacteristic
139C2×D3—64no—
140C2×D3—62no—
141C2×D3—121no—
142C2×D3—122no—
143C2×D3—121no—
144A4—43no—
145A4—83no—
146C3×C4—62no—
147C3×C4—62no—
148C3×C4—122no—
149C3×C4—121no—
150C3×C4—483no—
151Dic3—41no—
152C32—161no—
153C32—163no—
154C32—323no—
155C32—321no—
156C32#392⋊C311yescharacteristic, complemented
157C23—92no—
158C23—181no—
159C23—182no—
160C23—182no—
161C23—181no—
162C23C3×D3×A411yescharacteristic
163D4—188no—
164C2×C4—32no—
165C2×C4—62no—
166C2×C4—181no—
167C2×C3—21no—
168C2×C3—31no—
169C2×C3—31no—
170C2×C3—31no—
171C2×C3—31no—
172C2×C3—61no—
173C2×C3—61no—
174C2×C3—163no—
175C2×C3—323no—
176C2×C3—362no—
177C2×C3C3⋊(#127⋊C3)11yescharacteristic
178C2×C3C3×#127⋊C311yescharacteristic
179D3—122no—
180C22—31no—
181C22—31no—
182C22—184no—
183C22—182no—
184C22—361no—
185C22—362no—
186C22—361no—
187C22C3×C3⋊(#41⋊C3)11yescharacteristic
188C4—62no—
189C4—121no—
190C3—21no—
191C3—163no—
192C3—323no—
193C3C3⋊(#392⋊C3)11yescharacteristic, direct product factor
194C3C3×#392⋊C311yescharacteristic, complemented
195C2—31no—
196C2—31no—
197C2—362no—
198C2C3×C3⋊(#127⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC2×C3C3⋊(#127⋊C3)
commutator, cosocle, hypocenterC3×#95C2×C32
FrattiniC23C3×D3×A4
FittingC32×#95C2×C3
socleC23×C32C2×A4
LCSG ▷ C3×#95
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C32×#95⋊C3C2semidirect
2. C3×#4671C3semidirect
4. C3⋊(#392⋊C3)C3direct (N × H)
11. C3×#95⋊C3D3semidirect
12. C3×#95⋊C3C2×C3semidirect
15. #4671C32semidirect
35. #95⋊C3C3×D3semidirect
156. C32#392⋊C3semidirect
193. C3C3⋊(#392⋊C3)direct (N × H)
194. C3C3×#392⋊C3semidirect

Maximal subgroups

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

subgroupindex
C32×#95⋊C32
C3×#46713
C3×#392⋊C33
C3⋊(#392⋊C3)3
C3×Dic3×A44