Finite Group Databasebeta

← C3×C3⋊(#376⋊C3) #13157023

Subgroups — C3×C3⋊(#376⋊C3) #13157023

Order 1728.

255 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 255 conjugacy classes of subgroups — too many to draw. Only its 38 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
2C3×#4648C311yesmaximal, characteristic, complemented
3C3×#376⋊C3—31nomaximal
4C3⋊(#376⋊C3)C313yesmaximal, direct product factor
5C3×Dic3×A4—41nomaximal
6C2×C3×C4×Dic3—31no—
7C32×#95C2×C311yescharacteristic
8C3×C3⋊#95—31no—
9C3×#95⋊C3—21no—
10C3×#95⋊C3—23no—
11C3×#95⋊C3D311yescharacteristic
12C3×#95⋊C3C2×C313yes—
13C2×C32×A4—41no—
14C3×#376—31no—
15#4648C3211yescharacteristic, complemented
16#376⋊C3—33no—
17C22×C32×C4—31no—
18C22×C3×Dic3—31no—
19C22×C3×Dic3A411yescharacteristic
20C3×C4×A4—121no—
21Dic3×A4—43no—
22C3×C4×Dic3—32no—
23C3×C4×Dic3—32no—
24C32×A4—41no—
25C32×Dic3—161no—
26C2×C3×C42—91no—
27C2×C4×Dic3—31no—
28C3×#95—21no—
29C3×#95—91no—
30C3×#95C3×D311yescharacteristic
31C3×#95C2×C3211yescharacteristic
32C3⋊#95—31no—
33#95⋊C3—23no—
34#95⋊C3C3×D313yes—
35C23×C32C2×A411yescharacteristic
36C2×C3×A4—41no—
37C2×C3×A4—43no—
38C2×C3×A4—83no—
39C2×C3×A4—81no—
40C2×C32×C4—32no—
41C2×C32×C4—62no—
42C2×C3×Dic3—31no—
43C2×C3×Dic3—31no—
44C2×C3×Dic3—32no—
45C2×C3×Dic3—61no—
46C2×C3×Dic3—61no—
47#376—31noSylow
48C2×C33—161no—
49C22×C3×C4—31no—
50C22×C3×C4—31no—
51C22×C3×C4—31no—
52C22×C3×C4—61no—
53C22×C3×C4—91no—
54C22×Dic3—31no—
55C22×Dic3C3×A411yescharacteristic
56C4×A4—123no—
57C3×C42—92no—
58C3×C42—92no—
59C4×Dic3—32no—
60C4×Dic3—32no—
61C22×C32—31no—
62C22×C32—31no—
63C22×C32#41⋊C311yescharacteristic
64C3×A4—41no—
65C3×A4—43no—
66C3×A4—83no—
67C3×A4—81no—
68C32×C4—62no—
69C32×C4—481no—
70C3×Dic3—31no—
71C3×Dic3—62no—
72C3×Dic3—163no—
73C3×Dic3C42⋊C311yescharacteristic
74C2×C42—91no—
75#95—91no—
76#95C32×D311yescharacteristic
77C33—161noSylow
78C23×C3—21no—
79C23×C3D3×A411yescharacteristic
80C23×C3C2×C3×A411yescharacteristic
81C2×A4—43no—
82C2×A4—83no—
83C2×C3×C4—32no—
84C2×C3×C4—32no—
85C2×C3×C4—62no—
86C2×C3×C4—62no—
87C2×C3×C4—62no—
88C2×C3×C4—91no—
89C2×C3×C4—91no—
90C2×C3×C4—92no—
91C2×C3×C4—122no—
92C2×C3×C4—181no—
93C2×C3×C4—181no—
94C2×Dic3—31no—
95C2×Dic3—31no—
96C2×Dic3—32no—
97C2×Dic3—61no—
98C2×Dic3—61no—
99C2×C32—31no—
100C2×C32—31no—
101C2×C32—161no—
102C2×C32—163no—
103C2×C32—323no—
104C2×C32—321no—
105C2×C32C2×C42⋊C311yescharacteristic
106C22×C4—31no—
107C22×C4—31no—
108C22×C4—91no—
109C42—92no—
110C42—92no—
111C22×C3—21no—
112C22×C3—31no—
113C22×C3—31no—
114C22×C3—31no—
115C22×C3—31no—
116C22×C3—61no—
117C22×C3—61no—
118C22×C3C3⋊(#41⋊C3)11yescharacteristic
119C22×C3C3×#41⋊C311yescharacteristic
120A4—43no—
121A4—83no—
122C3×C4—31no—
123C3×C4—62no—
124C3×C4—62no—
125C3×C4—91no—
126C3×C4—122no—
127C3×C4—182no—
128C3×C4—483no—
129Dic3—31no—
130Dic3—62no—
131Dic3C3×C42⋊C311yescharacteristic
132C32—161no—
133C32—163no—
134C32—323no—
135C32—321no—
136C32#376⋊C311yescharacteristic, complemented
137C23C3×D3×A411yescharacteristic
138C2×C4—32no—
139C2×C4—62no—
140C2×C4—91no—
141C2×C4—91no—
142C2×C4—92no—
143C2×C4—181no—
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—163no—
153C2×C3—323no—
154C2×C3D3×C42⋊C311yescharacteristic
155C2×C3C2×C3×C42⋊C311yescharacteristic
156C22—31no—
157C22—31no—
158C22C3×C3⋊(#41⋊C3)11yescharacteristic
159C4—31no—
160C4—62no—
161C4—91no—
162C4—182no—
163C3—21no—
164C3—163no—
165C3—323no—
166C3C3⋊(#376⋊C3)11yescharacteristic, direct product factor
167C3C3×#376⋊C311yescharacteristic, complemented
168C2—31no—
169C2—31no—
170C2C3×D3×C42⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2×C3D3×C42⋊C3
commutator, cosocle, hypocenterC3×#95C2×C32
FrattiniC23C3×D3×A4
FittingC32×#95C2×C3
socleC23×C32C2×A4
prime radicalC32×#95⋊C3C2
LCSG ▷ C3×#95
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. C3×#4648C3semidirect
4. C3⋊(#376⋊C3)C3direct (N × H)
15. #4648C32semidirect
136. C32#376⋊C3semidirect
166. C3C3⋊(#376⋊C3)direct (N × H)
167. C3C3×#376⋊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×#46483
C3×#376⋊C33
C3⋊(#376⋊C3)3
C3×Dic3×A44