Finite Group Databasebeta

← C3×Dic3×C42⋊C3 #13157029

Subgroups — C3×Dic3×C42⋊C3 #13157029

Order 1728.

332 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 50 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×C32×C42⋊C3C211yesmaximal, characteristic
2C3×C42×Dic3C311yesmaximal, characteristic, complemented
3C3×C4×C42⋊C3—31nomaximal
4Dic3×C42⋊C3C313yesmaximal, direct product factor
5C3×Dic3×A4—41nomaximal
6C32×C42⋊C3C411yescharacteristic, complemented
7C2×C32×C42C2×C311yescharacteristic
8C2×C3×C4×Dic3—31no—
9C2×C3×C4×Dic3—31no—
10C2×C3×C42⋊C3—21no—
11C2×C3×C42⋊C3—23no—
12C2×C3×C42⋊C3D311yescharacteristic
13C2×C3×C42⋊C3C2×C313yes—
14C2×C32×A4—41no—
15C3×C43—31no—
16C42×Dic3C3211yescharacteristic, complemented
17C4×C42⋊C3—33no—
18C22×C32×C4—31no—
19C22×C3×Dic3—31no—
20C22×C3×Dic3A411yescharacteristic
21C3×C4×A4—121no—
22Dic3×A4—43no—
23C32×C42—31no—
24C32×C42C3×C411yescharacteristic, complemented
25C3×C4×Dic3—34no—
26C3×C4×Dic3—32no—
27C3×C4×Dic3—32no—
28C3×C42⋊C3—21no—
29C3×C42⋊C3—23no—
30C3×C42⋊C3Dic311yescharacteristic, direct product factor
31C3×C42⋊C3C3×C413yescomplemented
32C32×A4—41no—
33C32×Dic3—161no—
34C2×C3×C42—21no—
35C2×C3×C42—91no—
36C2×C3×C42—91no—
37C2×C3×C42C3×D311yescharacteristic
38C2×C3×C42C2×C3211yescharacteristic
39C2×C4×Dic3—31no—
40C2×C4×Dic3—31no—
41C2×C42⋊C3—23no—
42C2×C42⋊C3C3×D313yes—
43C23×C32C2×A411yescharacteristic
44C2×C3×A4—41no—
45C2×C3×A4—43no—
46C2×C3×A4—83no—
47C2×C3×A4—81no—
48C2×C32×C4—32no—
49C2×C32×C4—32no—
50C2×C32×C4—31no—
51C2×C32×C4—31no—
52C2×C3×Dic3—34no—
53C2×C3×Dic3—32no—
54C2×C3×Dic3—31no—
55C2×C3×Dic3—31no—
56C43—31noSylow
57C2×C33—161no—
58C22×C3×C4—31no—
59C22×C3×C4—31no—
60C22×C3×C4—31no—
61C22×C3×C4—61no—
62C22×C3×C4—91no—
63C22×Dic3—31no—
64C22×Dic3C3×A411yescharacteristic
65C4×A4—123no—
66C3×C42—21no—
67C3×C42—31no—
68C3×C42—31no—
69C3×C42—61no—
70C3×C42—92no—
71C3×C42—94no—
72C3×C42—92no—
73C3×C42C3×Dic311yescharacteristic, complemented
74C3×C42C32×C411yescharacteristic, complemented
75C4×Dic3—34no—
76C4×Dic3—32no—
77C4×Dic3—32no—
78C42⋊C3—23no—
79C42⋊C3C3×Dic313yesdirect product factor
80C22×C32—31no—
81C22×C32—31no—
82C22×C32C4×A411yescharacteristic
83C3×A4—41no—
84C3×A4—43no—
85C3×A4—83no—
86C3×A4—81no—
87C32×C4—32no—
88C32×C4—32no—
89C32×C4—481no—
90C3×Dic3—34no—
91C3×Dic3—31no—
92C3×Dic3—163no—
93C3×Dic3C42⋊C311yescharacteristic, direct product factor
94C2×C42—91no—
95C2×C42—91no—
96C2×C42C32×D311yescharacteristic
97C33—161noSylow
98C23×C3—21no—
99C23×C3D3×A411yescharacteristic
100C23×C3C2×C3×A411yescharacteristic
101C2×A4—43no—
102C2×A4—83no—
103C2×C3×C4—32no—
104C2×C3×C4—32no—
105C2×C3×C4—32no—
106C2×C3×C4—32no—
107C2×C3×C4—31no—
108C2×C3×C4—31no—
109C2×C3×C4—31no—
110C2×C3×C4—31no—
111C2×C3×C4—61no—
112C2×C3×C4—61no—
113C2×C3×C4—62no—
114C2×C3×C4—62no—
115C2×C3×C4—91no—
116C2×C3×C4—94no—
117C2×C3×C4—92no—
118C2×C3×C4—91no—
119C2×Dic3—34no—
120C2×Dic3—32no—
121C2×Dic3—31no—
122C2×Dic3—31no—
123C2×C32—31no—
124C2×C32—31no—
125C2×C32—161no—
126C2×C32—163no—
127C2×C32—323no—
128C2×C32—321no—
129C2×C32C2×C42⋊C311yescharacteristic
130C22×C4—31no—
131C22×C4—31no—
132C22×C4—91no—
133C42—31no—
134C42—92no—
135C42—94no—
136C42—92no—
137C42C32×Dic311yescharacteristic, complemented
138C22×C3—21no—
139C22×C3—31no—
140C22×C3—31no—
141C22×C3—31no—
142C22×C3—31no—
143C22×C3—61no—
144C22×C3—61no—
145C22×C3Dic3×A411yescharacteristic
146C22×C3C3×C4×A411yescharacteristic
147A4—43no—
148A4—83no—
149C3×C4—32no—
150C3×C4—32no—
151C3×C4—32no—
152C3×C4—32no—
153C3×C4—31no—
154C3×C4—62no—
155C3×C4—62no—
156C3×C4—94no—
157C3×C4—91no—
158C3×C4—483no—
159Dic3—34no—
160Dic3—31no—
161Dic3C3×C42⋊C311yescharacteristic, direct product factor
162C32—161no—
163C32—163no—
164C32—323no—
165C32—321no—
166C32C4×C42⋊C311yescharacteristic, complemented
167C23C3×D3×A411yescharacteristic
168C2×C4—32no—
169C2×C4—32no—
170C2×C4—31no—
171C2×C4—31no—
172C2×C4—91no—
173C2×C4—94no—
174C2×C4—92no—
175C2×C4—91no—
176C2×C3—21no—
177C2×C3—31no—
178C2×C3—31no—
179C2×C3—31no—
180C2×C3—31no—
181C2×C3—61no—
182C2×C3—61no—
183C2×C3—163no—
184C2×C3—323no—
185C2×C3D3×C42⋊C311yescharacteristic
186C2×C3C2×C3×C42⋊C311yescharacteristic
187C22—31no—
188C22—31no—
189C22C3×Dic3×A411yescharacteristic
190C4—32no—
191C4—32no—
192C4—31no—
193C4—94no—
194C4—91no—
195C3—21no—
196C3—163no—
197C3—323no—
198C3Dic3×C42⋊C311yescharacteristic, direct product factor
199C3C3×C4×C42⋊C311yescharacteristic, complemented
200C2—31no—
201C2—31no—
202C2C3×D3×C42⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2×C3D3×C42⋊C3
commutator, hypocenterC3×C42C32×C4
FrattiniC23C3×D3×A4
FittingC2×C32×C42C2×C3
socleC23×C32C2×A4
prime radicalC2×C32×C42⋊C3C2
cosocleC2×C3×C42C2×C32
LCSG ▷ C3×C42
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. C3×C42×Dic3C3semidirect
4. Dic3×C42⋊C3C3direct (N × H)
6. C32×C42⋊C3C4semidirect
16. C42×Dic3C32semidirect
24. C32×C42C3×C4semidirect
30. C3×C42⋊C3Dic3direct (N × H)
31. C3×C42⋊C3C3×C4semidirect
73. C3×C42C3×Dic3semidirect
74. C3×C42C32×C4semidirect
79. C42⋊C3C3×Dic3direct (N × H)
93. C3×Dic3C42⋊C3direct (N × H)
137. C42C32×Dic3semidirect
161. Dic3C3×C42⋊C3direct (N × H)
166. C32C4×C42⋊C3semidirect
198. C3Dic3×C42⋊C3direct (N × H)
199. C3C3×C4×C42⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C42⋊C32
C3×C42×Dic33
C3×C4×C42⋊C33
Dic3×C42⋊C33
C3×Dic3×A44