Finite Group Databasebeta

← Dic3×A42 #13180347

Subgroups — Dic3×A42 #13180347

Order 1728.

490 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 55 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×C3×A42C211yesmaximal, characteristic
2Dic3×C22⋊A4C312yesmaximal, complemented
3C22×Dic3×A4C312yesmaximal, complemented
4C4×A42—31nomaximal
5C3×A42C411yescharacteristic, complemented
6C3×Dic3×A4—42nomaximal
7C2×C3×C22⋊A4C2×C312yes—
8C23×C3×A4C2×C312yes—
9C2×A42—22no—
10C2×A42—22no—
11C2×A42D311yescharacteristic
12C2×Dic3×A4—32no—
13C2×Dic3×A4—32no—
14C2×C32×A4—42no—
15C24×Dic3C3211yescharacteristic, complemented
16C4×C22⋊A4—32no—
17C22×C4×A4—32no—
18C3×C22⋊A4C3×C412yescomplemented
19C22×C3×A4—32no—
20C22×C3×A4—32no—
21C22×C3×A4C3×C412yescomplemented
22A42—22no—
23A42—22no—
24A42Dic311yescharacteristic, direct product factor
25C22×C3×Dic3—42no—
26C3×C4×A4—122no—
27Dic3×A4—32no—
28Dic3×A4—44no—
29Dic3×A4—122no—
30Dic3×A4A412yesdirect product factor
31C32×A4—42no—
32C32×Dic3—161no—
33C25×C3C2×C3211yescharacteristic
34C2×C22⋊A4—22no—
35C2×C22⋊A4C3×D312yes—
36C23×A4—22no—
37C23×A4C3×D312yes—
38C23×Dic3—32no—
39C23×Dic3—32no—
40C23×Dic3—91no—
41C23×Dic3—91no—
42C2×C4×A4—92no—
43C2×C4×A4—92no—
44C23×C32—42no—
45C2×C3×A4—32no—
46C2×C3×A4—32no—
47C2×C3×A4—42no—
48C2×C3×A4—44no—
49C2×C3×A4—84no—
50C2×C3×A4—82no—
51C2×C3×A4—82no—
52C2×C3×A4—122no—
53C2×C3×A4C2×A412yes—
54C2×C3×Dic3—122no—
55C2×C3×Dic3—122no—
56C24×C4—31noSylow
57C2×C33—161no—
58C24×C3—32no—
59C24×C3—32no—
60C24×C3—91no—
61C24×C3—91no—
62C24×C3C32×C411yescharacteristic, complemented
63C22⋊A4—22no—
64C22⋊A4C3×Dic312yescomplemented
65C22×A4—22no—
66C22×A4—32no—
67C22×A4—32no—
68C22×A4—62no—
69C22×A4—62no—
70C22×A4C3×Dic312yescomplemented
71C22×C3×C4—122no—
72C22×Dic3—32no—
73C22×Dic3—32no—
74C22×Dic3—91no—
75C22×Dic3—92no—
76C22×Dic3—92no—
77C22×Dic3—92no—
78C22×Dic3—92no—
79C22×Dic3—94no—
80C22×Dic3—91no—
81C22×Dic3C3×A412yescomplemented
82C4×A4—32no—
83C4×A4—92no—
84C4×A4—124no—
85C4×A4—362no—
86C22×C32—42no—
87C22×C32—122no—
88C22×C32—122no—
89C3×A4—42no—
90C3×A4—44no—
91C3×A4—84no—
92C3×A4—82no—
93C3×A4—82no—
94C3×A4—122no—
95C3×A4C4×A412yescomplemented
96C32×C4—481no—
97C3×Dic3—42no—
98C3×Dic3—122no—
99C3×Dic3—162no—
100C25C32×D311yescharacteristic
101C23×C4—92no—
102C23×C4—92no—
103C23×C4—271no—
104C23×C4—271no—
105C33—161noSylow
106C23×C3—32no—
107C23×C3—32no—
108C23×C3—32no—
109C23×C3—42no—
110C23×C3—82no—
111C23×C3—91no—
112C23×C3—91no—
113C23×C3—92no—
114C23×C3—92no—
115C23×C3—92no—
116C23×C3—92no—
117C23×C3—91no—
118C23×C3—94no—
119C23×C3C2×C3×A412yes—
120C2×A4—22no—
121C2×A4—32no—
122C2×A4—32no—
123C2×A4—44no—
124C2×A4—62no—
125C2×A4—62no—
126C2×A4—84no—
127C2×A4—122no—
128C2×A4—242no—
129C2×A4D3×A412yes—
130C2×C3×C4—362no—
131C2×C3×C4—362no—
132C2×Dic3—32no—
133C2×Dic3—32no—
134C2×Dic3—91no—
135C2×Dic3—92no—
136C2×Dic3—94no—
137C2×Dic3—91no—
138C2×Dic3—92no—
139C2×Dic3—92no—
140C2×C32—42no—
141C2×C32—122no—
142C2×C32—122no—
143C2×C32—161no—
144C2×C32—162no—
145C2×C32—322no—
146C2×C32—322no—
147C24—32no—
148C24—32no—
149C24—91no—
150C24—91no—
151C24C32×Dic311yescharacteristic, complemented
152C22×C4—32no—
153C22×C4—92no—
154C22×C4—92no—
155C22×C4—271no—
156C22×C4—272no—
157C22×C4—272no—
158C22×C4—272no—
159C22×C4—272no—
160C22×C4—274no—
161C22×C4—271no—
162C22×C3—32no—
163C22×C3—32no—
164C22×C3—32no—
165C22×C3—42no—
166C22×C3—82no—
167C22×C3—91no—
168C22×C3—92no—
169C22×C3—91no—
170C22×C3—92no—
171C22×C3—92no—
172C22×C3—94no—
173C22×C3—92no—
174C22×C3—91no—
175C22×C3—122no—
176C22×C3—122no—
177C22×C3—242no—
178C22×C3—242no—
179C22×C3C3×C4×A412yescomplemented
180A4—22no—
181A4—44no—
182A4—84no—
183A4—122no—
184A4—242no—
185A4Dic3×A412yesdirect product factor
186C3×C4—122no—
187C3×C4—362no—
188C3×C4—482no—
189Dic3—32no—
190Dic3—91no—
191Dic3A4211yescharacteristic, direct product factor
192C32—42no—
193C32—161no—
194C32—162no—
195C32—322no—
196C32—322no—
197C23—32no—
198C23—32no—
199C23—32no—
200C23—91no—
201C23—91no—
202C23—92no—
203C23—92no—
204C23—92no—
205C23—92no—
206C23—91no—
207C23—94no—
208C23C3×D3×A412yes—
209C2×C4—92no—
210C2×C4—92no—
211C2×C4—271no—
212C2×C4—271no—
213C2×C4—272no—
214C2×C4—274no—
215C2×C4—272no—
216C2×C4—272no—
217C2×C3—32no—
218C2×C3—32no—
219C2×C3—42no—
220C2×C3—82no—
221C2×C3—91no—
222C2×C3—91no—
223C2×C3—122no—
224C2×C3—122no—
225C2×C3—162no—
226C2×C3—242no—
227C2×C3—242no—
228C2×C3—322no—
229C2×C3C2×A4211yescharacteristic
230C22—32no—
231C22—32no—
232C22—32no—
233C22—91no—
234C22—92no—
235C22—91no—
236C22—92no—
237C22—92no—
238C22—94no—
239C22—92no—
240C22—91no—
241C22C3×Dic3×A412yescomplemented
242C4—31no—
243C4—92no—
244C4—271no—
245C3—42no—
246C3—82no—
247C3—162no—
248C3—322no—
249C3C4×A4211yescharacteristic, complemented
250C2—32no—
251C2—32no—
252C2—91no—
253C2—91no—
254C2D3×A4211yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D3×A42
commutator, hypocenterC24×C3C32×C4
Fitting, socle, cosocleC25×C3C2×C32
prime radicalC2×C3×A42C2
LCSG ▷ C24×C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. Dic3×C22⋊A4C3semidirect
3. C22×Dic3×A4C3semidirect
5. C3×A42C4semidirect
15. C24×Dic3C32semidirect
18. C3×C22⋊A4C3×C4semidirect
21. C22×C3×A4C3×C4semidirect
24. A42Dic3direct (N × H)
30. Dic3×A4A4direct (N × H)
62. C24×C3C32×C4semidirect
64. C22⋊A4C3×Dic3semidirect
70. C22×A4C3×Dic3semidirect
81. C22×Dic3C3×A4semidirect
95. C3×A4C4×A4semidirect
151. C24C32×Dic3semidirect
179. C22×C3C3×C4×A4semidirect
185. A4Dic3×A4direct (N × H)
191. Dic3A42direct (N × H)
241. C22C3×Dic3×A4semidirect
249. C3C4×A42semidirect

Maximal subgroups

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

subgroupindex
C2×C3×A422
Dic3×C22⋊A43
C22×Dic3×A43
C4×A423
C3×Dic3×A44