Finite Group Databasebeta

← Dic32×A4 #13166164

Subgroups — Dic32×A4 #13166164

Order 1728.

682 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 108 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×A4×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×Dic3×A4C212yesmaximal
3C22×Dic32C311yesmaximal, characteristic, complemented
4C4×Dic3×A4—32nomaximal
5C22×C32×A4C2211yescharacteristic
6A4×C3⋊Dic3C412yescomplemented
7C3×Dic3×A4C414yescomplemented
8C3×Dic32—41nomaximal
9C23×C3⋊Dic3C2×C311yescharacteristic
10C23×C3×Dic3C2×C312yes—
11C2×C3×C4×A4—32no—
12C2×Dic3×A4—22no—
13C2×Dic3×A4—32no—
14C2×Dic3×A4—61no—
15C2×Dic3×A4D312yes—
16C2×Dic32—31no—
17C2×Dic32—31no—
18C2×Dic32—32no—
19C2×C32×A4C2×C411yescharacteristic
20C2×C32×A4C2×C412yes—
21C2×C3×C3⋊Dic3—41no—
22C2×C32×Dic3—42no—
23C22×C4×Dic3—32no—
24C42×A4—91no—
25C24×C32C22×C311yescharacteristic
26C22×C3×A4—22no—
27C22×C3×A4—21no—
28C22×C3×A4—41no—
29C22×C3×A4C2×D312yes—
30C22×C3⋊Dic3—31no—
31C22×C3⋊Dic3—32no—
32C22×C3⋊Dic3—31no—
33C22×C3⋊Dic3C3×C412yescomplemented
34C22×C3×Dic3—32no—
35C22×C3×Dic3—34no—
36C22×C3×Dic3—32no—
37C22×C3×Dic3C3×C414yescomplemented
38C3×C4×A4—34no—
39Dic3×A4—24no—
40Dic3×A4—34no—
41Dic3×A4—62no—
42Dic3×A4Dic314yesdirect product factor
43C3×C4×Dic3—122no—
44Dic32—32no—
45Dic32—31no—
46Dic32—32no—
47Dic32A411yescharacteristic, direct product factor
48C22×C33—41no—
49C32×A4C4211yescharacteristic, complemented
50C3×C3⋊Dic3—42no—
51C32×Dic3—44no—
52C23×C3×C4—32no—
53C23×Dic3—32no—
54C23×Dic3—61no—
55C23×Dic3C3×D312yes—
56C2×C4×A4—32no—
57C2×C4×A4—62no—
58C2×C4×A4—91no—
59C2×C4×Dic3—92no—
60C2×C4×Dic3—92no—
61C2×C4×Dic3—92no—
62C2×C4×Dic3—92no—
63C23×C32—32no—
64C23×C32—31no—
65C23×C32—31no—
66C23×C32C2×C3×C411yescharacteristic
67C23×C32C2×C3×C412yes—
68C2×C3×A4—22no—
69C2×C3×A4—22no—
70C2×C3×A4—22no—
71C2×C3×A4—22no—
72C2×C3×A4—21no—
73C2×C3×A4—42no—
74C2×C3×A4—41no—
75C2×C3×A4C4×D312yes—
76C2×C3×A4C4×D312yes—
77C2×C3×A4C2×Dic312yes—
78C2×C32×C4—122no—
79C2×C3⋊Dic3—32no—
80C2×C3⋊Dic3—31no—
81C2×C3⋊Dic3—32no—
82C2×C3⋊Dic3—32no—
83C2×C3⋊Dic3—32no—
84C2×C3⋊Dic3C2×A411yescharacteristic
85C2×C3×Dic3—34no—
86C2×C3×Dic3—32no—
87C2×C3×Dic3—34no—
88C2×C3×Dic3—34no—
89C2×C3×Dic3—34no—
90C2×C3×Dic3—42no—
91C2×C3×Dic3—82no—
92C2×C3×Dic3—122no—
93C2×C3×Dic3—241no—
94C2×C3×Dic3C2×A412yes—
95C22×C42—91noSylow
96C2×C33—42no—
97C2×C33—41no—
98C24×C3—21no—
99C24×C3C2×C3×D312yes—
100C22×A4—22no—
101C22×A4—41no—
102C22×A4D3211yescharacteristic
103C22×C3×C4—34no—
104C22×C3×C4—92no—
105C22×C3×C4—92no—
106C22×C3×C4—94no—
107C22×Dic3—32no—
108C22×Dic3—32no—
109C22×Dic3—34no—
110C22×Dic3—34no—
111C22×Dic3—62no—
112C22×Dic3—92no—
113C22×Dic3—92no—
114C22×Dic3—94no—
115C22×Dic3—181no—
116C22×Dic3—181no—
117C22×Dic3—182no—
118C22×Dic3C3×Dic314yescomplemented
119C4×A4—34no—
120C4×A4—64no—
121C4×A4—92no—
122C3×C42—361no—
123C4×Dic3—32no—
124C4×Dic3—92no—
125C4×Dic3—92no—
126C4×Dic3—94no—
127C4×Dic3—92no—
128C22×C32—31no—
129C22×C32—32no—
130C22×C32—32no—
131C22×C32—32no—
132C22×C32—32no—
133C22×C32—31no—
134C22×C32—31no—
135C22×C32—42no—
136C22×C32—81no—
137C22×C32—82no—
138C22×C32—161no—
139C22×C32C3×C4211yescharacteristic, complemented
140C22×C32C22×A411yescharacteristic
141C3×A4—22no—
142C3×A4—21no—
143C3×A4—41no—
144C3×A4C4×Dic312yescomplemented
145C32×C4—124no—
146C3⋊Dic3—32no—
147C3⋊Dic3C4×A412yescomplemented
148C3×Dic3—34no—
149C3×Dic3—44no—
150C3×Dic3—84no—
151C3×Dic3—124no—
152C3×Dic3—242no—
153C3×Dic3C4×A414yescomplemented
154C23×C4—32no—
155C23×C4—91no—
156C2×C42—271no—
157C2×C42—272no—
158C2×C42—271no—
159C33—41noSylow
160C23×C3—22no—
161C23×C3—21no—
162C23×C3—32no—
163C23×C3—32no—
164C23×C3—32no—
165C23×C3—32no—
166C23×C3—61no—
167C23×C3—61no—
168C23×C3—62no—
169C23×C3C3×C4×D312yes—
170C23×C3C3×C4×D312yes—
171C23×C3C2×C3×Dic312yes—
172C2×A4—22no—
173C2×A4—22no—
174C2×A4—22no—
175C2×A4—42no—
176C2×A4—41no—
177C2×A4D3×Dic312yes—
178C2×A4#62411yescharacteristic
179C2×C3×C4—32no—
180C2×C3×C4—94no—
181C2×C3×C4—94no—
182C2×C3×C4—94no—
183C2×C3×C4—92no—
184C2×C3×C4—94no—
185C2×C3×C4—122no—
186C2×C3×C4—242no—
187C2×C3×C4—361no—
188C2×Dic3—34no—
189C2×Dic3—32no—
190C2×Dic3—32no—
191C2×Dic3—34no—
192C2×Dic3—34no—
193C2×Dic3—34no—
194C2×Dic3—61no—
195C2×Dic3—94no—
196C2×Dic3—94no—
197C2×Dic3—94no—
198C2×Dic3—92no—
199C2×Dic3—94no—
200C2×Dic3—182no—
201C2×Dic3—182no—
202C2×Dic3—181no—
203C2×Dic3—182no—
204C2×Dic3—182no—
205C2×Dic3D3×A412yes—
206C2×C32—31no—
207C2×C32—32no—
208C2×C32—31no—
209C2×C32—42no—
210C2×C32—42no—
211C2×C32—42no—
212C2×C32—81no—
213C2×C32—82no—
214C2×C32—82no—
215C2×C32—82no—
216C2×C32—82no—
217C2×C32—162no—
218C2×C32—161no—
219C2×C32C2×C4×A411yescharacteristic
220C2×C32C2×C4×A412yes—
221C24C3×D3211yescharacteristic
222C22×C4—34no—
223C22×C4—92no—
224C22×C4—92no—
225C22×C4—94no—
226C22×C4—92no—
227C22×C4—271no—
228C22×C4—271no—
229C22×C4—272no—
230C42—91no—
231C42—272no—
232C42—271no—
233C42—272no—
234C22×C3—21no—
235C22×C3—21no—
236C22×C3—32no—
237C22×C3—32no—
238C22×C3—32no—
239C22×C3—34no—
240C22×C3—32no—
241C22×C3—32no—
242C22×C3—32no—
243C22×C3—32no—
244C22×C3—32no—
245C22×C3—32no—
246C22×C3—41no—
247C22×C3—61no—
248C22×C3—61no—
249C22×C3—62no—
250C22×C3—62no—
251C22×C3—62no—
252C22×C3—61no—
253C22×C3—62no—
254C22×C3—82no—
255C22×C3—161no—
256C22×C3C3×C4×Dic312yescomplemented
257C22×C3C2×D3×A412yes—
258A4—22no—
259A4—41no—
260A4Dic3211yescharacteristic, direct product factor
261C3×C4—34no—
262C3×C4—94no—
263C3×C4—124no—
264C3×C4—244no—
265C3×C4—362no—
266Dic3—34no—
267Dic3—34no—
268Dic3—62no—
269Dic3—94no—
270Dic3—182no—
271Dic3Dic3×A414yesdirect product factor
272C32—42no—
273C32—81no—
274C32—82no—
275C32—161no—
276C32C42×A411yescharacteristic, complemented
277C23—32no—
278C23—31no—
279C23—31no—
280C23C3×D3×Dic312yes—
281C23C3×#62411yescharacteristic
282C2×C4—32no—
283C2×C4—94no—
284C2×C4—94no—
285C2×C4—94no—
286C2×C4—91no—
287C2×C4—92no—
288C2×C4—94no—
289C2×C4—272no—
290C2×C4—272no—
291C2×C4—272no—
292C2×C4—271no—
293C2×C4—272no—
294C2×C3—22no—
295C2×C3—21no—
296C2×C3—32no—
297C2×C3—32no—
298C2×C3—32no—
299C2×C3—32no—
300C2×C3—42no—
301C2×C3—41no—
302C2×C3—61no—
303C2×C3—61no—
304C2×C3—62no—
305C2×C3—82no—
306C2×C3—82no—
307C2×C3—82no—
308C2×C3—162no—
309C2×C3—161no—
310C2×C3C4×D3×A412yes—
311C2×C3C4×D3×A412yes—
312C2×C3C2×Dic3×A412yes—
313C22—32no—
314C22—31no—
315C22—32no—
316C22—32no—
317C22—32no—
318C22—31no—
319C22—31no—
320C22C3×Dic3211yescharacteristic, complemented
321C22D32×A411yescharacteristic
322C4—34no—
323C4—94no—
324C4—92no—
325C4—272no—
326C3—21no—
327C3—41no—
328C3—82no—
329C3—161no—
330C3C4×Dic3×A412yescomplemented
331C2—31no—
332C2—32no—
333C2—31no—
334C2D3×Dic3×A412yes—
335C2A4×#62411yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×A4
commutator, hypocenterC22×C32C3×C42
Fitting, socle, cosocleC24×C32C22×C3
prime radicalC22×C32×A4C22
LCSG ▷ C22×C32
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
3. C22×Dic32C3semidirect
6. A4×C3⋊Dic3C4semidirect
7. C3×Dic3×A4C4semidirect
33. C22×C3⋊Dic3C3×C4semidirect
37. C22×C3×Dic3C3×C4semidirect
42. Dic3×A4Dic3direct (N × H)
47. Dic32A4direct (N × H)
49. C32×A4C42semidirect
118. C22×Dic3C3×Dic3semidirect
139. C22×C32C3×C42semidirect
144. C3×A4C4×Dic3semidirect
147. C3⋊Dic3C4×A4semidirect
153. C3×Dic3C4×A4semidirect
256. C22×C3C3×C4×Dic3semidirect
260. A4Dic32direct (N × H)
271. Dic3Dic3×A4direct (N × H)
276. C32C42×A4semidirect
320. C22C3×Dic32semidirect
330. C3C4×Dic3×A4semidirect

Maximal subgroups

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

subgroupindex
C2×A4×C3⋊Dic32
C2×C3×Dic3×A42
C22×Dic323
C4×Dic3×A43
C3×Dic324