Finite Group Databasebeta

← Dic3×#120⋊C3 #11921283

Subgroups — Dic3×#120⋊C3 #11921283

Order 1152.

527 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 527 conjugacy classes of subgroups — too many to draw. Only its 44 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
1Dic3×C22⋊A4C211yesmaximal, characteristic, complemented
2C2×C3×#120⋊C3C211yesmaximal, characteristic
3C3⋊(#379⋊C3)C211yesmaximal, characteristic, complemented
4Dic3×#120C311yesmaximal, characteristic, complemented
5C4×#120⋊C3—31nomaximal
6C2×C3×C22⋊A4C2211yescharacteristic
7C2×Dic3×A4—41nomaximal
8C3×#120⋊C3C412yescomplemented
9C24×Dic3C2×C311yescharacteristic, complemented
10C4×C22⋊A4—31no—
11C2×C3×#120C2×C311yescharacteristic
12C2×D4×Dic3—31no—
13C2×#120⋊C3—21no—
14C2×#120⋊C3D311yescharacteristic
15#5247C2×C311yescharacteristic, complemented
16#5220—31no—
17#4950—31no—
18Dic3×C22⋊C4—31no—
19#379⋊C3—31no—
20C3×C22⋊A4C2×C411yescharacteristic, complemented
21C22×C3×A4—41no—
22Dic3×A4—41no—
23Dic3×A4—41no—
24Dic3×A4—82no—
25C4×#120—31noSylow
26C25×C3C22×C311yescharacteristic
27C2×C22⋊A4—21no—
28C2×C22⋊A4C2×D311yescharacteristic
29C22×C3×D4—31no—
30C23×Dic3—31no—
31C23×Dic3—31no—
32C23×Dic3—62no—
33C23×Dic3—62no—
34C23×Dic3A411yescharacteristic, complemented
35C2×C4×A4—121no—
36C3×#120—32no—
37C3×#120C3×C412yescomplemented
38C2×C3×C22⋊C4—31no—
39C2×#217—31no—
40C2×#217—31no—
41C2×#217—31no—
42D4×Dic3—62no—
43D4×Dic3—62no—
44C2×C4⋊Dic3—31no—
45C2×C4×Dic3—31no—
46#120⋊C3—22no—
47#120⋊C3Dic312yesdirect product factor
48C3⋊#95—32no—
49C2×C3×A4—42no—
50C2×C3×A4—41no—
51C2×C3×A4—82no—
52C2×C3×Dic3—161no—
53C24×C4—31no—
54C2×#120C3×D311yescharacteristic
55C2×C4×D4—91no—
56#386—91no—
57#385—91no—
58#379—31no—
59C4×C22⋊C4—91no—
60C24×C3—31no—
61C24×C3—31no—
62C24×C3—62no—
63C24×C3—62no—
64C24×C3C2×C3×C411yescharacteristic, complemented
65C24×C3C2×A411yescharacteristic
66C22⋊A4—21no—
67C22⋊A4C2×Dic311yescharacteristic, complemented
68C22×A4—41no—
69C22×A4—81no—
70C2×C3×D4—32no—
71C2×C3×D4—32no—
72C2×C3×D4—62no—
73C2×C3×D4—62no—
74C22×C3×C4—31no—
75C22×Dic3—22no—
76C22×Dic3—32no—
77C22×Dic3—32no—
78C22×Dic3—31no—
79C22×Dic3—31no—
80C22×Dic3—61no—
81C22×Dic3—62no—
82C22×Dic3—62no—
83C22×Dic3—64no—
84C22×Dic3—61no—
85C22×Dic3—62no—
86C22×Dic3—62no—
87C22×Dic3—64no—
88C22×Dic3—62no—
89C22×Dic3—62no—
90C22×Dic3C2×A411yescharacteristic
91C22×Dic3C2×A411yescharacteristic
92C4×A4—121no—
93C4×A4—121no—
94C4×A4—242no—
95C3×C22⋊C4—32no—
96C3×C22⋊C4—32no—
97#217—62no—
98#217—62no—
99#217—62no—
100C4⋊Dic3—62no—
101C4×Dic3—61no—
102C4×Dic3—61no—
103C22×C32—161no—
104C3×A4—41no—
105C3×A4—82no—
106C3×Dic3—161no—
107C3×Dic3—161no—
108C25C2×C3×D311yescharacteristic
109C22×D4—31no—
110C23×C4—31no—
111C23×C4—91no—
112C23×C4—91no—
113C23×C4—182no—
114C23×C4—182no—
115#120—32no—
116#120C3×Dic312yescomplemented
117C4×D4—182no—
118C4×D4—182no—
119C2×C4⋊C4—91no—
120C2×C22⋊C4—31no—
121C2×C22⋊C4—91no—
122C2×C22⋊C4—91no—
123C2×C22⋊C4—91no—
124C2×C42—91no—
125#95—92no—
126C23×C3—22no—
127C23×C3—32no—
128C23×C3—32no—
129C23×C3—31no—
130C23×C3—31no—
131C23×C3—62no—
132C23×C3—62no—
133C23×C3—61no—
134C23×C3—62no—
135C23×C3—62no—
136C23×C3—62no—
137C23×C3—64no—
138C23×C3—61no—
139C23×C3—62no—
140C23×C3—62no—
141C23×C3—64no—
142C23×C3C4×A412yescomplemented
143C23×C3C22×A411yescharacteristic
144C2×A4—41no—
145C2×A4—42no—
146C2×A4—82no—
147C2×A4—81no—
148C2×A4—82no—
149C2×A4—162no—
150C3×D4—64no—
151C3×D4—64no—
152C2×C3×C4—32no—
153C2×C3×C4—61no—
154C2×C3×C4—61no—
155C2×C3×C4—481no—
156C2×Dic3—31no—
157C2×Dic3—31no—
158C2×Dic3—32no—
159C2×Dic3—41no—
160C2×Dic3—62no—
161C2×Dic3—64no—
162C2×Dic3—61no—
163C2×Dic3—62no—
164C2×Dic3—64no—
165C2×Dic3—62no—
166C2×Dic3—62no—
167C2×Dic3—62no—
168C2×Dic3—61no—
169C2×Dic3—62no—
170C2×Dic3—121no—
171C2×C32—162no—
172C2×C32—161no—
173C24—31no—
174C24—31no—
175C24—62no—
176C24—62no—
177C24C2×C3×Dic311yescharacteristic, complemented
178C24D3×A411yescharacteristic
179C2×D4—32no—
180C2×D4—32no—
181C2×D4—62no—
182C2×D4—62no—
183C22×C4—31no—
184C22×C4—31no—
185C22×C4—31no—
186C22×C4—62no—
187C22×C4—92no—
188C22×C4—92no—
189C22×C4—91no—
190C22×C4—91no—
191C22×C4—181no—
192C22×C4—182no—
193C22×C4—182no—
194C22×C4—184no—
195C22×C4—181no—
196C22×C4—182no—
197C22×C4—182no—
198C22×C4—184no—
199C22×C4—182no—
200C22×C4—182no—
201C4⋊C4—182no—
202C22⋊C4—32no—
203C22⋊C4—32no—
204C22⋊C4—182no—
205C22⋊C4—182no—
206C22⋊C4—182no—
207C42—181no—
208C42—181no—
209C22×C3—22no—
210C22×C3—31no—
211C22×C3—31no—
212C22×C3—32no—
213C22×C3—32no—
214C22×C3—41no—
215C22×C3—62no—
216C22×C3—62no—
217C22×C3—64no—
218C22×C3—62no—
219C22×C3—62no—
220C22×C3—62no—
221C22×C3—62no—
222C22×C3—62no—
223C22×C3—64no—
224C22×C3—62no—
225C22×C3—121no—
226C22×C3—161no—
227C22×C3—321no—
228C22×C3C2×C4×A411yescharacteristic
229A4—41no—
230A4—82no—
231A4—81no—
232A4—162no—
233C3×C4—62no—
234C3×C4—481no—
235C3×C4—481no—
236Dic3—31no—
237Dic3—41no—
238Dic3—62no—
239Dic3—121no—
240Dic3#120⋊C311yescharacteristic, direct product factor
241C32—161noSylow
242C23—22no—
243C23—32no—
244C23—32no—
245C23—31no—
246C23—31no—
247C23—62no—
248C23—62no—
249C23—61no—
250C23—62no—
251C23—62no—
252C23—62no—
253C23—64no—
254C23—61no—
255C23—62no—
256C23—62no—
257C23—64no—
258C23Dic3×A412yescomplemented
259C23C2×D3×A411yescharacteristic
260D4—64no—
261D4—64no—
262C2×C4—32no—
263C2×C4—61no—
264C2×C4—61no—
265C2×C4—91no—
266C2×C4—91no—
267C2×C4—92no—
268C2×C4—121no—
269C2×C4—182no—
270C2×C4—182no—
271C2×C4—184no—
272C2×C4—181no—
273C2×C4—182no—
274C2×C4—184no—
275C2×C4—182no—
276C2×C4—182no—
277C2×C4—181no—
278C2×C4—182no—
279C2×C4—361no—
280C2×C3—31no—
281C2×C3—31no—
282C2×C3—42no—
283C2×C3—62no—
284C2×C3—62no—
285C2×C3—162no—
286C2×C3—161no—
287C2×C3—322no—
288C2×C3—321no—
289C2×C3C2×#120⋊C311yescharacteristic
290C22—22no—
291C22—31no—
292C22—31no—
293C22—32no—
294C22—32no—
295C22—41no—
296C22—62no—
297C22—62no—
298C22—62no—
299C22—62no—
300C22—64no—
301C22—62no—
302C22—62no—
303C22—62no—
304C22—64no—
305C22—62no—
306C22—121no—
307C22C2×Dic3×A411yescharacteristic
308C4—31no—
309C4—62no—
310C4—91no—
311C4—121no—
312C4—182no—
313C4—361no—
314C3—161no—
315C3—321no—
316C3C4×#120⋊C311yescharacteristic, complemented
317C2—31no—
318C2—31no—
319C2—42no—
320C2—62no—
321C2—62no—
322C2D3×#120⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#120⋊C3
commutator, hypocenterC24×C3C2×C3×C4
FrattiniC23C2×D3×A4
FittingC2×C3×#120C2×C3
socleC23×C3C22×A4
prime radicalC2×C3×#120⋊C3C2
cosocleC25×C3C22×C3
LCSG ▷ C24×C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. Dic3×C22⋊A4C2semidirect
3. C3⋊(#379⋊C3)C2semidirect
4. Dic3×#120C3semidirect
8. C3×#120⋊C3C4semidirect
9. C24×Dic3C2×C3semidirect
15. #5247C2×C3semidirect
20. C3×C22⋊A4C2×C4semidirect
34. C23×Dic3A4semidirect
37. C3×#120C3×C4semidirect
47. #120⋊C3Dic3direct (N × H)
64. C24×C3C2×C3×C4semidirect
67. C22⋊A4C2×Dic3semidirect
116. #120C3×Dic3semidirect
142. C23×C3C4×A4semidirect
177. C24C2×C3×Dic3semidirect
240. Dic3#120⋊C3direct (N × H)
258. C23Dic3×A4semidirect
316. C3C4×#120⋊C3semidirect

Maximal subgroups

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

subgroupindex
Dic3×C22⋊A42
C2×C3×#120⋊C32
C3⋊(#379⋊C3)2
Dic3×#1203
C4×#120⋊C33
C2×Dic3×A44