Finite Group Databasebeta

← Dic3×#1202 #13085908

Subgroups — Dic3×#1202 #13085908

Order 1440.

410 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 106 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×Dic3×D15C211yesmaximal, characteristic, complemented
2C2×C3×#1202C211yesmaximal, characteristic
3C2×C3×D5×Dic3C211yesmaximal, characteristic, complemented
4#10623829C211yesmaximal, characteristic, complemented
5Dic3⋊Dic15C211yesmaximal, characteristic, complemented
6C5×Dic32C211yesmaximal, characteristic, complemented
7#10623770C211yesmaximal, characteristic, complemented
8C4×#1202—31nomaximal
9Dic3×D20—31nomaximal
10C22×C3×D15C2211yescharacteristic
11C22×C32×D5C2211yescharacteristic
12C2×C3⋊Dic15C2211yescharacteristic
13C2×C5×C3⋊Dic3C2211yescharacteristic
14C2×C3×Dic15C2211yescharacteristic
15C2×C3×C5×Dic3C2211yescharacteristic
16C2×C3×C5×Dic3C2211yescharacteristic
17Dic3×D15—22no—
18C3×#1202C414yescomplemented
19C3×D5×Dic3—22no—
20Dic3×#67—51nomaximal, Hall
21C2×C4×D15—31no—
22C2×C3×D20—31no—
23C2×C3×C4×D5—31no—
24C2×#1202D311yescharacteristic
25C2×D5×Dic3—31no—
26C2×D5×Dic3D311yescharacteristic, complemented
27C4⋊Dic15—31no—
28C4×C5×Dic3—31no—
29C4×C5×Dic3—31no—
30Dic3⋊Dic5—31no—
31#6667—31no—
32#6665—31no—
33#6665—31no—
34#6665—31no—
35#6665—61no—
36C22×C32×C5C2311yescharacteristic
37C2×C3×D15—21no—
38C2×C3×D15—21no—
39C2×C3×D15C2×C412yescomplemented
40C2×C32×D5—21no—
41C2×C32×D5—21no—
42C2×C32×D5C2×C412yescomplemented
43C3⋊Dic15—21no—
44C5×C3⋊Dic3—21no—
45C3×Dic15—21no—
46C3×C5×Dic3C2×C412yescomplemented
47C3×C5×Dic3D412yescomplemented
48C4×D20—91noHall
49C2×C3×#67—51no—
50C22×C3×Dic3—51no—
51C2×D3×Dic3—51no—
52#3757—51no—
53Dic3⋊Dic3—51no—
54(C2×D3)⋊Dic3—51no—
55Dic32D511yescharacteristic, complemented
56C22×D15C2×D311yescharacteristic
57C22×C3×D5—21no—
58C22×C3×D5—31no—
59C22×C3×D5C2×D311yescharacteristic
60C22×C3×D5C2×D311yescharacteristic
61C2×C3×C4×C5—31no—
62C2×C3×C4×C5—31no—
63C2×Dic15—31no—
64C2×Dic15—31no—
65C2×Dic15—61no—
66C2×Dic15C2×D311yescharacteristic
67C4×D15—62no—
68C2×C5×Dic3—31no—
69C2×C5×Dic3—31no—
70C2×C5×Dic3—61no—
71C2×C5×Dic3C2×D311yescharacteristic
72C2×C5×Dic3C2×D311yescharacteristic
73C2×C3×Dic5—31no—
74C3×D20—34no—
75C3×C4×D5—62no—
76#1202Dic314yesdirect product factor
77D5×Dic3—22no—
78D5×Dic3—62no—
79D4×Dic3—151no—
80C4×#67—151no—
81C2×C32×C5C22×C411yescharacteristic
82C2×C32×C5C2×D411yescharacteristic
83C2×C32×C5#4111yescharacteristic
84C3×D15—22no—
85C32×D5—22no—
86C2×D20—31no—
87C2×C4×D5—31no—
88C2×C4×D5—91no—
89C42×C5—91no—
90#685—91no—
91#685—91no—
92C4⋊Dic5—91no—
93C23×C32—51no—
94C22×C3×D3—51no—
95C2×C3⋊Dic3—51no—
96C2×C3⋊Dic3C2×D511yescharacteristic
97C3×#67—54no—
98C2×C3×Dic3—51no—
99C2×C3×Dic3—102no—
100C2×C3×Dic3C2×D511yescharacteristic
101C2×C3×Dic3C2×D511yescharacteristic
102D3×Dic3—102no—
103C22×C3×C5—21no—
104C22×C3×C5C22×D311yescharacteristic
105C22×C3×C5C22×D311yescharacteristic
106C2×D15—21no—
107C2×D15—21no—
108C2×D15C2×Dic312yescomplemented
109C2×C3×D5—21no—
110C2×C3×D5—21no—
111C2×C3×D5—21no—
112C2×C3×D5—21no—
113C2×C3×D5—22no—
114C2×C3×D5—32no—
115C2×C3×D5—41no—
116C2×C3×D5—41no—
117C2×C3×D5—61no—
118C2×C3×D5—61no—
119C2×C3×D5C4×D312yescomplemented
120C2×C3×D5C2×Dic312yescomplemented
121C3×C4×C5—32no—
122C3×C4×C5—32no—
123Dic15—21no—
124Dic15—61no—
125Dic15—61no—
126Dic15—121no—
127C3×Dic5—61no—
128C5×Dic3—61no—
129C5×Dic3—61no—
130C5×Dic3—121no—
131C5×Dic3C2×Dic312yescomplemented
132C5×Dic3#6712yescomplemented
133C2×C3×D4—151no—
134C22×C3×C4—151no—
135C2×#67—51no—
136C22×Dic3—51no—
137C22×Dic3—151no—
138C2×C4×D3—151no—
139#217—151no—
140#217—151no—
141#217—151no—
142#217—301no—
143(C2×D3)⋊C4—151no—
144C4⋊Dic3—151no—
145Dic3⋊C4—151no—
146C4×Dic3—31no—
147C4×Dic3—31no—
148C32×C5C4×D411yescharacteristic, complemented, Hall
149C22×D5—31no—
150C22×D5D3211yescharacteristic
151C2×C4×C5—31no—
152C2×C4×C5—31no—
153C2×C4×C5—91no—
154C2×Dic5—31no—
155C2×Dic5—91no—
156D20—34no—
157C4×D5—62no—
158C4×D5—182no—
159C22×C32—52no—
160C22×C32—101no—
161C22×C32—101no—
162C22×C32C22×D511yescharacteristic
163C2×C3×D3—52no—
164C2×C3×D3—101no—
165C2×C3×D3—101no—
166C3⋊Dic3—21no—
167C3⋊Dic3—101no—
168C3×Dic3—101no—
169C3×Dic3C4×D512yescomplemented
170C3×Dic3D2012yescomplemented
171C4×D4—451noSylow
172C2×C3×C5—21no—
173C2×C3×C5—21no—
174C2×C3×C5—21no—
175C2×C3×C5C2×C4×D311yescharacteristic
176C2×C3×C5#23511yescharacteristic
177C2×C3×C5D3×D411yescharacteristic
178C2×C3×C5#23711yescharacteristic
179C2×C3×C5C22×Dic311yescharacteristic
180C2×C3×C5C2×#6711yescharacteristic
181D15—22no—
182C3×D5—22no—
183C3×D5—22no—
184C3×D5—42no—
185C3×D5—62no—
186C23×C3—51no—
187C23×C3—51no—
188C23×C3—101no—
189C23×C3—151no—
190C22×D3—51no—
191C3×D4—154no—
192C2×C3×C4—31no—
193C2×C3×C4—31no—
194C2×C3×C4—151no—
195C2×C3×C4—302no—
196#67—54no—
197C2×Dic3—31no—
198C2×Dic3—31no—
199C2×Dic3—51no—
200C2×Dic3—61no—
201C2×Dic3—102no—
202C2×Dic3—151no—
203C2×Dic3—151no—
204C2×Dic3—301no—
205C2×Dic3—302no—
206C2×Dic3D3×D511yescharacteristic
207C2×Dic3D3×D511yescharacteristic
208C4×D3—302no—
209C22×C5C2×D3211yescharacteristic
210C2×D5—21no—
211C2×D5—21no—
212C2×D5—32no—
213C2×D5—61no—
214C2×D5—61no—
215C2×D5D3×Dic312yescomplemented
216C4×C5—32no—
217C4×C5—32no—
218C4×C5—181no—
219Dic5—61no—
220Dic5—181no—
221C2×C32—102no—
222C2×C32C2×C4×D511yescharacteristic
223C2×C32C2×D2011yescharacteristic
224C2×C32#70911yescharacteristic
225C3×D3—102no—
226C2×D4—151no—
227C22×C4—151no—
228C22×C4—451no—
229C4⋊C4—451no—
230C22⋊C4—451no—
231C22⋊C4—451no—
232C42—91no—
233C3×C5—21no—
234C3×C5C4×#6711yescharacteristic, complemented
235C3×C5D4×Dic311yescharacteristic, complemented
236C22×C3—21no—
237C22×C3—52no—
238C22×C3—52no—
239C22×C3—102no—
240C22×C3—101no—
241C22×C3—101no—
242C22×C3—101no—
243C22×C3—101no—
244C22×C3—152no—
245C22×C3—201no—
246C22×C3—201no—
247C22×C3—301no—
248C22×C3—301no—
249C22×C3C2×D3×D511yescharacteristic
250C22×C3C2×D3×D511yescharacteristic
251C2×D3—52no—
252C2×D3—101no—
253C2×D3—101no—
254C3×C4—32no—
255C3×C4—32no—
256C3×C4—301no—
257Dic3—61no—
258Dic3—61no—
259Dic3—101no—
260Dic3—121no—
261Dic3—301no—
262Dic3—301no—
263Dic3—601no—
264Dic3D5×Dic312yescomplemented
265Dic3#120212yesdirect product factor
266C2×C5C2×D3×Dic311yescharacteristic
267C2×C5#380411yescharacteristic
268C2×C5D3×#6711yescharacteristic
269D5—22no—
270D5—62no—
271C32C4×D2011yescharacteristic, complemented, Sylow
272C23—51no—
273C23—151no—
274D4—154no—
275C2×C4—31no—
276C2×C4—31no—
277C2×C4—91no—
278C2×C4—151no—
279C2×C4—302no—
280C2×C4—451no—
281C2×C4—902no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—102no—
286C2×C3—102no—
287C2×C3—202no—
288C2×C3—302no—
289C2×C3#676511yescharacteristic
290C2×C3#677111yescharacteristic
291C2×C3C4×D3×D511yescharacteristic
292C2×C3D3×D2011yescharacteristic
293C2×C3C2×D5×Dic311yescharacteristic
294C2×C3C2×#120211yescharacteristic
295D3—102no—
296C5Dic3×#6711yescharacteristic, complemented, Sylow
297C22—52no—
298C22—101no—
299C22—101no—
300C22—152no—
301C22—301no—
302C22—301no—
303C22D32×D511yescharacteristic
304C4—32no—
305C4—32no—
306C4—181no—
307C4—301no—
308C4—901no—
309C3—21no—
310C3Dic3×D2011yescharacteristic, complemented
311C3C4×#120211yescharacteristic, complemented
312C2—102no—
313C2—302no—
314C2D3×D5×Dic311yescharacteristic
315C2D3×#120211yescharacteristic
316C2#1062404211yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutatorC2×C32×C5C22×C4
Fitting, socle, cosocleC22×C32×C5C23
prime radicalC2×C3×#1202C2
hypocenterC32×C5C4×D4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×Dic3×D15C2semidirect
3. C2×C3×D5×Dic3C2semidirect
4. #10623829C2semidirect
5. Dic3⋊Dic15C2semidirect
6. C5×Dic32C2semidirect
7. #10623770C2semidirect
18. C3×#1202C4semidirect
26. C2×D5×Dic3D3semidirect
39. C2×C3×D15C2×C4semidirect
42. C2×C32×D5C2×C4semidirect
46. C3×C5×Dic3C2×C4semidirect
47. C3×C5×Dic3D4semidirect
55. Dic32D5semidirect
76. #1202Dic3direct (N × H)
108. C2×D15C2×Dic3semidirect
119. C2×C3×D5C4×D3semidirect
120. C2×C3×D5C2×Dic3semidirect
131. C5×Dic3C2×Dic3semidirect
132. C5×Dic3#67semidirect
148. C32×C5C4×D4semidirect
169. C3×Dic3C4×D5semidirect
170. C3×Dic3D20semidirect
215. C2×D5D3×Dic3semidirect
234. C3×C5C4×#67semidirect
235. C3×C5D4×Dic3semidirect
264. Dic3D5×Dic3semidirect
265. Dic3#1202direct (N × H)
271. C32C4×D20semidirect
296. C5Dic3×#67semidirect
310. C3Dic3×D20semidirect
311. C3C4×#1202semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×D152
C2×C3×#12022
C2×C3×D5×Dic32
#106238292
Dic3⋊Dic152
C5×Dic322
#106237702
C4×#12023
Dic3×D203
Dic3×#675