Finite Group Databasebeta

← D3×#6706 #13087264

Subgroups — D3×#6706 #13087264

Order 1440.

292 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 74 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
1D3×D60C211yesmaximal, characteristic
2D3×Dic30C211yesmaximal, characteristic, complemented
3#10623900C211yesmaximal, characteristic, complemented
4C3×#6706C211yesmaximal, characteristic, complemented
5C3×C5×D3×C8C211yesmaximal, characteristic, complemented
6#10623804C211yesmaximal, characteristic, complemented
7#10623803C211yesmaximal, characteristic, complemented
8C2×#6706—31nomaximal
9D3×#677—31nomaximal
10C2×D3×D15—21no—
11C4⋊(C3⋊D15)C2211yescharacteristic
12#67180C2211yescharacteristic, complemented
13C3×D60C2211yescharacteristic
14C3×Dic30C2211yescharacteristic, complemented
15C3×C4×C5×D3C2211yescharacteristic
16#67153—21no—
17#67151—21no—
18D3×Dic15—21no—
19C32×C5×C8C2211yescharacteristic, complemented
20C3×C5×C3⋊C8C2211yescharacteristic, complemented
21D3×#204—51nomaximal, Hall
22C2×D60—31no—
23C2×Dic30—31no—
24D3×D20—31no—
25D3×Dic10—31no—
26C2×C3×C5×C8—31no—
27#6706—31no—
28#6706—31no—
29#6706—31no—
30#6706—31no—
31#6706—61no—
32#6706D311yescharacteristic, direct product factor
33C5×D3×C8D311yescharacteristic, complemented
34C3×#677—31no—
35#6658—31no—
36#6657—31no—
37C2×C3⋊D15—21no—
38C2×C3×D15—21no—
39C2×C3×C5×D3D411yescharacteristic
40D3×D15—42no—
41C32×C4×C5C2311yescharacteristic
42C3⋊Dic15—21no—
43C3×Dic15—21no—
44C3×C5×Dic3D411yescharacteristic
45C2×#677—91noHall
46D3×D12—51no—
47D3×Dic6—51no—
48#3744—51no—
49C3×#204—51no—
50C3×D3×C8D511yescharacteristic, complemented
51#3717—51no—
52#3716—51no—
53C22×D15—61no—
54C2×D3×D5—61no—
55C2×C3×C4×C5—31no—
56C2×Dic15—61no—
57D60—31no—
58D60—31no—
59D60—61no—
60D60—61no—
61D60C2×D311yescharacteristic
62Dic30—31no—
63Dic30—31no—
64Dic30—61no—
65Dic30—61no—
66Dic30C2×D311yescharacteristic, complemented
67C4×C5×D3C2×D311yescharacteristic
68C3×D20—31no—
69C3×Dic10—31no—
70#1204—61no—
71#1202—61no—
72D3×Dic5—61no—
73C3×C5×C8—21no—
74C3×C5×C8—31no—
75C3×C5×C8C2×D311yescharacteristic, complemented
76C3×C5×C8C2×D311yescharacteristic, complemented
77C5×C3⋊C8C2×D311yescharacteristic, complemented
78D3×SD16—151no—
79C2×#204—151no—
80C2×C32×C5C2×D411yescharacteristic
81C3⋊D15—41no—
82C3×D15—41no—
83C3×C5×D3SD1612yescomplemented
84C2×D20—91no—
85C2×Dic10—91no—
86C2×C5×C8—31no—
87#677—31no—
88#677—91no—
89#677—91no—
90#677—91no—
91C2×D32—101no—
92C4⋊(C3⋊D3)—51no—
93#634—51no—
94C3×D12—51no—
95C3×C4×D3C2×D511yescharacteristic
96C3×Dic6—51no—
97#627—101no—
98#626—101no—
99D3×Dic3—101no—
100C32×C8C2×D511yescharacteristic, complemented
101C3×C3⋊C8C2×D511yescharacteristic, complemented
102C22×C3×C5—31no—
103C2×D15—21no—
104C2×D15—61no—
105C2×D15—61no—
106C2×D15—121no—
107C2×D15—122no—
108C2×C5×D3D1211yescharacteristic
109C2×C3×D5—61no—
110D3×D5—122no—
111C3×C4×C5—21no—
112C3×C4×C5—31no—
113C3×C4×C5C22×D311yescharacteristic
114C3×C4×C5C22×D311yescharacteristic
115Dic15—21no—
116Dic15—61no—
117Dic15—61no—
118Dic15—121no—
119C3×Dic5—61no—
120C5×Dic3D1211yescharacteristic
121D3×Q8—151no—
122D3×D4—151no—
123C2×D12—151no—
124C2×Dic6—151no—
125C3×SD16—151no—
126C2×C3×C8—31no—
127#215—151no—
128#214—151no—
129#204—51no—
130#204—151no—
131#204—151no—
132#204—151no—
133#204—151no—
134#204—301no—
135D3×C8D1511yescharacteristic, complemented
136C32×C5C2×SD1611yescharacteristic, complemented, Hall
137C22×D5—181no—
138C2×C4×C5—31no—
139C2×Dic5—181no—
140D20—31no—
141D20—91no—
142D20—181no—
143Dic10—31no—
144Dic10—91no—
145Dic10—181no—
146C5×C8—31no—
147C5×C8D3211yescharacteristic, complemented
148C2×C3⋊D3—101no—
149C2×C3×D3—101no—
150C2×C3×D3D2011yescharacteristic
151D32—202no—
152C32×C4C22×D511yescharacteristic
153C3⋊Dic3—101no—
154C3×Dic3—101no—
155C3×Dic3D2011yescharacteristic
156C2×SD16—451noSylow
157C2×C3×C5—21no—
158C2×C3×C5—32no—
159C2×C3×C5C2×D1211yescharacteristic
160C2×C3×C5D3×D411yescharacteristic
161D15—41no—
162D15—121no—
163D15—121no—
164D15—241no—
165C3×D5—121no—
166C5×D3#20412yescomplemented
167C22×D3—301no—
168C22×D3—301no—
169C3×Q8—151no—
170C3×D4—151no—
171C2×C3×C4—31no—
172#67—301no—
173C2×Dic3—301no—
174D12—51no—
175D12—151no—
176D12—151no—
177D12—301no—
178D12—301no—
179C4×D3—301no—
180C4×D3C2×D1511yescharacteristic
181Dic6—51no—
182Dic6—151no—
183Dic6—151no—
184Dic6—301no—
185Dic6—301no—
186Dic6—301no—
187C3×C8—21no—
188C3×C8—31no—
189C3×C8D3×D511yescharacteristic, complemented
190C3×C8C2×D1511yescharacteristic, complemented
191C3⋊C8C2×D1511yescharacteristic, complemented
192C22×C5—31no—
193C2×D5—61no—
194C2×D5—181no—
195C2×D5—362no—
196C4×C5—31no—
197C4×C5C2×D3211yescharacteristic
198Dic5—61no—
199Dic5—181no—
200C2×C32C2×D2011yescharacteristic
201C3⋊D3—201no—
202C3×D3—201no—
203C3×D3#67712yescomplemented
204C2×Q8—451no—
205C2×D4—451no—
206SD16—151no—
207SD16—451no—
208SD16—451no—
209SD16—451no—
210C2×C8—31no—
211C3×C5—21no—
212C3×C5C2×#20411yescharacteristic, complemented
213C3×C5D3×SD1611yescharacteristic, complemented
214C22×C3—31no—
215C22×C3—301no—
216C2×D3—101no—
217C2×D3—301no—
218C2×D3—301no—
219C2×D3—601no—
220C2×D3—602no—
221C2×D3—602no—
222C2×D3D6011yescharacteristic
223C3×C4—21no—
224C3×C4—31no—
225C3×C4—301no—
226C3×C4C2×D3×D511yescharacteristic
227C3×C4C22×D1511yescharacteristic
228Dic3—101no—
229Dic3—301no—
230Dic3—301no—
231Dic3—601no—
232Dic3D6011yescharacteristic
233C2×C5—32no—
234C2×C5D3×D1211yescharacteristic
235D5—121no—
236D5—361no—
237C32C2×#67711yescharacteristic, complemented, Sylow
238C23—901no—
239Q8—151no—
240Q8—451no—
241Q8—901no—
242D4—151no—
243D4—451no—
244D4—901no—
245C2×C4—31no—
246C2×C4—901no—
247C8—31no—
248C8D3×D1511yescharacteristic, complemented
249C2×C3—21no—
250C2×C3—32no—
251C2×C3—601no—
252C2×C3D3×D2011yescharacteristic
253C2×C3C2×D6011yescharacteristic
254D3—201no—
255D3—601no—
256D3—601no—
257D3—1201no—
258D3#670612yesdirect product factor
259C5D3×#20411yescharacteristic, complemented, Sylow
260C22—31no—
261C22—301no—
262C22—901no—
263C22—1802no—
264C4—31no—
265C4—301no—
266C4—901no—
267C4C2×D3×D1511yescharacteristic
268C3—21no—
269C3D3×#67711yescharacteristic, complemented
270C3C2×#670611yescharacteristic, complemented
271C2—32no—
272C2—601no—
273C2—1801no—
274C2D3×D6011yescharacteristic
subgroupG/H
centerC2D3×D60
commutator, cosocleC32×C4×C5C23
FrattiniC4C2×D3×D15
FittingC32×C5×C8C22
socleC2×C32×C5C2×D4
prime radicalD3×D60C2
hypercenterC8D3×D15
hypocenterC32×C5C2×SD16
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4 ◁ C8

Complements

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

NH ≅ G/Ntype
2. D3×Dic30C2semidirect
3. #10623900C2semidirect
4. C3×#6706C2semidirect
5. C3×C5×D3×C8C2semidirect
6. #10623804C2semidirect
7. #10623803C2semidirect
12. #67180C22semidirect
14. C3×Dic30C22semidirect
19. C32×C5×C8C22semidirect
20. C3×C5×C3⋊C8C22semidirect
32. #6706D3direct (N × H)
33. C5×D3×C8D3semidirect
50. C3×D3×C8D5semidirect
66. Dic30C2×D3semidirect
75. C3×C5×C8C2×D3semidirect
76. C3×C5×C8C2×D3semidirect
77. C5×C3⋊C8C2×D3semidirect
83. C3×C5×D3SD16semidirect
100. C32×C8C2×D5semidirect
101. C3×C3⋊C8C2×D5semidirect
135. D3×C8D15semidirect
136. C32×C5C2×SD16semidirect
147. C5×C8D32semidirect
166. C5×D3#204semidirect
189. C3×C8D3×D5semidirect
190. C3×C8C2×D15semidirect
191. C3⋊C8C2×D15semidirect
203. C3×D3#677semidirect
212. C3×C5C2×#204semidirect
213. C3×C5D3×SD16semidirect
237. C32C2×#677semidirect
248. C8D3×D15semidirect
258. D3#6706direct (N × H)
259. C5D3×#204semidirect
269. C3D3×#677semidirect
270. C3C2×#6706semidirect

Maximal subgroups

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

subgroupindex
D3×D602
D3×Dic302
#106239002
C3×#67062
C3×C5×D3×C82
#106238042
#106238032
C2×#67063
D3×#6773
D3×#2045