Finite Group Databasebeta

← D3×#470 #80902

Subgroups — D3×#470 #80902

Order 384.

492 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 135 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×D3×Q16C211yesmaximal, characteristic, complemented
2C2×D3×M16C211yesmaximal, characteristic
3D3×C22⋊Q8C212yesmaximal
4C3×#470C211yesmaximal, characteristic, complemented
5#5189C211yesmaximal, characteristic, complemented
6#5137C211yesmaximal, characteristic, complemented
7#5052C212yesmaximal, complemented
8#4867C211yesmaximal, characteristic, complemented
9D3×#106C211yesmaximal, characteristic, complemented
10#4816C212yesmaximal, complemented
11D3×#103C212yesmaximal, complemented
12C2×#470—31nomaximal, Sylow
13C2×D3×Q8C2212yes—
14C22×C4×D3C2211yescharacteristic
15C2×C3×Q16C2211yescharacteristic, complemented
16C2×C3×M16C2211yescharacteristic
17C3×C22⋊Q8C2212yes—
18#946C2212yes—
19C2×#216C2212yescomplemented
20#924C2212yes—
21C2×#208C2211yescharacteristic
22D3×Q16—24no—
23D3×M16—24no—
24C2×Dic12C2211yescharacteristic, complemented
25C2×ΓL(1,𝔽25)C2211yescharacteristic
26C2×ΓL(1,𝔽25)C2211yescharacteristic
27C2×D3×C8C2211yescharacteristic
28C2×D3×C8C2211yescharacteristic
29#897C2212yes—
30#896—22no—
31D3×C4⋊C4—22no—
32D3×C4⋊C4C2212yes—
33D3×C22⋊C4—22no—
34#878—22no—
35C3×#106C2211yescharacteristic, complemented
36C3×#103C2212yescomplemented
37#835C2212yescomplemented
38#817C2211yescharacteristic, complemented
39#816C2212yescomplemented
40#810C2212yescomplemented
41#808C2212yescomplemented
42C22×Q16—31no—
43C22×M16—31no—
44C2×C22⋊Q8—32no—
45#470—31no—
46#470—31no—
47#470—32no—
48#470—31no—
49#470—32no—
50#470D311yescharacteristic, direct product factor
51C2×#106—31no—
52C2×#103—32no—
53C23×D3D411yescharacteristic
54C2×C3×Q8C2312yes—
55C22×C3×C4C2311yescharacteristic
56C22×Dic3D411yescharacteristic
57D3×Q8—24no—
58D3×Q8—24no—
59C2×C4×D3—22no—
60C2×C4×D3—22no—
61C2×C4×D3—22no—
62C2×C4×D3—22no—
63C2×C4×D3D411yescharacteristic
64C2×C4×D3D411yescharacteristic
65C2×C4×D3C2311yescharacteristic
66C2×C4×D3C2311yescharacteristic
67C2×Dic6—22no—
68C2×Dic6C2312yes—
69C3×Q16—22no—
70C3×M16—22no—
71C2×C3×C8C2311yescharacteristic
72C2×C3×C8C2311yescharacteristic
73C3×C4⋊C4—22no—
74C3×C4⋊C4C2312yes—
75C3×C22⋊C4—22no—
76#217—22no—
77#216—24no—
78(C2×D3)⋊C4—22no—
79(C2×D3)⋊C4—22no—
80C4⋊Dic3—22no—
81C4⋊Dic3C2312yes—
82Dic3⋊C4—22no—
83Dic3⋊C4—22no—
84Dic3⋊C4—22no—
85#208—22no—
86C2×C3⋊C8C2311yescharacteristic
87C2×C3⋊C8C2311yescharacteristic
88Dic12—22no—
89ΓL(1,𝔽25)—22no—
90ΓL(1,𝔽25)—22no—
91D3×C8—22no—
92D3×C8D414yes—
93C22×Q8—32no—
94C23×C4—31no—
95C2×Q16—32no—
96C2×Q16—31no—
97C2×Q16—64no—
98C2×Q16C2×D311yescharacteristic, complemented
99C2×M16—31no—
100C2×M16—31no—
101C2×M16—31no—
102C2×M16—64no—
103C2×M16C2×D311yescharacteristic
104C22×C8—31no—
105C22×C8—31no—
106C22⋊Q8—32no—
107C22⋊Q8—32no—
108C22⋊Q8—32no—
109C22⋊Q8—62no—
110C22⋊Q8—62no—
111C22⋊Q8C2×D312yes—
112C2×C4⋊C4—32no—
113C2×C4⋊C4—62no—
114C2×C22⋊C4—62no—
115#106—31no—
116#106—32no—
117#106C2×D311yescharacteristic, complemented
118#103—32no—
119#103—32no—
120#103—32no—
121#103C2×D312yescomplemented
122C23×C3C2×D411yescharacteristic
123C22×D3—22no—
124C22×D3—24no—
125C22×D3C2×D411yescharacteristic
126C22×D3C2×D411yescharacteristic
127C3×Q8—22no—
128C3×Q8—22no—
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—22no—
132C2×C3×C4—22no—
133C2×C3×C4C2×D411yescharacteristic
134C2×C3×C4C2411yescharacteristic
135C2×Dic3—22no—
136C2×Dic3—22no—
137C2×Dic3—22no—
138C2×Dic3C2×D411yescharacteristic
139C2×Dic3C2×D411yescharacteristic
140C4×D3—22no—
141C4×D3—21no—
142C4×D3—21no—
143C4×D3—22no—
144C4×D3—44no—
145C4×D3—44no—
146C4×D3C2×D412yes—
147C4×D3#4112yes—
148Dic6—22no—
149Dic6—22no—
150Dic6—44no—
151C3×C8—21no—
152C3×C8C2×D412yes—
153C3⋊C8—21no—
154C3⋊C8C2×D412yes—
155C24—31no—
156C2×Q8—32no—
157C2×Q8—62no—
158C2×Q8—64no—
159C2×Q8—64no—
160C2×Q8C22×D312yes—
161C22×C4—31no—
162C22×C4—31no—
163C22×C4—31no—
164C22×C4—31no—
165C22×C4—31no—
166C22×C4—62no—
167C22×C4—62no—
168C22×C4—62no—
169C22×C4—62no—
170C22×C4C22×D311yescharacteristic
171Q16—22no—
172Q16—64no—
173Q16—62no—
174M16—22no—
175M16—62no—
176M16—62no—
177M16—62no—
178C2×C8—31no—
179C2×C8—34no—
180C2×C8—31no—
181C2×C8—62no—
182C2×C8C22×D311yescharacteristic
183C2×C8C22×D311yescharacteristic
184C4⋊C4—22no—
185C4⋊C4—32no—
186C4⋊C4—62no—
187C4⋊C4—62no—
188C4⋊C4—62no—
189C4⋊C4—62no—
190C4⋊C4C22×D312yes—
191C22⋊C4—22no—
192C22⋊C4—62no—
193C22⋊C4—62no—
194C22⋊C4—62no—
195C22×C3—21no—
196C22×C3—22no—
197C22×C3C22×D411yescharacteristic
198C2×D3—21no—
199C2×D3—22no—
200C2×D3—44no—
201C2×D3#12112yes—
202C2×D3#13714yes—
203C3×C4—21no—
204C3×C4—42no—
205C3×C4—42no—
206C3×C4C22×D411yescharacteristic
207C3×C4C2×#4111yescharacteristic
208Dic3—21no—
209Dic3—42no—
210Dic3—42no—
211Dic3#12112yes—
212C23—31no—
213C23—31no—
214C23—62no—
215C23—64no—
216C23D3×D411yescharacteristic
217Q8—22no—
218Q8—22no—
219Q8—62no—
220Q8—62no—
221Q8—124no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—31no—
227C2×C4—32no—
228C2×C4—32no—
229C2×C4—31no—
230C2×C4—62no—
231C2×C4—62no—
232C2×C4—62no—
233C2×C4—61no—
234C2×C4—61no—
235C2×C4—62no—
236C2×C4—62no—
237C2×C4—124no—
238C2×C4—124no—
239C2×C4D3×D411yescharacteristic
240C2×C4C23×D311yescharacteristic
241C8—21no—
242C8—32no—
243C8—61no—
244C8D3×D412yes—
245C2×C3—41no—
246C2×C3C2×#12111yescharacteristic
247C2×C3C2×#13712yes—
248D3—41no—
249D3#47014yesdirect product factor
250C22—22no—
251C22—21no—
252C22—34no—
253C22—32no—
254C22—62no—
255C22—61no—
256C22—124no—
257C22C2×D3×D411yescharacteristic
258C4—21no—
259C4—32no—
260C4—42no—
261C4—42no—
262C4—61no—
263C4—122no—
264C4—122no—
265C4C2×D3×D411yescharacteristic
266C4D3×#4111yescharacteristic
267C3C2×#47011yescharacteristic, complemented, Sylow
268C2—34no—
269C2—41no—
270C2—121no—
271C2D3×#12111yescharacteristic
272C2D3×#13712yes—
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#470C2
socleC22×C3C22×D4
prime radicalC23×D3D4
hypercenter#470D3
hypocenterC3C2×#470
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. C2×D3×Q16C2semidirect
4. C3×#470C2semidirect
5. #5189C2semidirect
6. #5137C2semidirect
7. #5052C2semidirect
8. #4867C2semidirect
9. D3×#106C2semidirect
10. #4816C2semidirect
11. D3×#103C2semidirect
15. C2×C3×Q16C22semidirect
19. C2×#216C22semidirect
24. C2×Dic12C22semidirect
35. C3×#106C22semidirect
36. C3×#103C22semidirect
37. #835C22semidirect
38. #817C22semidirect
39. #816C22semidirect
40. #810C22semidirect
41. #808C22semidirect
50. #470D3direct (N × H)
98. C2×Q16C2×D3semidirect
117. #106C2×D3semidirect
121. #103C2×D3semidirect
249. D3#470direct (N × H)
267. C3C2×#470semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Q162
C2×D3×M162
D3×C22⋊Q82
C3×#4702
#51892
#51372
#50522
#48672
D3×#1062
#48162
D3×#1032
C2×#4703