Finite Group Databasebeta

← D3×#485 #81514

Subgroups — D3×#485 #81514

Order 384.

416 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×C22⋊Q8C211yesmaximal, characteristic
2D3×#117C211yesmaximal, characteristic
3C3×#485C211yesmaximal, characteristic, complemented
4#5045C211yesmaximal, characteristic, complemented
5#4996C211yesmaximal, characteristic, complemented
6#4888C211yesmaximal, characteristic, complemented
7D3×#107C211yesmaximal, characteristic, complemented
8#4868C211yesmaximal, characteristic, complemented
9D3×#106C211yesmaximal, characteristic, complemented
10#4815C211yesmaximal, characteristic, complemented
11#4814C211yesmaximal, characteristic, complemented
12D3×#103C211yesmaximal, characteristic, complemented
13D3×#103C211yesmaximal, characteristic, complemented
14D3×C22⋊C8C211yesmaximal, characteristic
15#4723C211yesmaximal, characteristic, complemented
16C2×#485—31nomaximal, Sylow
17C2×D3×Q8C2211yescharacteristic
18C22×C4×D3C2211yescharacteristic
19C3×C22⋊Q8C2211yescharacteristic
20C3×#117C2211yescharacteristic
21#946C2211yescharacteristic
22#926C2211yescharacteristic
23#924C2211yescharacteristic
24C2×D3×C8C2211yescharacteristic
25C2×D3×C8C2211yescharacteristic
26#897C2211yescharacteristic
27#896—21no—
28#892C2211yescharacteristic
29#892C2211yescharacteristic
30D3×C4⋊C4—21no—
31D3×C4⋊C4C2211yescharacteristic
32D3×C4⋊C4C2211yescharacteristic
33D3×C4⋊C4C2211yescharacteristic
34D3×C22⋊C4—21no—
35D3×C22⋊C4—21no—
36#878—21no—
37#877—21no—
38#872—21no—
39C42×D3—21no—
40C3×#107C2211yescharacteristic, complemented
41C3×#106C2211yescharacteristic, complemented
42C3×#103C2211yescharacteristic, complemented
43C3×#103C2211yescharacteristic, complemented
44C3×C22⋊C8C2211yescharacteristic
45#835C2211yescharacteristic, complemented
46#835C2211yescharacteristic, complemented
47#830C2211yescharacteristic
48(C2×D3)⋊C8C2211yescharacteristic
49(C2×D3)⋊C8C2211yescharacteristic
50#818C2211yescharacteristic, complemented
51#817C2211yescharacteristic, complemented
52#816C2211yescharacteristic, complemented
53#816C2211yescharacteristic, complemented
54#810C2211yescharacteristic, complemented
55#810C2211yescharacteristic, complemented
56#808C2211yescharacteristic, complemented
57#808C2211yescharacteristic, complemented
58#807C2211yescharacteristic, complemented
59#807C2211yescharacteristic, complemented
60C2×C22⋊Q8—31no—
61C2×#117—31no—
62#485—31no—
63#485—31no—
64#485—31no—
65#485—31no—
66#485—31no—
67#485—31no—
68#485—31no—
69#485D311yescharacteristic, direct product factor
70C2×#107—31no—
71C2×#106—31no—
72C2×#103—31no—
73C2×#103—31no—
74C2×C22⋊C8—31no—
75C23×D3D411yescharacteristic
76C2×C3×Q8C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×Dic3D411yescharacteristic
79D3×Q8—22no—
80D3×Q8—22no—
81C2×C4×D3—22no—
82C2×C4×D3—22no—
83C2×C4×D3—21no—
84C2×C4×D3—21no—
85C2×C4×D3—21no—
86C2×C4×D3—21no—
87C2×C4×D3D411yescharacteristic
88C2×C4×D3D411yescharacteristic
89C2×C4×D3C2311yescharacteristic
90C2×C4×D3C2311yescharacteristic
91C2×Dic6—21no—
92C2×Dic6C2311yescharacteristic
93C2×C3×C8C2311yescharacteristic
94C2×C3×C8C2311yescharacteristic
95C3×C4⋊C4—21no—
96C3×C4⋊C4C2311yescharacteristic
97C3×C4⋊C4C2311yescharacteristic
98C3×C4⋊C4C2311yescharacteristic
99C3×C22⋊C4—21no—
100C3×C22⋊C4—21no—
101C3×C42—21no—
102#217—21no—
103#217—21no—
104(C2×D3)⋊C4—21no—
105(C2×D3)⋊C4—21no—
106(C2×D3)⋊C4—21no—
107(C2×D3)⋊C4—21no—
108C4⋊Dic3—21no—
109C4⋊Dic3C2311yescharacteristic
110C4⋊Dic3C2311yescharacteristic
111C4⋊Dic3C2311yescharacteristic
112Dic3⋊C4—21no—
113Dic3⋊C4—21no—
114Dic3⋊C4—21no—
115Dic3⋊C4—21no—
116Dic3⋊C4—21no—
117C4×Dic3—21no—
118C4×Dic3—21no—
119C4×Dic3—21no—
120C2×C3⋊C8C2311yescharacteristic
121C2×C3⋊C8C2311yescharacteristic
122D3×C8—22no—
123D3×C8—22no—
124C22×Q8—31no—
125C23×C4—31no—
126C22×C8—31no—
127C22×C8—31no—
128C22⋊Q8—31no—
129C22⋊Q8—31no—
130C22⋊Q8—31no—
131C22⋊Q8—61no—
132C22⋊Q8—61no—
133C22⋊Q8C2×D311yescharacteristic
134#117—31no—
135#117—31no—
136#117—31no—
137#117—61no—
138#117—61no—
139#117C2×D311yescharacteristic
140C2×C4⋊C4—31no—
141C2×C4⋊C4—31no—
142C2×C4⋊C4—31no—
143C2×C4⋊C4—61no—
144C2×C22⋊C4—61no—
145C2×C22⋊C4—61no—
146C2×C42—61no—
147#107—31no—
148#107—31no—
149#107—31no—
150#107C2×D311yescharacteristic, complemented
151#106—31no—
152#106—31no—
153#106—31no—
154#106C2×D311yescharacteristic, complemented
155#103—31no—
156#103—31no—
157#103—31no—
158#103—31no—
159#103—31no—
160#103—31no—
161#103C2×D311yescharacteristic, complemented
162#103C2×D311yescharacteristic, complemented
163C22⋊C8—31no—
164C22⋊C8—31no—
165C22⋊C8—31no—
166C22⋊C8C2×D311yescharacteristic
167C23×C3C2×D411yescharacteristic
168C22×D3—22no—
169C22×D3—22no—
170C22×D3—22no—
171C22×D3C2×D411yescharacteristic
172C22×D3C2×D411yescharacteristic
173C3×Q8—21no—
174C3×Q8—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4C2×D411yescharacteristic
182C2×C3×C4C2411yescharacteristic
183C2×Dic3—22no—
184C2×Dic3—21no—
185C2×Dic3—21no—
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3C2×D411yescharacteristic
189C2×Dic3C2×D411yescharacteristic
190C4×D3—22no—
191C4×D3—21no—
192C4×D3—21no—
193C4×D3—22no—
194C4×D3—42no—
195C4×D3—42no—
196C4×D3—42no—
197C4×D3—42no—
198C4×D3#4112yes—
199C4×D3#4112yes—
200Dic6—21no—
201Dic6—21no—
202Dic6—42no—
203C3×C8—21no—
204C3×C8—21no—
205C3⋊C8—21no—
206C3⋊C8—21no—
207C24—31no—
208C2×Q8—31no—
209C2×Q8—61no—
210C2×Q8—62no—
211C2×Q8—62no—
212C2×Q8C22×D311yescharacteristic
213C22×C4—31no—
214C22×C4—31no—
215C22×C4—31no—
216C22×C4—31no—
217C22×C4—31no—
218C22×C4—62no—
219C22×C4—62no—
220C22×C4—61no—
221C22×C4—61no—
222C22×C4—61no—
223C22×C4—61no—
224C22×C4C22×D311yescharacteristic
225C2×C8—31no—
226C2×C8—31no—
227C2×C8—62no—
228C2×C8—62no—
229C2×C8C22×D311yescharacteristic
230C2×C8C22×D311yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—31no—
233C4⋊C4—31no—
234C4⋊C4—31no—
235C4⋊C4—61no—
236C4⋊C4—61no—
237C4⋊C4—61no—
238C4⋊C4—61no—
239C4⋊C4—61no—
240C4⋊C4—61no—
241C4⋊C4C22×D311yescharacteristic
242C4⋊C4C22×D311yescharacteristic
243C4⋊C4C22×D311yescharacteristic
244C22⋊C4—21no—
245C22⋊C4—21no—
246C22⋊C4—61no—
247C22⋊C4—61no—
248C22⋊C4—61no—
249C22⋊C4—61no—
250C22⋊C4—61no—
251C22⋊C4—61no—
252C42—21no—
253C42—61no—
254C42—61no—
255C42—61no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3C22×D411yescharacteristic
260C2×D3—21no—
261C2×D3—21no—
262C2×D3—21no—
263C2×D3—44no—
264C2×D3#12312yes—
265C2×D3#13512yes—
266C2×D3#13712yes—
267C3×C4—21no—
268C3×C4—41no—
269C3×C4—41no—
270C3×C4—41no—
271C3×C4—41no—
272C3×C4C2×#4111yescharacteristic
273C3×C4C2×#4111yescharacteristic
274Dic3—21no—
275Dic3—41no—
276Dic3—41no—
277Dic3—41no—
278Dic3—41no—
279Dic3#12312yes—
280C23—31no—
281C23—31no—
282C23—62no—
283C23—62no—
284C23—62no—
285C23D3×D411yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—61no—
289Q8—61no—
290Q8—122no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—31no—
298C2×C4—32no—
299C2×C4—32no—
300C2×C4—31no—
301C2×C4—62no—
302C2×C4—62no—
303C2×C4—62no—
304C2×C4—61no—
305C2×C4—61no—
306C2×C4—61no—
307C2×C4—61no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4—122no—
311C2×C4—122no—
312C2×C4—122no—
313C2×C4—122no—
314C2×C4D3×D411yescharacteristic
315C2×C4C23×D311yescharacteristic
316C8—21no—
317C8—21no—
318C8—61no—
319C8—61no—
320C2×C3—41no—
321C2×C3C2×#12311yescharacteristic
322C2×C3C2×#13511yescharacteristic
323C2×C3C2×#13711yescharacteristic
324D3—41no—
325D3#48514yesdirect product factor
326C22—21no—
327C22—21no—
328C22—21no—
329C22—32no—
330C22—32no—
331C22—32no—
332C22—61no—
333C22—61no—
334C22—61no—
335C22—124no—
336C22C2×D3×D411yescharacteristic
337C4—21no—
338C4—32no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—61no—
344C4—121no—
345C4—121no—
346C4—121no—
347C4—121no—
348C4D3×#4111yescharacteristic
349C4D3×#4111yescharacteristic
350C3C2×#48511yescharacteristic, complemented, Sylow
351C2—34no—
352C2—41no—
353C2—121no—
354C2D3×#12311yescharacteristic
355C2D3×#13511yescharacteristic
356C2D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#485C2
socleC22×C3C22×D4
prime radicalC23×D3D4
hypercenter#485D3
hypocenterC3C2×#485
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. C3×#485C2semidirect
4. #5045C2semidirect
5. #4996C2semidirect
6. #4888C2semidirect
7. D3×#107C2semidirect
8. #4868C2semidirect
9. D3×#106C2semidirect
10. #4815C2semidirect
11. #4814C2semidirect
12. D3×#103C2semidirect
13. D3×#103C2semidirect
15. #4723C2semidirect
40. C3×#107C22semidirect
41. C3×#106C22semidirect
42. C3×#103C22semidirect
43. C3×#103C22semidirect
45. #835C22semidirect
46. #835C22semidirect
50. #818C22semidirect
51. #817C22semidirect
52. #816C22semidirect
53. #816C22semidirect
54. #810C22semidirect
55. #810C22semidirect
56. #808C22semidirect
57. #808C22semidirect
58. #807C22semidirect
59. #807C22semidirect
69. #485D3direct (N × H)
150. #107C2×D3semidirect
154. #106C2×D3semidirect
161. #103C2×D3semidirect
162. #103C2×D3semidirect
325. D3#485direct (N × H)
350. C3C2×#485semidirect

Maximal subgroups

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

subgroupindex
D3×C22⋊Q82
D3×#1172
C3×#4852
#50452
#49962
#48882
D3×#1072
#48682
D3×#1062
#48152
#48142
D3×#1032
D3×C22⋊C82
#47232
C2×#4853