Finite Group Databasebeta

← D3×#440 #79771

Subgroups — D3×#440 #79771

Order 384.

544 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×SD16C211yesmaximal, characteristic
2C4×D3×Q8C211yesmaximal, characteristic, complemented
3C4×D3×D4C211yesmaximal, characteristic
4C3×#440C211yesmaximal, characteristic, complemented
5#5164C211yesmaximal, characteristic, complemented
6#5026C211yesmaximal, characteristic, complemented
7#5018C211yesmaximal, characteristic, complemented
8#4889C211yesmaximal, characteristic, complemented
9D3×#107C211yesmaximal, characteristic, complemented
10#4817C211yesmaximal, characteristic, complemented
11D3×#103C211yesmaximal, characteristic, complemented
12D3×#102C211yesmaximal, characteristic
13#4757C211yesmaximal, characteristic, complemented
14#4710C211yesmaximal, characteristic, complemented
15D3×#97C211yesmaximal, characteristic, complemented
16C2×#440—31nomaximal, Sylow
17C2×D3×Q8C2211yescharacteristic
18C2×D3×D4C2211yescharacteristic
19C22×C4×D3—21no—
20C2×C3×SD16C2211yescharacteristic
21C3×C4×Q8C2211yescharacteristic, complemented
22C3×C4×D4C2211yescharacteristic
23Q8×Dic3C2211yescharacteristic, complemented
24C2×#215C2211yescharacteristic
25D4×Dic3C2211yescharacteristic
26C2×#214C2211yescharacteristic
27C4×#67—21no—
28D3×SD16C418yescomplemented
29C2×#204C2211yescharacteristic
30C2×D3×C8C2211yescharacteristic
31C2×D3×C8C2211yescharacteristic
32#893C2211yescharacteristic
33D3×C4⋊C4—21no—
34D3×C4⋊C4C2211yescharacteristic
35D3×C4⋊C4C2211yescharacteristic
36#887—21no—
37#887C2211yescharacteristic, complemented
38#67⋊C4—21no—
39D3×C22⋊C4—21no—
40C4×D12C2211yescharacteristic
41C42×D3—21no—
42C42×D3C2211yescharacteristic
43C4×Dic6—21no—
44C4×Dic6C2211yescharacteristic, complemented
45C3×#107C2211yescharacteristic, complemented
46C3×#103C2211yescharacteristic, complemented
47C3×#102C2211yescharacteristic
48C3×#97C2211yescharacteristic, complemented
49#835C2211yescharacteristic, complemented
50#832C2211yescharacteristic
51#821C2211yescharacteristic
52#818C2211yescharacteristic, complemented
53#816C2211yescharacteristic, complemented
54#815C2211yescharacteristic, complemented
55#815C2211yescharacteristic, complemented
56#810C2211yescharacteristic, complemented
57#809C2211yescharacteristic
58#807C2211yescharacteristic, complemented
59#807C2211yescharacteristic, complemented
60#803C2211yescharacteristic, complemented
61C22×SD16—31no—
62C2×C4×Q8—31no—
63C2×C4×D4—31no—
64#440—31no—
65#440—31no—
66#440—31no—
67#440—31no—
68#440—31no—
69#440—31no—
70#440—31no—
71#440D311yescharacteristic, direct product factor
72C2×#107—31no—
73C2×#103—31no—
74C2×#102—31no—
75C2×#97—31no—
76C23×D3—21no—
77C2×C3×Q8C2311yescharacteristic
78C2×C3×D4C2311yescharacteristic
79C22×C3×C4—21no—
80C2×#67—21no—
81C22×Dic3—21no—
82D3×Q8—22no—
83D3×Q8C2×C414yescomplemented
84D3×D4—22no—
85D3×D4C2×C414yes—
86C2×D12C2311yescharacteristic
87C2×C4×D3—21no—
88C2×C4×D3—21no—
89C2×C4×D3—21no—
90C2×C4×D3—21no—
91C2×C4×D3—21no—
92C2×C4×D3—44no—
93C2×C4×D3D411yescharacteristic
94C2×C4×D3D411yescharacteristic
95C2×C4×D3C2311yescharacteristic
96C2×Dic6—21no—
97C2×Dic6C2311yescharacteristic
98C3×SD16C2×C414yescomplemented
99C2×C3×C8C2311yescharacteristic
100C2×C3×C8C2311yescharacteristic
101C3×C4⋊C4—21no—
102C3×C4⋊C4C2311yescharacteristic
103C3×C4⋊C4C2311yescharacteristic
104C3×C22⋊C4—21no—
105C3×C42—21no—
106C3×C42C2311yescharacteristic
107#217—21no—
108#215C2×C414yescomplemented
109#214C2×C414yescomplemented
110(C2×D3)⋊C4—21no—
111(C2×D3)⋊C4—21no—
112C4⋊Dic3—21no—
113C4⋊Dic3C2311yescharacteristic
114C4⋊Dic3C2311yescharacteristic
115Dic3⋊C4—21no—
116Dic3⋊C4—21no—
117Dic3⋊C4—21no—
118Dic3⋊C4—21no—
119C4×Dic3—21no—
120C4×Dic3—21no—
121C4×Dic3—21no—
122C4×Dic3D411yescharacteristic
123C4×Dic3D411yescharacteristic
124C4×Dic3C2311yescharacteristic
125C2×C3⋊C8C2311yescharacteristic
126C2×C3⋊C8C2311yescharacteristic
127#204C2×C414yescomplemented
128D3×C8—22no—
129D3×C8C2×C414yescomplemented
130C22×Q8—31no—
131C22×D4—31no—
132C23×C4—61no—
133C2×SD16—31no—
134C2×SD16—31no—
135C2×SD16—38no—
136C2×SD16—31no—
137C2×SD16C2×D311yescharacteristic
138C22×C8—31no—
139C22×C8—31no—
140C4×Q8—31no—
141C4×Q8—31no—
142C4×Q8—31no—
143C4×Q8—61no—
144C4×Q8—61no—
145C4×Q8C2×D311yescharacteristic, complemented
146C4×D4—31no—
147C4×D4—31no—
148C4×D4—31no—
149C4×D4—61no—
150C4×D4—61no—
151C4×D4C2×D311yescharacteristic
152C2×C4⋊C4—31no—
153C2×C4⋊C4—31no—
154C2×C4⋊C4—61no—
155C2×C22⋊C4—61no—
156C2×C42—31no—
157C2×C42—61no—
158#107—31no—
159#107—31no—
160#107—31no—
161#107C2×D311yescharacteristic, complemented
162#103—31no—
163#103—31no—
164#103—31no—
165#103C2×D311yescharacteristic, complemented
166#102—31no—
167#102—31no—
168#102—31no—
169#102C2×D311yescharacteristic
170#97—31no—
171#97—31no—
172#97—31no—
173#97C2×D311yescharacteristic, complemented
174C23×C3—21no—
175C22×D3—21no—
176C22×D3—24no—
177C22×D3—42no—
178C22×D3—42no—
179C22×D3C2×D411yescharacteristic
180C3×Q8—21no—
181C3×Q8C22×C412yescomplemented
182C3×D4—21no—
183C3×D4C22×C412yes—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—42no—
188C2×C3×C4C2×D411yescharacteristic
189C2×C3×C4C2×D411yescharacteristic
190C2×C3×C4C2411yescharacteristic
191#67—24no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—21no—
195C2×Dic3—42no—
196C2×Dic3C2×D411yescharacteristic
197C2×Dic3C2×D411yescharacteristic
198C2×Dic3C2×D411yescharacteristic
199D12—21no—
200D12C22×C412yes—
201C4×D3—24no—
202C4×D3—22no—
203C4×D3—22no—
204C4×D3—42no—
205C4×D3—42no—
206C4×D3—42no—
207C4×D3—42no—
208C4×D3C22×C412yes—
209C4×D3#4112yes—
210Dic6—21no—
211Dic6—24no—
212Dic6C22×C412yescomplemented
213C3×C8—21no—
214C3×C8C22×C412yescomplemented
215C3⋊C8—21no—
216C3⋊C8C22×C412yescomplemented
217C24—61no—
218C2×Q8—34no—
219C2×Q8—31no—
220C2×Q8—61no—
221C2×Q8—62no—
222C2×Q8C22×D311yescharacteristic
223C2×D4—34no—
224C2×D4—31no—
225C2×D4—62no—
226C2×D4—61no—
227C2×D4C22×D311yescharacteristic
228C22×C4—21no—
229C22×C4—31no—
230C22×C4—31no—
231C22×C4—31no—
232C22×C4—61no—
233C22×C4—61no—
234C22×C4—61no—
235C22×C4—61no—
236C22×C4—61no—
237C22×C4—61no—
238C22×C4—124no—
239SD16—34no—
240SD16—34no—
241SD16—34no—
242SD16C4×D314yescomplemented
243C2×C8—31no—
244C2×C8—34no—
245C2×C8—31no—
246C2×C8—62no—
247C2×C8C22×D311yescharacteristic
248C2×C8C22×D311yescharacteristic
249C4⋊C4—21no—
250C4⋊C4—31no—
251C4⋊C4—31no—
252C4⋊C4—61no—
253C4⋊C4—61no—
254C4⋊C4—61no—
255C4⋊C4—61no—
256C4⋊C4—61no—
257C4⋊C4C22×D311yescharacteristic
258C4⋊C4C22×D311yescharacteristic
259C22⋊C4—21no—
260C22⋊C4—61no—
261C22⋊C4—61no—
262C22⋊C4—61no—
263C42—21no—
264C42—31no—
265C42—31no—
266C42—31no—
267C42—61no—
268C42—61no—
269C42—61no—
270C42C22×D311yescharacteristic
271C22×C3—22no—
272C22×C3—41no—
273C22×C3—41no—
274C22×C3C22×D411yescharacteristic
275C2×D3—22no—
276C2×D3—41no—
277C2×D3—41no—
278C2×D3—48no—
279C2×D3C4×D412yes—
280C2×D3AGL(1,ℤ/8)12yes—
281C2×D3#13712yes—
282C3×C4—22no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—41no—
286C3×C4—41no—
287C3×C4C23×C411yescharacteristic
288C3×C4C2×#4111yescharacteristic
289Dic3—22no—
290Dic3—21no—
291Dic3—21no—
292Dic3—41no—
293Dic3—41no—
294Dic3C4×D412yes—
295C23—21no—
296C23—31no—
297C23—64no—
298C23—61no—
299C23—122no—
300C23—122no—
301Q8—21no—
302Q8—32no—
303Q8—64no—
304Q8—61no—
305Q8C2×C4×D312yescomplemented
306D4—21no—
307D4—32no—
308D4—64no—
309D4—61no—
310D4C2×C4×D312yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—31no—
315C2×C4—32no—
316C2×C4—32no—
317C2×C4—31no—
318C2×C4—31no—
319C2×C4—42no—
320C2×C4—62no—
321C2×C4—62no—
322C2×C4—64no—
323C2×C4—61no—
324C2×C4—61no—
325C2×C4—61no—
326C2×C4—122no—
327C2×C4—122no—
328C2×C4—122no—
329C2×C4—122no—
330C2×C4—122no—
331C2×C4D3×D411yescharacteristic
332C2×C4D3×D411yescharacteristic
333C2×C4C23×D311yescharacteristic
334C8—21no—
335C8—32no—
336C8—61no—
337C8C2×C4×D312yescomplemented
338C2×C3—42no—
339C2×C3C2×C4×D411yescharacteristic
340C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
341C2×C3C2×#13711yescharacteristic
342D3—42no—
343D3#44014yesdirect product factor
344C22—22no—
345C22—32no—
346C22—32no—
347C22—32no—
348C22—41no—
349C22—41no—
350C22—62no—
351C22—128no—
352C22—121no—
353C22—121no—
354C22C2×D3×D411yescharacteristic
355C4—21no—
356C4—21no—
357C4—22no—
358C4—32no—
359C4—41no—
360C4—41no—
361C4—61no—
362C4—61no—
363C4—62no—
364C4—121no—
365C4—121no—
366C4C22×C4×D311yescharacteristic
367C4D3×#4111yescharacteristic
368C3C2×#44011yescharacteristic, complemented, Sylow
369C2—34no—
370C2—42no—
371C2—122no—
372C2C4×D3×D411yescharacteristic
373C2D3×AGL(1,ℤ/8)11yescharacteristic
374C2D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutatorC3×C4C23×C4
FrattiniC2×C4C23×D3
FittingC3×#440C2
socleC22×C3C22×D4
prime radicalC2×D3×D4C22
cosocleC2×C3×C4C24
hypercenter#440D3
hypocenterC3C2×#440
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×D3×Q8C2semidirect
4. C3×#440C2semidirect
5. #5164C2semidirect
6. #5026C2semidirect
7. #5018C2semidirect
8. #4889C2semidirect
9. D3×#107C2semidirect
10. #4817C2semidirect
11. D3×#103C2semidirect
13. #4757C2semidirect
14. #4710C2semidirect
15. D3×#97C2semidirect
21. C3×C4×Q8C22semidirect
23. Q8×Dic3C22semidirect
28. D3×SD16C4semidirect
37. #887C22semidirect
44. C4×Dic6C22semidirect
45. C3×#107C22semidirect
46. C3×#103C22semidirect
48. C3×#97C22semidirect
49. #835C22semidirect
52. #818C22semidirect
53. #816C22semidirect
54. #815C22semidirect
55. #815C22semidirect
56. #810C22semidirect
58. #807C22semidirect
59. #807C22semidirect
60. #803C22semidirect
71. #440D3direct (N × H)
83. D3×Q8C2×C4semidirect
98. C3×SD16C2×C4semidirect
108. #215C2×C4semidirect
109. #214C2×C4semidirect
127. #204C2×C4semidirect
129. D3×C8C2×C4semidirect
145. C4×Q8C2×D3semidirect
161. #107C2×D3semidirect
165. #103C2×D3semidirect
173. #97C2×D3semidirect
181. C3×Q8C22×C4semidirect
212. Dic6C22×C4semidirect
214. C3×C8C22×C4semidirect
216. C3⋊C8C22×C4semidirect
242. SD16C4×D3semidirect
305. Q8C2×C4×D3semidirect
337. C8C2×C4×D3semidirect
343. D3#440direct (N × H)
368. C3C2×#440semidirect

Maximal subgroups

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

subgroupindex
C2×D3×SD162
C4×D3×Q82
C4×D3×D42
C3×#4402
#51642
#50262
#50182
#48892
D3×#1072
#48172
D3×#1032
D3×#1022
#47572
#47102
D3×#972
C2×#4403