Finite Group Databasebeta

← #485×D47 #20253276

Subgroups — #485×D47 #20253276

Order 6016.

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
1C22⋊Q8×D47C211yesmaximal, characteristic
2#117×D47C211yesmaximal, characteristic
3#15689467C211yesmaximal, characteristic, complemented
4#15689466C211yesmaximal, characteristic, complemented
5#15689465C211yesmaximal, characteristic, complemented
6#15689464C211yesmaximal, characteristic, complemented
7#15689463C211yesmaximal, characteristic, complemented
8#15689462C211yesmaximal, characteristic, complemented
9#15689461C211yesmaximal, characteristic, complemented
10#107×D47C211yesmaximal, characteristic, complemented
11#106×D47C211yesmaximal, characteristic, complemented
12#103×D47C211yesmaximal, characteristic, complemented
13#103×D47C211yesmaximal, characteristic, complemented
14C22⋊C8×D47C211yesmaximal, characteristic
15C47×#485C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18C2×C8×D47C2211yescharacteristic
19C2×C8×D47C2211yescharacteristic
20#13094004C2211yescharacteristic
21#13094003C2211yescharacteristic
22#13094002—21no—
23#13094001—21no—
24#13094000C2211yescharacteristic
25#13093983C2211yescharacteristic
26#13093982C2211yescharacteristic
27#13093982C2211yescharacteristic
28#13093981—21no—
29#13093980—21no—
30C4⋊C4×D47—21no—
31C4⋊C4×D47C2211yescharacteristic
32C4⋊C4×D47C2211yescharacteristic
33C4⋊C4×D47C2211yescharacteristic
34C22⋊C4×D47—21no—
35C22⋊C4×D47—21no—
36C42×D47—21no—
37#13093958C2211yescharacteristic, complemented
38#13093957C2211yescharacteristic, complemented
39#13093957C2211yescharacteristic, complemented
40#13093956C2211yescharacteristic, complemented
41#13093955C2211yescharacteristic, complemented
42#13093955C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093948C2211yescharacteristic, complemented
46#13093948C2211yescharacteristic, complemented
47#13093947C2211yescharacteristic, complemented
48#13093947C2211yescharacteristic, complemented
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic
52C22⋊Q8×C47C2211yescharacteristic
53#117×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic, complemented
55#106×C47C2211yescharacteristic, complemented
56#103×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58C22⋊C8×C47C2211yescharacteristic
59C23×D47D411yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×Dic47D411yescharacteristic
63Q8×D47—22no—
64Q8×D47—22no—
65C2×C4×D47—22no—
66C2×C4×D47—22no—
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×C4×D47D411yescharacteristic
72C2×C4×D47D411yescharacteristic
73C2×C4×D47C2311yescharacteristic
74C2×C4×D47C2311yescharacteristic
75C2×Dic94—21no—
76C2×Dic94C2311yescharacteristic
77C2×C8×C47C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C4⋊C4×C47—21no—
80C4⋊C4×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C42×C47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C8×D47—22no—
107C8×D47—22no—
108C23×C47C2×D411yescharacteristic
109C22×D47—22no—
110C22×D47—22no—
111C22×D47—22no—
112C22×D47C2×D411yescharacteristic
113C22×D47C2×D411yescharacteristic
114Q8×C47—21no—
115Q8×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2411yescharacteristic
124C2×Dic47—22no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131C4×D47—22no—
132C4×D47—21no—
133C4×D47—21no—
134C4×D47—22no—
135C4×D47—42no—
136C4×D47—42no—
137C4×D47—42no—
138C4×D47—42no—
139C4×D47#4112yes—
140C4×D47#4112yes—
141Dic94—21no—
142Dic94—21no—
143Dic94—42no—
144C8×C47—21no—
145C8×C47—21no—
146C47⋊C8—21no—
147C47⋊C8—21no—
148C22×C47—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47C22×D411yescharacteristic
152C2×D47—21no—
153C2×D47—21no—
154C2×D47—21no—
155C2×D47—44no—
156C2×D47#12312yes—
157C2×D47#13512yes—
158C2×D47#13712yes—
159C4×C47—21no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47—41no—
163C4×C47—41no—
164C4×C47C2×#4111yescharacteristic
165C4×C47C2×#4111yescharacteristic
166Dic47—21no—
167Dic47—41no—
168Dic47—41no—
169Dic47—41no—
170Dic47—41no—
171Dic47#12312yes—
172C2×#485—471nomaximal, Sylow
173C2×C47—41no—
174C2×C47C2×#12311yescharacteristic
175C2×C47C2×#13511yescharacteristic
176C2×C47C2×#13711yescharacteristic
177D47—41no—
178D47#48514yesdirect product factor
179C2×C22⋊Q8—471no—
180C2×#117—471no—
181#485—471no—
182#485—471no—
183#485—471no—
184#485—471no—
185#485—471no—
186#485—471no—
187#485—471no—
188#485D4711yescharacteristic, direct product factor
189C2×#107—471no—
190C2×#106—471no—
191C2×#103—471no—
192C2×#103—471no—
193C2×C22⋊C8—471no—
194C47C2×#48511yescharacteristic, complemented, Sylow
195C22×Q8—471no—
196C23×C4—471no—
197C22×C8—471no—
198C22×C8—471no—
199C22⋊Q8—471no—
200C22⋊Q8—471no—
201C22⋊Q8—471no—
202C22⋊Q8—941no—
203C22⋊Q8—941no—
204C22⋊Q8C2×D4711yescharacteristic
205#117—471no—
206#117—471no—
207#117—471no—
208#117—941no—
209#117—941no—
210#117C2×D4711yescharacteristic
211C2×C4⋊C4—471no—
212C2×C4⋊C4—471no—
213C2×C4⋊C4—471no—
214C2×C4⋊C4—941no—
215C2×C22⋊C4—941no—
216C2×C22⋊C4—941no—
217C2×C42—941no—
218#107—471no—
219#107—471no—
220#107—471no—
221#107C2×D4711yescharacteristic, complemented
222#106—471no—
223#106—471no—
224#106—471no—
225#106C2×D4711yescharacteristic, complemented
226#103—471no—
227#103—471no—
228#103—471no—
229#103—471no—
230#103—471no—
231#103—471no—
232#103C2×D4711yescharacteristic, complemented
233#103C2×D4711yescharacteristic, complemented
234C22⋊C8—471no—
235C22⋊C8—471no—
236C22⋊C8—471no—
237C22⋊C8C2×D4711yescharacteristic
238C24—471no—
239C2×Q8—471no—
240C2×Q8—941no—
241C2×Q8—942no—
242C2×Q8—942no—
243C2×Q8C22×D4711yescharacteristic
244C22×C4—471no—
245C22×C4—471no—
246C22×C4—471no—
247C22×C4—471no—
248C22×C4—471no—
249C22×C4—942no—
250C22×C4—942no—
251C22×C4—941no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4—941no—
255C22×C4C22×D4711yescharacteristic
256C2×C8—471no—
257C2×C8—471no—
258C2×C8—942no—
259C2×C8—942no—
260C2×C8C22×D4711yescharacteristic
261C2×C8C22×D4711yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—471no—
264C4⋊C4—471no—
265C4⋊C4—471no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4C22×D4711yescharacteristic
273C4⋊C4C22×D4711yescharacteristic
274C4⋊C4C22×D4711yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C42—21no—
284C42—941no—
285C42—941no—
286C42—941no—
287C23—471no—
288C23—471no—
289C23—942no—
290C23—942no—
291C23—942no—
292C23D4×D4711yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—941no—
296Q8—941no—
297Q8—1882no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—471no—
305C2×C4—472no—
306C2×C4—472no—
307C2×C4—471no—
308C2×C4—942no—
309C2×C4—942no—
310C2×C4—942no—
311C2×C4—941no—
312C2×C4—941no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—1882no—
318C2×C4—1882no—
319C2×C4—1882no—
320C2×C4—1882no—
321C2×C4D4×D4711yescharacteristic
322C2×C4C23×D4711yescharacteristic
323C8—21no—
324C8—21no—
325C8—941no—
326C8—941no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—472no—
331C22—472no—
332C22—472no—
333C22—941no—
334C22—941no—
335C22—941no—
336C22—1884no—
337C22C2×D4×D4711yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—472no—
344C4—941no—
345C4—1881no—
346C4—1881no—
347C4—1881no—
348C4—1881no—
349C4#41×D4711yescharacteristic
350C4#41×D4711yescharacteristic
351C2—41no—
352C2—474no—
353C2—1881no—
354C2#123×D4711yescharacteristic
355C2#135×D4711yescharacteristic
356C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#485C2
socleC22×C47C22×D4
hypercenter#485D47
hypocenterC47C2×#485
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #15689467C2semidirect
4. #15689466C2semidirect
5. #15689465C2semidirect
6. #15689464C2semidirect
7. #15689463C2semidirect
8. #15689462C2semidirect
9. #15689461C2semidirect
10. #107×D47C2semidirect
11. #106×D47C2semidirect
12. #103×D47C2semidirect
13. #103×D47C2semidirect
15. C47×#485C2semidirect
37. #13093958C22semidirect
38. #13093957C22semidirect
39. #13093957C22semidirect
40. #13093956C22semidirect
41. #13093955C22semidirect
42. #13093955C22semidirect
43. #13093949C22semidirect
44. #13093949C22semidirect
45. #13093948C22semidirect
46. #13093948C22semidirect
47. #13093947C22semidirect
48. #13093947C22semidirect
54. #107×C47C22semidirect
55. #106×C47C22semidirect
56. #103×C47C22semidirect
57. #103×C47C22semidirect
178. D47#485direct (N × H)
188. #485D47direct (N × H)
194. C47C2×#485semidirect
221. #107C2×D47semidirect
225. #106C2×D47semidirect
232. #103C2×D47semidirect
233. #103C2×D47semidirect