Finite Group Databasebeta

← #20253305

Subgroups — #20253305

Order 6016.

420 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689635C211yesmaximal, characteristic
2#117×D47C211yesmaximal, characteristic, complemented
3#15689467C211yesmaximal, characteristic, complemented
4#15689466C211yesmaximal, characteristic, complemented
5#15689460C211yesmaximal, characteristic, complemented
6#15689455C211yesmaximal, characteristic, complemented
7#15689450C211yesmaximal, characteristic, complemented
8#15689449C211yesmaximal, characteristic, complemented
9#15689443C211yesmaximal, characteristic, complemented
10#15689438C211yesmaximal, characteristic, complemented
11#15689159C211yesmaximal, characteristic, complemented
12#15689120C211yesmaximal, characteristic, complemented
13#15689117C211yesmaximal, characteristic, complemented
14C2×(C2×D47)⋊C8C211yesmaximal, characteristic, complemented
15C47×#427C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18C22×C47⋊C8C2211yescharacteristic
19#13094008—21no—
20#13094004C2211yescharacteristic
21#13094004C2211yescharacteristic
22#13093999C2211yescharacteristic
23#13093999C2211yescharacteristic
24#13093994—21no—
25C4×D188—21no—
26C4×D188—21no—
27#13093983C2211yescharacteristic
28#13093982C2211yescharacteristic
29#13093982C2211yescharacteristic
30#13093981—21no—
31#13093980—21no—
32C4⋊C4×D47C2211yescharacteristic
33C4⋊C4×D47C2211yescharacteristic
34C22⋊C4×D47—21no—
35C42×D47—21no—
36#13093957C2211yescharacteristic, complemented
37#13093957C2211yescharacteristic, complemented
38#13093955C2211yescharacteristic, complemented
39#13093955C2211yescharacteristic, complemented
40#13093949C2211yescharacteristic, complemented
41#13093949C2211yescharacteristic, complemented
42#13093947C2211yescharacteristic, complemented
43#13093947C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic, complemented
46#13093944C2211yescharacteristic, complemented
47#13093944C2211yescharacteristic, complemented
48(C2×D47)⋊C8C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic
52C22×C8×C47C2211yescharacteristic
53#117×C47C2211yescharacteristic
54#117×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic, complemented
56#107×C47C2211yescharacteristic, complemented
57#106×C47C2211yescharacteristic, complemented
58#106×C47C2211yescharacteristic, complemented
59C23×D47D411yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C2×C22⋊D47—21no—
62C22×Dic47D411yescharacteristic
63#10625350—22no—
64#10625350—22no—
65C2×D188—21no—
66C2×D188—21no—
67C2×D188C2311yescharacteristic
68C2×C4×D47—22no—
69C2×C4×D47—22no—
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×C4×D47D411yescharacteristic
74C2×C4×D47D411yescharacteristic
75C2×C4×D47C2311yescharacteristic
76C2×C4×D47C2311yescharacteristic
77C2×Dic94C2311yescharacteristic
78C2×C8×C47—22no—
79C2×C8×C47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C4⋊C4×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C42×C47—21no—
88C42×C47—21no—
89C22⋊Dic47—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96C4⋊Dic47—21no—
97C4⋊Dic47—21no—
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105C2×C47⋊C8—22no—
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C23×C47C2×D411yescharacteristic
109C22×D47—22no—
110C22×D47—22no—
111C22×D47—21no—
112C22×D47—41no—
113C22×D47C2×D411yescharacteristic
114C22×D47C2×D411yescharacteristic
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47#4112yes—
121C2×C4×C47#4112yes—
122C2×C4×C47C2411yescharacteristic
123C22⋊D47—42no—
124C2×Dic47—22no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130D188—21no—
131D188—21no—
132D188—42no—
133D188—42no—
134C4×D47—22no—
135C4×D47—22no—
136C4×D47—21no—
137C4×D47—21no—
138C4×D47—21no—
139C4×D47—21no—
140C4×D47—42no—
141C4×D47—42no—
142C4×D47—42no—
143Dic94—21no—
144Dic94—21no—
145C8×C47—21no—
146C8×C47—21no—
147C47⋊C8—21no—
148C47⋊C8—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47#12312yes—
152C22×C47C22×D411yescharacteristic
153C2×D47—21no—
154C2×D47—21no—
155C2×D47—21no—
156C2×D47—21no—
157C2×D47—21no—
158C2×D47—44no—
159C2×D47—41no—
160C2×D47—41no—
161C2×D47—41no—
162C2×D47#13512yes—
163C4×C47—41no—
164C4×C47—41no—
165C4×C47—41no—
166C4×C47—41no—
167C4×C47#12312yes—
168C4×C47C2×#4111yescharacteristic
169C4×C47C2×#4111yescharacteristic
170Dic47—21no—
171Dic47—21no—
172Dic47—41no—
173Dic47—41no—
174Dic47—41no—
175#3091—471nomaximal, Sylow
176C2×C47—22no—
177C2×C47C2×#12311yescharacteristic
178C2×C47C2×#13511yescharacteristic
179C2×C47#57511yescharacteristic
180D47—22no—
181D47—41no—
182D47—81no—
183#525—471no—
184C2×#117—471no—
185#485—471no—
186#485—471no—
187#484—471no—
188#483—471no—
189#482—471no—
190#482—471no—
191#481—471no—
192#480—471no—
193#427—471no—
194#427D4711yescharacteristic, complemented
195#416—471no—
196#416—471no—
197C2×C22⋊C8—471no—
198C47#309111yescharacteristic, complemented, Sylow
199C2×#41—471no—
200C23×C4—471no—
201C22×C8—471no—
202C22×C8C2×D4711yescharacteristic
203#123—941no—
204C22⋊Q8—471no—
205C22⋊Q8—471no—
206#121—471no—
207#121—471no—
208#120—941no—
209C4×D4—941no—
210C4×D4—941no—
211#117—471no—
212#117—471no—
213#117—471no—
214#117—941no—
215#117—941no—
216#117C2×D4711yescharacteristic
217#117C2×D4711yescharacteristic
218C2×C4⋊C4—471no—
219C2×C4⋊C4—471no—
220C2×C22⋊C4—941no—
221C2×C42—941no—
222#107—471no—
223#107—471no—
224#107C2×D4711yescharacteristic, complemented
225#107C2×D4711yescharacteristic, complemented
226#106—471no—
227#106—471no—
228#106C2×D4711yescharacteristic, complemented
229#106C2×D4711yescharacteristic, complemented
230#103—471no—
231#103—471no—
232#103—471no—
233#103—471no—
234#102—471no—
235#102—471no—
236#102—471no—
237#102—471no—
238C22⋊C8—471no—
239C22⋊C8—471no—
240C22⋊C8—471no—
241C22⋊C8—471no—
242C24—471no—
243#41—942no—
244#41—942no—
245C2×Q8—471no—
246C2×D4—471no—
247C2×D4—941no—
248C2×D4—941no—
249C2×D4—941no—
250C22×C4—471no—
251C22×C4—471no—
252C22×C4—471no—
253C22×C4—471no—
254C22×C4—471no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4—942no—
258C22×C4—942no—
259C22×C4—941no—
260C22×C4C22×D4711yescharacteristic
261C2×C8—22no—
262C2×C8—471no—
263C2×C8—471no—
264C2×C8—942no—
265C2×C8C22×D4711yescharacteristic
266C2×C8C22×D4711yescharacteristic
267C4⋊C4—471no—
268C4⋊C4—471no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4C22×D4711yescharacteristic
274C4⋊C4C22×D4711yescharacteristic
275C4⋊C4C22×D4711yescharacteristic
276C4⋊C4C22×D4711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C42—21no—
287C42—21no—
288C42—941no—
289C42—941no—
290C42—941no—
291C23—471no—
292C23—471no—
293C23—942no—
294C23—942no—
295C23—941no—
296C23—1881no—
297C23D4×D4711yescharacteristic
298Q8—941no—
299Q8—941no—
300D4—941no—
301D4—941no—
302D4—1882no—
303D4—1882no—
304D4—1882no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—471no—
310C2×C4—471no—
311C2×C4—942no—
312C2×C4—942no—
313C2×C4—942no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—1882no—
322C2×C4—1882no—
323C2×C4—1882no—
324C2×C4#1062535012yes—
325C2×C4D4×D4711yescharacteristic
326C2×C4#1062535412yes—
327C2×C4C23×D4711yescharacteristic
328C8—21no—
329C8—21no—
330C8—941no—
331C8—941no—
332C22—21no—
333C22—21no—
334C22—472no—
335C22—941no—
336C22—941no—
337C22—941no—
338C22—941no—
339C22—941no—
340C22—1884no—
341C22—1881no—
342C22—1881no—
343C22—1881no—
344C22#1309400912yes—
345C22C2×D4×D4711yescharacteristic
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—941no—
351C4—941no—
352C4—1881no—
353C4—1881no—
354C4—1881no—
355C4#1309400912yes—
356C4C2×#1062535011yescharacteristic
357C4C2×#1062535411yescharacteristic
358C2—22no—
359C2—942no—
360C2—3761no—
361C2—1881no—
362C2C2×#1309400911yescharacteristic
363C2#135×D4711yescharacteristic
364C2#1568992011yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#427C2
socleC22×C47C22×D4
hypercenter#427D47
hypocenterC47#3091
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
2. #117×D47C2semidirect
3. #15689467C2semidirect
4. #15689466C2semidirect
5. #15689460C2semidirect
6. #15689455C2semidirect
7. #15689450C2semidirect
8. #15689449C2semidirect
9. #15689443C2semidirect
10. #15689438C2semidirect
11. #15689159C2semidirect
12. #15689120C2semidirect
13. #15689117C2semidirect
14. C2×(C2×D47)⋊C8C2semidirect
15. C47×#427C2semidirect
36. #13093957C22semidirect
37. #13093957C22semidirect
38. #13093955C22semidirect
39. #13093955C22semidirect
40. #13093949C22semidirect
41. #13093949C22semidirect
42. #13093947C22semidirect
43. #13093947C22semidirect
44. #13093946C22semidirect
45. #13093946C22semidirect
46. #13093944C22semidirect
47. #13093944C22semidirect
55. #107×C47C22semidirect
56. #107×C47C22semidirect
57. #106×C47C22semidirect
58. #106×C47C22semidirect
194. #427D47semidirect
198. C47#3091semidirect
224. #107C2×D47semidirect
225. #107C2×D47semidirect
228. #106C2×D47semidirect
229. #106C2×D47semidirect