Finite Group Databasebeta

← #20253634

Subgroups — #20253634

Order 6016.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689733C211yesmaximal, characteristic, complemented
2#15689598C211yesmaximal, characteristic
3#15689465C211yesmaximal, characteristic, complemented
4#15689461C211yesmaximal, characteristic, complemented
5#15689425C211yesmaximal, characteristic, complemented
6#15689421C211yesmaximal, characteristic, complemented
7#15689326C211yesmaximal, characteristic, complemented
8#15689326C211yesmaximal, characteristic, complemented
9#15689274C211yesmaximal, characteristic
10#15689224C211yesmaximal, characteristic, complemented
11#15689220C211yesmaximal, characteristic, complemented
12#15689214C211yesmaximal, characteristic, complemented
13SD16×Dic47C211yesmaximal, characteristic, complemented
14#15689181C211yesmaximal, characteristic, complemented
15C47×#450C211yesmaximal, characteristic
16C2×#10625335C2211yescharacteristic
17C2×#10625335C2211yescharacteristic
18#13094022C2211yescharacteristic, complemented
19#13094017—21no—
20#13094017—21no—
21#13094015—21no—
22#13094015C2211yescharacteristic, complemented
23#13094014—21no—
24#13094003C2211yescharacteristic
25Q8×Dic47C2211yescharacteristic, complemented
26#13093989C2211yescharacteristic, complemented
27D4×Dic47—21no—
28D4×Dic47—21no—
29D4×Dic47C2211yescharacteristic
30D4×Dic47C2211yescharacteristic
31D4×Dic47C2211yescharacteristic
32D4×Dic47C2211yescharacteristic
33#13093983C2211yescharacteristic
34#13093983C2211yescharacteristic
35C2×C22⋊Dic47—21no—
36C2×C22⋊Dic47—21no—
37#13093958C2211yescharacteristic, complemented
38#13093957C2211yescharacteristic, complemented
39#13093956C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41Dic47⋊C8C2211yescharacteristic, complemented
42Dic47⋊C8C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093948C2211yescharacteristic, complemented
46#13093948C2211yescharacteristic, complemented
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50#13093934C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C22×D4×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54C2×SD16×C47C2211yescharacteristic
55C22⋊Q8×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C24×C47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47—22no—
62C2×D4×C47—22no—
63C2×D4×C47—21no—
64C2×D4×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×Dic47—21no—
68C22×Dic47—21no—
69C22×Dic47—21no—
70C22×Dic47—21no—
71C2×Dic94C2311yescharacteristic
72SD16×C47—22no—
73SD16×C47—22no—
74C2×C8×C47C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C4⋊C4×C47—21no—
77C4⋊C4×C47C2311yescharacteristic
78C22⋊C4×C47—21no—
79C22⋊Dic47—21no—
80C22⋊Dic47—21no—
81C22⋊Dic47—21no—
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47D411yescharacteristic
86C22⋊Dic47D411yescharacteristic
87#10625335—22no—
88#10625335—22no—
89C4⋊Dic47—21no—
90C4⋊Dic47—21no—
91C4⋊Dic47D411yescharacteristic
92C4⋊Dic47D411yescharacteristic
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—
104C4×Dic47C2311yescharacteristic
105C4×Dic47C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C23×C47—24no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47—81no—
112C23×C47—81no—
113C23×C47C2×D411yescharacteristic
114Q8×C47—21no—
115Q8×C47—21no—
116D4×C47—24no—
117D4×C47—21no—
118D4×C47—21no—
119D4×C47#4112yes—
120D4×C47#4112yes—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2411yescharacteristic
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—81no—
132C2×Dic47—81no—
133C2×Dic47—81no—
134C2×Dic47—81no—
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137C2×Dic47C2×D411yescharacteristic
138C2×Dic47C2×D411yescharacteristic
139Dic94—21no—
140Dic94—21no—
141C8×C47—21no—
142C8×C47—21no—
143C47⋊C8—21no—
144C47⋊C8—21no—
145C22×C47—21no—
146C22×C47—22no—
147C22×C47—22no—
148C22×C47—21no—
149C22×C47—21no—
150C22×C47—41no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47—84no—
155C22×C47C22×D411yescharacteristic
156C4×C47—21no—
157C4×C47—41no—
158C4×C47—41no—
159C4×C47C2×#4111yescharacteristic
160C4×C47C2×#4111yescharacteristic
161Dic47—21no—
162Dic47—21no—
163Dic47—21no—
164Dic47—21no—
165Dic47—41no—
166Dic47—41no—
167Dic47—41no—
168Dic47—41no—
169#3123—471nomaximal, Sylow
170C2×C47—41no—
171C2×C47—42no—
172C2×C47—42no—
173C2×C47#52511yescharacteristic
174C2×C47#57711yescharacteristic
175C2×C47#57711yescharacteristic
176#541—471no—
177#518—471no—
178#485—471no—
179#485—471no—
180#478—471no—
181#478—471no—
182#461—471no—
183#461—471no—
184#450—471no—
185#450D4711yescharacteristic
186#440—471no—
187#440—471no—
188C4×SD16—471no—
189C4×SD16—471no—
190#433—471no—
191C47#312311yescharacteristic, complemented, Sylow
192C22×D4C2×D4711yescharacteristic
193C2×SD16—471no—
194C2×SD16—471no—
195C2×SD16C2×D4711yescharacteristic
196C2×SD16C2×D4711yescharacteristic
197C4⋊Q8—471no—
198#126—941no—
199#126—941no—
200#125—471no—
201#125—941no—
202#125—941no—
203C22⋊Q8—471no—
204C22⋊Q8C2×D4711yescharacteristic
205C4×Q8—471no—
206C4×Q8—471no—
207C4×D4—471no—
208C4×D4—471no—
209C4×D4—471no—
210C4×D4—471no—
211C4×D4—941no—
212C4×D4—941no—
213#117—471no—
214#117—471no—
215C2×C22⋊C4—941no—
216C2×C22⋊C4—941no—
217#107—471no—
218#107—471no—
219#106—471no—
220#106—471no—
221C4⋊C8—471no—
222C4⋊C8—471no—
223#103—471no—
224#103—471no—
225#103—471no—
226#103—471no—
227#102—471no—
228#102—471no—
229#102C2×D4711yescharacteristic
230#102C2×D4711yescharacteristic
231C22⋊C8—471no—
232C22⋊C8C2×D4711yescharacteristic
233#97—471no—
234C4×C8—471no—
235C24—21no—
236C2×Q8—471no—
237C2×Q8C22×D4711yescharacteristic
238C2×D4—22no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4C22×D4711yescharacteristic
242C2×D4C22×D4711yescharacteristic
243C22×C4—941no—
244C22×C4—941no—
245C22×C4—941no—
246C22×C4—941no—
247C22×C4C22×D4711yescharacteristic
248SD16—22no—
249SD16—22no—
250SD16—942no—
251SD16—942no—
252C2×C8—471no—
253C2×C8—471no—
254C2×C8C22×D4711yescharacteristic
255C2×C8C22×D4711yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—471no—
258C4⋊C4—471no—
259C4⋊C4—471no—
260C4⋊C4—471no—
261C4⋊C4—471no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4C22×D4711yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—471no—
272C22⋊C4—471no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4—941no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C42—471no—
280C42—471no—
281C42—941no—
282C42—941no—
283C42—941no—
284C23—24no—
285C23—21no—
286C23—21no—
287C23—81no—
288C23—81no—
289C23D4×D4711yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—941no—
293Q8—941no—
294D4—24no—
295D4—21no—
296D4—21no—
297D4#1062535212yes—
298D4#1062535212yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—471no—
304C2×C4—471no—
305C2×C4—471no—
306C2×C4—471no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—3761no—
312C2×C4—3761no—
313C2×C4—3761no—
314C2×C4—3761no—
315C2×C4D4×D4711yescharacteristic
316C2×C4C23×D4711yescharacteristic
317C8—21no—
318C8—21no—
319C8—941no—
320C8—941no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—84no—
331C22C2×D4×D4711yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—941no—
336C4—941no—
337C4—941no—
338C4—941no—
339C4—1881no—
340C4—1881no—
341C4—1881no—
342C4—1881no—
343C4C2×#1062535211yescharacteristic
344C4C2×#1062535211yescharacteristic
345C2—41no—
346C2—42no—
347C2—42no—
348C2#1568962911yescharacteristic
349C2#1568992911yescharacteristic
350C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#450C2
socleC22×C47C22×D4
hypercenter#450D47
hypocenterC47#3123
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #15689733C2semidirect
3. #15689465C2semidirect
4. #15689461C2semidirect
5. #15689425C2semidirect
6. #15689421C2semidirect
7. #15689326C2semidirect
8. #15689326C2semidirect
10. #15689224C2semidirect
11. #15689220C2semidirect
12. #15689214C2semidirect
13. SD16×Dic47C2semidirect
14. #15689181C2semidirect
18. #13094022C22semidirect
22. #13094015C22semidirect
25. Q8×Dic47C22semidirect
26. #13093989C22semidirect
37. #13093958C22semidirect
38. #13093957C22semidirect
39. #13093956C22semidirect
40. #13093955C22semidirect
41. Dic47⋊C8C22semidirect
42. Dic47⋊C8C22semidirect
43. #13093949C22semidirect
44. #13093949C22semidirect
45. #13093948C22semidirect
46. #13093948C22semidirect
50. #13093934C22semidirect
51. C8×Dic47C22semidirect
191. C47#3123semidirect