Finite Group Databasebeta

← #20253573

Subgroups — #20253573

Order 6016.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689746C211yesmaximal, characteristic, complemented
2#15689598C211yesmaximal, characteristic, complemented
3#15689461C211yesmaximal, characteristic, complemented
4#15689448C211yesmaximal, characteristic, complemented
5#15689411C211yesmaximal, characteristic, complemented
6#15689401C211yesmaximal, characteristic, complemented
7#15689340C211yesmaximal, characteristic, complemented
8#15689340C211yesmaximal, characteristic, complemented
9#15689257C211yesmaximal, characteristic
10#15689232C211yesmaximal, characteristic, complemented
11#15689224C211yesmaximal, characteristic, complemented
12SD16×Dic47C211yesmaximal, characteristic, complemented
13#15689203C211yesmaximal, characteristic, complemented
14#15689181C211yesmaximal, characteristic, complemented
15C47×#450C211yesmaximal, characteristic, complemented
16C2×#10625334C2211yescharacteristic
17C2×#10625334C2211yescharacteristic
18#13094023C2211yescharacteristic, complemented
19#13094019—21no—
20#13094013C2211yescharacteristic, complemented
21#13094010—21no—
22#13094006—21no—
23#13094004—21no—
24#13093998C2211yescharacteristic
25Q8×Dic47C2211yescharacteristic, complemented
26D4×Dic47—21no—
27D4×Dic47—21no—
28D4×Dic47C2211yescharacteristic
29D4×Dic47C2211yescharacteristic
30D4×Dic47C2211yescharacteristic
31D4×Dic47C2211yescharacteristic
32#13093986C2211yescharacteristic, complemented
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#13093948C2211yescharacteristic, complemented
44#13093948C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic, complemented
46#13093946C2211yescharacteristic, 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
67C2×C22⋊D47—21no—
68C22×Dic47—21no—
69C22×Dic47—21no—
70C22×Dic47—21no—
71C22×Dic47—21no—
72C2×D188C2311yescharacteristic
73C2×C4×D47—21no—
74C2×Dic94—21no—
75SD16×C47—22no—
76SD16×C47—22no—
77C2×C8×C47C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C4⋊C4×C47—21no—
80C4⋊C4×C47C2311yescharacteristic
81C22⋊C4×C47—21no—
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47D411yescharacteristic
88C22⋊Dic47D411yescharacteristic
89#10625334—22no—
90#10625334—22no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47D411yescharacteristic
97C4⋊Dic47D411yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101Dic47⋊C4—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
114C22×D47—21no—
115Q8×C47—21no—
116Q8×C47—21no—
117D4×C47—24no—
118D4×C47—21no—
119D4×C47—21no—
120D4×C47#4112yes—
121D4×C47#4112yes—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2411yescharacteristic
128C22⋊D47—81no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—81no—
133C2×Dic47—81no—
134C2×Dic47—81no—
135C2×Dic47—81no—
136C2×Dic47C2×D411yescharacteristic
137C2×Dic47C2×D411yescharacteristic
138C2×Dic47C2×D411yescharacteristic
139C2×Dic47C2×D411yescharacteristic
140D188—21no—
141D188—21no—
142C4×D47—81no—
143Dic94—81no—
144C8×C47—21no—
145C8×C47—21no—
146C47⋊C8—21no—
147C47⋊C8—21no—
148C22×C47—21no—
149C22×C47—22no—
150C22×C47—22no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47—84no—
158C22×C47C22×D411yescharacteristic
159C2×D47—41no—
160C2×D47—41no—
161C2×D47—41no—
162C4×C47—21no—
163C4×C47—41no—
164C4×C47—41no—
165C4×C47C2×#4111yescharacteristic
166C4×C47C2×#4111yescharacteristic
167Dic47—21no—
168Dic47—21no—
169Dic47—21no—
170Dic47—21no—
171Dic47—41no—
172Dic47—41no—
173Dic47—41no—
174#3118—471nomaximal, Sylow
175C2×C47—41no—
176C2×C47—42no—
177C2×C47—42no—
178C2×C47#52511yescharacteristic
179C2×C47#57611yescharacteristic
180C2×C47#57711yescharacteristic
181D47—81no—
182#542—471no—
183#518—471no—
184#485—471no—
185#482—471no—
186#476—471no—
187#474—471no—
188#463—471no—
189#463—471no—
190#450D4711yescharacteristic, complemented
191#447—471no—
192#442—471no—
193#440—471no—
194C4×SD16—471no—
195C4×D8—471no—
196#433—471no—
197C47#311811yescharacteristic, complemented, Sylow
198C22×D4C2×D4711yescharacteristic
199C2×SD16C2×D4711yescharacteristic
200C2×SD16C2×D4711yescharacteristic
201C2×D8—471no—
202C2×D8—471no—
203C4⋊Q8—471no—
204#126—941no—
205#124—471no—
206#124—941no—
207#123—941no—
208C22⋊Q8—941no—
209C22⋊Q8C2×D4711yescharacteristic
210#121—471no—
211C4×Q8—471no—
212C4×D4—471no—
213C4×D4—471no—
214C4×D4—471no—
215C4×D4—471no—
216C4×D4—471no—
217C4×D4—941no—
218C4×D4—941no—
219#117—471no—
220#117—471no—
221C2×C22⋊C4—941no—
222C2×C22⋊C4—941no—
223#107—471no—
224#107—471no—
225#106—471no—
226#106—471no—
227C4⋊C8—471no—
228C4⋊C8—471no—
229#103—471no—
230#103—471no—
231#102—471no—
232#102—471no—
233#102—471no—
234#102—471no—
235#102C2×D4711yescharacteristic
236#102C2×D4711yescharacteristic
237C22⋊C8—471no—
238C22⋊C8C2×D4711yescharacteristic
239#97—471no—
240C4×C8—471no—
241C24—21no—
242C2×Q8—941no—
243C2×Q8C22×D4711yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—471no—
248C2×D4—941no—
249C2×D4C22×D4711yescharacteristic
250C2×D4C22×D4711yescharacteristic
251C22×C4—941no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4—941no—
255C22×C4—941no—
256C22×C4C22×D4711yescharacteristic
257SD16—22no—
258SD16—22no—
259D8—942no—
260D8—942no—
261C2×C8—471no—
262C2×C8—471no—
263C2×C8C22×D4711yescharacteristic
264C2×C8C22×D4711yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—471no—
267C4⋊C4—471no—
268C4⋊C4—471no—
269C4⋊C4—471no—
270C4⋊C4—471no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4C22×D4711yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—471no—
276C22⋊C4—471no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C42—471no—
287C42—471no—
288C42—941no—
289C42—941no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—941no—
296C23D4×D4711yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—3761no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—941no—
304D4—941no—
305D4—3761no—
306D4#1062535212yes—
307D4#1062535212yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—471no—
313C2×C4—471no—
314C2×C4—471no—
315C2×C4—471no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—3761no—
320C2×C4—3761no—
321C2×C4—3761no—
322C2×C4—3761no—
323C2×C4—3761no—
324C2×C4D4×D4711yescharacteristic
325C2×C4C23×D4711yescharacteristic
326C8—21no—
327C8—21no—
328C8—941no—
329C8—941no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—1881no—
341C22—1881no—
342C22—1881no—
343C22C2×D4×D4711yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—941no—
348C4—941no—
349C4—941no—
350C4—941no—
351C4—1881no—
352C4—1881no—
353C4—1881no—
354C4C2×#1062535211yescharacteristic
355C4C2×#1062535211yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—3761no—
360C2#1568962911yescharacteristic
361C2#1568992711yescharacteristic
362C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#450C2
socleC22×C47C22×D4
hypercenter#450D47
hypocenterC47#3118
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. #15689746C2semidirect
2. #15689598C2semidirect
3. #15689461C2semidirect
4. #15689448C2semidirect
5. #15689411C2semidirect
6. #15689401C2semidirect
7. #15689340C2semidirect
8. #15689340C2semidirect
10. #15689232C2semidirect
11. #15689224C2semidirect
12. SD16×Dic47C2semidirect
13. #15689203C2semidirect
14. #15689181C2semidirect
15. C47×#450C2semidirect
18. #13094023C22semidirect
20. #13094013C22semidirect
25. Q8×Dic47C22semidirect
32. #13093986C22semidirect
37. #13093958C22semidirect
38. #13093957C22semidirect
39. #13093956C22semidirect
40. #13093955C22semidirect
41. Dic47⋊C8C22semidirect
42. Dic47⋊C8C22semidirect
43. #13093948C22semidirect
44. #13093948C22semidirect
45. #13093946C22semidirect
46. #13093946C22semidirect
50. #13093934C22semidirect
51. C8×Dic47C22semidirect
190. #450D47semidirect
197. C47#3118semidirect