Finite Group Databasebeta

← #20253572

Subgroups — #20253572

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#15689744C211yesmaximal, characteristic, complemented
2#15689464C211yesmaximal, characteristic, complemented
3#15689447C211yesmaximal, characteristic, complemented
4#15689413C211yesmaximal, characteristic, complemented
5#15689403C211yesmaximal, characteristic, complemented
6#15689338C211yesmaximal, characteristic, complemented
7#15689338C211yesmaximal, characteristic, complemented
8#15689274C211yesmaximal, characteristic, complemented
9#15689257C211yesmaximal, characteristic
10#15689233C211yesmaximal, characteristic, complemented
11#15689223C211yesmaximal, characteristic, complemented
12C4×#10625335C211yesmaximal, characteristic, complemented
13C4×#10625334C211yesmaximal, characteristic, complemented
14#15689184C211yesmaximal, characteristic, complemented
15C47×#518C211yesmaximal, characteristic, complemented
16C2×#10625335C2211yescharacteristic
17C2×#10625335C2211yescharacteristic
18C2×#10625334C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20#13094024C2211yescharacteristic, complemented
21#13094019—21no—
22#13094012C2211yescharacteristic, complemented
23#13094010—21no—
24#13094006—21no—
25#13094003C2211yescharacteristic
26#13094002—21no—
27#13093998C2211yescharacteristic
28C4×Dic94C2211yescharacteristic, complemented
29C4×D188C2211yescharacteristic, complemented
30#13093957C2211yescharacteristic, complemented
31#13093957C2211yescharacteristic, complemented
32#13093955C2211yescharacteristic, complemented
33#13093955C2211yescharacteristic, complemented
34C4⋊(C47⋊C8)C2211yescharacteristic, complemented
35C4⋊(C47⋊C8)C2211yescharacteristic, complemented
36#13093947C2211yescharacteristic, complemented
37#13093947C2211yescharacteristic, complemented
38#13093945C2211yescharacteristic
39#13093945C2211yescharacteristic
40#13093945C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093944C2211yescharacteristic, complemented
43#13093944C2211yescharacteristic, complemented
44C22⋊(C47⋊C8)C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46#13093935C2211yescharacteristic, complemented
47C4×C47⋊C8C2211yescharacteristic, complemented
48C22×D4×C47C2211yescharacteristic
49C4×D4×C47—21no—
50C4×D4×C47—21no—
51C4×D4×C47C2211yescharacteristic
52C4×D4×C47C2211yescharacteristic
53C4×D4×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55#117×C47C2211yescharacteristic
56#117×C47C2211yescharacteristic
57C2×C22⋊C4×C47—21no—
58C2×C22⋊C4×C47—21no—
59C24×C47—21no—
60C2×D4×C47—22no—
61C2×D4×C47—22no—
62C2×D4×C47—21no—
63C2×D4×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47—21no—
68C22×C4×C47—21no—
69C22×C4×C47C2311yescharacteristic
70C2×C22⋊D47—21no—
71C2×D188C2311yescharacteristic
72C2×C4×D47—21no—
73C2×Dic94—21no—
74C2×Dic94C2311yescharacteristic
75C4⋊C4×C47D411yescharacteristic
76C4⋊C4×C47D411yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C22⋊C4×C47—21no—
81C22⋊C4×C47—21no—
82C22⋊C4×C47—21no—
83C22⋊C4×C47—21no—
84C22⋊C4×C47D411yescharacteristic
85C22⋊C4×C47D411yescharacteristic
86C42×C47—21no—
87C42×C47C2311yescharacteristic
88C42×C47C2311yescharacteristic
89C22⋊Dic47—21no—
90#10625335—22no—
91#10625335—22no—
92#10625334—22no—
93#10625334—22no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98C4⋊Dic47—21no—
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103C4×Dic47—21no—
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
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—
115D4×C47—24no—
116D4×C47—21no—
117D4×C47—21no—
118D4×C47#4112yes—
119D4×C47#4112yes—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—81no—
125C2×C4×C47—81no—
126C2×C4×C47—81no—
127C2×C4×C47—81no—
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2×D411yescharacteristic
132C2×C4×C47C2×D411yescharacteristic
133C2×C4×C47C2411yescharacteristic
134C22⋊D47—81no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138D188—21no—
139D188—21no—
140C4×D47—81no—
141Dic94—21no—
142Dic94—21no—
143Dic94—81no—
144C47⋊C8—21no—
145C47⋊C8—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—21no—
164C4×C47—21no—
165C4×C47—21no—
166C4×C47—21no—
167C4×C47—41no—
168C4×C47—41no—
169C4×C47C2×#4111yescharacteristic
170C4×C47C2×#4111yescharacteristic
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#518D4711yescharacteristic, complemented
184#485—471no—
185#482—471no—
186#476—471no—
187#474—471no—
188#463—471no—
189#463—471no—
190#450—471no—
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×SD16—471no—
200C2×SD16—471no—
201C2×D8—471no—
202C2×D8—471no—
203C4⋊Q8—471no—
204#126—941no—
205#124—471no—
206#124—941no—
207#123—941no—
208C22⋊Q8—471no—
209C22⋊Q8—941no—
210#121—471no—
211C4×Q8—471no—
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—471no—
215C4×D4C2×D4711yescharacteristic
216C4×D4C2×D4711yescharacteristic
217C4×D4C2×D4711yescharacteristic
218C4×D4C2×D4711yescharacteristic
219#117C2×D4711yescharacteristic
220#117C2×D4711yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
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#102—471no—
236#102—471no—
237C22⋊C8—471no—
238C22⋊C8—471no—
239#97—471no—
240C4×C8—471no—
241C24—21no—
242C2×Q8—471no—
243C2×Q8—941no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—471no—
248C2×D4—941no—
249C2×D4C22×D4711yescharacteristic
250C2×D4C22×D4711yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—941no—
256C22×C4C22×D4711yescharacteristic
257SD16—942no—
258SD16—942no—
259D8—942no—
260D8—942no—
261C2×C8—471no—
262C2×C8—471no—
263C2×C8—471no—
264C2×C8—471no—
265C4⋊C4—471no—
266C4⋊C4—471no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4C22⋊D4711yescharacteristic
271C4⋊C4C22⋊D4711yescharacteristic
272C4⋊C4C22×D4711yescharacteristic
273C4⋊C4C22×D4711yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4C22⋊D4711yescharacteristic
285C22⋊C4C22⋊D4711yescharacteristic
286C42—21no—
287C42—941no—
288C42C22×D4711yescharacteristic
289C42C22×D4711yescharacteristic
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—941no—
296C23C2×C22⋊D4711yescharacteristic
297Q8—941no—
298Q8—941no—
299Q8—3761no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—941no—
304D4—941no—
305D4—3761no—
306D4#1062535012yes—
307D4#1062535012yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—3761no—
320C2×C4C2×C22⋊D4711yescharacteristic
321C2×C4C2×C22⋊D4711yescharacteristic
322C2×C4C2×C22⋊D4711yescharacteristic
323C2×C4C2×C22⋊D4711yescharacteristic
324C2×C4C2×C22⋊D4711yescharacteristic
325C2×C4C23×D4711yescharacteristic
326C8—941no—
327C8—941no—
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—
343C22C22×C22⋊D4711yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—1881no—
352C4—1881no—
353C4—1881no—
354C4C2×#1062535011yescharacteristic
355C4C2×#1062535011yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—3761no—
360C2#1568963411yescharacteristic
361C2#1568992611yescharacteristic
362C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#518C2
socleC22×C47C22×D4
hypercenter#518D47
hypocenterC47#3118
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #15689744C2semidirect
2. #15689464C2semidirect
3. #15689447C2semidirect
4. #15689413C2semidirect
5. #15689403C2semidirect
6. #15689338C2semidirect
7. #15689338C2semidirect
8. #15689274C2semidirect
10. #15689233C2semidirect
11. #15689223C2semidirect
12. C4×#10625335C2semidirect
13. C4×#10625334C2semidirect
14. #15689184C2semidirect
15. C47×#518C2semidirect
20. #13094024C22semidirect
22. #13094012C22semidirect
28. C4×Dic94C22semidirect
29. C4×D188C22semidirect
30. #13093957C22semidirect
31. #13093957C22semidirect
32. #13093955C22semidirect
33. #13093955C22semidirect
34. C4⋊(C47⋊C8)C22semidirect
35. C4⋊(C47⋊C8)C22semidirect
36. #13093947C22semidirect
37. #13093947C22semidirect
42. #13093944C22semidirect
43. #13093944C22semidirect
46. #13093935C22semidirect
47. C4×C47⋊C8C22semidirect
183. #518D47semidirect
197. C47#3118semidirect