Finite Group Databasebeta

← #20253566

Subgroups — #20253566

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#15689597C211yesmaximal, characteristic, complemented
2#15689461C211yesmaximal, characteristic, complemented
3#15689444C211yesmaximal, characteristic, complemented
4#15689410C211yesmaximal, characteristic, complemented
5#15689400C211yesmaximal, characteristic, complemented
6#15689335C211yesmaximal, characteristic, complemented
7#15689335C211yesmaximal, characteristic, complemented
8#15689273C211yesmaximal, characteristic, complemented
9#15689256C211yesmaximal, characteristic
10#15689233C211yesmaximal, characteristic, complemented
11#15689221C211yesmaximal, characteristic, complemented
12C4×#10625336C211yesmaximal, characteristic, complemented
13C4×#10625334C211yesmaximal, characteristic, complemented
14#15689184C211yesmaximal, characteristic, complemented
15C47×#542C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C2×#10625336C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20C2×#10625334C2211yescharacteristic
21C4×D188C2211yescharacteristic
22C4×D188C2211yescharacteristic
23C4×D188C2211yescharacteristic
24C4×D188C2211yescharacteristic
25#13093986—21no—
26#13093986—21no—
27#13093983C2211yescharacteristic
28C22⋊C4×D47—21no—
29C22⋊C4×D47—21no—
30#13093957C2211yescharacteristic, complemented
31#13093957C2211yescharacteristic, complemented
32#13093955C2211yescharacteristic, complemented
33#13093955C2211yescharacteristic, complemented
34C4⋊(C47⋊C8)C2211yescharacteristic, complemented
35C4⋊(C47⋊C8)C2211yescharacteristic, complemented
36#13093948C2211yescharacteristic, complemented
37#13093948C2211yescharacteristic, complemented
38#13093945C2211yescharacteristic, complemented
39#13093945C2211yescharacteristic, complemented
40#13093944C2211yescharacteristic
41#13093944C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44C22⋊(C47⋊C8)C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46#13093935C2211yescharacteristic, complemented
47C4×C47⋊C8C2211yescharacteristic, complemented
48C4⋊Q8×C47C2211yescharacteristic, complemented
49#126×C47—21no—
50#124×C47—21no—
51#124×C47C2211yescharacteristic, complemented
52#123×C47—21no—
53C22⋊Q8×C47—21no—
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56C4×Q8×C47C2211yescharacteristic, complemented
57C4×D4×C47C2211yescharacteristic, complemented
58#117×C47C2211yescharacteristic
59C23×D47—21no—
60C2×Q8×C47—21no—
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47—21no—
63C2×D4×C47C2311yescharacteristic
64C22×C4×C47—21no—
65C22×C4×C47C2311yescharacteristic
66C2×D188—21no—
67C2×D188—22no—
68C2×D188—22no—
69C2×D188C2311yescharacteristic
70C2×D188C2311yescharacteristic
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47—21no—
77C4⋊C4×C47—21no—
78C4⋊C4×C47D411yescharacteristic
79C4⋊C4×C47D411yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C22⋊C4×C47—21no—
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C22⋊C4×C47D411yescharacteristic
88C22⋊C4×C47D411yescharacteristic
89C42×C47—21no—
90C42×C47C2311yescharacteristic
91C42×C47C2311yescharacteristic
92C22⋊Dic47—21no—
93#10625336—22no—
94#10625336—22no—
95#10625334—22no—
96#10625334—22no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101C4⋊Dic47C2311yescharacteristic
102C4⋊Dic47C2311yescharacteristic
103C4×Dic47—21no—
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C23×C47—21no—
109C23×C47C2×D411yescharacteristic
110C22×D47—21no—
111C22×D47—21no—
112C22×D47—24no—
113C22×D47—81no—
114C22×D47—81no—
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47—81no—
118D4×C47—21no—
119D4×C47—21no—
120D4×C47—81no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—81no—
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2×D411yescharacteristic
132C2×C4×C47C2411yescharacteristic
133C2×Dic47—21no—
134C2×Dic47—21no—
135D188—24no—
136D188—21no—
137D188—21no—
138D188#4112yes—
139D188#4112yes—
140C4×D47—81no—
141C4×D47—81no—
142C4×D47—81no—
143C4×D47—81no—
144C47⋊C8—21no—
145C47⋊C8—21no—
146C47⋊C8—21no—
147C47⋊C8—21no—
148C22×C47—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47C22×D411yescharacteristic
155C2×D47—22no—
156C2×D47—22no—
157C2×D47—41no—
158C2×D47—41no—
159C2×D47—41no—
160C2×D47—41no—
161C2×D47—84no—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—21no—
165C4×C47—21no—
166C4×C47—21no—
167C4×C47—41no—
168C4×C47—41no—
169C4×C47—41no—
170C4×C47C2×#4111yescharacteristic
171C4×C47C2×#4111yescharacteristic
172Dic47—41no—
173Dic47—41no—
174#3118—471nomaximal, Sylow
175C2×C47—41no—
176C2×C47—81no—
177C2×C47#52511yescharacteristic
178C2×C47#57611yescharacteristic
179C2×C47#57711yescharacteristic
180D47—42no—
181D47—42no—
182#542D4711yescharacteristic, complemented
183#518—471no—
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×D4—471no—
199C2×SD16—471no—
200C2×SD16—471no—
201C2×D8—471no—
202C2×D8—471no—
203C4⋊Q8C2×D4711yescharacteristic, complemented
204#126—21no—
205#124—21no—
206#124C2×D4711yescharacteristic, complemented
207#123—21no—
208C22⋊Q8—21no—
209C22⋊Q8C2×D4711yescharacteristic
210#121C2×D4711yescharacteristic
211C4×Q8C2×D4711yescharacteristic, complemented
212C4×D4—471no—
213C4×D4—471no—
214C4×D4—471no—
215C4×D4—471no—
216C4×D4—941no—
217C4×D4—941no—
218C4×D4C2×D4711yescharacteristic, complemented
219#117—471no—
220#117C2×D4711yescharacteristic
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#102—471no—
236#102—471no—
237C22⋊C8—471no—
238C22⋊C8—471no—
239#97—471no—
240C4×C8—471no—
241C24—941no—
242C2×Q8—21no—
243C2×Q8C22×D4711yescharacteristic
244C2×D4—21no—
245C2×D4—471no—
246C2×D4—471no—
247C2×D4—942no—
248C2×D4—942no—
249C2×D4—941no—
250C2×D4C22×D4711yescharacteristic
251C22×C4—21no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4—941no—
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—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—471no—
269C4⋊C4—471no—
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—21no—
291C23—944no—
292C23—941no—
293C23—941no—
294C23—3761no—
295C23—3761no—
296C23C2×C22⋊D4711yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—81no—
300D4—21no—
301D4—21no—
302D4—81no—
303D4—472no—
304D4—472no—
305D4—944no—
306D4—941no—
307D4—941no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—81no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—3761no—
317C2×C4—3761no—
318C2×C4—3761no—
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—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—942no—
337C22—942no—
338C22—3764no—
339C22—1881no—
340C22—1881no—
341C22—1881no—
342C22—1881no—
343C22C22×C22⋊D4711yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—1881no—
353C4—1881no—
354C4#41×D4711yescharacteristic
355C4#41×D4711yescharacteristic
356C2—41no—
357C2—81no—
358C2—1882no—
359C2—1882no—
360C2#1568963011yescharacteristic
361C2#1568992611yescharacteristic
362C2#1568993111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#542C2
socleC22×C47C22×D4
hypercenter#542D47
hypocenterC47#3118
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #15689597C2semidirect
2. #15689461C2semidirect
3. #15689444C2semidirect
4. #15689410C2semidirect
5. #15689400C2semidirect
6. #15689335C2semidirect
7. #15689335C2semidirect
8. #15689273C2semidirect
10. #15689233C2semidirect
11. #15689221C2semidirect
12. C4×#10625336C2semidirect
13. C4×#10625334C2semidirect
14. #15689184C2semidirect
15. C47×#542C2semidirect
30. #13093957C22semidirect
31. #13093957C22semidirect
32. #13093955C22semidirect
33. #13093955C22semidirect
34. C4⋊(C47⋊C8)C22semidirect
35. C4⋊(C47⋊C8)C22semidirect
36. #13093948C22semidirect
37. #13093948C22semidirect
38. #13093945C22semidirect
39. #13093945C22semidirect
46. #13093935C22semidirect
47. C4×C47⋊C8C22semidirect
48. C4⋊Q8×C47C22semidirect
51. #124×C47C22semidirect
56. C4×Q8×C47C22semidirect
57. C4×D4×C47C22semidirect
182. #542D47semidirect
197. C47#3118semidirect
203. C4⋊Q8C2×D47semidirect
206. #124C2×D47semidirect
211. C4×Q8C2×D47semidirect
218. C4×D4C2×D47semidirect