Finite Group Databasebeta

← #20253569

Subgroups — #20253569

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#15689742C211yesmaximal, characteristic, complemented
2#15689595C211yesmaximal, characteristic, complemented
3#15689463C211yesmaximal, characteristic, complemented
4#15689445C211yesmaximal, characteristic, complemented
5#15689413C211yesmaximal, characteristic, complemented
6#15689404C211yesmaximal, characteristic, complemented
7#15689335C211yesmaximal, characteristic, complemented
8#15689272C211yesmaximal, characteristic, complemented
9#15689255C211yesmaximal, characteristic
10#15689232C211yesmaximal, characteristic, complemented
11#15689224C211yesmaximal, characteristic, complemented
12#15689208C211yesmaximal, characteristic, complemented
13D8×Dic47C211yesmaximal, characteristic, complemented
14#15689183C211yesmaximal, characteristic, complemented
15C47×#463C211yesmaximal, characteristic, complemented
16C2×D4×D47C2211yescharacteristic
17C2×#10625336C2211yescharacteristic
18C2×#10625334C2211yescharacteristic
19#13094024C2211yescharacteristic, complemented
20#13094017—21no—
21#13094010—21no—
22#13094008—21no—
23#13094001—21no—
24#13094000C2211yescharacteristic
25#13093995C2211yescharacteristic
26Q8×Dic47C2211yescharacteristic, complemented
27C4×D188C2211yescharacteristic
28D4×Dic47C2211yescharacteristic
29D4×Dic47C2211yescharacteristic, complemented
30#13093986C2211yescharacteristic
31C4×C22⋊D47—21no—
32(C22⋊D47)⋊C4—21no—
33#13093982C2211yescharacteristic
34#13093981C2211yescharacteristic
35C2×(C2×D47)⋊C4—21no—
36C22⋊C4×D47—21no—
37#13093958C2211yescharacteristic, complemented
38#13093958C2211yescharacteristic, complemented
39#13093955C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41C4⋊(C47⋊C8)C2211yescharacteristic, complemented
42#13093948C2211yescharacteristic, complemented
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093945C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic, complemented
48(C2×D47)⋊C8C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50#13093934C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C2×SD16×C47C2211yescharacteristic
53C2×D8×C47C2211yescharacteristic
54#124×C47C2211yescharacteristic, complemented
55C4×D4×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47—21no—
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C22×Dic47—21no—
67C22×Dic47—21no—
68D4×D47—22no—
69D4×D47—22no—
70C2×D188C2311yescharacteristic
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×C4×D47C2311yescharacteristic
74C2×Dic94—21no—
75SD16×C47—22no—
76D8×C47—22no—
77C2×C8×C47C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C22⋊C4×C47—21no—
81C22⋊C4×C47—21no—
82C22⋊C4×C47—21no—
83C42×C47C2311yescharacteristic
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87#10625336—22no—
88#10625334—22no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4D411yescharacteristic
94(C2×D47)⋊C4D411yescharacteristic
95C4⋊Dic47—21no—
96C4⋊Dic47—21no—
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100Dic47⋊C4—21no—
101Dic47⋊C4D411yescharacteristic
102Dic47⋊C4D411yescharacteristic
103C4×Dic47—21no—
104C4×Dic47—21no—
105C4×Dic47C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C23×C47—21no—
109C23×C47—21no—
110C22×D47—21no—
111C22×D47—24no—
112C22×D47—81no—
113C22×D47—81no—
114C22×D47C2×D411yescharacteristic
115Q8×C47—21no—
116Q8×C47—21no—
117D4×C47—21no—
118D4×C47—21no—
119D4×C47—21no—
120D4×C47#4112yes—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—81no—
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2411yescharacteristic
127C22⋊D47—24no—
128C22⋊D47—81no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—81no—
133C2×Dic47—81no—
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137D188—21no—
138D188#4112yes—
139C4×D47—21no—
140C4×D47—21no—
141C4×D47—81no—
142C4×D47—81no—
143Dic94—81no—
144C8×C47—21no—
145C8×C47—21no—
146C47⋊C8—21no—
147C47⋊C8—21no—
148C22×C47—22no—
149C22×C47—41no—
150C22×C47—41no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47C22×D411yescharacteristic
155C2×D47—21no—
156C2×D47—22no—
157C2×D47—21no—
158C2×D47—21no—
159C2×D47—41no—
160C2×D47—41no—
161C2×D47—84no—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—41no—
165C4×C47—41no—
166C4×C47C2×#4111yescharacteristic
167C4×C47C2×#4111yescharacteristic
168Dic47—21no—
169Dic47—21no—
170Dic47—21no—
171Dic47—41no—
172Dic47—41no—
173Dic47—41no—
174#3118—471nomaximal, Sylow
175C2×C47—42no—
176C2×C47—81no—
177C2×C47#52511yescharacteristic
178C2×C47#57611yescharacteristic
179C2×C47#57711yescharacteristic
180D47—41no—
181D47—42no—
182#542—471no—
183#518—471no—
184#485—471no—
185#482—471no—
186#476—471no—
187#474—471no—
188#463—471no—
189#463D4711yescharacteristic, complemented
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×SD16C2×D4711yescharacteristic
201C2×D8—471no—
202C2×D8C2×D4711yescharacteristic
203C4⋊Q8—471no—
204#126—941no—
205#124—941no—
206#124C2×D4711yescharacteristic, complemented
207#123—941no—
208C22⋊Q8—471no—
209C22⋊Q8—941no—
210#121—471no—
211C4×Q8—471no—
212C4×D4—471no—
213C4×D4—471no—
214C4×D4—471no—
215C4×D4—471no—
216C4×D4—941no—
217C4×D4—941no—
218C4×D4C2×D4711yescharacteristic
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⋊C8C2×D4711yescharacteristic, complemented
229#103—471no—
230#103C2×D4711yescharacteristic, complemented
231#102—471no—
232#102—471no—
233#102—471no—
234#102—471no—
235#102—471no—
236#102C2×D4711yescharacteristic, complemented
237C22⋊C8—471no—
238C22⋊C8—471no—
239#97—471no—
240C4×C8—471no—
241C24—941no—
242C2×Q8—941no—
243C2×Q8C22×D4711yescharacteristic
244C2×D4—471no—
245C2×D4—941no—
246C2×D4—942no—
247C2×D4—942no—
248C2×D4—941no—
249C2×D4C22×D4711yescharacteristic
250C2×D4C22×D4711yescharacteristic
251C22×C4—21no—
252C22×C4—471no—
253C22×C4—941no—
254C22×C4—941no—
255C22×C4—941no—
256C22×C4—941no—
257SD16—22no—
258SD16—942no—
259D8—22no—
260D8—942no—
261C2×C8—471no—
262C2×C8—471no—
263C2×C8C22×D4711yescharacteristic
264C2×C8C22×D4711yescharacteristic
265C4⋊C4—471no—
266C4⋊C4—471no—
267C4⋊C4—471no—
268C4⋊C4—471no—
269C4⋊C4—471no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4C22×D4711yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—471no—
278C22⋊C4—471no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C42—471no—
287C42—941no—
288C42—941no—
289C42C22×D4711yescharacteristic
290C23—21no—
291C23—21no—
292C23—471no—
293C23—944no—
294C23—941no—
295C23—3761no—
296C23—3761no—
297Q8—21no—
298Q8—21no—
299Q8—3761no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—472no—
304D4—944no—
305D4—941no—
306D4—3761no—
307D4#1062535212yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—471no—
312C2×C4—471no—
313C2×C4—471no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—3761no—
320C2×C4—3761no—
321C2×C4—3761no—
322C2×C4—3761no—
323C2×C4D4×D4711yescharacteristic
324C2×C4D4×D4711yescharacteristic
325C2×C4C23×D4711yescharacteristic
326C8—21no—
327C8—21no—
328C8—941no—
329C8—941no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—941no—
337C22—942no—
338C22—941no—
339C22—941no—
340C22—3764no—
341C22—1881no—
342C22—1881no—
343C22C2×D4×D4711yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—941no—
349C4—941no—
350C4—941no—
351C4—1881no—
352C4—1881no—
353C4—1881no—
354C4#41×D4711yescharacteristic
355C4C2×#1062535211yescharacteristic
356C2—42no—
357C2—81no—
358C2—1881no—
359C2—1882no—
360C2#1568963311yescharacteristic
361C2#1568992511yescharacteristic
362C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#463C2
socleC22×C47C22×D4
hypercenter#463D47
hypocenterC47#3118
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #15689742C2semidirect
2. #15689595C2semidirect
3. #15689463C2semidirect
4. #15689445C2semidirect
5. #15689413C2semidirect
6. #15689404C2semidirect
7. #15689335C2semidirect
8. #15689272C2semidirect
10. #15689232C2semidirect
11. #15689224C2semidirect
12. #15689208C2semidirect
13. D8×Dic47C2semidirect
14. #15689183C2semidirect
15. C47×#463C2semidirect
19. #13094024C22semidirect
26. Q8×Dic47C22semidirect
29. D4×Dic47C22semidirect
37. #13093958C22semidirect
38. #13093958C22semidirect
39. #13093955C22semidirect
40. #13093955C22semidirect
41. C4⋊(C47⋊C8)C22semidirect
42. #13093948C22semidirect
47. #13093945C22semidirect
50. #13093934C22semidirect
51. C8×Dic47C22semidirect
54. #124×C47C22semidirect
56. C4⋊C8×C47C22semidirect
57. #103×C47C22semidirect
58. #102×C47C22semidirect
189. #463D47semidirect
197. C47#3118semidirect
206. #124C2×D47semidirect
228. C4⋊C8C2×D47semidirect
230. #103C2×D47semidirect
236. #102C2×D47semidirect