Finite Group Databasebeta

← #481×D59 #21433992

Subgroups — #481×D59 #21433992

Order 7552.

512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×D59C211yesmaximal, characteristic
2C2×C4⋊C4×D59C211yesmaximal, characteristic, complemented
3#16837722C212yesmaximal, complemented
4#16837721C211yesmaximal, characteristic, complemented
5#16837720C211yesmaximal, characteristic, complemented
6#16837719C212yesmaximal, complemented
7#16837718C211yesmaximal, characteristic, complemented
8#106×D59C212yesmaximal, complemented
9#102×D59C212yesmaximal, complemented
10C22⋊C8×D59C211yesmaximal, characteristic, complemented
11C59×#481C211yesmaximal, characteristic, complemented
12C2×D4×D59—21no—
13C2×D4×D59C2211yescharacteristic
14C22×C4×D59—21no—
15C22×C4×D59C2211yescharacteristic
16C2×C8×D59C2212yes—
17#14273702C2211yescharacteristic
18#14273701C2211yescharacteristic
19#14273700—21no—
20#14273699—21no—
21#14273698C2211yescharacteristic
22C2×C4⋊Dic59C2211yescharacteristic, complemented
23C2×Dic59⋊C4—21no—
24C4⋊C4×D59—21no—
25C4⋊C4×D59—21no—
26C4⋊C4×D59C2211yescharacteristic
27C4⋊C4×D59C2212yes—
28C4⋊C4×D59C2212yescomplemented
29C22⋊C4×D59—21no—
30#14273659C2212yescomplemented
31#14273658C2212yescomplemented
32#14273658C2212yescomplemented
33#14273649C2212yescomplemented
34#14273648C2212yescomplemented
35#14273647C2212yescomplemented
36C22⋊(C59⋊C8)C2211yescharacteristic, complemented
37(C2×D59)⋊C8C2212yescomplemented
38#121×C59C2211yescharacteristic
39C2×C4⋊C4×C59C2211yescharacteristic, complemented
40#106×C59C2212yescomplemented
41#102×C59C2212yescomplemented
42C22⋊C8×C59C2211yescharacteristic, complemented
43C23×D59—21no—
44C23×D59D411yescharacteristic
45C2×D4×C59—21no—
46C2×D4×C59C2311yescharacteristic
47C22×C4×C59—21no—
48C22×C4×C59C2311yescharacteristic
49C2×C22⋊D59—21no—
50C2×C22⋊D59—21no—
51C2×C22⋊D59—21no—
52C22×Dic59—21no—
53C22×Dic59D411yescharacteristic
54D4×D59—24no—
55D4×D59—44no—
56C2×D236—21no—
57C2×D236C2311yescharacteristic
58C2×C4×D59—24no—
59C2×C4×D59—21no—
60C2×C4×D59—22no—
61C2×C4×D59—22no—
62C2×C4×D59—44no—
63C2×C4×D59D411yescharacteristic
64C2×C4×D59D411yescharacteristic
65C2×C4×D59C2311yescharacteristic
66C2×C4×D59C2311yescharacteristic
67C2×C8×C59C2312yes—
68C4⋊C4×C59—21no—
69C4⋊C4×C59C2312yes—
70C4⋊C4×C59C2311yescharacteristic
71C22⋊C4×C59—21no—
72C22⋊Dic59—21no—
73(C2×D59)⋊C4—21no—
74(C2×D59)⋊C4—21no—
75C4⋊Dic59—21no—
76C4⋊Dic59C2312yes—
77C4⋊Dic59C2311yescharacteristic
78Dic59⋊C4—22no—
79Dic59⋊C4—22no—
80Dic59⋊C4—21no—
81C2×C59⋊C8C2312yes—
82C8×D59—24no—
83C23×C59—21no—
84C23×C59C2×D411yescharacteristic
85C22×D59—22no—
86C22×D59—22no—
87C22×D59—21no—
88C22×D59—42no—
89C22×D59—42no—
90C22×D59—42no—
91C22×D59SD1614yes—
92C22×D59C2×D411yescharacteristic
93C22×D59C2×D411yescharacteristic
94D4×C59—22no—
95D4×C59—42no—
96C2×C4×C59—22no—
97C2×C4×C59—22no—
98C2×C4×C59—21no—
99C2×C4×C59—42no—
100C2×C4×C59C2×D411yescharacteristic
101C2×C4×C59C2411yescharacteristic
102C22⋊D59—42no—
103C22⋊D59—42no—
104C22⋊D59—42no—
105C2×Dic59—22no—
106C2×Dic59—22no—
107C2×Dic59—21no—
108C2×Dic59—42no—
109C2×Dic59C2×D411yescharacteristic
110C2×Dic59C2×D411yescharacteristic
111D236—22no—
112D236—42no—
113C4×D59—22no—
114C4×D59—22no—
115C4×D59—22no—
116C4×D59—44no—
117C4×D59—42no—
118C4×D59—44no—
119C4×D59#4114yes—
120C8×C59—22no—
121C59⋊C8—22no—
122C22×C59—21no—
123C22×C59—21no—
124C22×C59—41no—
125C22×C59—41no—
126C22×C59—41no—
127C22×C59C2×SD1612yes—
128C22×C59C22×D411yescharacteristic
129C2×D59—21no—
130C2×D59—21no—
131C2×D59—28no—
132C2×D59—41no—
133C2×D59—41no—
134C2×D59—41no—
135C2×D59—84no—
136C2×D59#12312yes—
137C2×D59C2×SD1612yes—
138C2×D59C2×SD1612yes—
139C2×D59AGL(1,ℤ/8)12yes—
140C4×C59—21no—
141C4×C59—41no—
142C4×C59—42no—
143C4×C59C2×#4112yes—
144Dic59—21no—
145Dic59—41no—
146Dic59—42no—
147Dic59#12312yes—
148C2×#481—591nomaximal, Sylow
149C2×C59—22no—
150C2×C59—81no—
151C2×C59C2×#12311yescharacteristic
152C2×C59C22×SD1611yescharacteristic
153C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
154D59—22no—
155D59—81no—
156D59#48114yesdirect product factor
157C2×#121—591no—
158C22×C4⋊C4—591no—
159#481—591no—
160#481—591no—
161#481—592no—
162#481—592no—
163#481—591no—
164#481D5911yescharacteristic, direct product factor
165C2×#106—592no—
166C2×#102—592no—
167C2×C22⋊C8—591no—
168C59C2×#48111yescharacteristic, complemented, Sylow
169C22×D4—591no—
170C22×D4—1181no—
171C23×C4—591no—
172C23×C4—1181no—
173C22×C8—592no—
174#121—591no—
175#121—591no—
176#121—591no—
177#121—1181no—
178#121—1181no—
179#121C2×D5911yescharacteristic
180C2×C4⋊C4—591no—
181C2×C4⋊C4—592no—
182C2×C4⋊C4—592no—
183C2×C4⋊C4—591no—
184C2×C4⋊C4—1181no—
185C2×C4⋊C4—1181no—
186C2×C4⋊C4—1181no—
187C2×C4⋊C4C2×D5911yescharacteristic, complemented
188C2×C22⋊C4—1181no—
189#106—592no—
190#106—592no—
191#106—592no—
192#106C2×D5912yescomplemented
193#102—592no—
194#102—592no—
195#102—592no—
196#102C2×D5912yescomplemented
197C22⋊C8—591no—
198C22⋊C8—592no—
199C22⋊C8C2×D5911yescharacteristic, complemented
200C24—591no—
201C24—1181no—
202C2×D4—21no—
203C2×D4—591no—
204C2×D4—1181no—
205C2×D4—1184no—
206C2×D4—1181no—
207C2×D4—1181no—
208C2×D4—1181no—
209C2×D4—2364no—
210C2×D4C22×D5911yescharacteristic
211C22×C4—21no—
212C22×C4—591no—
213C22×C4—591no—
214C22×C4—591no—
215C22×C4—591no—
216C22×C4—591no—
217C22×C4—1184no—
218C22×C4—1181no—
219C22×C4—1182no—
220C22×C4—1182no—
221C22×C4—1181no—
222C22×C4—2364no—
223C22×C4C22×D5911yescharacteristic
224C2×C8—592no—
225C2×C8—1184no—
226C2×C8C22×D5912yes—
227C4⋊C4—21no—
228C4⋊C4—592no—
229C4⋊C4—591no—
230C4⋊C4—1182no—
231C4⋊C4—1182no—
232C4⋊C4—1181no—
233C4⋊C4—1181no—
234C4⋊C4C22×D5912yes—
235C4⋊C4C22×D5911yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—1181no—
238C22⋊C4—1181no—
239C22⋊C4—1181no—
240C23—21no—
241C23—591no—
242C23—594no—
243C23—591no—
244C23—1182no—
245C23—1182no—
246C23—1181no—
247C23—2362no—
248C23—2362no—
249C23—2362no—
250C23D4×D5911yescharacteristic
251D4—22no—
252D4—42no—
253D4—1182no—
254D4—2362no—
255D4—2362no—
256D4—2362no—
257D4—2362no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—591no—
263C2×C4—594no—
264C2×C4—591no—
265C2×C4—1182no—
266C2×C4—1182no—
267C2×C4—1182no—
268C2×C4—1182no—
269C2×C4—1181no—
270C2×C4—1182no—
271C2×C4—2364no—
272C2×C4—2362no—
273C2×C4—2364no—
274C2×C4—2362no—
275C2×C4D4×D5911yescharacteristic
276C2×C4C23×D5911yescharacteristic
277C8—22no—
278C8—1182no—
279C22—21no—
280C22—21no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—592no—
285C22—592no—
286C22—592no—
287C22—592no—
288C22—1188no—
289C22—1181no—
290C22—1181no—
291C22—4724no—
292C22—2361no—
293C22—2361no—
294C22—2361no—
295C22SD16×D5912yes—
296C22C2×D4×D5911yescharacteristic
297C4—21no—
298C4—41no—
299C4—42no—
300C4—592no—
301C4—1181no—
302C4—2361no—
303C4—2362no—
304C4#41×D5912yes—
305C2—22no—
306C2—81no—
307C2—594no—
308C2—1182no—
309C2—4721no—
310C2#123×D5911yescharacteristic
311C2C2×SD16×D5911yescharacteristic
312C2AGL(1,ℤ/8)×D5911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#481C2
socleC22×C59C22×D4
hypercenter#481D59
hypocenterC59C2×#481
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D59C2semidirect
3. #16837722C2semidirect
4. #16837721C2semidirect
5. #16837720C2semidirect
6. #16837719C2semidirect
7. #16837718C2semidirect
8. #106×D59C2semidirect
9. #102×D59C2semidirect
10. C22⋊C8×D59C2semidirect
11. C59×#481C2semidirect
22. C2×C4⋊Dic59C22semidirect
28. C4⋊C4×D59C22semidirect
30. #14273659C22semidirect
31. #14273658C22semidirect
32. #14273658C22semidirect
33. #14273649C22semidirect
34. #14273648C22semidirect
35. #14273647C22semidirect
36. C22⋊(C59⋊C8)C22semidirect
37. (C2×D59)⋊C8C22semidirect
39. C2×C4⋊C4×C59C22semidirect
40. #106×C59C22semidirect
41. #102×C59C22semidirect
42. C22⋊C8×C59C22semidirect
156. D59#481direct (N × H)
164. #481D59direct (N × H)
168. C59C2×#481semidirect
187. C2×C4⋊C4C2×D59semidirect
192. #106C2×D59semidirect
196. #102C2×D59semidirect
199. C22⋊C8C2×D59semidirect