Finite Group Databasebeta

← #21435036

Subgroups — #21435036

Order 7552.

488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 123 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#16837956C211yesmaximal, characteristic, complemented
2#127×D59C211yesmaximal, characteristic
3#16837773C212yesmaximal, complemented
4#16837747C212yesmaximal, complemented
5#16837603C211yesmaximal, characteristic, complemented
6#16837602C211yesmaximal, characteristic, complemented
7#16837599C211yesmaximal, characteristic, complemented
8#16837554C212yesmaximal, complemented
9#16837551C212yesmaximal, complemented
10#16837454C211yesmaximal, characteristic, complemented
11C59×#460C211yesmaximal, characteristic, complemented
12C2×D4×D59—21no—
13C2×D4×D59—21no—
14C2×D4×D59C2212yes—
15C2×#11745660C2212yescomplemented
16C2×#11745670C2212yescomplemented
17C2×#11745671C2212yescomplemented
18#14273726C2211yescharacteristic, complemented
19#14273725C2211yescharacteristic, complemented
20#14273724C2211yescharacteristic
21#14273723—21no—
22#14273723—21no—
23#14273723C2212yes—
24#14273717—21no—
25#14273707C2211yescharacteristic
26#14273705—21no—
27#14273703C2211yescharacteristic
28C4×Dic118—21no—
29C4×Dic118C2211yescharacteristic, complemented
30#14273684—21no—
31C42×D59C2211yescharacteristic
32C4⋊(C59⋊C8)C2211yescharacteristic, complemented
33#14273649C2212yescomplemented
34#14273648C2212yescomplemented
35#14273647C2212yescomplemented
36(C2×D59)⋊C8C2212yes—
37C8×Dic59C2212yescomplemented
38C2×SD16×C59C2212yescomplemented
39#127×C59C2211yescharacteristic
40C4×Q8×C59C2211yescharacteristic, complemented
41C4⋊C8×C59C2211yescharacteristic, complemented
42#102×C59C2212yescomplemented
43C23×D59—22no—
44C2×Q8×C59C2311yescharacteristic
45C2×D4×C59—21no—
46C2×D4×C59—21no—
47C2×D4×C59C2312yes—
48C2×C22⋊D59—22no—
49C2×C22⋊D59—22no—
50C2×C22⋊D59—22no—
51D4×D59—42no—
52D4×D59—42no—
53D4×D59—44no—
54D4×D59—44no—
55C2×D236—21no—
56C2×D236—21no—
57C2×D236C2312yes—
58C2×C4×D59D411yescharacteristic
59C2×C4×D59D411yescharacteristic
60C2×C4×D59C2311yescharacteristic
61C2×Dic118—21no—
62C2×Dic118C2311yescharacteristic
63SD16×C59—42no—
64C2×C8×C59C2312yes—
65C4⋊C4×C59—21no—
66C4⋊C4×C59C2311yescharacteristic
67C42×C59—21no—
68C42×C59C2311yescharacteristic
69#11745671—42no—
70#11745670—42no—
71(C2×D59)⋊C4—21no—
72(C2×D59)⋊C4—21no—
73C4⋊Dic59—21no—
74C4⋊Dic59C2311yescharacteristic
75Dic59⋊C4—21no—
76Dic59⋊C4—21no—
77Dic59⋊C4—21no—
78Dic59⋊C4—21no—
79Dic59⋊C4—21no—
80C4×Dic59—21no—
81C4×Dic59D411yescharacteristic
82C4×Dic59D411yescharacteristic
83C4×Dic59C2311yescharacteristic
84C2×C59⋊C8C2312yes—
85#11745660—42no—
86C23×C59—22no—
87C22×D59—22no—
88C22×D59—44no—
89C22×D59—44no—
90C22×D59—44no—
91C22×D59C2×D411yescharacteristic
92Q8×C59—21no—
93Q8×C59—21no—
94D4×C59—22no—
95D4×C59—22no—
96D4×C59—42no—
97D4×C59—42no—
98C2×C4×C59—21no—
99C2×C4×C59—21no—
100C2×C4×C59C2×D411yescharacteristic
101C2×C4×C59C2×D411yescharacteristic
102C2×C4×C59C2411yescharacteristic
103C22⋊D59—44no—
104C22⋊D59—44no—
105C22⋊D59—44no—
106C2×Dic59—21no—
107C2×Dic59—21no—
108C2×Dic59C2×D411yescharacteristic
109C2×Dic59C2×D411yescharacteristic
110C2×Dic59C2×D411yescharacteristic
111D236—22no—
112D236—22no—
113D236—42no—
114D236—42no—
115C4×D59—21no—
116C4×D59—21no—
117C4×D59—22no—
118C4×D59SD1614yescomplemented
119Dic118—21no—
120Dic118—21no—
121Dic118—42no—
122C8×C59—22no—
123C59⋊C8—22no—
124C22×C59—42no—
125C22×C59—42no—
126C22×C59—42no—
127C22×C59C22×D411yescharacteristic
128C2×D59—21no—
129C2×D59—21no—
130C2×D59—42no—
131C2×D59—42no—
132C2×D59—42no—
133C2×D59—88no—
134C2×D59C2×SD1612yes—
135C4×C59—21no—
136C4×C59—41no—
137C4×C59—41no—
138C4×C59C2×SD1612yes—
139C4×C59H(5,𝔽2)11yescharacteristic
140C4×C59H(5,𝔽2)11yescharacteristic
141Dic59—21no—
142Dic59—41no—
143Dic59—41no—
144Dic59C2×SD1612yes—
145Dic59AGL(1,ℤ/8)12yes—
146#3208—591nomaximal, Sylow
147C2×C59—82no—
148C2×C59#53511yescharacteristic
149C2×C59C22×SD1611yescharacteristic
150C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
151D59—22no—
152D59—82no—
153#533—591no—
154C2×#127—591no—
155#492—592no—
156#486—592no—
157#460—591no—
158#460—591no—
159#460—591no—
160#460D5911yescharacteristic, complemented
161#450—592no—
162#450—592no—
163#431—591no—
164C59#320811yescharacteristic, complemented, Sylow
165C22×D4—592no—
166C22×D4—1181no—
167C22×D4—1181no—
168C2×SD16—592no—
169C2×SD16—592no—
170C2×SD16—592no—
171C2×SD16C2×D5912yescomplemented
172C4⋊Q8—591no—
173C4⋊Q8—591no—
174#127—592no—
175#127—591no—
176#127—1181no—
177#127—1181no—
178#127C2×D5911yescharacteristic
179#125—1181no—
180C22⋊Q8—591no—
181C22⋊Q8—591no—
182C22⋊Q8—1181no—
183C4×Q8—591no—
184C4×Q8—1181no—
185C4×Q8C2×D5911yescharacteristic, complemented
186#117—1181no—
187C2×C42—591no—
188C4⋊C8—591no—
189C4⋊C8C2×D5911yescharacteristic, complemented
190#102—592no—
191#102—592no—
192#102—592no—
193#102C2×D5912yescomplemented
194C22⋊C8—592no—
195C4×C8—592no—
196C24—1182no—
197C2×Q8—591no—
198C2×Q8—1181no—
199C2×Q8C22×D5911yescharacteristic
200C2×D4—21no—
201C2×D4—21no—
202C2×D4—592no—
203C2×D4—1182no—
204C2×D4—1182no—
205C2×D4—1182no—
206C2×D4—1181no—
207C2×D4—1181no—
208C2×D4—2364no—
209C2×D4—2362no—
210C2×D4—2362no—
211C2×D4—2364no—
212C2×D4C22×D5912yes—
213C22×C4—591no—
214C22×C4—591no—
215C22×C4—591no—
216SD16—42no—
217SD16—2362no—
218SD16—2362no—
219SD16—2362no—
220C2×C8—592no—
221C2×C8C22×D5912yes—
222C4⋊C4—21no—
223C4⋊C4—591no—
224C4⋊C4—1181no—
225C4⋊C4—1181no—
226C4⋊C4—1181no—
227C4⋊C4—1181no—
228C4⋊C4—1181no—
229C4⋊C4—1181no—
230C4⋊C4C22×D5911yescharacteristic
231C22⋊C4—1181no—
232C22⋊C4—1181no—
233C42—21no—
234C42—591no—
235C42—591no—
236C42—591no—
237C42—1181no—
238C42C22×D5911yescharacteristic
239C23—22no—
240C23—591no—
241C23—1182no—
242C23—2364no—
243C23—2364no—
244C23—2364no—
245Q8—21no—
246Q8—21no—
247Q8—1181no—
248Q8—1181no—
249Q8—2362no—
250D4—22no—
251D4—22no—
252D4—42no—
253D4—42no—
254D4—1182no—
255D4—1182no—
256D4—2362no—
257D4—2364no—
258D4—2364no—
259D4—2364no—
260D4—2362no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—591no—
264C2×C4—591no—
265C2×C4—594no—
266C2×C4—591no—
267C2×C4—1182no—
268C2×C4—1181no—
269C2×C4—1181no—
270C2×C4—1181no—
271C2×C4—1181no—
272C2×C4D4×D5911yescharacteristic
273C2×C4D4×D5911yescharacteristic
274C2×C4C23×D5911yescharacteristic
275C8—22no—
276C8—1182no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—592no—
281C22—1181no—
282C22—1181no—
283C22—4728no—
284C22—2362no—
285C22—2362no—
286C22—2362no—
287C22C2×D4×D5911yescharacteristic
288C4—21no—
289C4—41no—
290C4—41no—
291C4—592no—
292C4—592no—
293C4—1181no—
294C4—2361no—
295C4—2361no—
296C4SD16×D5912yes—
297C4#1427377211yescharacteristic
298C4#1427377311yescharacteristic
299C2—82no—
300C2—1182no—
301C2—4722no—
302C2#1683796811yescharacteristic
303C2C2×SD16×D5911yescharacteristic
304C2AGL(1,ℤ/8)×D5911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#460C2
socleC22×C59C22×D4
hypercenter#460D59
hypocenterC59#3208
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #16837956C2semidirect
3. #16837773C2semidirect
4. #16837747C2semidirect
5. #16837603C2semidirect
6. #16837602C2semidirect
7. #16837599C2semidirect
8. #16837554C2semidirect
9. #16837551C2semidirect
10. #16837454C2semidirect
11. C59×#460C2semidirect
15. C2×#11745660C22semidirect
16. C2×#11745670C22semidirect
17. C2×#11745671C22semidirect
18. #14273726C22semidirect
19. #14273725C22semidirect
29. C4×Dic118C22semidirect
32. C4⋊(C59⋊C8)C22semidirect
33. #14273649C22semidirect
34. #14273648C22semidirect
35. #14273647C22semidirect
37. C8×Dic59C22semidirect
38. C2×SD16×C59C22semidirect
40. C4×Q8×C59C22semidirect
41. C4⋊C8×C59C22semidirect
42. #102×C59C22semidirect
118. C4×D59SD16semidirect
160. #460D59semidirect
164. C59#3208semidirect
171. C2×SD16C2×D59semidirect
185. C4×Q8C2×D59semidirect
189. C4⋊C8C2×D59semidirect
193. #102C2×D59semidirect