Finite Group Databasebeta

← #21435078

Subgroups — #21435078

Order 7552.

444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 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#16837950C211yesmaximal, characteristic, complemented
2#124×D59C211yesmaximal, characteristic, complemented
3#16837789C211yesmaximal, characteristic, complemented
4#16837762C211yesmaximal, characteristic, complemented
5#16837761C211yesmaximal, characteristic, complemented
6#16837619C212yesmaximal, complemented
7#16837615C212yesmaximal, complemented
8#16837539C212yesmaximal, complemented
9#16837534C212yesmaximal, complemented
10#16837457C211yesmaximal, characteristic, complemented
11C59×#496C211yesmaximal, characteristic, complemented
12C2×#11745687—21no—
13C2×Q8×D59C2211yescharacteristic
14C2×D4×D59C2211yescharacteristic
15C2×#11745670C2212yescomplemented
16C2×#11745669C2212yes—
17#14273727C2211yescharacteristic, complemented
18#14273716C2211yescharacteristic
19#14273715C2211yescharacteristic
20#14273714—21no—
21#14273714C2211yescharacteristic
22#14273713—21no—
23#14273713—21no—
24#14273698—21no—
25#14273698C2212yes—
26D4×Dic59—21no—
27D4×Dic59C2212yescomplemented
28C22⋊C4×D59—21no—
29C22⋊C4×D59—21no—
30C42×D59C2211yescharacteristic
31Dic59⋊C8C2212yescomplemented
32#14273652C2212yescomplemented
33#14273651C2212yescomplemented
34#14273649C2212yes—
35#14273648C2212yes—
36(C2×D59)⋊C8C2212yes—
37#14273638C2211yescharacteristic, complemented
38C2×SD16×C59C2212yescomplemented
39C2×D8×C59C2212yes—
40#127×C59C2211yescharacteristic, complemented
41#124×C59C2211yescharacteristic
42#97×C59C2211yescharacteristic, complemented
43C23×D59—21no—
44C2×Q8×C59C2311yescharacteristic
45C2×D4×C59—21no—
46C2×D4×C59—21no—
47C2×D4×C59C2311yescharacteristic
48C2×D4×C59C2312yes—
49C2×C22⋊D59—22no—
50C2×C22⋊D59—21no—
51C22×Dic59—22no—
52Q8×D59—42no—
53#11745687—44no—
54D4×D59—42no—
55C2×D236C2311yescharacteristic
56C2×C4×D59—21no—
57C2×C4×D59D411yescharacteristic
58C2×C4×D59D411yescharacteristic
59C2×C4×D59C2311yescharacteristic
60C2×Dic118—21no—
61C2×Dic118—21no—
62C2×Dic118C2311yescharacteristic
63SD16×C59—42no—
64D8×C59—42no—
65C2×C8×C59C2312yes—
66C22⋊C4×C59—21no—
67C22⋊C4×C59—21no—
68C42×C59C2311yescharacteristic
69C22⋊Dic59—21no—
70C22⋊Dic59—21no—
71C22⋊Dic59—22no—
72C22⋊Dic59—22no—
73#11745670—42no—
74#11745669—42no—
75(C2×D59)⋊C4—21no—
76(C2×D59)⋊C4—21no—
77(C2×D59)⋊C4—21no—
78(C2×D59)⋊C4—21no—
79C4⋊Dic59—21no—
80C4⋊Dic59C2312yes—
81C4×Dic59D411yescharacteristic
82C4×Dic59D411yescharacteristic
83C4×Dic59C2311yescharacteristic
84C2×C59⋊C8C2312yes—
85C23×C59—21no—
86C23×C59—22no—
87C22×D59—21no—
88C22×D59—42no—
89C22×D59—42no—
90C22×D59—42no—
91C22×D59C2×D411yescharacteristic
92Q8×C59—22no—
93D4×C59—22no—
94D4×C59—22no—
95D4×C59—22no—
96D4×C59—42no—
97D4×C59—42no—
98C2×C4×C59—21no—
99C2×C4×C59C2×D411yescharacteristic
100C2×C4×C59C2×D411yescharacteristic
101C2×C4×C59C2411yescharacteristic
102C22⋊D59—42no—
103C22⋊D59—44no—
104C2×Dic59—22no—
105C2×Dic59—21no—
106C2×Dic59—44no—
107C2×Dic59C2×D411yescharacteristic
108C2×Dic59C2×D411yescharacteristic
109C2×Dic59C2×D411yescharacteristic
110D236—22no—
111C4×D59—22no—
112C4×D59—22no—
113C4×D59—41no—
114C4×D59—42no—
115Dic118—22no—
116Dic118—42no—
117Dic118—42no—
118C8×C59—22no—
119C59⋊C8—22no—
120C22×C59—41no—
121C22×C59—42no—
122C22×C59—42no—
123C22×C59—41no—
124C22×C59—42no—
125C22×C59—41no—
126C22×C59C22×D411yescharacteristic
127C2×D59—21no—
128C2×D59—21no—
129C2×D59—41no—
130C2×D59—41no—
131C2×D59—41no—
132C2×D59—84no—
133C2×D59AGL(1,ℤ/8)12yes—
134C4×C59—21no—
135C4×C59—21no—
136C4×C59—41no—
137C4×C59H(5,𝔽2)12yes—
138Dic59—21no—
139Dic59—21no—
140Dic59—21no—
141Dic59—41no—
142Dic59—42no—
143#3213—591nomaximal, Sylow
144C2×C59—81no—
145C2×C59—82no—
146C2×C59#53511yescharacteristic
147C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
148C2×C59#57511yescharacteristic
149D59—22no—
150D59—81no—
151#532—591no—
152C2×#124—591no—
153#496—591no—
154#496D5911yescharacteristic, complemented
155#489—591no—
156#489—591no—
157#463—592no—
158#463—592no—
159#448—592no—
160#447—592no—
161#432—591no—
162C59#321311yescharacteristic, complemented, Sylow
163C2×#41—1181no—
164C22×Q8—591no—
165C22×D4—591no—
166C2×SD16—592no—
167C2×SD16C2×D5912yescomplemented
168C2×D8—592no—
169C2×D8C2×D5912yes—
170C4⋊Q8—591no—
171#127C2×D5911yescharacteristic, complemented
172#124—591no—
173#124—591no—
174#124—591no—
175#124—1181no—
176#124—1181no—
177#124—1181no—
178#124C2×D5911yescharacteristic
179#121—592no—
180#121—1181no—
181C4×D4—592no—
182C4×D4—1181no—
183C2×C22⋊C4—1181no—
184C2×C22⋊C4—1181no—
185C2×C42—591no—
186C4⋊C8—592no—
187#103—592no—
188#103—592no—
189#102—592no—
190#102—592no—
191C22⋊C8—592no—
192#97—591no—
193#97C2×D5911yescharacteristic, complemented
194C24—1181no—
195#41—2364no—
196C2×Q8—591no—
197C2×Q8—1181no—
198C2×Q8—1181no—
199C2×Q8—2362no—
200C2×Q8C22×D5911yescharacteristic
201C2×D4—21no—
202C2×D4—21no—
203C2×D4—591no—
204C2×D4—1181no—
205C2×D4—1182no—
206C2×D4—2362no—
207C2×D4C22×D5911yescharacteristic
208C2×D4C22×D5912yes—
209C22×C4—591no—
210C22×C4—591no—
211C22×C4—591no—
212C22×C4—1181no—
213C22×C4—1182no—
214SD16—42no—
215SD16—2362no—
216D8—42no—
217D8—2362no—
218C2×C8—592no—
219C2×C8C22×D5912yes—
220C4⋊C4—592no—
221C4⋊C4—1181no—
222C22⋊C4—21no—
223C22⋊C4—21no—
224C22⋊C4—1181no—
225C22⋊C4—1181no—
226C22⋊C4—1181no—
227C22⋊C4—1181no—
228C22⋊C4—1182no—
229C22⋊C4—1182no—
230C22⋊C4—1181no—
231C22⋊C4—1181no—
232C42—591no—
233C42—591no—
234C42—591no—
235C42C22×D5911yescharacteristic
236C23—21no—
237C23—22no—
238C23—591no—
239C23—1181no—
240C23—2362no—
241C23—2362no—
242C23—2362no—
243Q8—22no—
244Q8—1182no—
245Q8—2362no—
246Q8—2362no—
247D4—22no—
248D4—22no—
249D4—22no—
250D4—42no—
251D4—42no—
252D4—1182no—
253D4—2362no—
254D4—2364no—
255C2×C4—21no—
256C2×C4—591no—
257C2×C4—591no—
258C2×C4—591no—
259C2×C4—1182no—
260C2×C4—1182no—
261C2×C4—1181no—
262C2×C4—1182no—
263C2×C4—2361no—
264C2×C4—2362no—
265C2×C4—2364no—
266C2×C4D4×D5911yescharacteristic
267C2×C4D4×D5911yescharacteristic
268C2×C4C23×D5911yescharacteristic
269C8—22no—
270C8—1182no—
271C22—42no—
272C22—41no—
273C22—42no—
274C22—41no—
275C22—41no—
276C22—42no—
277C22—592no—
278C22—1181no—
279C22—1181no—
280C22—4724no—
281C22—2361no—
282C22—2361no—
283C22—2361no—
284C22C2×D4×D5911yescharacteristic
285C4—21no—
286C4—21no—
287C4—41no—
288C4—1181no—
289C4—1181no—
290C4—1181no—
291C4—2362no—
292C4—2361no—
293C4#1427377212yes—
294C2—81no—
295C2—82no—
296C2—1182no—
297C2—4721no—
298C2#1683796511yescharacteristic
299C2AGL(1,ℤ/8)×D5911yescharacteristic
300C2#1683819811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#496C2
socleC22×C59C22×D4
hypercenter#496D59
hypocenterC59#3213
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #16837950C2semidirect
2. #124×D59C2semidirect
3. #16837789C2semidirect
4. #16837762C2semidirect
5. #16837761C2semidirect
6. #16837619C2semidirect
7. #16837615C2semidirect
8. #16837539C2semidirect
9. #16837534C2semidirect
10. #16837457C2semidirect
11. C59×#496C2semidirect
15. C2×#11745670C22semidirect
17. #14273727C22semidirect
27. D4×Dic59C22semidirect
31. Dic59⋊C8C22semidirect
32. #14273652C22semidirect
33. #14273651C22semidirect
37. #14273638C22semidirect
38. C2×SD16×C59C22semidirect
40. #127×C59C22semidirect
42. #97×C59C22semidirect
154. #496D59semidirect
162. C59#3213semidirect
167. C2×SD16C2×D59semidirect
171. #127C2×D59semidirect
193. #97C2×D59semidirect