Finite Group Databasebeta

← #21436341

Subgroups — #21436341

Order 7552.

460 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 115 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#16838117C211yesmaximal, characteristic, complemented
2#16838037C211yesmaximal, characteristic, complemented
3#16837748C211yesmaximal, characteristic, complemented
4#16837725C212yesmaximal, complemented
5#16837693C211yesmaximal, characteristic, complemented
6#16837652C212yesmaximal, complemented
7#16837534C212yesmaximal, complemented
8C4×#11745669C211yesmaximal, characteristic, complemented
9#16837479C211yesmaximal, characteristic, complemented
10#16837405C212yesmaximal, complemented
11C59×#459C211yesmaximal, characteristic, complemented
12C2×D4×D59—21no—
13C2×D4×D59C2212yes—
14C2×#11745669C2211yescharacteristic
15C2×#11745659C2212yescomplemented
16#14273727C2211yescharacteristic, complemented
17#14273713—22no—
18#14273701—21no—
19#14273698—21no—
20#14273698C2212yes—
21#14273698C2212yescomplemented
22#14273695—22no—
23C4×D236C2211yescharacteristic
24C4×D236C2211yescharacteristic
25#14273686—21no—
26#14273685C2212yescomplemented
27#14273660C2211yescharacteristic, complemented
28#14273659C2212yescomplemented
29#14273649C2212yes—
30#14273648C2211yescharacteristic, complemented
31#14273648C2212yescomplemented
32#14273648C2212yescomplemented
33#14273647C2211yescharacteristic
34(C2×D59)⋊C8C2212yescomplemented
35C4×C59⋊C8C2211yescharacteristic, complemented
36C2×D8×C59C2212yescomplemented
37#127×C59C2211yescharacteristic
38C4×D4×C59C2211yescharacteristic, complemented
39C4⋊C8×C59C2211yescharacteristic, complemented
40#102×C59C2212yescomplemented
41C23×D59—22no—
42C2×D4×C59—21no—
43C2×D4×C59—21no—
44C2×D4×C59C2312yes—
45C2×D4×C59C2311yescharacteristic
46C22×C4×C59—21no—
47C2×C22⋊D59—22no—
48C2×C22⋊D59—22no—
49C2×C22⋊D59—22no—
50D4×D59—24no—
51D4×D59—42no—
52D4×D59—44no—
53C2×D236D411yescharacteristic
54C2×D236C2311yescharacteristic
55C2×C4×D59—21no—
56C2×C4×D59C2312yes—
57C2×Dic118—21no—
58D8×C59—42no—
59C2×C8×C59C2312yes—
60C4⋊C4×C59C2311yescharacteristic
61C22⋊C4×C59—21no—
62C42×C59C2311yescharacteristic
63C22⋊Dic59—22no—
64C22⋊Dic59—22no—
65#11745669—22no—
66(C2×D59)⋊C4—22no—
67(C2×D59)⋊C4—21no—
68(C2×D59)⋊C4D412yes—
69C4⋊Dic59—21no—
70C4⋊Dic59D411yescharacteristic
71C4⋊Dic59C2312yes—
72C4⋊Dic59C2311yescharacteristic
73C4×Dic59—22no—
74C2×C59⋊C8C2311yescharacteristic
75C2×C59⋊C8C2311yescharacteristic
76#11745659—42no—
77C23×C59—21no—
78C23×C59—22no—
79C22×D59—21no—
80C22×D59—44no—
81C22×D59—44no—
82C22×D59—82no—
83C22×D59C2×D412yes—
84D4×C59—21no—
85D4×C59—22no—
86D4×C59—21no—
87D4×C59—22no—
88D4×C59—42no—
89D4×C59—81no—
90C2×C4×C59—21no—
91C2×C4×C59—42no—
92C2×C4×C59C2×D411yescharacteristic
93C2×C4×C59C2×D411yescharacteristic
94C2×C4×C59C2411yescharacteristic
95C22⋊D59—44no—
96C22⋊D59—44no—
97C22⋊D59—82no—
98C2×Dic59—22no—
99C2×Dic59—21no—
100C2×Dic59C2×D412yes—
101D236—22no—
102D236—21no—
103D236#4112yes—
104C4×D59—22no—
105C4×D59—22no—
106C4×D59—42no—
107Dic118—81no—
108C8×C59—22no—
109C59⋊C8—21no—
110C59⋊C8—21no—
111C22×C59—42no—
112C22×C59—41no—
113C22×C59—42no—
114C22×C59—41no—
115C22×C59—41no—
116C22×C59—42no—
117C22×C59C22×D411yescharacteristic
118C2×D59—22no—
119C2×D59—22no—
120C2×D59—22no—
121C2×D59—22no—
122C2×D59—41no—
123C2×D59—41no—
124C2×D59—88no—
125C4×C59—21no—
126C4×C59—41no—
127C4×C59AGL(1,ℤ/8)12yes—
128C4×C59C2×#4111yescharacteristic
129C4×C59H(5,𝔽2)11yescharacteristic
130Dic59—22no—
131Dic59—41no—
132Dic59—42no—
133#3325—591nomaximal, Sylow
134C2×C59—82no—
135C2×C59—81no—
136C2×C59#54611yescharacteristic
137C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C59#57611yescharacteristic
139D59—42no—
140D59—42no—
141#555—591no—
142D42—591no—
143#486—591no—
144#482—592no—
145#476—591no—
146#469—592no—
147#459D5911yescharacteristic, complemented
148#447—592no—
149C4×D8—591no—
150#436—591no—
151#418—592no—
152C59#332511yescharacteristic, complemented, Sylow
153C22×D4—592no—
154C22×D4—1181no—
155C2×D8—591no—
156C2×D8C2×D5912yescomplemented
157C2×M16—592no—
158C4⋊Q8—591no—
159#127C2×D5911yescharacteristic
160#124—1182no—
161#121—592no—
162#121—592no—
163#121—1181no—
164#121—1181no—
165#120—1182no—
166C4×D4—591no—
167C4×D4—591no—
168C4×D4C2×D5911yescharacteristic, complemented
169#117—592no—
170#117—1181no—
171#107—591no—
172#106—592no—
173C4⋊C8C2×D5911yescharacteristic, complemented
174#102—592no—
175#102—591no—
176#102—592no—
177#102—592no—
178#102—591no—
179#102C2×D5912yescomplemented
180C22⋊C8—592no—
181C4×C8—591no—
182C24—1182no—
183C2×Q8—1181no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—591no—
187C2×D4—591no—
188C2×D4—1182no—
189C2×D4—1184no—
190C2×D4—1182no—
191C2×D4—1182no—
192C2×D4—2362no—
193C2×D4—2364no—
194C2×D4C22×D5912yes—
195C2×D4C22×D5911yescharacteristic
196C22×C4—21no—
197C22×C4—592no—
198C22×C4—1181no—
199D8—42no—
200D8—1182no—
201M16—2362no—
202C2×C8—591no—
203C2×C8—591no—
204C2×C8C22×D5912yes—
205C4⋊C4—591no—
206C4⋊C4—592no—
207C4⋊C4—591no—
208C4⋊C4—1181no—
209C4⋊C4C22×D5911yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—592no—
212C22⋊C4—1182no—
213C22⋊C4—1182no—
214C22⋊C4—1182no—
215C22⋊C4—1181no—
216C42—1182no—
217C42C22×D5911yescharacteristic
218C23—21no—
219C23—22no—
220C23—592no—
221C23—1181no—
222C23—4722no—
223C23—2364no—
224C23—2364no—
225Q8—4721no—
226D4—21no—
227D4—22no—
228D4—21no—
229D4—22no—
230D4—42no—
231D4—81no—
232D4—592no—
233D4—1182no—
234D4—1181no—
235D4—4722no—
236D4—2364no—
237D4—2364no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—592no—
241C2×C4—1182no—
242C2×C4—1182no—
243C2×C4—1182no—
244C2×C4—1181no—
245C2×C4—2362no—
246C2×C4D4×D5911yescharacteristic
247C2×C4D4×D5911yescharacteristic
248C2×C4C23×D5911yescharacteristic
249C8—22no—
250C8—1181no—
251C8—1181no—
252C22—41no—
253C22—42no—
254C22—42no—
255C22—41no—
256C22—42no—
257C22—41no—
258C22—1182no—
259C22—1182no—
260C22—1182no—
261C22—1182no—
262C22—4728no—
263C22—2361no—
264C22—2361no—
265C22C2×D4×D5911yescharacteristic
266C4—21no—
267C4—41no—
268C4—1182no—
269C4—2361no—
270C4—2362no—
271C4#1427375112yes—
272C4#41×D5911yescharacteristic
273C4#1427377211yescharacteristic
274C2—82no—
275C2—81no—
276C2—2362no—
277C2—2362no—
278C2#1683804911yescharacteristic
279C2C2×#1427375111yescharacteristic
280C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#459C2
socleC22×C59C22×D4
hypercenter#459D59
hypocenterC59#3325
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #16838117C2semidirect
2. #16838037C2semidirect
3. #16837748C2semidirect
4. #16837725C2semidirect
5. #16837693C2semidirect
6. #16837652C2semidirect
7. #16837534C2semidirect
8. C4×#11745669C2semidirect
9. #16837479C2semidirect
10. #16837405C2semidirect
11. C59×#459C2semidirect
15. C2×#11745659C22semidirect
16. #14273727C22semidirect
21. #14273698C22semidirect
26. #14273685C22semidirect
27. #14273660C22semidirect
28. #14273659C22semidirect
30. #14273648C22semidirect
31. #14273648C22semidirect
32. #14273648C22semidirect
34. (C2×D59)⋊C8C22semidirect
35. C4×C59⋊C8C22semidirect
36. C2×D8×C59C22semidirect
38. C4×D4×C59C22semidirect
39. C4⋊C8×C59C22semidirect
40. #102×C59C22semidirect
147. #459D59semidirect
152. C59#3325semidirect
156. C2×D8C2×D59semidirect
168. C4×D4C2×D59semidirect
173. C4⋊C8C2×D59semidirect
179. #102C2×D59semidirect