Finite Group Databasebeta

← #21436338

Subgroups — #21436338

Order 7552.

460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 125 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#16837748C211yesmaximal, characteristic, complemented
3#16837723C212yesmaximal, complemented
4#16837692C211yesmaximal, characteristic, complemented
5#16837653C212yesmaximal, complemented
6#16837594C211yesmaximal, characteristic, complemented
7#16837536C212yesmaximal, complemented
8C4×#11745669C211yesmaximal, characteristic, complemented
9#16837480C211yesmaximal, characteristic, complemented
10#16837407C212yesmaximal, complemented
11D42×C59C211yesmaximal, characteristic, complemented
12C2×#11745669C2211yescharacteristic
13C2×#11745669C2212yescomplemented
14C2×#11745664C2212yescomplemented
15#14273727C2211yescharacteristic, complemented
16#14273713—22no—
17#14273701C2212yescomplemented
18#14273698—21no—
19C4×D236C2211yescharacteristic, complemented
20#14273686C2212yescomplemented
21#14273685—21no—
22#14273660C2211yescharacteristic, complemented
23#14273658C2212yescomplemented
24C4⋊(C59⋊C8)C2211yescharacteristic, complemented
25#14273648C2211yescharacteristic
26#14273648C2212yes—
27#14273648C2212yescomplemented
28#14273648C2212yescomplemented
29#14273648C2212yescomplemented
30#14273647C2211yescharacteristic, complemented
31C22⋊(C59⋊C8)C2212yescomplemented
32C4×C59⋊C8C2211yescharacteristic, complemented
33C22×D4×C59—21no—
34C22×D4×C59C2212yes—
35#127×C59C2211yescharacteristic
36#121×C59—21no—
37#121×C59C2212yes—
38#120×C59—22no—
39C4×D4×C59C2211yescharacteristic
40C4×D4×C59C2211yescharacteristic
41C24×C59—22no—
42C2×D4×C59—24no—
43C2×D4×C59—22no—
44C2×D4×C59—22no—
45C2×D4×C59—21no—
46C2×D4×C59—21no—
47C2×D4×C59—42no—
48C2×D4×C59—44no—
49C2×D4×C59D411yescharacteristic
50C2×D4×C59C2312yes—
51C2×D4×C59C2311yescharacteristic
52C22×C4×C59—21no—
53C22×C4×C59C2312yes—
54C2×C22⋊D59—22no—
55C2×D236C2311yescharacteristic
56C2×C4×D59—21no—
57C2×Dic118—21no—
58C4⋊C4×C59D411yescharacteristic
59C4⋊C4×C59C2311yescharacteristic
60C22⋊C4×C59—21no—
61C22⋊C4×C59—22no—
62C22⋊C4×C59D412yes—
63C42×C59C2311yescharacteristic
64C22⋊Dic59—22no—
65#11745669—22no—
66#11745669—42no—
67(C2×D59)⋊C4—22no—
68(C2×D59)⋊C4—21no—
69C4⋊Dic59—21no—
70C4⋊Dic59C2312yes—
71C4⋊Dic59C2311yescharacteristic
72C4×Dic59—22no—
73#11745664—42no—
74C2×C59⋊C8C2311yescharacteristic
75C2×C59⋊C8C2311yescharacteristic
76C2×C59⋊C8C2312yes—
77C23×C59—21no—
78C23×C59—22no—
79C23×C59—44no—
80C23×C59—44no—
81C23×C59—82no—
82C23×C59C2×D412yes—
83C22×D59—21no—
84D4×C59—22no—
85D4×C59—22no—
86D4×C59—21no—
87D4×C59—22no—
88D4×C59—44no—
89D4×C59—44no—
90D4×C59—42no—
91D4×C59—81no—
92D4×C59#4112yes—
93C2×C4×C59—22no—
94C2×C4×C59—22no—
95C2×C4×C59—21no—
96C2×C4×C59—42no—
97C2×C4×C59C2×D412yes—
98C2×C4×C59C2×D411yescharacteristic
99C2×C4×C59C2×D411yescharacteristic
100C2×C4×C59C2411yescharacteristic
101C22⋊D59—82no—
102C2×Dic59—21no—
103C2×Dic59—22no—
104D236—21no—
105D236—21no—
106C4×D59—42no—
107Dic118—81no—
108C59⋊C8—21no—
109C59⋊C8—21no—
110C59⋊C8—22no—
111C22×C59—22no—
112C22×C59—22no—
113C22×C59—22no—
114C22×C59—22no—
115C22×C59—41no—
116C22×C59—41no—
117C22×C59—42no—
118C22×C59—42no—
119C22×C59—42no—
120C22×C59—88no—
121C22×C59C22×D411yescharacteristic
122C2×D59—41no—
123C2×D59—41no—
124C2×D59—41no—
125C4×C59—22no—
126C4×C59—21no—
127C4×C59—41no—
128C4×C59AGL(1,ℤ/8)12yes—
129C4×C59C2×#4111yescharacteristic
130C4×C59H(5,𝔽2)11yescharacteristic
131Dic59—41no—
132Dic59—42no—
133#3325—591nomaximal, Sylow
134C2×C59—42no—
135C2×C59—42no—
136C2×C59—82no—
137C2×C59#54611yescharacteristic
138C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
139C2×C59#57611yescharacteristic
140D59—81no—
141#555—591no—
142D42D5911yescharacteristic, complemented
143#486—591no—
144#482—592no—
145#476—591no—
146#469—592no—
147#459—591no—
148#447—592no—
149C4×D8—591no—
150#436—591no—
151#418—592no—
152C59#332511yescharacteristic, complemented, Sylow
153C22×D4—21no—
154C22×D4C2×D5912yes—
155C2×D8—591no—
156C2×D8—592no—
157C2×M16—592no—
158C4⋊Q8—591no—
159#127C2×D5911yescharacteristic
160#124—1182no—
161#121—21no—
162#121—592no—
163#121—1181no—
164#121C2×D5912yes—
165#120—22no—
166C4×D4—591no—
167C4×D4C2×D5911yescharacteristic
168C4×D4C2×D5911yescharacteristic
169#117—592no—
170#117—1181no—
171#107—591no—
172#106—592no—
173C4⋊C8—591no—
174#102—591no—
175#102—592no—
176#102—592no—
177#102—592no—
178#102—592no—
179#102—591no—
180C22⋊C8—592no—
181C4×C8—591no—
182C24—22no—
183C2×Q8—1181no—
184C2×D4—24no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—42no—
190C2×D4—44no—
191C2×D4—591no—
192C2×D4—1182no—
193C2×D4C22⋊D5911yescharacteristic
194C2×D4C22×D5912yes—
195C2×D4C22×D5911yescharacteristic
196C22×C4—21no—
197C22×C4—1181no—
198C22×C4C22×D5912yes—
199D8—1182no—
200D8—2362no—
201M16—2362no—
202C2×C8—591no—
203C2×C8—591no—
204C2×C8—592no—
205C4⋊C4—592no—
206C4⋊C4—591no—
207C4⋊C4—1181no—
208C4⋊C4C22⋊D5911yescharacteristic
209C4⋊C4C22×D5911yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—22no—
212C22⋊C4—1182no—
213C22⋊C4—1182no—
214C22⋊C4—1181no—
215C22⋊C4C22⋊D5912yes—
216C42—1182no—
217C42C22×D5911yescharacteristic
218C23—21no—
219C23—22no—
220C23—44no—
221C23—44no—
222C23—82no—
223C23—1181no—
224C23C2×C22⋊D5912yes—
225Q8—4721no—
226D4—22no—
227D4—22no—
228D4—21no—
229D4—22no—
230D4—44no—
231D4—44no—
232D4—42no—
233D4—81no—
234D4—1181no—
235D4—1181no—
236D4—4722no—
237D4#1174568712yes—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—1181no—
243C2×C4—1182no—
244C2×C4—2362no—
245C2×C4C2×C22⋊D5912yes—
246C2×C4C2×C22⋊D5911yescharacteristic
247C2×C4C2×C22⋊D5911yescharacteristic
248C2×C4C23×D5911yescharacteristic
249C8—1181no—
250C8—1181no—
251C8—1182no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—41no—
257C22—41no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—88no—
262C22—2361no—
263C22—2361no—
264C22—2361no—
265C22C22×C22⋊D5911yescharacteristic
266C4—21no—
267C4—22no—
268C4—41no—
269C4—2361no—
270C4—2362no—
271C4#1427375312yes—
272C4C2×#1174568711yescharacteristic
273C4#1427377211yescharacteristic
274C2—42no—
275C2—42no—
276C2—82no—
277C2—4721no—
278C2#1683804611yescharacteristic
279C2C2×#1427375311yescharacteristic
280C2#1683820511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingD42×C59C2
socleC22×C59C22×D4
hypercenterD42D59
hypocenterC59#3325
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #16838117C2semidirect
2. #16837748C2semidirect
3. #16837723C2semidirect
4. #16837692C2semidirect
5. #16837653C2semidirect
6. #16837594C2semidirect
7. #16837536C2semidirect
8. C4×#11745669C2semidirect
9. #16837480C2semidirect
10. #16837407C2semidirect
11. D42×C59C2semidirect
13. C2×#11745669C22semidirect
14. C2×#11745664C22semidirect
15. #14273727C22semidirect
17. #14273701C22semidirect
19. C4×D236C22semidirect
20. #14273686C22semidirect
22. #14273660C22semidirect
23. #14273658C22semidirect
24. C4⋊(C59⋊C8)C22semidirect
27. #14273648C22semidirect
28. #14273648C22semidirect
29. #14273648C22semidirect
30. #14273647C22semidirect
31. C22⋊(C59⋊C8)C22semidirect
32. C4×C59⋊C8C22semidirect
142. D42D59semidirect
152. C59#3325semidirect