Finite Group Databasebeta

← #21435692

Subgroups — #21435692

Order 7552.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#14273753C212yesmaximal, complemented
2#16838057C211yesmaximal, characteristic, complemented
3#16837774C211yesmaximal, characteristic, complemented
4#16837646C212yesmaximal, complemented
5#16837607C211yesmaximal, characteristic, complemented
6#16837594C211yesmaximal, characteristic, complemented
7#16837553C212yesmaximal, complemented
8#16837545C212yesmaximal, complemented
9C4×#11745669C211yesmaximal, characteristic, complemented
10#16837480C211yesmaximal, characteristic, complemented
11D42×C59C211yesmaximal, characteristic, complemented
12C2×#11745685C2212yescomplemented
13#14273753—28no—
14C2×#11745670C2212yes—
15C2×#11745670C2212yescomplemented
16C2×#11745670C2212yescomplemented
17C2×#11745669C2211yescharacteristic
18C2×#11745669C2212yescomplemented
19C2×#11745664C2212yescomplemented
20#14273727C2211yescharacteristic, complemented
21#14273709—22no—
22#14273706C2212yescomplemented
23#14273698—21no—
24C4×D236C2211yescharacteristic, complemented
25C4⋊C4×D59—21no—
26#14273660C2211yescharacteristic, complemented
27C4⋊(C59⋊C8)C2211yescharacteristic, complemented
28#14273650C2212yescomplemented
29#14273648C2211yescharacteristic
30#14273648C2212yescomplemented
31#14273647C2211yescharacteristic, complemented
32C22⋊(C59⋊C8)C2212yescomplemented
33C4×C59⋊C8C2211yescharacteristic, complemented
34C22×D4×C59—21no—
35C22×D4×C59C2212yes—
36#127×C59C2211yescharacteristic
37#121×C59—21no—
38#121×C59C2212yes—
39#120×C59—22no—
40C4×D4×C59C2211yescharacteristic
41C4×D4×C59C2211yescharacteristic
42C24×C59—22no—
43C2×D4×C59—24no—
44C2×D4×C59—22no—
45C2×D4×C59—22no—
46C2×D4×C59—21no—
47C2×D4×C59—21no—
48C2×D4×C59—42no—
49C2×D4×C59—44no—
50C2×D4×C59D411yescharacteristic
51C2×D4×C59C2312yes—
52C2×D4×C59C2311yescharacteristic
53C22×C4×C59—21no—
54C22×C4×C59C2312yes—
55C2×C22⋊D59—22no—
56#11745685—24no—
57#11745685—42no—
58C2×D236C2311yescharacteristic
59C2×C4×D59—21no—
60C2×C4×D59—22no—
61C2×Dic118C2312yes—
62C4⋊C4×C59D411yescharacteristic
63C4⋊C4×C59C2311yescharacteristic
64C22⋊C4×C59—21no—
65C22⋊C4×C59—22no—
66C22⋊C4×C59D412yes—
67C42×C59C2311yescharacteristic
68C22⋊Dic59—22no—
69#11745670—24no—
70#11745670—24no—
71#11745670—42no—
72#11745669—24no—
73#11745669D414yescomplemented
74(C2×D59)⋊C4—21no—
75C4⋊Dic59—21no—
76C4⋊Dic59—21no—
77C4⋊Dic59C2311yescharacteristic
78Dic59⋊C4—22no—
79#11745664—24no—
80C2×C59⋊C8C2311yescharacteristic
81C2×C59⋊C8C2312yes—
82C2×C59⋊C8C2311yescharacteristic
83C23×C59—21no—
84C23×C59—22no—
85C23×C59—44no—
86C23×C59—44no—
87C23×C59—82no—
88C23×C59C2×D412yes—
89C22×D59—21no—
90D4×C59—22no—
91D4×C59—22no—
92D4×C59—21no—
93D4×C59—22no—
94D4×C59—44no—
95D4×C59—44no—
96D4×C59—42no—
97D4×C59—81no—
98D4×C59C2×D412yes—
99C2×C4×C59—22no—
100C2×C4×C59—22no—
101C2×C4×C59—21no—
102C2×C4×C59—42no—
103C2×C4×C59C2×D412yes—
104C2×C4×C59C2×D411yescharacteristic
105C2×C4×C59C2×D411yescharacteristic
106C2×C4×C59C2411yescharacteristic
107C22⋊D59—44no—
108C2×Dic59—21no—
109C2×Dic59—22no—
110D236—21no—
111D236C2×D412yescomplemented
112C4×D59—44no—
113C4×D59—42no—
114Dic118—22no—
115Dic118—22no—
116C59⋊C8—22no—
117C59⋊C8—21no—
118C59⋊C8C2×D412yescomplemented
119C22×C59—22no—
120C22×C59—22no—
121C22×C59—22no—
122C22×C59—22no—
123C22×C59—41no—
124C22×C59—41no—
125C22×C59—42no—
126C22×C59—42no—
127C22×C59—42no—
128C22×C59—88no—
129C22×C59C22×D411yescharacteristic
130C2×D59—22no—
131C2×D59—41no—
132C2×D59—41no—
133C4×C59—22no—
134C4×C59—21no—
135C4×C59—41no—
136C4×C59AGL(1,ℤ/8)12yescomplemented
137C4×C59C22×D411yescharacteristic
138C4×C59H(5,𝔽2)11yescharacteristic
139Dic59—42no—
140Dic59—41no—
141#3272—591nomaximal, Sylow
142C2×C59—42no—
143C2×C59—42no—
144C2×C59—82no—
145C2×C59D4211yescharacteristic
146C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
147C2×C59#57711yescharacteristic
148D59—42no—
149C2×AGL(1,ℤ/8)—592no—
150#547—591no—
151D42D5911yescharacteristic, complemented
152#492—591no—
153#468—592no—
154#461—591no—
155#459—591no—
156#450—592no—
157#449—592no—
158C4×D8—591no—
159#436—591no—
160C59#327211yescharacteristic, complemented, Sylow
161C2×#41—592no—
162C22×D4—21no—
163C22×D4C2×D5912yes—
164AGL(1,ℤ/8)—1188no—
165C2×SD16—592no—
166C2×SD16—592no—
167C2×SD16—592no—
168C2×D8—591no—
169C2×D8—592no—
170C2×M16—592no—
171C4⋊Q8—591no—
172#127C2×D5911yescharacteristic
173#123—1182no—
174C22⋊Q8—592no—
175#121—21no—
176#121—1181no—
177#121C2×D5912yes—
178#120—22no—
179C4×D4—591no—
180C4×D4C2×D5911yescharacteristic
181C4×D4C2×D5911yescharacteristic
182C2×C4⋊C4—1181no—
183#107—591no—
184C4⋊C8—591no—
185#103—592no—
186#102—591no—
187#102—592no—
188#102—591no—
189C22⋊C8—592no—
190C4×C8—591no—
191C24—22no—
192#41—1184no—
193#41—2362no—
194C2×Q8—592no—
195C2×D4—24no—
196C2×D4—22no—
197C2×D4—22no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—42no—
201C2×D4—44no—
202C2×D4—591no—
203C2×D4—1182no—
204C2×D4C22⋊D5911yescharacteristic
205C2×D4C22×D5912yes—
206C2×D4C22×D5911yescharacteristic
207C22×C4—21no—
208C22×C4—1181no—
209C22×C4—1182no—
210C22×C4C22×D5912yes—
211SD16—1184no—
212SD16—1184no—
213SD16—2362no—
214D8—594no—
215D8—1184no—
216M16—1184no—
217C2×C8—591no—
218C2×C8—591no—
219C2×C8—592no—
220C4⋊C4—591no—
221C4⋊C4—1181no—
222C4⋊C4—1182no—
223C4⋊C4—1181no—
224C4⋊C4C22⋊D5911yescharacteristic
225C4⋊C4C22×D5911yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—22no—
228C22⋊C4—1182no—
229C22⋊C4—1181no—
230C22⋊C4C22⋊D5912yes—
231C42C22×D5911yescharacteristic
232C23—21no—
233C23—22no—
234C23—44no—
235C23—44no—
236C23—82no—
237C23—1181no—
238C23C2×C22⋊D5912yes—
239Q8—1182no—
240Q8—1182no—
241D4—22no—
242D4—22no—
243D4—21no—
244D4—22no—
245D4—44no—
246D4—44no—
247D4—42no—
248D4—81no—
249D4—592no—
250D4—1181no—
251D4—2364no—
252D4D4×D5912yes—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—1181no—
258C2×C4—1182no—
259C2×C4—2364no—
260C2×C4—2362no—
261C2×C4C2×C22⋊D5911yescharacteristic
262C2×C4C2×C22⋊D5912yes—
263C2×C4C2×C22⋊D5911yescharacteristic
264C2×C4C23×D5911yescharacteristic
265C8—592no—
266C8—1182no—
267C8—1181no—
268C22—22no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22—41no—
273C22—41no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—88no—
278C22—1182no—
279C22—2361no—
280C22—2361no—
281C22C22×C22⋊D5911yescharacteristic
282C4—21no—
283C4—22no—
284C4—41no—
285C4—2361no—
286C4—2362no—
287C4#1427375312yescomplemented
288C4C2×D4×D5911yescharacteristic
289C4#1427377211yescharacteristic
290C2—42no—
291C2—42no—
292C2—82no—
293C2—2362no—
294C2D4×C22⋊D5911yescharacteristic
295C2C2×#1427375311yescharacteristic
296C2#1683821311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingD42×C59C2
socleC22×C59C22×D4
hypercenterD42D59
hypocenterC59#3272
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. C2×#14273753C2semidirect
2. #16838057C2semidirect
3. #16837774C2semidirect
4. #16837646C2semidirect
5. #16837607C2semidirect
6. #16837594C2semidirect
7. #16837553C2semidirect
8. #16837545C2semidirect
9. C4×#11745669C2semidirect
10. #16837480C2semidirect
11. D42×C59C2semidirect
12. C2×#11745685C22semidirect
15. C2×#11745670C22semidirect
16. C2×#11745670C22semidirect
18. C2×#11745669C22semidirect
19. C2×#11745664C22semidirect
20. #14273727C22semidirect
22. #14273706C22semidirect
24. C4×D236C22semidirect
26. #14273660C22semidirect
27. C4⋊(C59⋊C8)C22semidirect
28. #14273650C22semidirect
30. #14273648C22semidirect
31. #14273647C22semidirect
32. C22⋊(C59⋊C8)C22semidirect
33. C4×C59⋊C8C22semidirect
73. #11745669D4semidirect
111. D236C2×D4semidirect
118. C59⋊C8C2×D4semidirect
136. C4×C59AGL(1,ℤ/8)semidirect
151. D42D59semidirect
160. C59#3272semidirect
287. C4#14273753semidirect