Finite Group Databasebeta

← #21435063

Subgroups — #21435063

Order 7552.

410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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#16837936C211yesmaximal, characteristic, complemented
2C2×#14273715C211yesmaximal, characteristic, complemented
3#16837786C212yesmaximal, complemented
4#16837757C212yesmaximal, complemented
5#16837625C212yesmaximal, complemented
6#16837618C212yesmaximal, complemented
7#16837560C211yesmaximal, characteristic, complemented
8#16837555C211yesmaximal, characteristic, complemented
9#16837543C211yesmaximal, characteristic, complemented
10#16837538C211yesmaximal, characteristic
11C59×#431C211yesmaximal, characteristic, complemented
12C22×Dic118C2211yescharacteristic
13C22×D236C2211yescharacteristic
14C2×Dic236C2212yescomplemented
15C2×#11745660C2212yes—
16C2×#11745660C2212yescomplemented
17C2×D472C2212yes—
18#14273721—21no—
19#14273719C2211yescharacteristic, complemented
20#14273715—21no—
21#14273715—21no—
22#14273715C2212yes—
23#14273715C2212yes—
24#14273715C2211yescharacteristic, complemented
25#14273710—21no—
26#14273706C2211yescharacteristic
27#14273701C2211yescharacteristic
28C4×Dic118C2211yescharacteristic, complemented
29C4×D236C2211yescharacteristic, complemented
30C4×C22⋊D59—21no—
31#14273684—21no—
32C2×(C2×D59)⋊C4—21no—
33C2×(C2×D59)⋊C4—21no—
34#14273652C2212yescomplemented
35#14273652C2212yescomplemented
36#14273649C2212yes—
37#14273649C2212yes—
38C2×C42×C59C2211yescharacteristic
39C4⋊C8×C59C2212yescomplemented
40C22⋊C8×C59C2211yescharacteristic
41C22⋊C8×C59C2211yescharacteristic
42C4×C8×C59C2212yescomplemented
43C23×D59—21no—
44C22×C4×C59D411yescharacteristic
45C22×C4×C59D411yescharacteristic
46C22×C4×C59C2311yescharacteristic
47C2×C22⋊D59—21no—
48C22×Dic59—21no—
49C2×D236—21no—
50C2×D236—42no—
51C2×D236C2312yes—
52C2×D236C2311yescharacteristic
53C2×C4×D59—21no—
54C2×Dic118—21no—
55C2×Dic118—42no—
56C2×Dic118C2312yes—
57C2×Dic118C2311yescharacteristic
58C2×C8×C59C2312yes—
59C2×C8×C59C2312yes—
60C42×C59D411yescharacteristic
61C42×C59D411yescharacteristic
62C42×C59C2311yescharacteristic
63C42×C59C2311yescharacteristic
64C22⋊Dic59—21no—
65(C2×D59)⋊C4—22no—
66(C2×D59)⋊C4—22no—
67(C2×D59)⋊C4—22no—
68(C2×D59)⋊C4—22no—
69(C2×D59)⋊C4—21no—
70(C2×D59)⋊C4—21no—
71(C2×D59)⋊C4—21no—
72(C2×D59)⋊C4—21no—
73C4⋊Dic59C2311yescharacteristic
74C4⋊Dic59C2311yescharacteristic
75Dic59⋊C4—21no—
76Dic59⋊C4—21no—
77Dic59⋊C4—21no—
78Dic59⋊C4—21no—
79C4×Dic59—21no—
80Dic236—42no—
81D472—42no—
82#11745660—42no—
83#11745660—42no—
84C23×C59C2×D411yescharacteristic
85C22×D59—21no—
86C22×D59—22no—
87C22×D59—42no—
88C22×D59—42no—
89C22×D59—42no—
90C2×C4×C59—22no—
91C2×C4×C59—22no—
92C2×C4×C59—41no—
93C2×C4×C59C2×D411yescharacteristic
94C2×C4×C59C2×D411yescharacteristic
95C2×C4×C59C2×D411yescharacteristic
96C2×C4×C59C2×D411yescharacteristic
97C2×C4×C59C2×D411yescharacteristic
98C2×C4×C59C2411yescharacteristic
99C22⋊D59—42no—
100C2×Dic59—21no—
101C2×Dic59—21no—
102C2×Dic59—21no—
103C2×Dic59—22no—
104C2×Dic59—42no—
105D236—22no—
106D236—22no—
107D236—22no—
108D236—42no—
109C4×D59—42no—
110Dic118—22no—
111Dic118—22no—
112Dic118—22no—
113Dic118—42no—
114C8×C59—22no—
115C8×C59—22no—
116C22×C59—21no—
117C22×C59—21no—
118C22×C59#13512yes—
119C22×C59C22×D411yescharacteristic
120C2×D59—42no—
121C2×D59—41no—
122C2×D59—41no—
123C2×D59—42no—
124C2×D59—41no—
125C2×D59—42no—
126C2×D59—84no—
127C4×C59—21no—
128C4×C59—21no—
129C4×C59—21no—
130C4×C59—21no—
131C4×C59—21no—
132C4×C59H(5,𝔽2)12yes—
133Dic59—42no—
134Dic59—41no—
135Dic59—41no—
136Dic59—41no—
137#3211—591nomaximal, Sylow
138C2×C59—22no—
139C2×C59#53511yescharacteristic
140C2×C59C2×#13511yescharacteristic
141C2×C59#57511yescharacteristic
142D59—81no—
143D59—82no—
144#529—591no—
145C2×#124—591no—
146#495—592no—
147#488—592no—
148#464—592no—
149#463—592no—
150#451—591no—
151#450—591no—
152#448—591no—
153#447—591no—
154#431D5911yescharacteristic, complemented
155C59#321111yescharacteristic, complemented, Sylow
156C22×Q8—591no—
157C22×D4—591no—
158C2×Q16—592no—
159C2×SD16—592no—
160C2×SD16—592no—
161C2×D8—592no—
162#126—1181no—
163#125—591no—
164#124—592no—
165#124—592no—
166#124—591no—
167#124—1181no—
168#124—1181no—
169#123—1181no—
170C22⋊Q8—591no—
171#121—591no—
172C4×Q8—591no—
173C4×D4—591no—
174C4×D4—1181no—
175#117—1181no—
176C2×C22⋊C4—1181no—
177C2×C22⋊C4—1181no—
178C2×C42C2×D5911yescharacteristic
179C4⋊C8C2×D5912yescomplemented
180#103—592no—
181#103—592no—
182#102—592no—
183#102—592no—
184C22⋊C8C2×D5911yescharacteristic
185C22⋊C8C2×D5911yescharacteristic
186C4×C8C2×D5912yescomplemented
187C24—1181no—
188C2×Q8—592no—
189C2×Q8—591no—
190C2×Q8—1181no—
191C2×Q8—2362no—
192C2×D4—592no—
193C2×D4—591no—
194C2×D4—1181no—
195C2×D4—1181no—
196C2×D4—2362no—
197C22×C4—1181no—
198C22×C4—1181no—
199C22×C4D23611yescharacteristic
200C22×C4D23611yescharacteristic
201C22×C4C22×D5911yescharacteristic
202Q16—2362no—
203SD16—2362no—
204SD16—2362no—
205D8—2362no—
206C2×C8C22×D5912yes—
207C2×C8C22×D5912yes—
208C4⋊C4—591no—
209C4⋊C4—591no—
210C4⋊C4—1181no—
211C4⋊C4—1181no—
212C4⋊C4—1181no—
213C4⋊C4—1181no—
214C22⋊C4—1181no—
215C22⋊C4—1182no—
216C22⋊C4—1182no—
217C22⋊C4—1182no—
218C22⋊C4—1182no—
219C22⋊C4—1181no—
220C22⋊C4—1181no—
221C22⋊C4—1181no—
222C22⋊C4—1181no—
223C42—1181no—
224C42D23611yescharacteristic
225C42D23611yescharacteristic
226C42C22×D5911yescharacteristic
227C42C22×D5911yescharacteristic
228C23—1181no—
229C23—1182no—
230C23—2362no—
231C23—2362no—
232C23—2362no—
233C23C2×D23611yescharacteristic
234Q8—1182no—
235Q8—1182no—
236Q8—1182no—
237Q8—2362no—
238D4—1182no—
239D4—1182no—
240D4—1182no—
241D4—2362no—
242D4—2362no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—1181no—
247C2×C4—1181no—
248C2×C4—1182no—
249C2×C4—1181no—
250C2×C4—2362no—
251C2×C4—2362no—
252C2×C4C2×D23611yescharacteristic
253C2×C4C2×D23611yescharacteristic
254C2×C4C2×D23611yescharacteristic
255C2×C4C2×D23611yescharacteristic
256C2×C4C2×D23611yescharacteristic
257C2×C4C23×D5911yescharacteristic
258C8—22no—
259C8—22no—
260C22—21no—
261C22—21no—
262C22—4724no—
263C22—2361no—
264C22—2362no—
265C22—2361no—
266C22—2362no—
267C22—2362no—
268C22—2361no—
269C22#1427374912yes—
270C22C22×D23611yescharacteristic
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—2361no—
277C4—2361no—
278C4—2362no—
279C4—2361no—
280C4#1427377312yes—
281C2—22no—
282C2—4722no—
283C2—4721no—
284C2#1683797111yescharacteristic
285C2C2×#1427374911yescharacteristic
286C2#1683820211yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#431C2
socleC22×C59C22×D4
hypercenter#431D59
hypocenterC59#3211
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #16837936C2semidirect
2. C2×#14273715C2semidirect
3. #16837786C2semidirect
4. #16837757C2semidirect
5. #16837625C2semidirect
6. #16837618C2semidirect
7. #16837560C2semidirect
8. #16837555C2semidirect
9. #16837543C2semidirect
11. C59×#431C2semidirect
14. C2×Dic236C22semidirect
16. C2×#11745660C22semidirect
19. #14273719C22semidirect
24. #14273715C22semidirect
28. C4×Dic118C22semidirect
29. C4×D236C22semidirect
34. #14273652C22semidirect
35. #14273652C22semidirect
39. C4⋊C8×C59C22semidirect
42. C4×C8×C59C22semidirect
154. #431D59semidirect
155. C59#3211semidirect
179. C4⋊C8C2×D59semidirect
186. C4×C8C2×D59semidirect