Finite Group Databasebeta

← #21434093

Subgroups — #21434093

Order 7552.

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

normal subgroups only

This group has 492 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#16837947C211yesmaximal, characteristic, complemented
2C2×#14273689C211yesmaximal, characteristic, complemented
3#16837715C211yesmaximal, characteristic, complemented
4#16837681C212yesmaximal, complemented
5#16837596C212yesmaximal, complemented
6#16837538C211yesmaximal, characteristic, complemented
7#16837535C211yesmaximal, characteristic, complemented
8#16837484C212yesmaximal, complemented
9#16837482C212yesmaximal, complemented
10#16837452C211yesmaximal, characteristic, complemented
11C59×#480C211yesmaximal, characteristic, complemented
12C2×#11745687—21no—
13C22×D236C2211yescharacteristic
14C22×C4×D59—21no—
15C2×D472C2212yes—
16C2×#11745669C2212yes—
17#14273726C2211yescharacteristic, complemented
18#14273723C2211yescharacteristic, complemented
19#14273713—21no—
20#14273701C2211yescharacteristic
21#14273699—21no—
22D4×Dic59C2211yescharacteristic, complemented
23#14273689—21no—
24#14273689—21no—
25#14273689C2212yes—
26#14273689C2212yes—
27#14273689C2211yescharacteristic, complemented
28(C22⋊D59)⋊C4—21no—
29C2×(C2×D59)⋊C4—21no—
30C2×C4×Dic59C2211yescharacteristic
31#14273660C2212yescomplemented
32Dic59⋊C8C2212yescomplemented
33#14273649C2212yes—
34#14273647C2212yes—
35#14273647C2212yescomplemented
36C22⋊(C59⋊C8)C2211yescharacteristic
37C8×Dic59C2212yescomplemented
38#121×C59C2211yescharacteristic
39C2×C4⋊C4×C59C2211yescharacteristic
40#107×C59C2212yescomplemented
41#102×C59C2212yescomplemented
42C22⋊C8×C59C2211yescharacteristic
43C23×D59—21no—
44C2×D4×C59—21no—
45C2×D4×C59C2311yescharacteristic
46C22×C4×C59—21no—
47C22×C4×C59C2311yescharacteristic
48C2×C22⋊D59—21no—
49C2×C22⋊D59—21no—
50C2×C22⋊D59—21no—
51C22×Dic59—21no—
52C22×Dic59D411yescharacteristic
53C22×Dic59D411yescharacteristic
54#11745687—44no—
55C2×D236—21no—
56C2×D236—24no—
57C2×D236C2311yescharacteristic
58C2×D236C2312yes—
59C2×C4×D59—21no—
60C2×C4×D59—22no—
61C2×C4×D59—22no—
62C2×C4×D59—44no—
63C2×Dic118—21no—
64C2×C8×C59C2312yes—
65C4⋊C4×C59—21no—
66C4⋊C4×C59C2312yes—
67C4⋊C4×C59C2311yescharacteristic
68C22⋊C4×C59—21no—
69C22⋊Dic59—21no—
70#11745669—24no—
71(C2×D59)⋊C4—21no—
72(C2×D59)⋊C4—22no—
73(C2×D59)⋊C4—22no—
74(C2×D59)⋊C4—21no—
75C4⋊Dic59C2311yescharacteristic
76Dic59⋊C4—21no—
77C4×Dic59D411yescharacteristic
78C4×Dic59D411yescharacteristic
79C4×Dic59C2311yescharacteristic
80C4×Dic59C2311yescharacteristic
81C2×C59⋊C8C2312yes—
82D472—24no—
83C23×C59—21no—
84C23×C59C2×D411yescharacteristic
85C22×D59—24no—
86C22×D59—22no—
87C22×D59—21no—
88C22×D59—42no—
89C22×D59—42no—
90D4×C59—22no—
91D4×C59—42no—
92C2×C4×C59—22no—
93C2×C4×C59—21no—
94C2×C4×C59—22no—
95C2×C4×C59—42no—
96C2×C4×C59C2×D411yescharacteristic
97C2×C4×C59C2411yescharacteristic
98C22⋊D59—42no—
99C22⋊D59—42no—
100C22⋊D59—42no—
101C2×Dic59—21no—
102C2×Dic59—41no—
103C2×Dic59—42no—
104C2×Dic59D814yescomplemented
105C2×Dic59C2×D411yescharacteristic
106C2×Dic59C2×D411yescharacteristic
107C2×Dic59C2×D411yescharacteristic
108C2×Dic59C2×D411yescharacteristic
109D236—24no—
110D236—22no—
111D236—22no—
112D236#4114yescomplemented
113C4×D59—44no—
114C4×D59—44no—
115C4×D59—42no—
116Dic118—42no—
117C8×C59—22no—
118C59⋊C8—22no—
119C22×C59—21no—
120C22×C59—21no—
121C22×C59—41no—
122C22×C59—41no—
123C22×C59—41no—
124C22×C59C2×D812yes—
125C22×C59C22×D411yescharacteristic
126C2×D59—24no—
127C2×D59—48no—
128C2×D59—42no—
129C2×D59—42no—
130C2×D59—41no—
131C2×D59—41no—
132C2×D59—41no—
133C4×C59—21no—
134C4×C59—41no—
135C4×C59—42no—
136C4×C59C2×#4112yes—
137Dic59—21no—
138Dic59—21no—
139Dic59—41no—
140Dic59C2×D812yes—
141Dic59C2×D812yes—
142#3100—591nomaximal, Sylow
143C2×C59—22no—
144C2×C59—81no—
145C2×C59#52511yescharacteristic
146C2×C59C22×D811yescharacteristic
147C2×C59#57511yescharacteristic
148D59—44no—
149D59—81no—
150#532—591no—
151C2×C4×D4—591no—
152#480—591no—
153#480D5911yescharacteristic, complemented
154#474—592no—
155#459—592no—
156#447—591no—
157#447—591no—
158C4×D8—592no—
159C4×D8—592no—
160#431—591no—
161C59#310011yescharacteristic, complemented, Sylow
162C2×#41—1181no—
163C22×D4—591no—
164C23×C4—1181no—
165C2×D8—592no—
166C2×D8—592no—
167C4⋊Q8—591no—
168#127—591no—
169#124—1181no—
170#121—591no—
171#121—1181no—
172#121C2×D5911yescharacteristic
173C4×D4—591no—
174C4×D4—592no—
175C4×D4—592no—
176C4×D4—591no—
177C4×D4—1181no—
178C4×D4—1181no—
179C4×D4—1181no—
180C2×C4⋊C4C2×D5911yescharacteristic
181C2×C22⋊C4—1181no—
182C2×C42—591no—
183#107—592no—
184#107C2×D5912yescomplemented
185C4⋊C8—592no—
186#102—592no—
187#102—592no—
188#102—592no—
189#102C2×D5912yescomplemented
190C22⋊C8—591no—
191C22⋊C8C2×D5911yescharacteristic
192C4×C8—592no—
193C24—1181no—
194#41—2364no—
195C2×Q8—1181no—
196C2×D4—21no—
197C2×D4—592no—
198C2×D4—591no—
199C2×D4—1184no—
200C2×D4—1181no—
201C2×D4—1181no—
202C2×D4—1181no—
203C2×D4—1181no—
204C2×D4C22×D5911yescharacteristic
205C22×C4—21no—
206C22×C4—591no—
207C22×C4—591no—
208C22×C4—1182no—
209C22×C4—1182no—
210C22×C4—1181no—
211C22×C4—1181no—
212C22×C4—2364no—
213C22×C4C22×D5911yescharacteristic
214D8—1184no—
215D8—1184no—
216C2×C8—592no—
217C2×C8C22×D5912yes—
218C4⋊C4—21no—
219C4⋊C4—591no—
220C4⋊C4—1181no—
221C4⋊C4C22×D5911yescharacteristic
222C4⋊C4C22×D5912yes—
223C22⋊C4—21no—
224C22⋊C4—1182no—
225C22⋊C4—1182no—
226C22⋊C4—1181no—
227C22⋊C4—1181no—
228C22⋊C4—1181no—
229C42—591no—
230C42—591no—
231C42—591no—
232C42—591no—
233C23—21no—
234C23—1184no—
235C23—1182no—
236C23—1181no—
237C23—2362no—
238C23—2362no—
239C23D4×D5911yescharacteristic
240Q8—2362no—
241D4—22no—
242D4—42no—
243D4—594no—
244D4—1184no—
245D4—1182no—
246D4—1182no—
247D4—2362no—
248D4—2362no—
249D4—2362no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—594no—
255C2×C4—591no—
256C2×C4—591no—
257C2×C4—591no—
258C2×C4—591no—
259C2×C4—1181no—
260C2×C4—2364no—
261C2×C4—2364no—
262C2×C4—2362no—
263C2×C4—2362no—
264C2×C4—2361no—
265C2×C4D4×D5911yescharacteristic
266C2×C4C23×D5911yescharacteristic
267C8—22no—
268C8—1182no—
269C22—21no—
270C22—21no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—1184no—
275C22—2368no—
276C22—2361no—
277C22—2361no—
278C22—2361no—
279C22—2362no—
280C22—2362no—
281C22D8×D5912yes—
282C22C2×D4×D5911yescharacteristic
283C4—21no—
284C4—42no—
285C4—41no—
286C4—592no—
287C4—592no—
288C4—1181no—
289C4—1181no—
290C4—2361no—
291C4#41×D5912yes—
292C2—22no—
293C2—81no—
294C2—4721no—
295C2—2364no—
296C2#1683791011yescharacteristic
297C2C2×D8×D5911yescharacteristic
298C2#1683820111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#480C2
socleC22×C59C22×D4
hypercenter#480D59
hypocenterC59#3100
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #16837947C2semidirect
2. C2×#14273689C2semidirect
3. #16837715C2semidirect
4. #16837681C2semidirect
5. #16837596C2semidirect
6. #16837538C2semidirect
7. #16837535C2semidirect
8. #16837484C2semidirect
9. #16837482C2semidirect
10. #16837452C2semidirect
11. C59×#480C2semidirect
17. #14273726C22semidirect
18. #14273723C22semidirect
22. D4×Dic59C22semidirect
27. #14273689C22semidirect
31. #14273660C22semidirect
32. Dic59⋊C8C22semidirect
35. #14273647C22semidirect
37. C8×Dic59C22semidirect
40. #107×C59C22semidirect
41. #102×C59C22semidirect
104. C2×Dic59D8semidirect
112. D236#41semidirect
153. #480D59semidirect
161. C59#3100semidirect
184. #107C2×D59semidirect
189. #102C2×D59semidirect