Finite Group Databasebeta

← #21436339

Subgroups — #21436339

Order 7552.

460 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 123 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
2D4×D236C211yesmaximal, characteristic, complemented
3#16837749C211yesmaximal, characteristic, complemented
4#16837727C212yesmaximal, complemented
5#16837693C211yesmaximal, characteristic, complemented
6#16837655C212yesmaximal, complemented
7#16837598C211yesmaximal, characteristic, complemented
8#16837538C212yesmaximal, complemented
9C4×D472C211yesmaximal, characteristic, complemented
10#16837408C212yesmaximal, complemented
11C59×#436C211yesmaximal, characteristic, complemented
12C22×D236C2212yes—
13C2×D4×D59—21no—
14C2×D472C2211yescharacteristic
15C2×D472C2212yescomplemented
16#14273727C2211yescharacteristic, complemented
17#14273724C2211yescharacteristic
18#14273713—22no—
19#14273702—21no—
20#14273701C2212yes—
21#14273701C2212yescomplemented
22#14273698—21no—
23#14273697—22no—
24C4×D236C2211yescharacteristic
25C4×D236C2211yescharacteristic, complemented
26#14273686C2212yescomplemented
27#14273685—21no—
28#14273661C2211yescharacteristic, complemented
29#14273659C2212yescomplemented
30#14273649C2211yescharacteristic
31#14273649C2212yes—
32#14273649C2211yescharacteristic, complemented
33#14273649C2212yescomplemented
34#14273649C2212yescomplemented
35#14273649C2212yescomplemented
36C2×M16×C59C2212yescomplemented
37C4×D4×C59C2211yescharacteristic
38C4⋊C8×C59C2211yescharacteristic, complemented
39C22⋊C8×C59C2212yescomplemented
40C4×C8×C59C2211yescharacteristic, complemented
41C23×D59—22no—
42C2×D4×C59D411yescharacteristic
43C22×C4×C59C2312yes—
44C2×C22⋊D59—22no—
45C2×C22⋊D59—22no—
46D4×D59—44no—
47C2×D236—24no—
48C2×D236—22no—
49C2×D236—21no—
50C2×D236—21no—
51C2×D236—42no—
52C2×D236C2312yes—
53C2×D236C2311yescharacteristic
54C2×D236C2311yescharacteristic
55C2×C4×D59—21no—
56C2×C4×D59—21no—
57C2×Dic118—21no—
58M16×C59—42no—
59C2×C8×C59C2311yescharacteristic
60C2×C8×C59C2311yescharacteristic
61C2×C8×C59C2312yes—
62C4⋊C4×C59D411yescharacteristic
63C22⋊C4×C59D412yes—
64C42×C59C2311yescharacteristic
65C22⋊Dic59—22no—
66(C2×D59)⋊C4—22no—
67(C2×D59)⋊C4—21no—
68(C2×D59)⋊C4—21no—
69(C2×D59)⋊C4—22no—
70C4⋊Dic59—21no—
71C4⋊Dic59C2312yes—
72C4⋊Dic59C2311yescharacteristic
73C4⋊Dic59C2311yescharacteristic
74C4×Dic59—22no—
75D472—22no—
76D472—42no—
77C23×C59C2×D412yes—
78C22×D59—21no—
79C22×D59—21no—
80C22×D59—22no—
81C22×D59—44no—
82C22×D59—44no—
83C22×D59—82no—
84D4×C59—22no—
85C2×C4×C59—22no—
86C2×C4×C59—22no—
87C2×C4×C59C2×D412yes—
88C2×C4×C59C2×D411yescharacteristic
89C2×C4×C59C2×D411yescharacteristic
90C2×C4×C59C2411yescharacteristic
91C22⋊D59—44no—
92C22⋊D59—82no—
93C2×Dic59—21no—
94C2×Dic59—22no—
95C2×Dic59—21no—
96D236—21no—
97D236—22no—
98D236—21no—
99D236—21no—
100D236—22no—
101D236—44no—
102D236—42no—
103D236—81no—
104D236#4112yes—
105C4×D59—42no—
106C4×D59—42no—
107Dic118—81no—
108C8×C59—21no—
109C8×C59—22no—
110C8×C59—21no—
111C22×C59—22no—
112C22×C59—22no—
113C22×C59—22no—
114C22×C59C22×D411yescharacteristic
115C2×D59—22no—
116C2×D59—41no—
117C2×D59—41no—
118C2×D59—42no—
119C2×D59—41no—
120C2×D59—41no—
121C2×D59—42no—
122C2×D59—42no—
123C2×D59—41no—
124C2×D59—88no—
125C4×C59—22no—
126C4×C59—21no—
127C4×C59AGL(1,ℤ/8)12yes—
128C4×C59C2×#4111yescharacteristic
129C4×C59H(5,𝔽2)11yescharacteristic
130Dic59—41no—
131Dic59—41no—
132Dic59—42no—
133#3325—591nomaximal, Sylow
134C2×C59—42no—
135C2×C59#54611yescharacteristic
136C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C59#57611yescharacteristic
138D59—42no—
139D59—81no—
140D59—82no—
141#555—591no—
142D42—591no—
143#486—591no—
144#482—592no—
145#476—591no—
146#469—592no—
147#459—591no—
148#447—592no—
149C4×D8—591no—
150#436D5911yescharacteristic, complemented
151#418—592no—
152C59#332511yescharacteristic, complemented, Sylow
153C22×D4—592no—
154C22×D4—1181no—
155C2×D8—591no—
156C2×D8—592no—
157C2×M16C2×D5912yescomplemented
158C4⋊Q8—591no—
159#127—591no—
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
169#117—592no—
170#117—1181no—
171#107—591no—
172#106—592no—
173C4⋊C8C2×D5911yescharacteristic, complemented
174#102—591no—
175#102—592no—
176#102—592no—
177#102—592no—
178#102—591no—
179#102—592no—
180C22⋊C8C2×D5912yescomplemented
181C4×C8C2×D5911yescharacteristic, complemented
182C24—1182no—
183C2×Q8—1181no—
184C2×D4—591no—
185C2×D4—592no—
186C2×D4—591no—
187C2×D4—1184no—
188C2×D4—1182no—
189C2×D4—1182no—
190C2×D4—1181no—
191C2×D4—1182no—
192C2×D4—1181no—
193C2×D4—2362no—
194C2×D4—2364no—
195C2×D4D23611yescharacteristic
196C22×C4—1181no—
197C22×C4—1181no—
198C22×C4C22×D5912yes—
199D8—1182no—
200D8—2362no—
201M16—42no—
202C2×C8C22×D5911yescharacteristic
203C2×C8C22×D5911yescharacteristic
204C2×C8C22×D5912yes—
205C4⋊C4—592no—
206C4⋊C4—591no—
207C4⋊C4—591no—
208C4⋊C4—1181no—
209C4⋊C4D23611yescharacteristic
210C22⋊C4—1182no—
211C22⋊C4—1182no—
212C22⋊C4—1181no—
213C22⋊C4—1181no—
214C22⋊C4—1182no—
215C22⋊C4D23612yes—
216C42—1182no—
217C42C22×D5911yescharacteristic
218C23—1181no—
219C23—1181no—
220C23—1182no—
221C23—4722no—
222C23—2364no—
223C23—2364no—
224C23C2×D23612yes—
225Q8—4721no—
226D4—22no—
227D4—592no—
228D4—1181no—
229D4—1182no—
230D4—1181no—
231D4—1181no—
232D4—1182no—
233D4—4721no—
234D4—4722no—
235D4—2364no—
236D4—2364no—
237D4—2362no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—1181no—
241C2×C4—1182no—
242C2×C4—1181no—
243C2×C4—2362no—
244C2×C4—2362no—
245C2×C4C2×D23612yes—
246C2×C4C2×D23611yescharacteristic
247C2×C4C2×D23611yescharacteristic
248C2×C4C23×D5911yescharacteristic
249C8—21no—
250C8—21no—
251C8—22no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—1182no—
256C22—4728no—
257C22—2361no—
258C22—2362no—
259C22—2361no—
260C22—2362no—
261C22—2362no—
262C22—2361no—
263C22—2361no—
264C22—2361no—
265C22C22×D23611yescharacteristic
266C4—21no—
267C4—22no—
268C4—2361no—
269C4—2361no—
270C4—2362no—
271C4#1427375512yes—
272C4#41×D5911yescharacteristic
273C4#1427377211yescharacteristic
274C2—42no—
275C2—4722no—
276C2—4721no—
277C2—2362no—
278C2#1683804711yescharacteristic
279C2C2×#1427375511yescharacteristic
280C2#1683820711yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#436C2
socleC22×C59C22×D4
hypercenter#436D59
hypocenterC59#3325
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #16838117C2semidirect
2. D4×D236C2semidirect
3. #16837749C2semidirect
4. #16837727C2semidirect
5. #16837693C2semidirect
6. #16837655C2semidirect
7. #16837598C2semidirect
8. #16837538C2semidirect
9. C4×D472C2semidirect
10. #16837408C2semidirect
11. C59×#436C2semidirect
15. C2×D472C22semidirect
16. #14273727C22semidirect
21. #14273701C22semidirect
25. C4×D236C22semidirect
26. #14273686C22semidirect
28. #14273661C22semidirect
29. #14273659C22semidirect
32. #14273649C22semidirect
33. #14273649C22semidirect
34. #14273649C22semidirect
35. #14273649C22semidirect
36. C2×M16×C59C22semidirect
38. C4⋊C8×C59C22semidirect
39. C22⋊C8×C59C22semidirect
40. C4×C8×C59C22semidirect
150. #436D59semidirect
152. C59#3325semidirect
157. C2×M16C2×D59semidirect
173. C4⋊C8C2×D59semidirect
180. C22⋊C8C2×D59semidirect
181. C4×C8C2×D59semidirect