Finite Group Databasebeta

← #21436337

Subgroups — #21436337

Order 7552.

460 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 115 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#16838118C211yesmaximal, characteristic, complemented
2#16838037C211yesmaximal, characteristic, complemented
3#16837724C212yesmaximal, complemented
4#16837689C211yesmaximal, characteristic, complemented
5#16837654C212yesmaximal, complemented
6#16837594C211yesmaximal, characteristic, complemented
7#16837537C212yesmaximal, complemented
8C4×D472C211yesmaximal, characteristic, complemented
9#16837481C211yesmaximal, characteristic, complemented
10#16837405C212yesmaximal, complemented
11C59×#486C211yesmaximal, characteristic, complemented
12C2×D4×D59—21no—
13C2×D4×D59C2212yes—
14C2×D472C2211yescharacteristic
15C2×#11745669C2212yescomplemented
16C2×#11745659C2212yescomplemented
17#14273716—22no—
18#14273702—21no—
19#14273702C2212yescomplemented
20#14273698—21no—
21#14273698C2212yes—
22#14273695—22no—
23C4×D236C2211yescharacteristic
24C4×D236C2211yescharacteristic
25C4×D236C2211yescharacteristic, complemented
26#14273685—21no—
27#14273685C2212yescomplemented
28#14273661C2211yescharacteristic, complemented
29#14273658C2212yescomplemented
30C4⋊(C59⋊C8)C2211yescharacteristic, complemented
31#14273649C2211yescharacteristic
32#14273649C2211yescharacteristic, complemented
33#14273648C2212yescomplemented
34#14273647C2212yes—
35(C2×D59)⋊C8C2212yescomplemented
36C4⋊Q8×C59C2211yescharacteristic, complemented
37#127×C59C2211yescharacteristic
38#102×C59C2212yescomplemented
39#102×C59C2212yescomplemented
40C4×C8×C59C2211yescharacteristic, complemented
41C23×D59—22no—
42C2×Q8×C59—21no—
43C2×D4×C59—21no—
44C2×D4×C59—21no—
45C2×D4×C59C2312yes—
46C2×C22⋊D59—22no—
47C2×C22⋊D59—22no—
48D4×D59—24no—
49D4×D59—42no—
50D4×D59—44no—
51C2×D236—22no—
52C2×D236D411yescharacteristic
53C2×D236C2311yescharacteristic
54C2×D236C2311yescharacteristic
55C2×C4×D59—21no—
56C2×C4×D59—21no—
57C2×C4×D59C2312yes—
58C2×C8×C59C2311yescharacteristic
59C2×C8×C59C2311yescharacteristic
60C4⋊C4×C59—21no—
61C4⋊C4×C59C2312yes—
62C42×C59C2311yescharacteristic
63C22⋊Dic59—22no—
64#11745669—42no—
65(C2×D59)⋊C4—22no—
66(C2×D59)⋊C4—21no—
67(C2×D59)⋊C4—21no—
68(C2×D59)⋊C4—22no—
69(C2×D59)⋊C4D412yes—
70C4⋊Dic59D411yescharacteristic
71C4⋊Dic59C2311yescharacteristic
72C4⋊Dic59C2311yescharacteristic
73C4×Dic59—22no—
74C2×C59⋊C8C2312yes—
75D472—22no—
76#11745659—42no—
77C23×C59—22no—
78C22×D59—21no—
79C22×D59—21no—
80C22×D59—44no—
81C22×D59—44no—
82C22×D59—82no—
83C22×D59C2×D412yes—
84Q8×C59—81no—
85D4×C59—22no—
86D4×C59—22no—
87D4×C59—42no—
88D4×C59—81no—
89C2×C4×C59—22no—
90C2×C4×C59C2×D411yescharacteristic
91C2×C4×C59C2×D411yescharacteristic
92C2×C4×C59C2411yescharacteristic
93C22⋊D59—44no—
94C22⋊D59—44no—
95C2×Dic59—21no—
96C2×Dic59—21no—
97C2×Dic59C2×D412yes—
98D236—22no—
99D236—21no—
100D236—21no—
101D236—21no—
102D236—82no—
103D236#4112yes—
104C4×D59—22no—
105C4×D59—22no—
106C4×D59—42no—
107C4×D59—42no—
108C8×C59—21no—
109C8×C59—21no—
110C59⋊C8—22no—
111C22×C59—42no—
112C22×C59—42no—
113C22×C59—42no—
114C22×C59C22×D411yescharacteristic
115C2×D59—22no—
116C2×D59—22no—
117C2×D59—22no—
118C2×D59—22no—
119C2×D59—41no—
120C2×D59—41no—
121C2×D59—41no—
122C2×D59—41no—
123C2×D59—41no—
124C2×D59—88no—
125C4×C59—21no—
126C4×C59—42no—
127C4×C59AGL(1,ℤ/8)12yes—
128C4×C59C2×#4111yescharacteristic
129C4×C59H(5,𝔽2)11yescharacteristic
130Dic59—22no—
131Dic59—41no—
132Dic59—41no—
133#3325—591nomaximal, Sylow
134C2×C59—82no—
135C2×C59#54611yescharacteristic
136C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C59#57611yescharacteristic
138D59—42no—
139D59—42no—
140D59—81no—
141#555—591no—
142D42—591no—
143#486D5911yescharacteristic, complemented
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—592no—
154C22×D4—1181no—
155C2×D8—592no—
156C2×D8—591no—
157C2×M16—592no—
158C4⋊Q8C2×D5911yescharacteristic, complemented
159#127C2×D5911yescharacteristic
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×D4—591no—
169#117—592no—
170#117—1181no—
171#107—591no—
172#106—592no—
173C4⋊C8—591no—
174#102—592no—
175#102—591no—
176#102—591no—
177#102—592no—
178#102C2×D5912yescomplemented
179#102C2×D5912yescomplemented
180C22⋊C8—592no—
181C4×C8C2×D5911yescharacteristic, complemented
182C24—1182no—
183C2×Q8—21no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—591no—
187C2×D4—591no—
188C2×D4—591no—
189C2×D4—1182no—
190C2×D4—1182no—
191C2×D4—1184no—
192C2×D4—1182no—
193C2×D4—2362no—
194C2×D4—2364no—
195C2×D4C22×D5912yes—
196C22×C4—592no—
197C22×C4—1181no—
198C22×C4—1181no—
199D8—1182no—
200D8—2362no—
201M16—2362no—
202C2×C8—592no—
203C2×C8C22×D5911yescharacteristic
204C2×C8C22×D5911yescharacteristic
205C4⋊C4—21no—
206C4⋊C4—591no—
207C4⋊C4—591no—
208C4⋊C4—591no—
209C4⋊C4C22×D5912yes—
210C22⋊C4—592no—
211C22⋊C4—1182no—
212C22⋊C4—1182no—
213C22⋊C4—1182no—
214C22⋊C4—1181no—
215C22⋊C4—1181no—
216C42—1182no—
217C42C22×D5911yescharacteristic
218C23—22no—
219C23—592no—
220C23—1181no—
221C23—1181no—
222C23—4722no—
223C23—2364no—
224C23—2364no—
225Q8—81no—
226D4—22no—
227D4—22no—
228D4—42no—
229D4—81no—
230D4—592no—
231D4—1182no—
232D4—1181no—
233D4—1181no—
234D4—1181no—
235D4—4722no—
236D4—2364no—
237D4—2364no—
238C2×C4—22no—
239C2×C4—592no—
240C2×C4—1182no—
241C2×C4—1182no—
242C2×C4—1181no—
243C2×C4—1181no—
244C2×C4—2362no—
245C2×C4—2362no—
246C2×C4D4×D5911yescharacteristic
247C2×C4D4×D5911yescharacteristic
248C2×C4C23×D5911yescharacteristic
249C8—21no—
250C8—21no—
251C8—1182no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—1182no—
256C22—1182no—
257C22—1182no—
258C22—1182no—
259C22—4728no—
260C22—2361no—
261C22—2361no—
262C22—2361no—
263C22—2361no—
264C22—2361no—
265C22C2×D4×D5911yescharacteristic
266C4—21no—
267C4—42no—
268C4—1182no—
269C4—2361no—
270C4—2361no—
271C4#1427375412yes—
272C4#41×D5911yescharacteristic
273C4#1427377311yescharacteristic
274C2—82no—
275C2—4721no—
276C2—2362no—
277C2—2362no—
278C2#1683804511yescharacteristic
279C2C2×#1427375411yescharacteristic
280C2#1683820311yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#486C2
socleC22×C59C22×D4
hypercenter#486D59
hypocenterC59#3325
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #16838118C2semidirect
2. #16838037C2semidirect
3. #16837724C2semidirect
4. #16837689C2semidirect
5. #16837654C2semidirect
6. #16837594C2semidirect
7. #16837537C2semidirect
8. C4×D472C2semidirect
9. #16837481C2semidirect
10. #16837405C2semidirect
11. C59×#486C2semidirect
15. C2×#11745669C22semidirect
16. C2×#11745659C22semidirect
19. #14273702C22semidirect
25. C4×D236C22semidirect
27. #14273685C22semidirect
28. #14273661C22semidirect
29. #14273658C22semidirect
30. C4⋊(C59⋊C8)C22semidirect
32. #14273649C22semidirect
33. #14273648C22semidirect
35. (C2×D59)⋊C8C22semidirect
36. C4⋊Q8×C59C22semidirect
38. #102×C59C22semidirect
39. #102×C59C22semidirect
40. C4×C8×C59C22semidirect
143. #486D59semidirect
152. C59#3325semidirect
158. C4⋊Q8C2×D59semidirect
178. #102C2×D59semidirect
179. #102C2×D59semidirect
181. C4×C8C2×D59semidirect