Finite Group Databasebeta

← #21435015

Subgroups — #21435015

Order 7552.

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

normal subgroups only

This group has 532 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#16837953C211yesmaximal, characteristic, complemented
2#127×D59C211yesmaximal, characteristic, complemented
3#16837779C211yesmaximal, characteristic, complemented
4#16837778C211yesmaximal, characteristic, complemented
5#16837750C211yesmaximal, characteristic, complemented
6#16837596C214yesmaximal, complemented
7#16837537C214yesmaximal, complemented
8#16837453C211yesmaximal, characteristic, complemented
9C59×#486C211yesmaximal, characteristic, complemented
10C2×#11745689—21no—
11C2×D4×D59—21no—
12C2×D4×D59—21no—
13C2×D4×D59C2212yes—
14C2×D472C2214yescomplemented
15C2×#11745669C2214yescomplemented
16#14273724C2211yescharacteristic
17#14273724C2211yescharacteristic, complemented
18#14273723—21no—
19#14273723—21no—
20#14273723C2212yes—
21#14273716—21no—
22#14273702—21no—
23#14273702C2212yes—
24#14273689—21no—
25#14273689C2212yescomplemented
26C42×D59C2211yescharacteristic
27Dic59⋊C8C2212yescomplemented
28#14273647C2214yescomplemented
29(C2×D59)⋊C8C2212yes—
30C4×C59⋊C8C2211yescharacteristic, complemented
31C4⋊Q8×C59C2211yescharacteristic, complemented
32#127×C59C2211yescharacteristic
33#102×C59C2214yescomplemented
34C4×C8×C59C2211yescharacteristic, complemented
35C23×D59—22no—
36C2×Q8×C59—21no—
37C2×D4×C59—21no—
38C2×D4×C59—21no—
39C2×D4×C59C2312yes—
40C2×C22⋊D59—22no—
41C2×C22⋊D59—22no—
42C2×C22⋊D59—22no—
43#11745689—44no—
44D4×D59—44no—
45D4×D59—44no—
46D4×D59—44no—
47C2×D236—22no—
48C2×D236—21no—
49C2×D236—21no—
50C2×D236—21no—
51C2×D236—21no—
52C2×D236C2312yes—
53C2×D236C2312yes—
54C2×C4×D59—22no—
55C2×C4×D59D411yescharacteristic
56C2×C4×D59D411yescharacteristic
57C2×C4×D59C2311yescharacteristic
58C2×C8×C59C2312yes—
59C4⋊C4×C59—21no—
60C4⋊C4×C59C2312yes—
61C42×C59C2311yescharacteristic
62#11745669—44no—
63(C2×D59)⋊C4—22no—
64(C2×D59)⋊C4—22no—
65C4×Dic59D411yescharacteristic
66C4×Dic59D411yescharacteristic
67C4×Dic59C2311yescharacteristic
68C2×C59⋊C8C2312yes—
69D472—44no—
70C23×C59—22no—
71C22×D59—22no—
72C22×D59—22no—
73C22×D59—44no—
74C22×D59—44no—
75C22×D59—44no—
76C22×D59C2×D411yescharacteristic
77Q8×C59—42no—
78D4×C59—24no—
79D4×C59—42no—
80D4×C59—42no—
81C2×C4×C59—22no—
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59C2×D411yescharacteristic
84C2×C4×C59C2411yescharacteristic
85C22⋊D59—44no—
86C22⋊D59—44no—
87C22⋊D59—44no—
88C2×Dic59C2×D411yescharacteristic
89C2×Dic59C2×D411yescharacteristic
90C2×Dic59C2×D411yescharacteristic
91D236—24no—
92D236—24no—
93D236—44no—
94D236—42no—
95D236—42no—
96D236—42no—
97D236—42no—
98C4×D59—22no—
99C4×D59—22no—
100C4×D59—44no—
101C4×D59D814yescomplemented
102C8×C59—22no—
103C59⋊C8—22no—
104C22×C59—42no—
105C22×C59—42no—
106C22×C59—42no—
107C22×C59C22×D411yescharacteristic
108C2×D59—21no—
109C2×D59—21no—
110C2×D59—42no—
111C2×D59—42no—
112C2×D59—42no—
113C2×D59—42no—
114C2×D59—42no—
115C2×D59—42no—
116C2×D59—88no—
117C2×D59C2×D812yes—
118C4×C59—42no—
119C4×C59C2×D812yes—
120C4×C59AGL(1,ℤ/8)12yes—
121C4×C59H(5,𝔽2)12yes—
122Dic59—21no—
123Dic59—21no—
124Dic59C2×D812yes—
125#3205—591nomaximal, Sylow
126C2×C59—82no—
127C2×C59#53511yescharacteristic
128C2×C59C22×D811yescharacteristic
129C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
130D59—22no—
131D59—82no—
132D59—82no—
133#532—591no—
134C2×#127—591no—
135#493—591no—
136#493—591no—
137#486—591no—
138#486D5911yescharacteristic, complemented
139#459—594no—
140#447—594no—
141#431—591no—
142C59#320511yescharacteristic, complemented, Sylow
143C2×#41—1181no—
144C22×D4—592no—
145C22×D4—1181no—
146C22×D4—1181no—
147C2×D8—594no—
148C2×D8—594no—
149C4⋊Q8C2×D5911yescharacteristic, complemented
150#127—592no—
151#127—591no—
152#127—591no—
153#127—1181no—
154#127—1181no—
155#127C2×D5911yescharacteristic
156#124—1181no—
157#121—592no—
158#121—1181no—
159C4×D4—592no—
160C4×D4—1181no—
161C2×C42—591no—
162C4⋊C8—592no—
163#102—594no—
164#102C2×D5914yescomplemented
165C22⋊C8—592no—
166C4×C8—591no—
167C4×C8C2×D5911yescharacteristic, complemented
168C24—1182no—
169#41—2364no—
170C2×Q8—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—592no—
174C2×D4—592no—
175C2×D4—1182no—
176C2×D4—1182no—
177C2×D4—1182no—
178C2×D4—1182no—
179C2×D4—1181no—
180C2×D4—1181no—
181C2×D4—1181no—
182C2×D4—1181no—
183C2×D4—2364no—
184C2×D4—2364no—
185C2×D4—2364no—
186C2×D4C22×D5912yes—
187C22×C4—591no—
188C22×C4—591no—
189C22×C4—591no—
190C22×C4—1182no—
191D8—2364no—
192D8—2364no—
193C2×C8—592no—
194C2×C8C22×D5912yes—
195C4⋊C4—21no—
196C4⋊C4C22×D5912yes—
197C22⋊C4—1182no—
198C22⋊C4—1182no—
199C42—591no—
200C42—591no—
201C42—591no—
202C42C22×D5911yescharacteristic
203C23—22no—
204C23—591no—
205C23—1182no—
206C23—1182no—
207C23—2364no—
208C23—2364no—
209C23—2364no—
210Q8—42no—
211D4—24no—
212D4—42no—
213D4—42no—
214D4—1184no—
215D4—1184no—
216D4—2364no—
217D4—2364no—
218D4—2364no—
219D4—2364no—
220D4—2362no—
221D4—2362no—
222D4—2362no—
223D4—2362no—
224C2×C4—22no—
225C2×C4—591no—
226C2×C4—594no—
227C2×C4—591no—
228C2×C4—591no—
229C2×C4—1182no—
230C2×C4—1182no—
231C2×C4—2364no—
232C2×C4D4×D5911yescharacteristic
233C2×C4D4×D5911yescharacteristic
234C2×C4C23×D5911yescharacteristic
235C8—22no—
236C8—1182no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—592no—
241C22—1181no—
242C22—1181no—
243C22—4728no—
244C22—2362no—
245C22—2362no—
246C22—2362no—
247C22—2362no—
248C22—2362no—
249C22—2362no—
250C22C2×D4×D5911yescharacteristic
251C4—42no—
252C4—592no—
253C4—1181no—
254C4—1181no—
255C4D8×D5912yes—
256C4#1427375412yes—
257C4#1427377312yes—
258C2—82no—
259C2—1182no—
260C2—4722no—
261C2—4722no—
262C2#1683797011yescharacteristic
263C2C2×D8×D5911yescharacteristic
264C2C2×#1427375411yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#486C2
socleC22×C59C22×D4
hypercenter#486D59
hypocenterC59#3205
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. #16837953C2semidirect
2. #127×D59C2semidirect
3. #16837779C2semidirect
4. #16837778C2semidirect
5. #16837750C2semidirect
6. #16837596C2semidirect
7. #16837537C2semidirect
8. #16837453C2semidirect
9. C59×#486C2semidirect
14. C2×D472C22semidirect
15. C2×#11745669C22semidirect
17. #14273724C22semidirect
25. #14273689C22semidirect
27. Dic59⋊C8C22semidirect
28. #14273647C22semidirect
30. C4×C59⋊C8C22semidirect
31. C4⋊Q8×C59C22semidirect
33. #102×C59C22semidirect
34. C4×C8×C59C22semidirect
101. C4×D59D8semidirect
138. #486D59semidirect
142. C59#3205semidirect
149. C4⋊Q8C2×D59semidirect
164. #102C2×D59semidirect
167. C4×C8C2×D59semidirect