Finite Group Databasebeta

← #21431143

Subgroups — #21431143

Order 7552.

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

normal subgroups only

This group has 560 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#16837329C212yesmaximal, complemented
2#16837315C212yesmaximal, complemented
3#16837314C211yesmaximal, characteristic, complemented
4#16837295C212yesmaximal, complemented
5#16837294C212yesmaximal, complemented
6#16837292C212yesmaximal, complemented
7#16837257C212yesmaximal
8#16837257C211yesmaximal, characteristic
9C59×#397C211yesmaximal, characteristic, complemented
10C24×D59C2211yescharacteristic
11C22×Dic118C2211yescharacteristic, complemented
12C2×C4⋊Dic59C2212yescomplemented
13C2×C22⋊Dic59C2211yescharacteristic
14C2×C22⋊Dic59C2212yes—
15C2×(C2×D59)⋊C4C2212yes—
16C2×(C2×D59)⋊C4C2212yes—
17C2×(C2×D59)⋊C4C2212yes—
18C2×(C2×D59)⋊C4C2212yes—
19C2×(C2×D59)⋊C4C2212yes—
20C2×(C2×D59)⋊C4C2212yes—
21C2×C4×Dic59C2212yescomplemented
22C59⋊#95C2212yescomplemented
23C59⋊#95C2212yescomplemented
24C59⋊#95C2211yescharacteristic, complemented
25C59⋊#95C2212yescomplemented
26C2×C4⋊C4×C59C2211yescharacteristic, complemented
27C2×C22⋊C4×C59C2212yes—
28C2×C22⋊C4×C59C2211yescharacteristic
29#95×C59C2212yescomplemented
30#95×C59C2211yescharacteristic, complemented
31C24×C59C2311yescharacteristic
32C23×D59—22no—
33C23×D59—24no—
34C23×D59—41no—
35C23×D59—42no—
36C23×D59—41no—
37C23×D59C2312yes—
38C22×C4×C59C2312yes—
39C22×C4×C59C2311yescharacteristic
40C22×C4×C59C2311yescharacteristic
41C22×C4×C59C2312yes—
42C22×Dic59C2312yes—
43C22×Dic59C2312yes—
44C22×Dic59C2312yes—
45C2×Dic118—41no—
46C2×Dic118—42no—
47C4⋊C4×C59—41no—
48C22⋊C4×C59—24no—
49C22⋊C4×C59—41no—
50C22⋊Dic59—41no—
51C22⋊Dic59—42no—
52(C2×D59)⋊C4—24no—
53(C2×D59)⋊C4—24no—
54(C2×D59)⋊C4—42no—
55(C2×D59)⋊C4—42no—
56(C2×D59)⋊C4—42no—
57(C2×D59)⋊C4—42no—
58C4⋊Dic59—42no—
59C4×Dic59—42no—
60C23×C59—22no—
61C23×C59—21no—
62C23×C59—22no—
63C23×C59—21no—
64C23×C59#4112yes—
65C23×C59C2411yescharacteristic
66C22×D59—22no—
67C22×D59—22no—
68C22×D59—22no—
69C22×D59—22no—
70C22×D59—22no—
71C22×D59—22no—
72C22×D59—44no—
73C22×D59—48no—
74C22×D59—48no—
75C22×D59—44no—
76C22×D59—44no—
77C22×D59#4114yes—
78C2×C4×C59—22no—
79C2×C4×C59—22no—
80C2×C4×C59—22no—
81C2×C4×C59—22no—
82C2×C4×C59—22no—
83C2×C4×C59—22no—
84C2×C4×C59—22no—
85C2×C4×C59—22no—
86C2×C4×C59—21no—
87C2×C4×C59—21no—
88C2×Dic59—22no—
89C2×Dic59—22no—
90C2×Dic59—22no—
91C2×Dic59—22no—
92C2×Dic59—22no—
93C2×Dic59—22no—
94C2×Dic59—22no—
95C2×Dic59—22no—
96C2×Dic59—22no—
97Dic118—44no—
98C22×C59—22no—
99C22×C59—24no—
100C22×C59—42no—
101C22×C59—41no—
102C22×C59—41no—
103C22×C59C2×#4112yes—
104C22×C59C2×#4111yescharacteristic
105C22×C59H(5,𝔽2)11yescharacteristic
106C22×C59H(5,𝔽2)11yescharacteristic
107C22×C59H(5,𝔽2)12yes—
108C2×D59—24no—
109C2×D59—24no—
110C2×D59—24no—
111C2×D59—416no—
112C2×D59—42no—
113C2×D59—42no—
114C2×D59—42no—
115C2×D59—42no—
116C4×C59—42no—
117C4×C59—42no—
118C4×C59—41no—
119C4×C59—41no—
120Dic59—42no—
121Dic59—42no—
122Dic59—42no—
123#2736—591nomaximal, Sylow
124C2×C59—42no—
125C2×C59#53811yescharacteristic
126C2×C59#53812yes—
127C2×C59#55112yes—
128C2×C59#55111yescharacteristic
129C2×C59H(3,𝔽4)11yescharacteristic
130D59—44no—
131#397—592no—
132#397D5911yescharacteristic, complemented
133#393—591no—
134#393—592no—
135#388—592no—
136#388—592no—
137#388—592no—
138#379—591no—
139#379—592no—
140C59#273611yescharacteristic, complemented, Sylow
141C25—591no—
142C22×Q8—591no—
143C2×C4⋊C4—592no—
144C2×C4⋊C4C2×D5911yescharacteristic, complemented
145C2×C22⋊C4—592no—
146C2×C22⋊C4—592no—
147C2×C22⋊C4—591no—
148C2×C22⋊C4—592no—
149C2×C22⋊C4—592no—
150C2×C22⋊C4—592no—
151C2×C22⋊C4—592no—
152C2×C22⋊C4—592no—
153C2×C22⋊C4C2×D5912yes—
154C2×C22⋊C4C2×D5911yescharacteristic
155C2×C42—592no—
156#95—592no—
157#95—591no—
158#95—592no—
159#95—592no—
160#95C2×D5912yescomplemented
161#95C2×D5911yescharacteristic, complemented
162C24—592no—
163C24—1184no—
164C24—1182no—
165C24—2361no—
166C24—2362no—
167C24—2361no—
168C24C22×D5911yescharacteristic
169C2×Q8—2361no—
170C2×Q8—2362no—
171C22×C4—592no—
172C22×C4—592no—
173C22×C4—592no—
174C22×C4C22×D5911yescharacteristic
175C22×C4C22×D5912yes—
176C22×C4C22×D5911yescharacteristic
177C22×C4C22×D5912yes—
178C4⋊C4—41no—
179C4⋊C4—2362no—
180C22⋊C4—24no—
181C22⋊C4—41no—
182C22⋊C4—1184no—
183C22⋊C4—1184no—
184C22⋊C4—2362no—
185C22⋊C4—2362no—
186C22⋊C4—2362no—
187C22⋊C4—2362no—
188C22⋊C4—2361no—
189C22⋊C4—2362no—
190C42—2362no—
191C23—22no—
192C23—21no—
193C23—21no—
194C23—22no—
195C23—594no—
196C23—1182no—
197C23—1182no—
198C23—1182no—
199C23—1182no—
200C23—1182no—
201C23—1182no—
202C23—2368no—
203C23—2364no—
204C23—2364no—
205C23—2368no—
206C23—2364no—
207C23#1174568712yes—
208C23C23×D5911yescharacteristic
209Q8—2364no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—1182no—
221C2×C4—1182no—
222C2×C4—1182no—
223C2×C4—1182no—
224C2×C4—1182no—
225C2×C4—1182no—
226C2×C4—1182no—
227C2×C4—1182no—
228C2×C4—1182no—
229C22—22no—
230C22—24no—
231C22—41no—
232C22—42no—
233C22—41no—
234C22—1184no—
235C22—1184no—
236C22—1184no—
237C22—23616no—
238C22—2362no—
239C22—2362no—
240C22—2362no—
241C22—2362no—
242C22#41×D5912yes—
243C22C2×#1174568711yescharacteristic
244C22#1427377211yescharacteristic
245C22#1427377312yes—
246C22#1427377311yescharacteristic
247C4—41no—
248C4—42no—
249C4—42no—
250C4—41no—
251C4—2362no—
252C4—2362no—
253C4—2362no—
254C2—42no—
255C2—2364no—
256C2#1683798911yescharacteristic
257C2#1683799112yes—
258C2#1683807512yes—
259C2#1683808011yescharacteristic
260C2#1683814411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#397C2
hypercenter#397D59
hypocenterC59#2736
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #16837329C2semidirect
2. #16837315C2semidirect
3. #16837314C2semidirect
4. #16837295C2semidirect
5. #16837294C2semidirect
6. #16837292C2semidirect
9. C59×#397C2semidirect
11. C22×Dic118C22semidirect
12. C2×C4⋊Dic59C22semidirect
21. C2×C4×Dic59C22semidirect
22. C59⋊#95C22semidirect
23. C59⋊#95C22semidirect
24. C59⋊#95C22semidirect
25. C59⋊#95C22semidirect
26. C2×C4⋊C4×C59C22semidirect
29. #95×C59C22semidirect
30. #95×C59C22semidirect
132. #397D59semidirect
140. C59#2736semidirect
144. C2×C4⋊C4C2×D59semidirect
160. #95C2×D59semidirect
161. #95C2×D59semidirect