Finite Group Databasebeta

← #21431142

Subgroups — #21431142

Order 7552.

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

normal subgroups only

This group has 560 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#16837330C212yesmaximal, complemented
2#16837327C211yesmaximal, characteristic, complemented
3#16837314C212yesmaximal, complemented
4#16837314C211yesmaximal, characteristic, complemented
5#16837296C212yesmaximal, complemented
6#16837295C212yesmaximal, complemented
7#16837290C212yesmaximal, complemented
8#16837258C212yesmaximal
9C59×#379C211yesmaximal, characteristic
10C22×Dic118C2211yescharacteristic, complemented
11C2×C4⋊Dic59C2211yescharacteristic, complemented
12C2×Dic59⋊C4C2212yescomplemented
13C2×C22⋊Dic59C2212yes—
14C2×C22⋊Dic59C2212yes—
15C2×C22⋊Dic59C2212yes—
16C2×C22⋊Dic59C2212yes—
17C2×C22⋊Dic59C2212yes—
18C2×C22⋊Dic59C2212yes—
19C2×C4×Dic59C2212yescomplemented
20C59⋊#95C2212yescomplemented
21C59⋊#95C2212yescomplemented
22C59⋊#95C2212yescomplemented
23C59⋊#95C2211yescharacteristic, complemented
24C59⋊#95C2212yescomplemented
25C59⋊#95C2211yescharacteristic, complemented
26C25×C59C2211yescharacteristic
27C2×C22⋊C4×C59C2212yes—
28C2×C22⋊C4×C59C2211yescharacteristic
29C2×C22⋊C4×C59C2212yes—
30C2×C22⋊C4×C59C2211yescharacteristic
31C24×C59—22no—
32C24×C59—24no—
33C24×C59—42no—
34C24×C59—41no—
35C24×C59—41no—
36C24×C59C2312yes—
37C24×C59C2311yescharacteristic
38C22×C4×C59C2311yescharacteristic
39C22×C4×C59C2311yescharacteristic
40C22×C4×C59C2312yes—
41C22×Dic59C2312yes—
42C22×Dic59C2312yes—
43C22×Dic59C2312yes—
44C22×Dic59C2312yes—
45C2×Dic118—42no—
46C2×Dic118—41no—
47C22⋊C4×C59—24no—
48C22⋊C4×C59—41no—
49C22⋊C4×C59—42no—
50C22⋊C4×C59—41no—
51C22⋊Dic59—24no—
52C22⋊Dic59—24no—
53C22⋊Dic59—42no—
54C22⋊Dic59—42no—
55C22⋊Dic59—42no—
56C22⋊Dic59—42no—
57C4⋊Dic59—41no—
58Dic59⋊C4—42no—
59C4×Dic59—42no—
60C23×C59—22no—
61C23×C59—22no—
62C23×C59—22no—
63C23×C59—22no—
64C23×C59—22no—
65C23×C59—22no—
66C23×C59—22no—
67C23×C59—21no—
68C23×C59—21no—
69C23×C59—22no—
70C23×C59—48no—
71C23×C59—44no—
72C23×C59—48no—
73C23×C59—44no—
74C23×C59—44no—
75C23×C59#4112yes—
76C23×C59#4114yes—
77C23×C59C2411yescharacteristic
78C2×C4×C59—22no—
79C2×C4×C59—22no—
80C2×C4×C59—22no—
81C2×C4×C59—22no—
82C2×C4×C59—21no—
83C2×C4×C59—22no—
84C2×C4×C59—21no—
85C2×Dic59—22no—
86C2×Dic59—22no—
87C2×Dic59—22no—
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—24no—
99C22×C59—22no—
100C22×C59—24no—
101C22×C59—24no—
102C22×C59—24no—
103C22×C59—416no—
104C22×C59—42no—
105C22×C59—42no—
106C22×C59—42no—
107C22×C59—42no—
108C22×C59—41no—
109C22×C59—42no—
110C22×C59—41no—
111C22×C59C2×#4112yes—
112C22×C59C2×#4111yescharacteristic
113C22×C59H(5,𝔽2)11yescharacteristic
114C22×C59H(5,𝔽2)12yes—
115C22×C59H(5,𝔽2)11yescharacteristic
116C4×C59—42no—
117C4×C59—41no—
118C4×C59—41no—
119Dic59—42no—
120Dic59—42no—
121Dic59—42no—
122Dic59—42no—
123#2736—591nomaximal, Sylow
124C2×C59—44no—
125C2×C59—42no—
126C2×C59#53812yes—
127C2×C59#53811yescharacteristic
128C2×C59#55112yes—
129C2×C59#55111yescharacteristic
130C2×C59H(3,𝔽4)11yescharacteristic
131#397—591no—
132#397—592no—
133#393—591no—
134#393—592no—
135#388—592no—
136#388—592no—
137#388—592no—
138#379—592no—
139#379D5911yescharacteristic
140C59#273611yescharacteristic, complemented, Sylow
141C25C2×D5911yescharacteristic
142C22×Q8—591no—
143C2×C4⋊C4—592no—
144C2×C4⋊C4—591no—
145C2×C22⋊C4—592no—
146C2×C22⋊C4—592no—
147C2×C22⋊C4—592no—
148C2×C22⋊C4—592no—
149C2×C22⋊C4—592no—
150C2×C22⋊C4—592no—
151C2×C22⋊C4C2×D5912yes—
152C2×C22⋊C4C2×D5911yescharacteristic
153C2×C22⋊C4C2×D5912yes—
154C2×C22⋊C4C2×D5911yescharacteristic
155C2×C42—592no—
156#95—592no—
157#95—591no—
158#95—592no—
159#95—592no—
160#95—592no—
161#95—591no—
162C24—22no—
163C24—24no—
164C24—41no—
165C24—42no—
166C24—41no—
167C24C22×D5911yescharacteristic
168C24C22×D5912yes—
169C2×Q8—2362no—
170C2×Q8—2361no—
171C22×C4—592no—
172C22×C4—592no—
173C22×C4—592no—
174C22×C4—592no—
175C22×C4C22×D5911yescharacteristic
176C22×C4C22×D5911yescharacteristic
177C22×C4C22×D5912yes—
178C4⋊C4—2362no—
179C4⋊C4—2361no—
180C22⋊C4—24no—
181C22⋊C4—41no—
182C22⋊C4—42no—
183C22⋊C4—41no—
184C22⋊C4—1184no—
185C22⋊C4—1184no—
186C22⋊C4—2362no—
187C22⋊C4—2362no—
188C22⋊C4—2362no—
189C22⋊C4—2362no—
190C42—2362no—
191C23—22no—
192C23—22no—
193C23—22no—
194C23—21no—
195C23—21no—
196C23—22no—
197C23—22no—
198C23—22no—
199C23—22no—
200C23—22no—
201C23—48no—
202C23—44no—
203C23—48no—
204C23—44no—
205C23—44no—
206C23#1174568512yes—
207C23#1174568714yes—
208C23C23×D5911yescharacteristic
209Q8—2364no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—1182no—
218C2×C4—1182no—
219C2×C4—1182no—
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—24no—
230C22—22no—
231C22—24no—
232C22—24no—
233C22—24no—
234C22—416no—
235C22—42no—
236C22—41no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—41no—
242C22C2×#1174568712yes—
243C22C2×#1174568511yescharacteristic
244C22#1427377212yes—
245C22#1427377211yescharacteristic
246C22#1427377211yescharacteristic
247C4—41no—
248C4—42no—
249C4—41no—
250C4—2362no—
251C4—2362no—
252C4—2362no—
253C4—2362no—
254C2—44no—
255C2—42no—
256C2#1683798712yes—
257C2#1683799011yescharacteristic
258C2#1683807812yes—
259C2#1683808311yescharacteristic
260C2#1683814511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#379C2
hypercenter#379D59
hypocenterC59#2736
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #16837330C2semidirect
2. #16837327C2semidirect
3. #16837314C2semidirect
4. #16837314C2semidirect
5. #16837296C2semidirect
6. #16837295C2semidirect
7. #16837290C2semidirect
10. C22×Dic118C22semidirect
11. C2×C4⋊Dic59C22semidirect
12. C2×Dic59⋊C4C22semidirect
19. C2×C4×Dic59C22semidirect
20. C59⋊#95C22semidirect
21. C59⋊#95C22semidirect
22. C59⋊#95C22semidirect
23. C59⋊#95C22semidirect
24. C59⋊#95C22semidirect
25. C59⋊#95C22semidirect
140. C59#2736semidirect