Finite Group Databasebeta

← #21429966

Subgroups — #21429966

Order 7552.

512 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C2×#14273717C211yesmaximal, characteristic, complemented
2C2×#14273689C211yesmaximal, characteristic
3#16837337C212yesmaximal, complemented
4#16837333C211yesmaximal, characteristic, complemented
5#16837331C212yesmaximal, complemented
6#16837320C211yesmaximal, characteristic
7#16837319C211yesmaximal, characteristic
8#16837276C212yesmaximal, complemented
9#16837273C212yesmaximal, complemented
10#16837269C211yesmaximal, characteristic, complemented
11C59×#398C211yesmaximal, characteristic, complemented
12C22×D236C2211yescharacteristic
13C22×C4×D59C2212yes—
14#14273717—24no—
15#14273689—24no—
16C2×C4⋊Dic59C2211yescharacteristic
17C2×Dic59⋊C4C2211yescharacteristic
18C2×Dic59⋊C4C2211yescharacteristic
19C2×Dic59⋊C4C2211yescharacteristic
20C2×Dic59⋊C4C2211yescharacteristic
21C2×Dic59⋊C4C2212yes—
22C2×(C2×D59)⋊C4C2212yes—
23C2×(C2×D59)⋊C4C2212yes—
24C2×(C2×D59)⋊C4C2212yes—
25C2×(C2×D59)⋊C4C2212yes—
26C2×(C2×D59)⋊C4C2212yes—
27C2×C4×Dic59C2211yescharacteristic
28C59⋊#95C2212yes—
29C59⋊#95C2211yescharacteristic
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C2×C4⋊C4×C59C2211yescharacteristic
33C2×C4⋊C4×C59C2211yescharacteristic
34C2×C4⋊C4×C59C2212yes—
35#95×C59C2211yescharacteristic
36#95×C59C2212yes—
37C23×D59C2312yes—
38C22×C4×C59C2312yes—
39C22×C4×C59C2311yescharacteristic
40C22×C4×C59C2312yes—
41C22×C4×C59C2311yescharacteristic
42C22×C4×C59C2311yescharacteristic
43C22×Dic59C2312yes—
44C22×Dic59C2311yescharacteristic
45C22×Dic59C2311yescharacteristic
46C22×Dic59C2311yescharacteristic
47C22×Dic59C2311yescharacteristic
48C2×D236—24no—
49C2×D236—22no—
50C2×C4×D59—24no—
51C2×C4×D59—42no—
52C2×C4×D59—42no—
53C4⋊C4×C59—22no—
54C4⋊C4×C59—22no—
55C4⋊C4×C59—42no—
56(C2×D59)⋊C4—24no—
57(C2×D59)⋊C4—24no—
58(C2×D59)⋊C4—24no—
59(C2×D59)⋊C4—42no—
60(C2×D59)⋊C4—42no—
61C4⋊Dic59—22no—
62Dic59⋊C4—22no—
63Dic59⋊C4—22no—
64Dic59⋊C4—22no—
65Dic59⋊C4—22no—
66Dic59⋊C4—42no—
67C4×Dic59D414yes—
68C23×C59C2411yescharacteristic
69C22×D59—22no—
70C22×D59—22no—
71C22×D59—22no—
72C22×D59—22no—
73C22×D59—22no—
74C22×D59—22no—
75C22×D59#4114yes—
76C2×C4×C59—22no—
77C2×C4×C59—21no—
78C2×C4×C59—21no—
79C2×C4×C59—22no—
80C2×C4×C59—22no—
81C2×C4×C59—22no—
82C2×C4×C59—22no—
83C2×C4×C59—21no—
84C2×C4×C59—22no—
85C2×C4×C59—21no—
86C2×C4×C59—22no—
87C2×C4×C59—22no—
88C2×C4×C59C2×D412yes—
89C2×Dic59—21no—
90C2×Dic59—21no—
91C2×Dic59—22no—
92C2×Dic59—21no—
93C2×Dic59—21no—
94C2×Dic59—22no—
95C2×Dic59—22no—
96C2×Dic59—21no—
97C2×Dic59—22no—
98C2×Dic59—21no—
99C2×Dic59—22no—
100C2×Dic59C2×D412yes—
101C2×Dic59C2×D412yes—
102D236—28no—
103C4×D59—48no—
104C22×C59C22×D411yescharacteristic
105C22×C59C2×#4112yes—
106C22×C59H(5,𝔽2)11yescharacteristic
107C22×C59H(5,𝔽2)11yescharacteristic
108C22×C592−1+412yes—
109C2×D59—24no—
110C2×D59—24no—
111C2×D59—24no—
112C2×D59—42no—
113C2×D59—42no—
114C2×D59—42no—
115C2×D59—42no—
116C4×C59—22no—
117C4×C59—41no—
118C4×C59—42no—
119C4×C59—41no—
120C4×C59—42no—
121Dic59—22no—
122Dic59—22no—
123Dic59—41no—
124Dic59—41no—
125Dic59—42no—
126#2633—591nomaximal, Sylow
127C2×C59#52511yescharacteristic
128C2×C59#53511yescharacteristic
129C2×C59#53611yescharacteristic
130C2×C59#53912yes—
131C2×C59#53912yes—
132D59—44no—
133C2×#125—591no—
134C2×C4×D4—591no—
135#399—592no—
136#398—591no—
137#398D5911yescharacteristic, complemented
138#397—592no—
139#394—591no—
140#394—591no—
141#385—592no—
142#385—592no—
143#383—591no—
144C59#263311yescharacteristic, complemented, Sylow
145C22×D4—591no—
146C23×C4—592no—
147#125—1184no—
148C4×D4—1184no—
149C2×C4⋊C4—591no—
150C2×C4⋊C4—591no—
151C2×C4⋊C4—591no—
152C2×C4⋊C4—591no—
153C2×C4⋊C4—591no—
154C2×C4⋊C4—592no—
155C2×C4⋊C4C2×D5911yescharacteristic
156C2×C4⋊C4C2×D5911yescharacteristic
157C2×C4⋊C4C2×D5912yes—
158C2×C22⋊C4—592no—
159C2×C22⋊C4—592no—
160C2×C22⋊C4—592no—
161C2×C22⋊C4—592no—
162C2×C22⋊C4—592no—
163C2×C42—591no—
164#95—592no—
165#95—591no—
166#95—592no—
167#95—592no—
168#95C2×D5911yescharacteristic
169#95C2×D5912yes—
170C24—592no—
171C2×D4—1184no—
172C2×D4—1182no—
173C22×C4—591no—
174C22×C4—591no—
175C22×C4—592no—
176C22×C4—591no—
177C22×C4—591no—
178C22×C4—1184no—
179C22×C4—2362no—
180C22×C4—2362no—
181C22×C4C22×D5912yes—
182C22×C4C22×D5912yes—
183C22×C4C22×D5911yescharacteristic
184C22×C4C22×D5911yescharacteristic
185C22×C4C22×D5911yescharacteristic
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—42no—
189C4⋊C4—1182no—
190C4⋊C4—1182no—
191C4⋊C4—1182no—
192C4⋊C4—1182no—
193C4⋊C4—1182no—
194C4⋊C4—2362no—
195C22⋊C4—1184no—
196C22⋊C4—1184no—
197C22⋊C4—1184no—
198C22⋊C4—2362no—
199C22⋊C4—2362no—
200C42—594no—
201C23—594no—
202C23—1182no—
203C23—1182no—
204C23—1182no—
205C23—1182no—
206C23—1182no—
207C23—1182no—
208C23C23×D5911yescharacteristic
209D4—1188no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—592no—
223C2×C4—592no—
224C2×C4—1181no—
225C2×C4—1181no—
226C2×C4—1182no—
227C2×C4—1181no—
228C2×C4—1181no—
229C2×C4—1182no—
230C2×C4—1182no—
231C2×C4—1181no—
232C2×C4—1182no—
233C2×C4—1181no—
234C2×C4—1182no—
235C2×C4—2368no—
236C2×C4D4×D5912yes—
237C22—1184no—
238C22—1184no—
239C22—1184no—
240C22—2362no—
241C22—2362no—
242C22—2362no—
243C22—2362no—
244C22C2×D4×D5911yescharacteristic
245C22#41×D5912yes—
246C22#1427377211yescharacteristic
247C22#1427377311yescharacteristic
248C22#1427377512yes—
249C4—22no—
250C4—41no—
251C4—42no—
252C4—41no—
253C4—42no—
254C4—1182no—
255C4—1182no—
256C4—2361no—
257C4—2361no—
258C4—2362no—
259C2—2364no—
260C2#1683791011yescharacteristic
261C2#1683796811yescharacteristic
262C2#1683797711yescharacteristic
263C2#1683799812yes—
264C2#1683800012yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#398C2
hypercenter#398D59
hypocenterC59#2633
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14273717C2semidirect
3. #16837337C2semidirect
4. #16837333C2semidirect
5. #16837331C2semidirect
8. #16837276C2semidirect
9. #16837273C2semidirect
10. #16837269C2semidirect
11. C59×#398C2semidirect
137. #398D59semidirect
144. C59#2633semidirect