Finite Group Databasebeta

← #21432152

Subgroups — #21432152

Order 7552.

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

normal subgroups only

This group has 464 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
1C2×#14273718C211yesmaximal, characteristic, complemented
2C2×#14273713C211yesmaximal, characteristic
3#16837339C211yesmaximal, characteristic, complemented
4#16837338C211yesmaximal, characteristic, complemented
5#16837328C211yesmaximal, characteristic, complemented
6#16837326C212yesmaximal, complemented
7#16837325C212yesmaximal, complemented
8#16837323C212yesmaximal, complemented
9#16837318C212yesmaximal
10#16837266C211yesmaximal, characteristic, complemented
11C59×#397C211yesmaximal, characteristic, complemented
12C22×Dic118C2211yescharacteristic
13C22×C22⋊D59C2211yescharacteristic
14#14273718—24no—
15#14273713—24no—
16C2×C4⋊Dic59C2212yes—
17C2×C4⋊Dic59C2211yescharacteristic
18C2×C4⋊Dic59C2212yes—
19C2×Dic59⋊C4C2212yes—
20C2×Dic59⋊C4C2212yes—
21C2×Dic59⋊C4C2212yes—
22C2×C22⋊Dic59C2211yescharacteristic
23C2×C22⋊Dic59C2212yes—
24C2×(C2×D59)⋊C4C2211yescharacteristic
25C2×(C2×D59)⋊C4C2211yescharacteristic
26C2×(C2×D59)⋊C4C2212yes—
27C2×(C2×D59)⋊C4C2212yes—
28C2×C4×Dic59C2211yescharacteristic
29C59⋊#95C2212yes—
30C59⋊#95C2211yescharacteristic
31C59⋊#95C2212yes—
32C2×C4⋊C4×C59C2211yescharacteristic
33C2×C22⋊C4×C59C2211yescharacteristic
34C2×C22⋊C4×C59C2212yes—
35#95×C59C2211yescharacteristic
36#95×C59C2212yes—
37C24×C59C2311yescharacteristic
38C23×D59C2311yescharacteristic
39C22×C4×C59C2312yes—
40C22×C4×C59C2311yescharacteristic
41C22×C4×C59C2312yes—
42C22×C4×C59C2311yescharacteristic
43C2×C22⋊D59—22no—
44C2×C22⋊D59—42no—
45C22×Dic59C2312yes—
46C22×Dic59C2311yescharacteristic
47C22×Dic59C2312yes—
48C22×Dic59C2311yescharacteristic
49C22×Dic59C2311yescharacteristic
50C2×Dic118—22no—
51C2×Dic118—42no—
52C4⋊C4×C59—22no—
53C22⋊C4×C59—22no—
54C22⋊C4×C59—42no—
55C22⋊Dic59—22no—
56C22⋊Dic59—42no—
57(C2×D59)⋊C4—22no—
58(C2×D59)⋊C4—22no—
59(C2×D59)⋊C4—42no—
60(C2×D59)⋊C4—42no—
61C4⋊Dic59—22no—
62C4⋊Dic59—24no—
63C4⋊Dic59—42no—
64Dic59⋊C4—24no—
65Dic59⋊C4—42no—
66Dic59⋊C4—42no—
67C4×Dic59D414yes—
68C23×C59—21no—
69C23×C59—22no—
70C23×C59—21no—
71C23×C59—22no—
72C23×C59—21no—
73C23×C59C2411yescharacteristic
74C22×D59—21no—
75C22×D59—21no—
76C22×D59—22no—
77C22×D59—22no—
78C22×D59—21no—
79C2×C4×C59—22no—
80C2×C4×C59—22no—
81C2×C4×C59—21no—
82C2×C4×C59—22no—
83C2×C4×C59—22no—
84C2×C4×C59—22no—
85C2×C4×C59—22no—
86C2×C4×C59—22no—
87C2×C4×C59—22no—
88C2×C4×C59C2×D412yes—
89C22⋊D59—44no—
90C2×Dic59—21no—
91C2×Dic59—22no—
92C2×Dic59—21no—
93C2×Dic59—22no—
94C2×Dic59—21no—
95C2×Dic59—22no—
96C2×Dic59—22no—
97C2×Dic59—22no—
98C2×Dic59—22no—
99C2×Dic59—22no—
100C2×Dic59—22no—
101C2×Dic59C2×D412yes—
102C2×Dic59C2×D412yes—
103Dic118—44no—
104C22×C59—41no—
105C22×C59—41no—
106C22×C59—41no—
107C22×C59—42no—
108C22×C59—42no—
109C22×C59C22×D411yescharacteristic
110C22×C59H(5,𝔽2)11yescharacteristic
111C22×C59H(5,𝔽2)12yes—
112C22×C592−1+412yes—
113C22×C592−1+411yescharacteristic
114C2×D59—41no—
115C2×D59—41no—
116C2×D59—41no—
117C2×D59—42no—
118C2×D59—42no—
119C4×C59—22no—
120C4×C59—41no—
121C4×C59—42no—
122C4×C59—42no—
123Dic59—22no—
124Dic59—22no—
125Dic59—41no—
126Dic59—42no—
127Dic59—42no—
128#2820—591nomaximal, Sylow
129C2×C59—81no—
130C2×C59#53511yescharacteristic
131C2×C59#53611yescharacteristic
132C2×C59#53711yescharacteristic
133C2×C59#56212yes—
134C2×C59#56312yes—
135D59—81no—
136C2×#125—591no—
137C2×#124—591no—
138#399—591no—
139#399—591no—
140#397—591no—
141#397D5911yescharacteristic, complemented
142#396—592no—
143#396—592no—
144#395—592no—
145#394—592no—
146#382—591no—
147C59#282011yescharacteristic, complemented, Sylow
148C22×Q8—591no—
149C22×D4—591no—
150#125—1184no—
151#124—1184no—
152C2×C4⋊C4—592no—
153C2×C4⋊C4—592no—
154C2×C4⋊C4—591no—
155C2×C4⋊C4—592no—
156C2×C4⋊C4—592no—
157C2×C4⋊C4—592no—
158C2×C4⋊C4C2×D5911yescharacteristic
159C2×C22⋊C4—591no—
160C2×C22⋊C4—591no—
161C2×C22⋊C4—591no—
162C2×C22⋊C4—592no—
163C2×C22⋊C4—592no—
164C2×C22⋊C4—592no—
165C2×C22⋊C4C2×D5911yescharacteristic
166C2×C22⋊C4C2×D5912yes—
167C2×C42—591no—
168#95—592no—
169#95—591no—
170#95—592no—
171#95C2×D5911yescharacteristic
172#95C2×D5912yes—
173C24—591no—
174C24C22×D5911yescharacteristic
175C2×Q8—1182no—
176C2×Q8—2362no—
177C2×D4—1182no—
178C2×D4—2362no—
179C22×C4—591no—
180C22×C4—591no—
181C22×C4—592no—
182C22×C4—591no—
183C22×C4—592no—
184C22×C4C22×D5912yes—
185C22×C4C22×D5912yes—
186C22×C4C22×D5911yescharacteristic
187C22×C4C22×D5911yescharacteristic
188C4⋊C4—22no—
189C4⋊C4—1184no—
190C4⋊C4—1184no—
191C4⋊C4—1182no—
192C4⋊C4—2362no—
193C4⋊C4—2362no—
194C4⋊C4—2362no—
195C22⋊C4—22no—
196C22⋊C4—42no—
197C22⋊C4—1182no—
198C22⋊C4—1182no—
199C22⋊C4—1182no—
200C22⋊C4—2362no—
201C22⋊C4—2362no—
202C22⋊C4—2362no—
203C42—594no—
204C23—21no—
205C23—21no—
206C23—22no—
207C23—22no—
208C23—21no—
209C23—1181no—
210C23—1181no—
211C23—1182no—
212C23—1182no—
213C23—1181no—
214C23C23×D5911yescharacteristic
215Q8—2364no—
216D4—2364no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—592no—
227C2×C4—592no—
228C2×C4—1181no—
229C2×C4—1182no—
230C2×C4—1181no—
231C2×C4—1181no—
232C2×C4—1182no—
233C2×C4—1182no—
234C2×C4—1182no—
235C2×C4—1182no—
236C2×C4—1182no—
237C2×C4—1182no—
238C2×C4—1182no—
239C2×C4D4×D5912yes—
240C22—42no—
241C22—42no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—2362no—
246C22—2362no—
247C22—2361no—
248C22—2361no—
249C22—2361no—
250C22C2×D4×D5911yescharacteristic
251C22#1427377211yescharacteristic
252C22#1427377312yes—
253C22#1427377412yes—
254C22#1427377411yescharacteristic
255C4—22no—
256C4—42no—
257C4—41no—
258C4—42no—
259C4—1182no—
260C4—1182no—
261C4—2362no—
262C4—2361no—
263C4—2362no—
264C2—81no—
265C2—4721no—
266C2#1683797011yescharacteristic
267C2#1683797411yescharacteristic
268C2#1683798111yescharacteristic
269C2#1683814912yes—
270C2#1683815412yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#397C2
hypercenter#397D59
hypocenterC59#2820
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#14273718C2semidirect
3. #16837339C2semidirect
4. #16837338C2semidirect
5. #16837328C2semidirect
6. #16837326C2semidirect
7. #16837325C2semidirect
8. #16837323C2semidirect
10. #16837266C2semidirect
11. C59×#397C2semidirect
141. #397D59semidirect
147. C59#2820semidirect