Finite Group Databasebeta

← #21432149

Subgroups — #21432149

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×#14273717C211yesmaximal, characteristic, complemented
2C2×#14273714C211yesmaximal, characteristic
3#16837338C212yesmaximal, complemented
4#16837330C212yesmaximal, complemented
5#16837325C212yesmaximal, complemented
6#16837325C212yesmaximal, complemented
7#16837323C211yesmaximal, characteristic, complemented
8#16837322C211yesmaximal, characteristic, complemented
9#16837316C211yesmaximal, characteristic
10#16837266C211yesmaximal, characteristic, complemented
11C59×#394C211yesmaximal, characteristic
12C22×Dic118C2211yescharacteristic
13#14273717—24no—
14#14273714—24no—
15C2×C4⋊Dic59C2211yescharacteristic
16C2×C4⋊Dic59C2212yes—
17C2×Dic59⋊C4C2211yescharacteristic
18C2×Dic59⋊C4C2211yescharacteristic
19C2×Dic59⋊C4C2211yescharacteristic
20C2×Dic59⋊C4C2211yescharacteristic
21C2×Dic59⋊C4C2212yes—
22C2×Dic59⋊C4C2212yes—
23C2×C22⋊Dic59C2212yes—
24C2×C22⋊Dic59C2212yes—
25C2×C22⋊Dic59C2212yes—
26C2×C22⋊Dic59C2212yes—
27C2×C4×Dic59C2211yescharacteristic
28C59⋊#95C2211yescharacteristic
29C59⋊#95C2212yes—
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C22×D4×C59C2211yescharacteristic
33C2×C4⋊C4×C59C2211yescharacteristic
34C2×C22⋊C4×C59C2212yes—
35C2×C22⋊C4×C59C2212yes—
36#95×C59C2211yescharacteristic
37C24×C59C2312yes—
38C2×D4×C59—22no—
39C2×D4×C59—42no—
40C22×C4×C59C2312yes—
41C22×C4×C59C2311yescharacteristic
42C22×C4×C59C2311yescharacteristic
43C22×C4×C59C2311yescharacteristic
44C22×Dic59C2312yes—
45C22×Dic59C2311yescharacteristic
46C22×Dic59C2312yes—
47C22×Dic59C2311yescharacteristic
48C22×Dic59C2311yescharacteristic
49C22×Dic59C2311yescharacteristic
50C2×Dic118—22no—
51C2×Dic118—42no—
52C4⋊C4×C59—22no—
53C22⋊C4×C59—42no—
54C22⋊C4×C59—42no—
55C22⋊Dic59—24no—
56C22⋊Dic59—24no—
57C22⋊Dic59—42no—
58C22⋊Dic59—42no—
59C4⋊Dic59—22no—
60C4⋊Dic59—42no—
61Dic59⋊C4—22no—
62Dic59⋊C4—22no—
63Dic59⋊C4—22no—
64Dic59⋊C4—22no—
65Dic59⋊C4—42no—
66Dic59⋊C4—42no—
67C4×Dic59D414yes—
68C23×C59—22no—
69C23×C59—22no—
70C23×C59—22no—
71C23×C59—22no—
72C23×C59—22no—
73C23×C59—22no—
74C23×C59—22no—
75C23×C59C2411yescharacteristic
76D4×C59—44no—
77C2×C4×C59—22no—
78C2×C4×C59—21no—
79C2×C4×C59—21no—
80C2×C4×C59—22no—
81C2×C4×C59—22no—
82C2×C4×C59—22no—
83C2×C4×C59—21no—
84C2×C4×C59—21no—
85C2×C4×C59—22no—
86C2×C4×C59C2×D412yes—
87C2×Dic59—21no—
88C2×Dic59—22no—
89C2×Dic59—21no—
90C2×Dic59—21no—
91C2×Dic59—21no—
92C2×Dic59—22no—
93C2×Dic59—22no—
94C2×Dic59—22no—
95C2×Dic59—22no—
96C2×Dic59—22no—
97C2×Dic59—22no—
98C2×Dic59—21no—
99C2×Dic59—21no—
100C2×Dic59—22no—
101C2×Dic59C2×D412yes—
102C2×Dic59C2×D412yes—
103Dic118—44no—
104C22×C59—42no—
105C22×C59—42no—
106C22×C59—42no—
107C22×C59—42no—
108C22×C59—42no—
109C22×C59—42no—
110C22×C59—42no—
111C22×C59C22×D411yescharacteristic
112C22×C59H(5,𝔽2)12yes—
113C22×C59H(5,𝔽2)11yescharacteristic
114C22×C592−1+412yes—
115C22×C592−1+411yescharacteristic
116C4×C59—22no—
117C4×C59—41no—
118C4×C59—41no—
119C4×C59—42no—
120Dic59—22no—
121Dic59—22no—
122Dic59—42no—
123Dic59—41no—
124Dic59—41no—
125Dic59—42no—
126#2820—591nomaximal, Sylow
127C2×C59—82no—
128C2×C59#53511yescharacteristic
129C2×C59#53611yescharacteristic
130C2×C59#53711yescharacteristic
131C2×C59#56212yes—
132C2×C59#56312yes—
133C2×#125—591no—
134C2×#124—591no—
135#399—592no—
136#397—592no—
137#396—592no—
138#396—592no—
139#395—591no—
140#395—591no—
141#394—591no—
142#394D5911yescharacteristic
143#382—591no—
144C59#282011yescharacteristic, complemented, Sylow
145C22×Q8—591no—
146C22×D4C2×D5911yescharacteristic
147#125—1184no—
148#124—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⋊C4—592no—
156C2×C4⋊C4—592no—
157C2×C4⋊C4C2×D5911yescharacteristic
158C2×C22⋊C4—592no—
159C2×C22⋊C4—592no—
160C2×C22⋊C4—592no—
161C2×C22⋊C4—592no—
162C2×C22⋊C4C2×D5912yes—
163C2×C22⋊C4C2×D5912yes—
164C2×C42—591no—
165#95—591no—
166#95—592no—
167#95—592no—
168#95—592no—
169#95C2×D5911yescharacteristic
170C24C22×D5912yes—
171C2×Q8—1182no—
172C2×Q8—2362no—
173C2×D4—22no—
174C2×D4—42no—
175C22×C4—591no—
176C22×C4—591no—
177C22×C4—592no—
178C22×C4—591no—
179C22×C4—592no—
180C22×C4—591no—
181C22×C4C22×D5912yes—
182C22×C4C22×D5911yescharacteristic
183C22×C4C22×D5911yescharacteristic
184C22×C4C22×D5911yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—1182no—
187C4⋊C4—1182no—
188C4⋊C4—1182no—
189C4⋊C4—1182no—
190C4⋊C4—1182no—
191C4⋊C4—2362no—
192C4⋊C4—2362no—
193C4⋊C4—2362no—
194C22⋊C4—42no—
195C22⋊C4—42no—
196C22⋊C4—1184no—
197C22⋊C4—1184no—
198C22⋊C4—2362no—
199C22⋊C4—2362no—
200C42—594no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23C23×D5911yescharacteristic
209Q8—2364no—
210D4—44no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—592no—
221C2×C4—592no—
222C2×C4—1181no—
223C2×C4—1182no—
224C2×C4—1181no—
225C2×C4—1182no—
226C2×C4—1181no—
227C2×C4—1181no—
228C2×C4—1181no—
229C2×C4—1182no—
230C2×C4—1182no—
231C2×C4—1182no—
232C2×C4—1182no—
233C2×C4—1182no—
234C2×C4—1182no—
235C2×C4—1181no—
236C2×C4D4×D5912yes—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—42no—
244C22C2×D4×D5911yescharacteristic
245C22#1427377211yescharacteristic
246C22#1427377212yes—
247C22#1427377412yes—
248C22#1427377411yescharacteristic
249C4—22no—
250C4—42no—
251C4—41no—
252C4—41no—
253C4—1182no—
254C4—1182no—
255C4—2362no—
256C4—2362no—
257C4—2361no—
258C4—2361no—
259C2—82no—
260C2#1683796711yescharacteristic
261C2#1683797211yescharacteristic
262C2#1683798111yescharacteristic
263C2#1683814712yes—
264C2#1683815512yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#394C2
hypercenter#394D59
hypocenterC59#2820
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14273717C2semidirect
3. #16837338C2semidirect
4. #16837330C2semidirect
5. #16837325C2semidirect
6. #16837325C2semidirect
7. #16837323C2semidirect
8. #16837322C2semidirect
10. #16837266C2semidirect
144. C59#2820semidirect