Finite Group Databasebeta

← #21429969

Subgroups — #21429969

Order 7552.

512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 131 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×(C22⋊D59)⋊C4C211yesmaximal, characteristic
3#16837339C211yesmaximal, characteristic, complemented
4#16837338C211yesmaximal, characteristic, complemented
5#16837336C212yesmaximal, complemented
6#16837328C211yesmaximal, characteristic, complemented
7#16837317C212yesmaximal
8#16837277C212yesmaximal, complemented
9#16837276C212yesmaximal, complemented
10#16837269C211yesmaximal, characteristic, complemented
11C59×#397C211yesmaximal, characteristic, complemented
12C22×C22⋊D59C2211yescharacteristic
13C23×Dic59C2211yescharacteristic
14C22×C4×D59C2211yescharacteristic
15#14273718—24no—
16(C22⋊D59)⋊C4—24no—
17C2×C4⋊Dic59C2212yes—
18C2×C4⋊Dic59C2211yescharacteristic
19C2×C4⋊Dic59C2212yes—
20C2×Dic59⋊C4C2212yes—
21C2×Dic59⋊C4C2211yescharacteristic
22C2×Dic59⋊C4C2212yes—
23C2×C22⋊Dic59C2212yes—
24C2×(C2×D59)⋊C4C2212yes—
25C2×(C2×D59)⋊C4C2211yescharacteristic
26C2×(C2×D59)⋊C4C2212yes—
27C2×C4×Dic59C2211yescharacteristic
28C59⋊#95C2212yes—
29C59⋊#95C2212yes—
30C59⋊#95C2211yescharacteristic
31C59⋊#95C2212yes—
32C2×C4⋊C4×C59C2211yescharacteristic
33C2×C22⋊C4×C59C2212yes—
34C2×C22⋊C4×C59C2211yescharacteristic
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—22no—
45C2×C22⋊D59—22no—
46C22×Dic59—22no—
47C22×Dic59—42no—
48C22×Dic59C2312yes—
49C22×Dic59C2311yescharacteristic
50C22×Dic59C2312yes—
51C22×Dic59C2311yescharacteristic
52C22×Dic59C2311yescharacteristic
53C2×C4×D59—22no—
54C2×C4×D59—42no—
55C4⋊C4×C59—22no—
56C22⋊C4×C59—24no—
57C22⋊C4×C59—22no—
58C22⋊Dic59—42no—
59(C2×D59)⋊C4—24no—
60(C2×D59)⋊C4—22no—
61(C2×D59)⋊C4—42no—
62C4⋊Dic59—22no—
63C4⋊Dic59—24no—
64C4⋊Dic59—42no—
65Dic59⋊C4—22no—
66Dic59⋊C4—24no—
67Dic59⋊C4—42no—
68C4×Dic59D414yes—
69C23×C59—21no—
70C23×C59—21no—
71C23×C59—22no—
72C23×C59—22no—
73C23×C59#4112yes—
74C23×C59C2411yescharacteristic
75C22×D59—21no—
76C22×D59—21no—
77C22×D59—22no—
78C22×D59—22no—
79C22×D59#4112yes—
80C2×C4×C59—22no—
81C2×C4×C59—22no—
82C2×C4×C59—21no—
83C2×C4×C59—22no—
84C2×C4×C59—22no—
85C2×C4×C59—22no—
86C2×C4×C59—22no—
87C2×C4×C59—22no—
88C2×C4×C59—22no—
89C2×C4×C59C2×D412yes—
90C22⋊D59—28no—
91C2×Dic59—21no—
92C2×Dic59—21no—
93C2×Dic59—22no—
94C2×Dic59—22no—
95C2×Dic59—21no—
96C2×Dic59—22no—
97C2×Dic59—22no—
98C2×Dic59—22no—
99C2×Dic59—22no—
100C2×Dic59—22no—
101C2×Dic59—22no—
102C2×Dic59—44no—
103C2×Dic59C2×D412yes—
104C2×Dic59C2×D412yes—
105C4×D59—44no—
106C22×C59—22no—
107C22×C59—24no—
108C22×C59—41no—
109C22×C59—41no—
110C22×C59—42no—
111C22×C59C22×D411yescharacteristic
112C22×C59C2×#4111yescharacteristic
113C22×C59C2×#4111yescharacteristic
114C22×C59H(5,𝔽2)12yes—
115C22×C592−1+412yes—
116C2×D59—22no—
117C2×D59—24no—
118C2×D59—41no—
119C2×D59—41no—
120C2×D59—42no—
121C4×C59—22no—
122C4×C59—42no—
123C4×C59—41no—
124C4×C59—42no—
125Dic59—22no—
126Dic59—22no—
127Dic59—42no—
128Dic59—41no—
129Dic59—42no—
130#2633—591nomaximal, Sylow
131C2×C59—42no—
132C2×C59#52511yescharacteristic
133C2×C59#53511yescharacteristic
134C2×C59#53611yescharacteristic
135C2×C59#53912yes—
136C2×C59#53912yes—
137D59—42no—
138C2×#125—591no—
139C2×C4×D4—591no—
140#399—591no—
141#399—591no—
142#398—592no—
143#397—591no—
144#397D5911yescharacteristic, complemented
145#394—592no—
146#385—592no—
147#385—592no—
148#383—591no—
149C59#263311yescharacteristic, complemented, Sylow
150C22×D4—591no—
151C23×C4—591no—
152C23×C4—591no—
153#125—1184no—
154C4×D4—1184no—
155C2×C4⋊C4—591no—
156C2×C4⋊C4—592no—
157C2×C4⋊C4—592no—
158C2×C4⋊C4—591no—
159C2×C4⋊C4—592no—
160C2×C4⋊C4—592no—
161C2×C4⋊C4C2×D5911yescharacteristic
162C2×C22⋊C4—591no—
163C2×C22⋊C4—592no—
164C2×C22⋊C4—592no—
165C2×C22⋊C4—592no—
166C2×C22⋊C4C2×D5911yescharacteristic
167C2×C22⋊C4C2×D5912yes—
168C2×C42—591no—
169#95—592no—
170#95—592no—
171#95—591no—
172#95—592no—
173#95C2×D5911yescharacteristic
174#95C2×D5912yes—
175C24—591no—
176C24C22×D5911yescharacteristic
177C2×D4—1182no—
178C2×D4—1182no—
179C2×D4—1182no—
180C22×C4—591no—
181C22×C4—591no—
182C22×C4—592no—
183C22×C4—591no—
184C22×C4—592no—
185C22×C4—1182no—
186C22×C4—1182no—
187C22×C4—2362no—
188C22×C4—2362no—
189C22×C4C22×D5912yes—
190C22×C4C22×D5912yes—
191C22×C4C22×D5911yescharacteristic
192C22×C4C22×D5911yescharacteristic
193C4⋊C4—22no—
194C4⋊C4—1182no—
195C4⋊C4—1184no—
196C4⋊C4—1184no—
197C4⋊C4—1182no—
198C4⋊C4—2362no—
199C4⋊C4—2362no—
200C22⋊C4—24no—
201C22⋊C4—22no—
202C22⋊C4—1184no—
203C22⋊C4—1182no—
204C22⋊C4—2362no—
205C22⋊C4—2362no—
206C42—594no—
207C23—21no—
208C23—21no—
209C23—22no—
210C23—22no—
211C23—592no—
212C23—1181no—
213C23—1181no—
214C23—1182no—
215C23—1182no—
216C23#1174568712yes—
217C23C23×D5911yescharacteristic
218D4—1188no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—592no—
229C2×C4—592no—
230C2×C4—1181no—
231C2×C4—1181no—
232C2×C4—1182no—
233C2×C4—1181no—
234C2×C4—1182no—
235C2×C4—1182no—
236C2×C4—1182no—
237C2×C4—1182no—
238C2×C4—1182no—
239C2×C4—1182no—
240C2×C4—1182no—
241C2×C4—2364no—
242C2×C4—2364no—
243C2×C4D4×D5912yes—
244C22—22no—
245C22—24no—
246C22—41no—
247C22—41no—
248C22—42no—
249C22—1182no—
250C22—1184no—
251C22—2361no—
252C22—2361no—
253C22—2362no—
254C22C2×D4×D5911yescharacteristic
255C22#41×D5911yescharacteristic
256C22C2×#1174568711yescharacteristic
257C22#1427377312yes—
258C22#1427377412yes—
259C4—22no—
260C4—42no—
261C4—41no—
262C4—42no—
263C4—1182no—
264C4—1182no—
265C4—2361no—
266C4—2362no—
267C4—2362no—
268C2—42no—
269C2—2362no—
270C2#1683791211yescharacteristic
271C2#1683797011yescharacteristic
272C2#1683797411yescharacteristic
273C2#1683799312yes—
274C2#1683799612yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#397C2
hypercenter#397D59
hypocenterC59#2633
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. #16837336C2semidirect
6. #16837328C2semidirect
8. #16837277C2semidirect
9. #16837276C2semidirect
10. #16837269C2semidirect
11. C59×#397C2semidirect
144. #397D59semidirect
149. C59#2633semidirect