Finite Group Databasebeta

← #21430322

Subgroups — #21430322

Order 7552.

796 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 796 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14273713C212yesmaximal, complemented
2C2×#14273696C212yesmaximal, complemented
3#16837317C212yesmaximal, complemented
4#16837314C211yesmaximal, characteristic, complemented
5#16837311C212yesmaximal, complemented
6#16837311C211yesmaximal, characteristic, complemented
7#16837302C212yesmaximal, complemented
8#16837296C212yesmaximal, complemented
9C59×#379C211yesmaximal, characteristic, complemented
10C22×Dic118C2211yescharacteristic, complemented
11C22×D236C2211yescharacteristic, complemented
12C22×C22⋊D59C2212yes—
13C22×C22⋊D59C2212yes—
14C22×C22⋊D59C2212yes—
15#14273713—28no—
16#14273696—28no—
17C2×Dic59⋊C4C2212yescomplemented
18C2×C22⋊Dic59C2212yes—
19C2×C22⋊Dic59C2212yes—
20C2×C22⋊Dic59C2212yes—
21C2×(C2×D59)⋊C4C2212yescomplemented
22C2×(C2×D59)⋊C4C2212yescomplemented
23C2×(C2×D59)⋊C4C2212yescomplemented
24C2×C4×Dic59C2212yescomplemented
25C59⋊#95C2211yescharacteristic, complemented
26C59⋊#95C2212yescomplemented
27C59⋊#95C2211yescharacteristic, complemented
28C25×C59C2211yescharacteristic
29C2×C22⋊C4×C59C2212yes—
30C2×C22⋊C4×C59C2212yes—
31C2×C22⋊C4×C59C2211yescharacteristic
32C2×C22⋊C4×C59C2211yescharacteristic
33C24×C59—24no—
34C24×C59—22no—
35C24×C59—41no—
36C24×C59—42no—
37C24×C59—41no—
38C24×C59C2312yes—
39C24×C59C2311yescharacteristic
40C23×D59C2312yes—
41C22×C4×C59C2311yescharacteristic
42C22×C4×C59C2311yescharacteristic
43C22×C4×C59C2312yes—
44C2×C22⋊D59—24no—
45C2×C22⋊D59—24no—
46C2×C22⋊D59—24no—
47C2×C22⋊D59—24no—
48C2×C22⋊D59—24no—
49C2×C22⋊D59—42no—
50C2×C22⋊D59—42no—
51C2×C22⋊D59—42no—
52C2×C22⋊D59—42no—
53C22×Dic59C2312yes—
54C22×Dic59C2312yes—
55C22×Dic59C2312yes—
56C2×D236—42no—
57C2×D236—41no—
58C2×Dic118—24no—
59C2×Dic118—41no—
60C22⋊C4×C59—24no—
61C22⋊C4×C59—42no—
62C22⋊C4×C59—41no—
63C22⋊C4×C59—41no—
64C22⋊Dic59—24no—
65C22⋊Dic59—24no—
66C22⋊Dic59D418yescomplemented
67(C2×D59)⋊C4—24no—
68(C2×D59)⋊C4—24no—
69(C2×D59)⋊C4—42no—
70Dic59⋊C4—42no—
71C4×Dic59—24no—
72C23×C59—22no—
73C23×C59—22no—
74C23×C59—22no—
75C23×C59—21no—
76C23×C59—21no—
77C23×C59—22no—
78C23×C59—22no—
79C23×C59—22no—
80C23×C59—22no—
81C23×C59—22no—
82C23×C59—44no—
83C23×C59—48no—
84C23×C59—48no—
85C23×C59—44no—
86C23×C59—44no—
87C23×C59C2×D414yes—
88C23×C59#4112yes—
89C23×C59C2411yescharacteristic
90C22×D59—22no—
91C22×D59—22no—
92C22×D59—22no—
93C22×D59—22no—
94C22×D59—22no—
95C22×D59—22no—
96C22×D59—22no—
97C2×C4×C59—22no—
98C2×C4×C59—22no—
99C2×C4×C59—22no—
100C2×C4×C59—22no—
101C2×C4×C59—21no—
102C2×C4×C59—22no—
103C2×C4×C59—21no—
104C22⋊D59—48no—
105C22⋊D59—48no—
106C22⋊D59—48no—
107C2×Dic59—22no—
108C2×Dic59—22no—
109C2×Dic59—22no—
110C2×Dic59—22no—
111C2×Dic59—22no—
112C2×Dic59—22no—
113C2×Dic59—22no—
114C2×Dic59C2×D414yes—
115C2×Dic59C2×D414yes—
116D236—44no—
117Dic118—44no—
118C22×C59—24no—
119C22×C59—22no—
120C22×C59—24no—
121C22×C59—24no—
122C22×C59—24no—
123C22×C59—416no—
124C22×C59—42no—
125C22×C59—42no—
126C22×C59—42no—
127C22×C59—41no—
128C22×C59—42no—
129C22×C59—42no—
130C22×C59—41no—
131C22×C59C22×D412yes—
132C22×C59C2×#4111yescharacteristic
133C22×C59H(5,𝔽2)11yescharacteristic
134C22×C59H(5,𝔽2)12yes—
135C22×C59H(5,𝔽2)11yescharacteristic
136C2×D59—42no—
137C2×D59—42no—
138C2×D59—42no—
139C2×D59—42no—
140C2×D59—42no—
141C2×D59—42no—
142C2×D59—42no—
143C4×C59—42no—
144C4×C59—41no—
145C4×C59—41no—
146Dic59—24no—
147Dic59—24no—
148Dic59—42no—
149#2670—591nomaximal, Sylow
150C2×C59—44no—
151C2×C59—42no—
152C2×C59#53512yes—
153C2×C59#53811yescharacteristic
154C2×C59D4211yescharacteristic
155C2×C59#54612yes—
156C2×C59H(3,𝔽4)11yescharacteristic
157D59—82no—
158C2×#124—592no—
159C2×#120—592no—
160#394—592no—
161#393—591no—
162#392—591no—
163#392—592no—
164#390—592no—
165#388—592no—
166#379D5911yescharacteristic, complemented
167C59#267011yescharacteristic, complemented, Sylow
168C25C2×D5911yescharacteristic
169C22×Q8—591no—
170C22×D4—592no—
171C22×D4—592no—
172C22×D4—592no—
173C22×D4—591no—
174#124—1188no—
175#120—1188no—
176C2×C4⋊C4—592no—
177C2×C22⋊C4—592no—
178C2×C22⋊C4—592no—
179C2×C22⋊C4—592no—
180C2×C22⋊C4—592no—
181C2×C22⋊C4—592no—
182C2×C22⋊C4—592no—
183C2×C22⋊C4C2×D5912yes—
184C2×C22⋊C4C2×D5912yes—
185C2×C22⋊C4C2×D5911yescharacteristic
186C2×C22⋊C4C2×D5911yescharacteristic
187C2×C42—592no—
188#95—591no—
189#95—592no—
190#95—591no—
191C24—22no—
192C24—24no—
193C24—41no—
194C24—42no—
195C24—41no—
196C24—592no—
197C24C22×D5911yescharacteristic
198C24C22×D5912yes—
199C2×Q8—1184no—
200C2×Q8—2361no—
201C2×D4—1184no—
202C2×D4—1184no—
203C2×D4—1184no—
204C2×D4—1184no—
205C2×D4—1184no—
206C2×D4—2362no—
207C2×D4—2361no—
208C2×D4—2362no—
209C2×D4—2362no—
210C2×D4—2362no—
211C2×D4—2362no—
212C22×C4—592no—
213C22×C4—592no—
214C22×C4—592no—
215C22×C4C22×D5911yescharacteristic
216C22×C4C22×D5911yescharacteristic
217C22×C4C22×D5912yes—
218C4⋊C4—2362no—
219C22⋊C4—24no—
220C22⋊C4—41no—
221C22⋊C4—42no—
222C22⋊C4—41no—
223C22⋊C4—598no—
224C22⋊C4—1184no—
225C22⋊C4—1184no—
226C22⋊C4—1184no—
227C22⋊C4—1184no—
228C22⋊C4—2362no—
229C42—1184no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—44no—
241C23—48no—
242C23—48no—
243C23—44no—
244C23—44no—
245C23—1182no—
246C23—1182no—
247C23—1182no—
248C23—1182no—
249C23—1182no—
250C23—1182no—
251C23—1182no—
252C23#1174568512yes—
253C23D4×D5914yes—
254C23C23×D5911yescharacteristic
255Q8—2364no—
256D4—2364no—
257D4—2368no—
258D4—2368no—
259D4—2368no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—594no—
268C2×C4—594no—
269C2×C4—1182no—
270C2×C4—1182no—
271C2×C4—1182no—
272C2×C4—1182no—
273C2×C4—1182no—
274C2×C4—1182no—
275C2×C4—1182no—
276C22—24no—
277C22—22no—
278C22—24no—
279C22—24no—
280C22—24no—
281C22—416no—
282C22—42no—
283C22—41no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—41no—
288C22—42no—
289C22—2362no—
290C22—2362no—
291C22—2362no—
292C22—2362no—
293C22—2362no—
294C22—2362no—
295C22—2362no—
296C22C2×D4×D5912yes—
297C22C2×#1174568511yescharacteristic
298C22#1427377212yes—
299C22#1427377211yescharacteristic
300C22#1427377211yescharacteristic
301C4—41no—
302C4—42no—
303C4—41no—
304C4—1184no—
305C4—1184no—
306C4—2362no—
307C2—44no—
308C2—42no—
309C2—4722no—
310C2#1683796712yes—
311C2#1683799011yescharacteristic
312C2#1683803411yescharacteristic
313C2#1683804212yes—
314C2#1683814511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#379C2
hypercenter#379D59
hypocenterC59#2670
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#14273713C2semidirect
2. C2×#14273696C2semidirect
3. #16837317C2semidirect
4. #16837314C2semidirect
5. #16837311C2semidirect
6. #16837311C2semidirect
7. #16837302C2semidirect
8. #16837296C2semidirect
9. C59×#379C2semidirect
10. C22×Dic118C22semidirect
11. C22×D236C22semidirect
17. C2×Dic59⋊C4C22semidirect
21. C2×(C2×D59)⋊C4C22semidirect
22. C2×(C2×D59)⋊C4C22semidirect
23. C2×(C2×D59)⋊C4C22semidirect
24. C2×C4×Dic59C22semidirect
25. C59⋊#95C22semidirect
26. C59⋊#95C22semidirect
27. C59⋊#95C22semidirect
66. C22⋊Dic59D4semidirect
166. #379D59semidirect
167. C59#2670semidirect