Finite Group Databasebeta

← #21427335

Subgroups — #21427335

Order 7552.

696 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 155 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×D4×Dic59C211yesmaximal, characteristic, complemented
2C2×(C22⋊D59)⋊C4C212yesmaximal, complemented
3C2×#14273685C211yesmaximal, characteristic, complemented
4#16837332C211yesmaximal, characteristic, complemented
5#16837329C211yesmaximal, characteristic, complemented
6#16837325C212yesmaximal, complemented
7#16837317C212yesmaximal, complemented
8#16837310C211yesmaximal, characteristic
9#16837253C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic59C212yesmaximal, complemented
11C59×#394C211yesmaximal, characteristic, complemented
12C22×C22⋊D59C2212yes—
13C23×Dic59C2212yes—
14C22×C4×D59C2211yescharacteristic
15D4×Dic59—24no—
16(C22⋊D59)⋊C4—28no—
17#14273685—24no—
18C2×C4⋊Dic59C2211yescharacteristic
19C2×C4⋊Dic59C2211yescharacteristic
20C2×Dic59⋊C4C2212yes—
21C2×Dic59⋊C4C2212yes—
22C2×C22⋊Dic59C2212yes—
23C2×C22⋊Dic59C2212yes—
24C2×(C2×D59)⋊C4C2211yescharacteristic
25C2×(C2×D59)⋊C4C2211yescharacteristic
26C2×(C2×D59)⋊C4C2212yes—
27C2×C4×Dic59C2211yescharacteristic
28C2×C4×Dic59C2212yes—
29C2×C4×Dic59C2211yescharacteristic
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C59⋊#95C2211yescharacteristic
33C22×D4×C59C2211yescharacteristic
34C2×C4⋊C4×C59C2211yescharacteristic
35C2×C22⋊C4×C59C2212yes—
36C2×C22⋊C4×C59C2212yes—
37#95×C59C2211yescharacteristic
38C24×C59C2312yes—
39C23×D59C2311yescharacteristic
40C2×D4×C59—24no—
41C2×D4×C59—22no—
42C22×C4×C59C2312yes—
43C22×C4×C59C2311yescharacteristic
44C22×C4×C59C2311yescharacteristic
45C22×C4×C59C2311yescharacteristic
46C2×C22⋊D59—24no—
47C2×C22⋊D59—24no—
48C2×C22⋊D59—24no—
49C22×Dic59—24no—
50C22×Dic59—24no—
51C22×Dic59—24no—
52C22×Dic59C2311yescharacteristic
53C22×Dic59C2312yes—
54C22×Dic59C2311yescharacteristic
55C22×Dic59C2312yes—
56C22×Dic59C2311yescharacteristic
57C2×C4×D59—22no—
58C2×C4×D59—22no—
59C2×C4×D59D414yescomplemented
60C4⋊C4×C59—22no—
61C22⋊C4×C59—24no—
62C22⋊C4×C59—24no—
63C22⋊Dic59—24no—
64C22⋊Dic59—24no—
65(C2×D59)⋊C4—24no—
66(C2×D59)⋊C4—22no—
67(C2×D59)⋊C4—22no—
68C4⋊Dic59—22no—
69C4⋊Dic59—22no—
70Dic59⋊C4—24no—
71Dic59⋊C4—24no—
72C4×Dic59—22no—
73C4×Dic59—24no—
74C4×Dic59D414yescomplemented
75C23×C59—22no—
76C23×C59—22no—
77C23×C59—22no—
78C23×C59—22no—
79C23×C59—22no—
80C23×C59—22no—
81C23×C59#4114yes—
82C23×C59C2411yescharacteristic
83C22×D59—21no—
84C22×D59—21no—
85C22×D59—22no—
86C22×D59—22no—
87C22×D59C2×D412yes—
88D4×C59—28no—
89C2×C4×C59—21no—
90C2×C4×C59—21no—
91C2×C4×C59—22no—
92C2×C4×C59—22no—
93C2×C4×C59—21no—
94C2×C4×C59—22no—
95C2×C4×C59—22no—
96C2×C4×C59—22no—
97C2×C4×C59C2×D412yes—
98C2×C4×C59C2×D412yes—
99C22⋊D59—216no—
100C2×Dic59—22no—
101C2×Dic59—22no—
102C2×Dic59—22no—
103C2×Dic59—21no—
104C2×Dic59—22no—
105C2×Dic59—22no—
106C2×Dic59—22no—
107C2×Dic59—22no—
108C2×Dic59—48no—
109C2×Dic59C2×D412yes—
110C2×Dic59C2×D412yes—
111C2×Dic59C2×D412yes—
112C2×Dic59#4114yes—
113C2×Dic59#4112yes—
114C4×D59—28no—
115C22×C59—24no—
116C22×C59—24no—
117C22×C59—24no—
118C22×C59—42no—
119C22×C59—42no—
120C22×C59—42no—
121C22×C59—42no—
122C22×C59C22×D411yescharacteristic
123C22×C59C22×D411yescharacteristic
124C22×C59C2×#4111yescharacteristic
125C22×C59C2×#4112yes—
126C22×C59C2×#4112yes—
127C2×D59—22no—
128C2×D59—24no—
129C2×D59—41no—
130C2×D59—42no—
131C2×D59—41no—
132C4×C59—22no—
133C4×C59—22no—
134C4×C59—41no—
135C4×C59—42no—
136Dic59—24no—
137Dic59—22no—
138Dic59—42no—
139Dic59—41no—
140Dic59#12114yes—
141#2392—591nomaximal, Sylow
142C2×C59—44no—
143C2×C59C2×#12111yescharacteristic
144C2×C59#52511yescharacteristic
145C2×C59#52512yes—
146C2×C59#52912yes—
147C2×C59#53211yescharacteristic
148D59—42no—
149C2×C4×D4—591no—
150C2×C4×D4—592no—
151C2×#117—591no—
152#398—591no—
153#397—591no—
154#396—592no—
155#394—592no—
156#394D5911yescharacteristic, complemented
157#392—591no—
158C4×C4⋊C4—591no—
159C4×C22⋊C4—592no—
160C59#239211yescharacteristic, complemented, Sylow
161C22×D4—592no—
162C22×D4C2×D5911yescharacteristic
163C23×C4—591no—
164C23×C4—592no—
165C4×D4—1184no—
166C4×D4—1188no—
167#117—1184no—
168C2×C4⋊C4—591no—
169C2×C4⋊C4—592no—
170C2×C4⋊C4—591no—
171C2×C4⋊C4—592no—
172C2×C4⋊C4C2×D5911yescharacteristic
173C2×C22⋊C4—592no—
174C2×C22⋊C4—592no—
175C2×C22⋊C4—591no—
176C2×C22⋊C4—591no—
177C2×C22⋊C4—592no—
178C2×C22⋊C4C2×D5912yes—
179C2×C22⋊C4C2×D5912yes—
180C2×C42—591no—
181C2×C42—591no—
182C2×C42—592no—
183#95—592no—
184#95—592no—
185#95—591no—
186#95C2×D5911yescharacteristic
187C24—591no—
188C24C22×D5912yes—
189C2×D4—24no—
190C2×D4—22no—
191C2×D4—1184no—
192C2×D4—1184no—
193C2×D4—1184no—
194C22×C4—591no—
195C22×C4—592no—
196C22×C4—591no—
197C22×C4—594no—
198C22×C4—591no—
199C22×C4—592no—
200C22×C4—1182no—
201C22×C4—1182no—
202C22×C4—1184no—
203C22×C4—1184no—
204C22×C4—1184no—
205C22×C4C22×D5911yescharacteristic
206C22×C4C22×D5912yes—
207C22×C4C22×D5911yescharacteristic
208C22×C4C22×D5911yescharacteristic
209C4⋊C4—22no—
210C4⋊C4—1182no—
211C4⋊C4—1184no—
212C4⋊C4—1184no—
213C4⋊C4—1182no—
214C22⋊C4—24no—
215C22⋊C4—24no—
216C22⋊C4—1182no—
217C22⋊C4—1184no—
218C22⋊C4—1184no—
219C22⋊C4—1184no—
220C22⋊C4—1182no—
221C42—594no—
222C42—1182no—
223C42—1184no—
224C23—22no—
225C23—22no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—592no—
231C23—1181no—
232C23—1181no—
233C23—1182no—
234C23—1182no—
235C23#1174568714yes—
236C23C23×D5911yescharacteristic
237D4—28no—
238D4—11816no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—592no—
248C2×C4—592no—
249C2×C4—592no—
250C2×C4—592no—
251C2×C4—594no—
252C2×C4—1188no—
253C2×C4—1182no—
254C2×C4—1182no—
255C2×C4—1182no—
256C2×C4—1181no—
257C2×C4—1182no—
258C2×C4—1182no—
259C2×C4—1182no—
260C2×C4—1182no—
261C2×C4—2368no—
262C2×C4D4×D5912yes—
263C2×C4D4×D5912yes—
264C22—24no—
265C22—24no—
266C22—24no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—1182no—
272C22—1184no—
273C22—2361no—
274C22—2362no—
275C22—2361no—
276C22C2×D4×D5911yescharacteristic
277C22C2×D4×D5911yescharacteristic
278C22#41×D5911yescharacteristic
279C22#41×D5912yes—
280C22C2×#1174568712yes—
281C4—22no—
282C4—22no—
283C4—41no—
284C4—42no—
285C4—594no—
286C4—1184no—
287C4—1182no—
288C4—2362no—
289C4—2361no—
290C2—44no—
291C2—2362no—
292C2#121×D5911yescharacteristic
293C2#1683790811yescharacteristic
294C2#1683791212yes—
295C2#1683792912yes—
296C2#1683795111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#394C2
hypercenter#394D59
hypocenterC59#2392
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic59C2semidirect
2. C2×(C22⋊D59)⋊C4C2semidirect
3. C2×#14273685C2semidirect
4. #16837332C2semidirect
5. #16837329C2semidirect
6. #16837325C2semidirect
7. #16837317C2semidirect
9. #16837253C2semidirect
10. C22⋊C4×Dic59C2semidirect
11. C59×#394C2semidirect
59. C2×C4×D59D4semidirect
74. C4×Dic59D4semidirect
156. #394D59semidirect
160. C59#2392semidirect