Finite Group Databasebeta

← #21429448

Subgroups — #21429448

Order 7552.

584 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 153 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×(C22⋊D59)⋊C4C211yesmaximal, characteristic
2C22×Dic59⋊C4C211yesmaximal, characteristic, complemented
3#16837333C212yesmaximal, complemented
4#16837326C212yesmaximal, complemented
5#16837284C212yesmaximal, complemented
6#16837281C211yesmaximal, characteristic
7#16837279C211yesmaximal, characteristic
8#16837274C211yesmaximal, characteristic, complemented
9#16837273C212yesmaximal, complemented
10#16837260C211yesmaximal, characteristic, complemented
11C59×#385C211yesmaximal, characteristic, complemented
12C22×C22⋊D59C2211yescharacteristic
13C23×Dic59C2211yescharacteristic
14C23×Dic59C2211yescharacteristic
15C22×C4×D59C2211yescharacteristic
16(C22⋊D59)⋊C4—24no—
17C2×Dic59⋊C4—24no—
18C2×Dic59⋊C4C2212yes—
19C2×Dic59⋊C4C2212yes—
20C2×Dic59⋊C4C2212yes—
21C2×Dic59⋊C4C2211yescharacteristic
22C2×Dic59⋊C4C2212yes—
23C2×C22⋊Dic59C2211yescharacteristic
24C2×(C2×D59)⋊C4C2212yes—
25C2×(C2×D59)⋊C4C2211yescharacteristic
26C2×(C2×D59)⋊C4C2212yes—
27C2×C4×Dic59C2211yescharacteristic
28C59⋊#95C2212yes—
29C59⋊#95C2212yes—
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C23×C4×C59C2211yescharacteristic
33C2×C4⋊C4×C59C2212yes—
34C2×C22⋊C4×C59C2211yescharacteristic
35C2×C22⋊C4×C59C2211yescharacteristic
36#95×C59C2212yes—
37C24×C59C2311yescharacteristic
38C23×D59C2311yescharacteristic
39C22×C4×C59—22no—
40C22×C4×C59—42no—
41C22×C4×C59C2311yescharacteristic
42C22×C4×C59C2312yes—
43C22×C4×C59C2312yes—
44C22×C4×C59C2311yescharacteristic
45C2×C22⋊D59—22no—
46C2×C22⋊D59—22no—
47C2×C22⋊D59Q814yes—
48C22×Dic59—22no—
49C22×Dic59—24no—
50C22×Dic59—42no—
51C22×Dic59D414yes—
52C22×Dic59C2312yes—
53C22×Dic59C2311yescharacteristic
54C22×Dic59C2311yescharacteristic
55C22×Dic59C2311yescharacteristic
56C22×Dic59C2312yes—
57C2×C4×D59—22no—
58C2×C4×D59—42no—
59C4⋊C4×C59—42no—
60C22⋊C4×C59—22no—
61C22⋊C4×C59—22no—
62C22⋊Dic59—22no—
63(C2×D59)⋊C4—22no—
64(C2×D59)⋊C4—24no—
65(C2×D59)⋊C4—42no—
66Dic59⋊C4—24no—
67Dic59⋊C4—24no—
68Dic59⋊C4—22no—
69Dic59⋊C4—24no—
70Dic59⋊C4—42no—
71C4×Dic59—22no—
72C23×C59—22no—
73C23×C59—22no—
74C23×C59C2×D412yes—
75C23×C59C2×Q812yes—
76C23×C59#4112yes—
77C23×C59C2411yescharacteristic
78C22×D59—21no—
79C22×D59—22no—
80C22×D59—21no—
81C22×D59—22no—
82C22×D59C2×Q812yes—
83C2×C4×C59—21no—
84C2×C4×C59—22no—
85C2×C4×C59—21no—
86C2×C4×C59—22no—
87C2×C4×C59—22no—
88C2×C4×C59—22no—
89C2×C4×C59—22no—
90C2×C4×C59—22no—
91C2×C4×C59—22no—
92C2×C4×C59—22no—
93C2×C4×C59—44no—
94C22⋊D59—28no—
95C2×Dic59—28no—
96C2×Dic59—21no—
97C2×Dic59—22no—
98C2×Dic59—22no—
99C2×Dic59—21no—
100C2×Dic59—22no—
101C2×Dic59—22no—
102C2×Dic59—22no—
103C2×Dic59—22no—
104C2×Dic59—22no—
105C2×Dic59—44no—
106C2×Dic59C2×D412yes—
107C2×Dic59C2×D412yes—
108C2×Dic59C2×Q812yes—
109C2×Dic59#4114yes—
110C4×D59—44no—
111C22×C59—22no—
112C22×C59—22no—
113C22×C59—24no—
114C22×C59—24no—
115C22×C59C22⋊Q814yes—
116C22×C59C22×D411yescharacteristic
117C22×C59C22×Q811yescharacteristic
118C22×C59C2×#4112yes—
119C22×C59C2×#4111yescharacteristic
120C22×C59H(5,𝔽2)12yes—
121C2×D59—22no—
122C2×D59—24no—
123C2×D59—41no—
124C2×D59—41no—
125C2×D59—42no—
126C4×C59—41no—
127C4×C59—41no—
128C4×C59—42no—
129C4×C59—42no—
130Dic59—22no—
131Dic59—24no—
132Dic59—22no—
133Dic59—22no—
134Dic59—42no—
135#2579—591nomaximal, Sylow
136C2×C59—24no—
137C2×C59C2×C22⋊Q811yescharacteristic
138C2×C59#52511yescharacteristic
139C2×C59#53411yescharacteristic
140C2×C59#55312yes—
141C2×C59#55412yes—
142D59—42no—
143C2×C4×D4—591no—
144C22×C4⋊C4—591no—
145#398—592no—
146#396—592no—
147#387—592no—
148#386—591no—
149#386—591no—
150#385—592no—
151#385—591no—
152#385D5911yescharacteristic, complemented
153#380—591no—
154C59#257911yescharacteristic, complemented, Sylow
155C22×D4—591no—
156C23×C4—591no—
157C23×C4—591no—
158C23×C4—591no—
159C23×C4C2×D5911yescharacteristic
160C4×D4—1184no—
161C2×C4⋊C4—592no—
162C2×C4⋊C4—592no—
163C2×C4⋊C4—591no—
164C2×C4⋊C4—592no—
165C2×C4⋊C4—592no—
166C2×C4⋊C4—1184no—
167C2×C4⋊C4C2×D5912yes—
168C2×C22⋊C4—591no—
169C2×C22⋊C4—591no—
170C2×C22⋊C4—592no—
171C2×C22⋊C4—592no—
172C2×C22⋊C4C2×D5911yescharacteristic
173C2×C22⋊C4C2×D5911yescharacteristic
174C2×C42—591no—
175#95—592no—
176#95—592no—
177#95—592no—
178#95—592no—
179#95C2×D5912yes—
180C24—591no—
181C24C22×D5911yescharacteristic
182C2×D4—594no—
183C2×D4—1182no—
184C2×D4—1182no—
185C22×C4—22no—
186C22×C4—42no—
187C22×C4—591no—
188C22×C4—591no—
189C22×C4—592no—
190C22×C4—591no—
191C22×C4—594no—
192C22×C4—592no—
193C22×C4—1182no—
194C22×C4—1184no—
195C22×C4—1182no—
196C22×C4—2362no—
197C22×C4—2362no—
198C22×C4C22×D5912yes—
199C22×C4C22×D5911yescharacteristic
200C22×C4C22×D5912yes—
201C22×C4C22×D5911yescharacteristic
202C4⋊C4—42no—
203C4⋊C4—1184no—
204C4⋊C4—1184no—
205C4⋊C4—1182no—
206C4⋊C4—1184no—
207C4⋊C4—2362no—
208C22⋊C4—22no—
209C22⋊C4—22no—
210C22⋊C4—1182no—
211C22⋊C4—1184no—
212C22⋊C4—1182no—
213C22⋊C4—2362no—
214C42—1182no—
215C23—22no—
216C23—22no—
217C23—592no—
218C23—1181no—
219C23—1182no—
220C23—1181no—
221C23—1182no—
222C23#1174568512yes—
223C23D4×D5912yes—
224C23Q8×D5912yes—
225C23C23×D5911yescharacteristic
226D4—1188no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—44no—
238C2×C4—592no—
239C2×C4—592no—
240C2×C4—592no—
241C2×C4—594no—
242C2×C4—1188no—
243C2×C4—1181no—
244C2×C4—1182no—
245C2×C4—1182no—
246C2×C4—1181no—
247C2×C4—1182no—
248C2×C4—1182no—
249C2×C4—1182no—
250C2×C4—1182no—
251C2×C4—1182no—
252C2×C4—2364no—
253C2×C4—2364no—
254C22—22no—
255C22—22no—
256C22—24no—
257C22—24no—
258C22—1182no—
259C22—1184no—
260C22—2361no—
261C22—2361no—
262C22—2362no—
263C22#1427370514yes—
264C22C2×D4×D5911yescharacteristic
265C22C2×Q8×D5911yescharacteristic
266C22#41×D5912yes—
267C22C2×#1174568511yescharacteristic
268C22#1427377212yes—
269C4—41no—
270C4—42no—
271C4—41no—
272C4—42no—
273C4—1182no—
274C4—1184no—
275C4—1182no—
276C4—1182no—
277C4—2362no—
278C2—24no—
279C2—2362no—
280C2C2×#1427370511yescharacteristic
281C2#1683791011yescharacteristic
282C2#1683796211yescharacteristic
283C2#1683810112yes—
284C2#1683810612yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#385C2
hypercenter#385D59
hypocenterC59#2579
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C22×Dic59⋊C4C2semidirect
3. #16837333C2semidirect
4. #16837326C2semidirect
5. #16837284C2semidirect
8. #16837274C2semidirect
9. #16837273C2semidirect
10. #16837260C2semidirect
11. C59×#385C2semidirect
152. #385D59semidirect
154. C59#2579semidirect