Finite Group Databasebeta

← #484×D59 #21433998

Subgroups — #484×D59 #21433998

Order 7552.

460 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 135 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
1C22⋊Q8×D59C211yesmaximal, characteristic
2C2×C4⋊C4×D59C211yesmaximal, characteristic
3#16837739C212yesmaximal, complemented
4#16837738C211yesmaximal, characteristic, complemented
5#16837737C211yesmaximal, characteristic, complemented
6#16837736C212yesmaximal, complemented
7#16837735C211yesmaximal, characteristic, complemented
8#107×D59C212yesmaximal, complemented
9#103×D59C212yesmaximal, complemented
10C22⋊C8×D59C211yesmaximal, characteristic
11C59×#484C211yesmaximal, characteristic, complemented
12C2×Q8×D59C2211yescharacteristic
13C22×C4×D59—21no—
14C22×C4×D59C2211yescharacteristic
15C2×C8×D59C2212yes—
16#14273707C2211yescharacteristic
17#14273706C2211yescharacteristic
18#14273705—21no—
19#14273704—21no—
20#14273703C2211yescharacteristic
21C2×C4⋊Dic59C2211yescharacteristic
22C2×Dic59⋊C4—21no—
23C4⋊C4×D59—21no—
24C4⋊C4×D59—21no—
25C4⋊C4×D59—21no—
26C4⋊C4×D59C2211yescharacteristic
27C4⋊C4×D59C2212yes—
28C4⋊C4×D59C2212yes—
29C22⋊C4×D59—21no—
30#14273661C2212yescomplemented
31#14273660C2212yescomplemented
32#14273660C2212yescomplemented
33#14273652C2212yescomplemented
34#14273651C2212yescomplemented
35#14273650C2212yescomplemented
36C22⋊(C59⋊C8)C2211yescharacteristic
37(C2×D59)⋊C8C2212yes—
38C22⋊Q8×C59C2211yescharacteristic
39C2×C4⋊C4×C59C2211yescharacteristic
40#107×C59C2212yescomplemented
41#103×C59C2212yescomplemented
42C22⋊C8×C59C2211yescharacteristic
43C23×D59D411yescharacteristic
44C2×Q8×C59C2311yescharacteristic
45C22×C4×C59—21no—
46C22×C4×C59C2311yescharacteristic
47C22×Dic59—21no—
48C22×Dic59D411yescharacteristic
49Q8×D59—24no—
50C2×C4×D59—24no—
51C2×C4×D59—21no—
52C2×C4×D59—21no—
53C2×C4×D59—22no—
54C2×C4×D59—22no—
55C2×C4×D59—44no—
56C2×C4×D59D411yescharacteristic
57C2×C4×D59D411yescharacteristic
58C2×C4×D59C2311yescharacteristic
59C2×C4×D59C2311yescharacteristic
60C2×Dic118—21no—
61C2×Dic118C2311yescharacteristic
62C2×C8×C59C2312yes—
63C4⋊C4×C59—21no—
64C4⋊C4×C59—21no—
65C4⋊C4×C59C2312yes—
66C4⋊C4×C59C2311yescharacteristic
67C22⋊C4×C59—21no—
68C22⋊Dic59—21no—
69(C2×D59)⋊C4—21no—
70(C2×D59)⋊C4—21no—
71C4⋊Dic59—21no—
72C4⋊Dic59—21no—
73C4⋊Dic59C2312yes—
74C4⋊Dic59C2311yescharacteristic
75Dic59⋊C4—21no—
76Dic59⋊C4—22no—
77Dic59⋊C4—22no—
78Dic59⋊C4—21no—
79Dic59⋊C4—21no—
80C2×C59⋊C8C2312yes—
81C8×D59—24no—
82C23×C59C2×D411yescharacteristic
83C22×D59—22no—
84C22×D59—22no—
85C22×D59Q1614yes—
86C22×D59C2×D411yescharacteristic
87C22×D59C2×D411yescharacteristic
88Q8×C59—22no—
89C2×C4×C59—22no—
90C2×C4×C59—22no—
91C2×C4×C59—21no—
92C2×C4×C59—21no—
93C2×C4×C59—42no—
94C2×C4×C59C2×D411yescharacteristic
95C2×C4×C59C2411yescharacteristic
96C2×Dic59—22no—
97C2×Dic59—21no—
98C2×Dic59—22no—
99C2×Dic59—21no—
100C2×Dic59—42no—
101C2×Dic59C2×D411yescharacteristic
102C2×Dic59C2×D411yescharacteristic
103C4×D59—22no—
104C4×D59—22no—
105C4×D59—22no—
106C4×D59—44no—
107C4×D59—42no—
108C4×D59—42no—
109C4×D59—44no—
110C4×D59#4114yes—
111Dic118—22no—
112Dic118—42no—
113C8×C59—22no—
114C59⋊C8—22no—
115C22×C59—21no—
116C22×C59—21no—
117C22×C59C2×Q1612yes—
118C22×C59C22×D411yescharacteristic
119C2×D59—21no—
120C2×D59—21no—
121C2×D59—28no—
122C2×D59#12312yes—
123C2×D59C2×Q1612yes—
124C2×D59C2×Q1612yes—
125C2×D59AGL(1,ℤ/8)12yes—
126C4×C59—21no—
127C4×C59—41no—
128C4×C59—42no—
129C4×C59—41no—
130C4×C59C2×#4112yes—
131Dic59—21no—
132Dic59—41no—
133Dic59—42no—
134Dic59—41no—
135Dic59#12312yes—
136C2×#484—591nomaximal, Sylow
137C2×C59—22no—
138C2×C59C2×#12311yescharacteristic
139C2×C59C22×Q1611yescharacteristic
140C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
141D59—22no—
142D59#48414yesdirect product factor
143C2×C22⋊Q8—591no—
144C22×C4⋊C4—591no—
145#484—591no—
146#484—591no—
147#484—592no—
148#484—592no—
149#484—591no—
150#484D5911yescharacteristic, direct product factor
151C2×#107—592no—
152C2×#103—592no—
153C2×C22⋊C8—591no—
154C59C2×#48411yescharacteristic, complemented, Sylow
155C22×Q8—591no—
156C23×C4—591no—
157C23×C4—1181no—
158C22×C8—592no—
159C22⋊Q8—591no—
160C22⋊Q8—591no—
161C22⋊Q8—591no—
162C22⋊Q8—1181no—
163C22⋊Q8—1181no—
164C22⋊Q8C2×D5911yescharacteristic
165C2×C4⋊C4—591no—
166C2×C4⋊C4—592no—
167C2×C4⋊C4—592no—
168C2×C4⋊C4—591no—
169C2×C4⋊C4—1181no—
170C2×C4⋊C4—1181no—
171C2×C4⋊C4—1181no—
172C2×C4⋊C4—1181no—
173C2×C4⋊C4C2×D5911yescharacteristic
174C2×C22⋊C4—1181no—
175#107—592no—
176#107—592no—
177#107—592no—
178#107C2×D5912yescomplemented
179#103—592no—
180#103—592no—
181#103—592no—
182#103C2×D5912yescomplemented
183C22⋊C8—591no—
184C22⋊C8—592no—
185C22⋊C8C2×D5911yescharacteristic
186C24—591no—
187C2×Q8—591no—
188C2×Q8—1181no—
189C2×Q8—1184no—
190C2×Q8C22×D5911yescharacteristic
191C22×C4—21no—
192C22×C4—591no—
193C22×C4—591no—
194C22×C4—591no—
195C22×C4—591no—
196C22×C4—591no—
197C22×C4—1184no—
198C22×C4—1181no—
199C22×C4—1181no—
200C22×C4—1182no—
201C22×C4—1182no—
202C22×C4—1181no—
203C22×C4—2364no—
204C22×C4C22×D5911yescharacteristic
205C2×C8—592no—
206C2×C8—1184no—
207C2×C8C22×D5912yes—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—592no—
211C4⋊C4—591no—
212C4⋊C4—1182no—
213C4⋊C4—1182no—
214C4⋊C4—1181no—
215C4⋊C4—1181no—
216C4⋊C4—1181no—
217C4⋊C4—1181no—
218C4⋊C4—1181no—
219C4⋊C4C22×D5912yes—
220C4⋊C4C22×D5911yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—1181no—
223C22⋊C4—1181no—
224C22⋊C4—1181no—
225C23—591no—
226C23—594no—
227C23—591no—
228C23—1182no—
229C23—1182no—
230C23D4×D5911yescharacteristic
231Q8—22no—
232Q8—1182no—
233Q8—2362no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—591no—
240C2×C4—594no—
241C2×C4—591no—
242C2×C4—1182no—
243C2×C4—1182no—
244C2×C4—1182no—
245C2×C4—1182no—
246C2×C4—1181no—
247C2×C4—1181no—
248C2×C4—1182no—
249C2×C4—2362no—
250C2×C4—2364no—
251C2×C4—2362no—
252C2×C4—2364no—
253C2×C4—2362no—
254C2×C4D4×D5911yescharacteristic
255C2×C4C23×D5911yescharacteristic
256C8—22no—
257C8—1182no—
258C22—21no—
259C22—21no—
260C22—592no—
261C22—592no—
262C22—592no—
263C22—592no—
264C22—1188no—
265C22—1181no—
266C22—1181no—
267C22Q16×D5912yes—
268C22C2×D4×D5911yescharacteristic
269C4—21no—
270C4—41no—
271C4—42no—
272C4—41no—
273C4—592no—
274C4—1181no—
275C4—2361no—
276C4—2362no—
277C4—2361no—
278C4#41×D5912yes—
279C2—22no—
280C2—594no—
281C2—1182no—
282C2#123×D5911yescharacteristic
283C2C2×Q16×D5911yescharacteristic
284C2AGL(1,ℤ/8)×D5911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#484C2
socleC22×C59C22×D4
hypercenter#484D59
hypocenterC59C2×#484
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #16837739C2semidirect
4. #16837738C2semidirect
5. #16837737C2semidirect
6. #16837736C2semidirect
7. #16837735C2semidirect
8. #107×D59C2semidirect
9. #103×D59C2semidirect
11. C59×#484C2semidirect
30. #14273661C22semidirect
31. #14273660C22semidirect
32. #14273660C22semidirect
33. #14273652C22semidirect
34. #14273651C22semidirect
35. #14273650C22semidirect
40. #107×C59C22semidirect
41. #103×C59C22semidirect
142. D59#484direct (N × H)
150. #484D59direct (N × H)
154. C59C2×#484semidirect
178. #107C2×D59semidirect
182. #103C2×D59semidirect