Finite Group Databasebeta

← #21435698

Subgroups — #21435698

Order 7552.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14273755C212yesmaximal, complemented
2#16838057C211yesmaximal, characteristic, complemented
3D4×D236C211yesmaximal, characteristic, complemented
4#16837775C211yesmaximal, characteristic, complemented
5#16837648C212yesmaximal, complemented
6#16837608C211yesmaximal, characteristic, complemented
7#16837598C211yesmaximal, characteristic, complemented
8#16837555C212yesmaximal, complemented
9#16837549C212yesmaximal, complemented
10C4×D472C211yesmaximal, characteristic, complemented
11C59×#436C211yesmaximal, characteristic, complemented
12C2×#11745685C2212yescomplemented
13C22×D236C2212yes—
14C2×D4×D59—21no—
15#14273755—28no—
16C2×#11745660C2212yes—
17C2×#11745660C2212yescomplemented
18C2×#11745660C2212yescomplemented
19C2×D472C2211yescharacteristic
20C2×D472C2212yescomplemented
21#14273727C2211yescharacteristic, complemented
22#14273724C2211yescharacteristic
23#14273709—22no—
24#14273706C2212yescomplemented
25#14273702—21no—
26#14273701C2212yes—
27#14273698—21no—
28#14273697—22no—
29C4×D236C2211yescharacteristic
30C4×D236C2211yescharacteristic, complemented
31C4⋊C4×D59—21no—
32#14273661C2211yescharacteristic, complemented
33#14273652C2212yescomplemented
34#14273649C2211yescharacteristic
35#14273649C2212yescomplemented
36#14273649C2211yescharacteristic, complemented
37C2×M16×C59C2212yescomplemented
38C4×D4×C59C2211yescharacteristic
39C4⋊C8×C59C2211yescharacteristic, complemented
40C22⋊C8×C59C2212yescomplemented
41C4×C8×C59C2211yescharacteristic, complemented
42C23×D59—22no—
43C2×D4×C59D411yescharacteristic
44C22×C4×C59C2312yes—
45C2×C22⋊D59—22no—
46C2×C22⋊D59—22no—
47D4×D59—44no—
48#11745685—24no—
49#11745685—42no—
50C2×D236—24no—
51C2×D236—22no—
52C2×D236—21no—
53C2×D236—21no—
54C2×D236—42no—
55C2×D236C2312yes—
56C2×D236C2311yescharacteristic
57C2×D236C2311yescharacteristic
58C2×C4×D59—21no—
59C2×C4×D59—22no—
60C2×C4×D59—21no—
61C2×Dic118C2312yes—
62M16×C59—24no—
63C2×C8×C59C2311yescharacteristic
64C2×C8×C59C2312yes—
65C2×C8×C59C2311yescharacteristic
66C4⋊C4×C59D411yescharacteristic
67C22⋊C4×C59D412yes—
68C42×C59C2311yescharacteristic
69C22⋊Dic59—22no—
70(C2×D59)⋊C4—21no—
71(C2×D59)⋊C4—21no—
72(C2×D59)⋊C4—22no—
73C4⋊Dic59—21no—
74C4⋊Dic59—21no—
75C4⋊Dic59C2311yescharacteristic
76C4⋊Dic59C2311yescharacteristic
77Dic59⋊C4—22no—
78D472—24no—
79D472D414yescomplemented
80#11745660—24no—
81#11745660—24no—
82#11745660—42no—
83C23×C59C2×D412yes—
84C22×D59—21no—
85C22×D59—21no—
86C22×D59—22no—
87C22×D59—44no—
88C22×D59—44no—
89C22×D59—82no—
90D4×C59—22no—
91C2×C4×C59—22no—
92C2×C4×C59—22no—
93C2×C4×C59C2×D412yes—
94C2×C4×C59C2×D411yescharacteristic
95C2×C4×C59C2×D411yescharacteristic
96C2×C4×C59C2411yescharacteristic
97C22⋊D59—44no—
98C22⋊D59—44no—
99C2×Dic59—21no—
100C2×Dic59—22no—
101C2×Dic59—21no—
102D236—22no—
103D236—21no—
104D236—21no—
105D236—22no—
106D236—44no—
107D236—42no—
108D236—81no—
109D236C2×D412yes—
110D236C2×D412yescomplemented
111C4×D59—44no—
112C4×D59—42no—
113C4×D59—42no—
114Dic118—22no—
115Dic118—22no—
116C8×C59—22no—
117C8×C59—21no—
118C8×C59C2×D412yescomplemented
119C22×C59—22no—
120C22×C59—22no—
121C22×C59—22no—
122C22×C59C22×D411yescharacteristic
123C2×D59—22no—
124C2×D59—22no—
125C2×D59—41no—
126C2×D59—41no—
127C2×D59—41no—
128C2×D59—41no—
129C2×D59—42no—
130C2×D59—42no—
131C2×D59—42no—
132C2×D59—88no—
133C4×C59—22no—
134C4×C59—21no—
135C4×C59AGL(1,ℤ/8)12yescomplemented
136C4×C59C22×D411yescharacteristic
137C4×C59H(5,𝔽2)11yescharacteristic
138Dic59—42no—
139Dic59—41no—
140Dic59—41no—
141#3272—591nomaximal, Sylow
142C2×C59—42no—
143C2×C59D4211yescharacteristic
144C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
145C2×C59#57711yescharacteristic
146D59—42no—
147D59—42no—
148D59—82no—
149C2×AGL(1,ℤ/8)—592no—
150#547—591no—
151D42—591no—
152#492—591no—
153#468—592no—
154#461—591no—
155#459—591no—
156#450—592no—
157#449—592no—
158C4×D8—591no—
159#436D5911yescharacteristic, complemented
160C59#327211yescharacteristic, complemented, Sylow
161C2×#41—592no—
162C22×D4—592no—
163C22×D4—1181no—
164AGL(1,ℤ/8)—1188no—
165C2×SD16—592no—
166C2×SD16—592no—
167C2×SD16—592no—
168C2×D8—591no—
169C2×D8—592no—
170C2×M16C2×D5912yescomplemented
171C4⋊Q8—591no—
172#127—591no—
173#123—1182no—
174C22⋊Q8—592no—
175#121—592no—
176#121—1181no—
177#121—1181no—
178#120—1182no—
179C4×D4—591no—
180C4×D4—591no—
181C4×D4C2×D5911yescharacteristic
182C2×C4⋊C4—1181no—
183#107—591no—
184C4⋊C8C2×D5911yescharacteristic, complemented
185#103—592no—
186#102—591no—
187#102—591no—
188#102—592no—
189C22⋊C8C2×D5912yescomplemented
190C4×C8C2×D5911yescharacteristic, complemented
191C24—1182no—
192#41—1184no—
193#41—2362no—
194C2×Q8—592no—
195C2×D4—591no—
196C2×D4—591no—
197C2×D4—592no—
198C2×D4—1184no—
199C2×D4—1182no—
200C2×D4—1182no—
201C2×D4—1181no—
202C2×D4—1182no—
203C2×D4—1181no—
204C2×D4—2362no—
205C2×D4—2364no—
206C2×D4D23611yescharacteristic
207C22×C4—1181no—
208C22×C4—1182no—
209C22×C4—1181no—
210C22×C4C22×D5912yes—
211SD16—1184no—
212SD16—1184no—
213SD16—2362no—
214D8—594no—
215D8—1184no—
216M16—24no—
217C2×C8C22×D5911yescharacteristic
218C2×C8C22×D5912yes—
219C2×C8C22×D5911yescharacteristic
220C4⋊C4—591no—
221C4⋊C4—591no—
222C4⋊C4—1181no—
223C4⋊C4—1182no—
224C4⋊C4—1181no—
225C4⋊C4D23611yescharacteristic
226C22⋊C4—1182no—
227C22⋊C4—1181no—
228C22⋊C4—1181no—
229C22⋊C4—1182no—
230C22⋊C4D23612yes—
231C42C22×D5911yescharacteristic
232C23—1181no—
233C23—1181no—
234C23—1182no—
235C23—4722no—
236C23—2364no—
237C23—2364no—
238C23C2×D23612yes—
239Q8—1182no—
240Q8—1182no—
241D4—22no—
242D4—592no—
243D4—592no—
244D4—1182no—
245D4—1181no—
246D4—1181no—
247D4—1182no—
248D4—4721no—
249D4—2364no—
250D4—2364no—
251D4—2364no—
252D4—2362no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—1181no—
256C2×C4—1181no—
257C2×C4—1182no—
258C2×C4—2364no—
259C2×C4—2362no—
260C2×C4—2362no—
261C2×C4C2×D23611yescharacteristic
262C2×C4C2×D23612yes—
263C2×C4C2×D23611yescharacteristic
264C2×C4C23×D5911yescharacteristic
265C8—22no—
266C8—21no—
267C8D4×D5912yescomplemented
268C22—22no—
269C22—22no—
270C22—22no—
271C22—1182no—
272C22—1182no—
273C22—4728no—
274C22—2362no—
275C22—2362no—
276C22—2362no—
277C22—2361no—
278C22—2361no—
279C22—2361no—
280C22—2361no—
281C22C22×D23611yescharacteristic
282C4—21no—
283C4—22no—
284C4—2361no—
285C4—2361no—
286C4—2362no—
287C4#1427375512yescomplemented
288C4C2×D4×D5911yescharacteristic
289C4#1427377311yescharacteristic
290C2—42no—
291C2—4722no—
292C2—2362no—
293C2—2362no—
294C2D4×D23611yescharacteristic
295C2C2×#1427375511yescharacteristic
296C2#1683821411yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#436C2
socleC22×C59C22×D4
hypercenter#436D59
hypocenterC59#3272
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#14273755C2semidirect
2. #16838057C2semidirect
3. D4×D236C2semidirect
4. #16837775C2semidirect
5. #16837648C2semidirect
6. #16837608C2semidirect
7. #16837598C2semidirect
8. #16837555C2semidirect
9. #16837549C2semidirect
10. C4×D472C2semidirect
11. C59×#436C2semidirect
12. C2×#11745685C22semidirect
17. C2×#11745660C22semidirect
18. C2×#11745660C22semidirect
20. C2×D472C22semidirect
21. #14273727C22semidirect
24. #14273706C22semidirect
30. C4×D236C22semidirect
32. #14273661C22semidirect
33. #14273652C22semidirect
35. #14273649C22semidirect
36. #14273649C22semidirect
37. C2×M16×C59C22semidirect
39. C4⋊C8×C59C22semidirect
40. C22⋊C8×C59C22semidirect
41. C4×C8×C59C22semidirect
79. D472D4semidirect
110. D236C2×D4semidirect
118. C8×C59C2×D4semidirect
135. C4×C59AGL(1,ℤ/8)semidirect
159. #436D59semidirect
160. C59#3272semidirect
170. C2×M16C2×D59semidirect
184. C4⋊C8C2×D59semidirect
189. C22⋊C8C2×D59semidirect
190. C4×C8C2×D59semidirect
267. C8D4×D59semidirect
287. C4#14273755semidirect