Finite Group Databasebeta

← #21436328

Subgroups — #21436328

Order 7552.

448 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 123 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
1#16838122C211yesmaximal, characteristic, complemented
2D4×D236C211yesmaximal, characteristic
3#16837749C211yesmaximal, characteristic, complemented
4#16837727C212yesmaximal, complemented
5#16837683C211yesmaximal, characteristic, complemented
6#16837648C212yesmaximal, complemented
7#16837603C211yesmaximal, characteristic, complemented
8#16837555C212yesmaximal, complemented
9C4×#11745660C211yesmaximal, characteristic, complemented
10#16837408C212yesmaximal, complemented
11C59×#436C211yesmaximal, characteristic, complemented
12C22×D236C2212yes—
13C2×D4×D59—21no—
14C2×#11745660C2211yescharacteristic
15C2×#11745660C2212yescomplemented
16#14273727C2211yescharacteristic, complemented
17#14273724C2211yescharacteristic
18#14273720—22no—
19#14273714—21no—
20#14273706C2212yescomplemented
21#14273702—21no—
22#14273701C2212yes—
23#14273697—22no—
24C4×Dic118C2211yescharacteristic, complemented
25#14273692—21no—
26C4×D236C2211yescharacteristic
27#14273686C2212yescomplemented
28#14273661C2212yescomplemented
29#14273659C2211yescharacteristic, complemented
30#14273652C2211yescharacteristic, complemented
31#14273649C2211yescharacteristic
32#14273649C2212yes—
33#14273649C2212yescomplemented
34#14273649C2212yescomplemented
35#14273649C2212yescomplemented
36C2×M16×C59C2212yescomplemented
37C4×D4×C59C2211yescharacteristic
38C4⋊C8×C59C2211yescharacteristic, complemented
39C22⋊C8×C59C2212yescomplemented
40C4×C8×C59C2211yescharacteristic, complemented
41C23×D59—22no—
42C2×D4×C59D411yescharacteristic
43C22×C4×C59C2312yes—
44C2×C22⋊D59—22no—
45D4×D59—44no—
46C2×D236—24no—
47C2×D236—22no—
48C2×D236—21no—
49C2×D236—21no—
50C2×D236—42no—
51C2×D236C2312yes—
52C2×D236C2311yescharacteristic
53C2×C4×D59—21no—
54C2×Dic118—21no—
55C2×Dic118C2311yescharacteristic
56M16×C59—42no—
57C2×C8×C59C2311yescharacteristic
58C2×C8×C59C2311yescharacteristic
59C2×C8×C59C2312yes—
60C4⋊C4×C59D411yescharacteristic
61C22⋊C4×C59D412yes—
62C42×C59C2311yescharacteristic
63C22⋊Dic59—22no—
64C22⋊Dic59—22no—
65(C2×D59)⋊C4—21no—
66(C2×D59)⋊C4—22no—
67C4⋊Dic59—21no—
68C4⋊Dic59C2311yescharacteristic
69C4⋊Dic59C2312yes—
70C4⋊Dic59C2311yescharacteristic
71Dic59⋊C4—22no—
72Dic59⋊C4—21no—
73C4×Dic59—22no—
74C4×Dic59—21no—
75#11745660—22no—
76#11745660—42no—
77C23×C59C2×D412yes—
78C22×D59—21no—
79C22×D59—22no—
80C22×D59—44no—
81C22×D59—44no—
82C22×D59—82no—
83D4×C59—22no—
84C2×C4×C59—22no—
85C2×C4×C59—22no—
86C2×C4×C59C2×D412yes—
87C2×C4×C59C2×D411yescharacteristic
88C2×C4×C59C2×D411yescharacteristic
89C2×C4×C59C2411yescharacteristic
90C22⋊D59—44no—
91C2×Dic59—21no—
92C2×Dic59—21no—
93C2×Dic59—22no—
94C2×Dic59—21no—
95D236—22no—
96D236—21no—
97D236—22no—
98D236—44no—
99D236—42no—
100D236—81no—
101D236#4112yes—
102C4×D59—42no—
103Dic118—21no—
104Dic118—21no—
105Dic118—42no—
106C8×C59—21no—
107C8×C59—22no—
108C8×C59—21no—
109C22×C59—22no—
110C22×C59—22no—
111C22×C59—22no—
112C22×C59C22×D411yescharacteristic
113C2×D59—22no—
114C2×D59—41no—
115C2×D59—41no—
116C2×D59—42no—
117C2×D59—42no—
118C2×D59—42no—
119C2×D59—88no—
120C4×C59—22no—
121C4×C59—21no—
122C4×C59AGL(1,ℤ/8)12yes—
123C4×C59C2×#4111yescharacteristic
124C4×C59H(5,𝔽2)11yescharacteristic
125Dic59—41no—
126Dic59—42no—
127Dic59—41no—
128Dic59—41no—
129#3324—591nomaximal, Sylow
130C2×C59—42no—
131C2×C59#54611yescharacteristic
132C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
133C2×C59#57711yescharacteristic
134D59—42no—
135D59—82no—
136#556—591no—
137D42—591no—
138#486—591no—
139#482—592no—
140#474—591no—
141#468—592no—
142#460—591no—
143#450—592no—
144C4×SD16—591no—
145#436D5911yescharacteristic, complemented
146#418—592no—
147C59#332411yescharacteristic, complemented, Sylow
148C22×D4—592no—
149C22×D4—1181no—
150C2×SD16—591no—
151C2×SD16—592no—
152C2×M16C2×D5912yescomplemented
153C4⋊Q8—591no—
154#127—591no—
155#126—1182no—
156#124—1181no—
157C22⋊Q8—592no—
158#121—592no—
159#121—1181no—
160#120—1182no—
161C4×Q8—591no—
162C4×Q8—1181no—
163C4×D4—591no—
164C4×D4C2×D5911yescharacteristic
165#117—592no—
166#107—592no—
167#106—591no—
168C4⋊C8C2×D5911yescharacteristic, complemented
169#103—591no—
170#102—591no—
171#102—592no—
172#102—592no—
173#102—592no—
174#102—592no—
175C22⋊C8C2×D5912yescomplemented
176C4×C8C2×D5911yescharacteristic, complemented
177C24—1182no—
178C2×Q8—591no—
179C2×Q8—1181no—
180C2×D4—591no—
181C2×D4—592no—
182C2×D4—1184no—
183C2×D4—1182no—
184C2×D4—1181no—
185C2×D4—1182no—
186C2×D4—1181no—
187C2×D4—2362no—
188C2×D4—2364no—
189C2×D4D23611yescharacteristic
190C22×C4—1181no—
191C22×C4C22×D5912yes—
192SD16—1182no—
193SD16—2362no—
194M16—42no—
195C2×C8C22×D5911yescharacteristic
196C2×C8C22×D5911yescharacteristic
197C2×C8C22×D5912yes—
198C4⋊C4—591no—
199C4⋊C4—592no—
200C4⋊C4—591no—
201C4⋊C4—1181no—
202C4⋊C4—1182no—
203C4⋊C4—1181no—
204C4⋊C4D23611yescharacteristic
205C22⋊C4—1182no—
206C22⋊C4—1182no—
207C22⋊C4—1181no—
208C22⋊C4—1182no—
209C22⋊C4D23612yes—
210C42—1182no—
211C42—1181no—
212C42C22×D5911yescharacteristic
213C23—1181no—
214C23—1182no—
215C23—4722no—
216C23—2364no—
217C23—2364no—
218C23C2×D23612yes—
219Q8—1181no—
220Q8—1181no—
221Q8—2362no—
222D4—22no—
223D4—592no—
224D4—1182no—
225D4—1181no—
226D4—1182no—
227D4—4721no—
228D4—2364no—
229D4—2364no—
230D4—2362no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—1181no—
234C2×C4—1182no—
235C2×C4—1181no—
236C2×C4—1181no—
237C2×C4—2362no—
238C2×C4C2×D23612yes—
239C2×C4C2×D23611yescharacteristic
240C2×C4C2×D23611yescharacteristic
241C2×C4C23×D5911yescharacteristic
242C8—21no—
243C8—21no—
244C8—22no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—1182no—
249C22—4728no—
250C22—2362no—
251C22—2362no—
252C22—2362no—
253C22—2361no—
254C22—2361no—
255C22C22×D23611yescharacteristic
256C4—21no—
257C4—22no—
258C4—2361no—
259C4—2362no—
260C4—2361no—
261C4—2361no—
262C4#1427375512yes—
263C4#41×D5911yescharacteristic
264C4#1427377211yescharacteristic
265C2—42no—
266C2—4722no—
267C2—2362no—
268C2#1683804711yescharacteristic
269C2C2×#1427375511yescharacteristic
270C2#1683821411yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#436C2
socleC22×C59C22×D4
hypercenter#436D59
hypocenterC59#3324
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. #16838122C2semidirect
3. #16837749C2semidirect
4. #16837727C2semidirect
5. #16837683C2semidirect
6. #16837648C2semidirect
7. #16837603C2semidirect
8. #16837555C2semidirect
9. C4×#11745660C2semidirect
10. #16837408C2semidirect
11. C59×#436C2semidirect
15. C2×#11745660C22semidirect
16. #14273727C22semidirect
20. #14273706C22semidirect
24. C4×Dic118C22semidirect
27. #14273686C22semidirect
28. #14273661C22semidirect
29. #14273659C22semidirect
30. #14273652C22semidirect
33. #14273649C22semidirect
34. #14273649C22semidirect
35. #14273649C22semidirect
36. C2×M16×C59C22semidirect
38. C4⋊C8×C59C22semidirect
39. C22⋊C8×C59C22semidirect
40. C4×C8×C59C22semidirect
145. #436D59semidirect
147. C59#3324semidirect
152. C2×M16C2×D59semidirect
168. C4⋊C8C2×D59semidirect
175. C22⋊C8C2×D59semidirect
176. C4×C8C2×D59semidirect