Finite Group Databasebeta

← #21435708

Subgroups — #21435708

Order 7552.

520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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#16838048C212yesmaximal, complemented
3#16837786C211yesmaximal, characteristic, complemented
4#16837648C212yesmaximal, complemented
5#16837618C212yesmaximal, complemented
6#16837566C212yesmaximal, complemented
7#16837538C212yesmaximal, complemented
8C4×D472C211yesmaximal, characteristic, complemented
9C59×#436C211yesmaximal, characteristic, complemented
10C2×#11745685C2212yes—
11C22×D236C2212yescomplemented
12#14273755—28no—
13C2×Dic236C2211yescharacteristic, complemented
14C2×#11745660C2212yescomplemented
15C2×#11745660C2212yescomplemented
16C2×D472C2212yes—
17C2×D472C2211yescharacteristic
18C2×D472C2211yescharacteristic
19#14273715C2212yescomplemented
20#14273712—22no—
21#14273706C2212yescomplemented
22#14273701C2212yes—
23#14273700—22no—
24#14273695—22no—
25C4×D236C2212yescomplemented
26C22⋊C4×D59—22no—
27#14273661C2211yescharacteristic, complemented
28#14273652C2212yescomplemented
29#14273649C2212yescomplemented
30#14273649C2212yescomplemented
31C2×M16×C59C2212yescomplemented
32C4×D4×C59C2211yescharacteristic
33C4⋊C8×C59C2211yescharacteristic, complemented
34C22⋊C8×C59C2212yescomplemented
35C4×C8×C59C2211yescharacteristic, complemented
36C23×D59—22no—
37C2×D4×C59D411yescharacteristic
38C22×C4×C59C2312yes—
39C2×C22⋊D59—22no—
40C2×C22⋊D59—22no—
41#11745685—24no—
42#11745685—42no—
43C2×D236—24no—
44C2×D236—22no—
45C2×D236—42no—
46C2×D236C2312yes—
47C2×D236C2312yes—
48C2×C4×D59—22no—
49C2×C4×D59—22no—
50C2×Dic118C2312yes—
51M16×C59—24no—
52C2×C8×C59C2311yescharacteristic
53C2×C8×C59C2312yes—
54C2×C8×C59C2311yescharacteristic
55C4⋊C4×C59D411yescharacteristic
56C22⋊C4×C59D412yes—
57C42×C59C2311yescharacteristic
58C22⋊Dic59—22no—
59(C2×D59)⋊C4—22no—
60(C2×D59)⋊C4—22no—
61(C2×D59)⋊C4—22no—
62(C2×D59)⋊C4—22no—
63C4⋊Dic59C2312yes—
64Dic59⋊C4—22no—
65Dic236—41no—
66D472—24no—
67D472—41no—
68D472D414yescomplemented
69#11745660—24no—
70#11745660—24no—
71C23×C59C2×D412yes—
72C22×D59—22no—
73C22×D59—22no—
74C22×D59—44no—
75C22×D59—44no—
76C22×D59—82no—
77D4×C59—41no—
78C2×C4×C59—22no—
79C2×C4×C59—22no—
80C2×C4×C59C2×D412yes—
81C2×C4×C59C2×D411yescharacteristic
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59C2411yescharacteristic
84C22⋊D59—44no—
85C22⋊D59—82no—
86C2×Dic59—22no—
87C2×Dic59—22no—
88D236—22no—
89D236—22no—
90D236—22no—
91D236—44no—
92D236C2×D414yes—
93C4×D59—44no—
94C4×D59—82no—
95Dic118—22no—
96Dic118—22no—
97C8×C59—22no—
98C8×C59—21no—
99C8×C59C2×D412yes—
100C22×C59—22no—
101C22×C59—22no—
102C22×C59—22no—
103C22×C59C22×D411yescharacteristic
104C2×D59—24no—
105C2×D59—42no—
106C2×D59—42no—
107C2×D59—42no—
108C2×D59—42no—
109C2×D59—42no—
110C2×D59—88no—
111C4×C59—22no—
112C4×C59—21no—
113C4×C59—21no—
114C4×C59C22×D411yescharacteristic
115C4×C59H(5,𝔽2)11yescharacteristic
116Dic59—42no—
117Dic59—42no—
118#3273—591nomaximal, Sylow
119C2×C59—42no—
120C2×C59D4211yescharacteristic
121C2×C59#57511yescharacteristic
122C2×C59#57611yescharacteristic
123D59—44no—
124D59—82no—
125C2×AGL(1,ℤ/8)—592no—
126#546—592no—
127#495—591no—
128#468—592no—
129#463—592no—
130#452—592no—
131#447—592no—
132C4×D8—591no—
133#436D5911yescharacteristic, complemented
134C59#327311yescharacteristic, complemented, Sylow
135C2×#41—592no—
136C22×D4—592no—
137AGL(1,ℤ/8)—1188no—
138C2×Q16—591no—
139C2×SD16—592no—
140C2×SD16—592no—
141C2×D8—591no—
142C2×D8—592no—
143C2×D8—591no—
144C2×M16C2×D5912yescomplemented
145#124—592no—
146#123—1182no—
147C22⋊Q8—592no—
148#121—592no—
149#121—1182no—
150#120—1182no—
151C4×D4—592no—
152C4×D4C2×D5911yescharacteristic
153C2×C22⋊C4—1182no—
154#107—591no—
155C4⋊C8C2×D5911yescharacteristic, complemented
156#103—592no—
157#102—592no—
158#102—592no—
159C22⋊C8C2×D5912yescomplemented
160C4×C8C2×D5911yescharacteristic, complemented
161C24—1182no—
162#41—1184no—
163#41—2362no—
164C2×Q8—592no—
165C2×D4—592no—
166C2×D4—592no—
167C2×D4—1184no—
168C2×D4—1182no—
169C2×D4—1182no—
170C2×D4—1182no—
171C2×D4—2362no—
172C2×D4D23611yescharacteristic
173C22×C4—1182no—
174C22×C4—1182no—
175C22×C4C22×D5912yes—
176Q16—2361no—
177SD16—1184no—
178SD16—1184no—
179D8—594no—
180D8—1184no—
181D8—2361no—
182M16—24no—
183C2×C8C22×D5911yescharacteristic
184C2×C8C22×D5912yes—
185C2×C8C22×D5911yescharacteristic
186C4⋊C4—592no—
187C4⋊C4—1182no—
188C4⋊C4D23611yescharacteristic
189C22⋊C4—1182no—
190C22⋊C4—1182no—
191C22⋊C4—1182no—
192C22⋊C4—1182no—
193C22⋊C4—1182no—
194C22⋊C4D23612yes—
195C42C22×D5911yescharacteristic
196C23—1182no—
197C23—1182no—
198C23—4722no—
199C23—2364no—
200C23—2364no—
201C23C2×D23612yes—
202Q8—1182no—
203Q8—1182no—
204D4—41no—
205D4—594no—
206D4—1182no—
207D4—1182no—
208D4—1182no—
209D4—4722no—
210D4—2364no—
211D4—2364no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—1182no—
215C2×C4—1182no—
216C2×C4—4722no—
217C2×C4—2364no—
218C2×C4C2×D23611yescharacteristic
219C2×C4C2×D23611yescharacteristic
220C2×C4C2×D23612yes—
221C2×C4C23×D5911yescharacteristic
222C8—22no—
223C8—21no—
224C8D4×D5912yes—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—1184no—
229C22—4728no—
230C22—2362no—
231C22—2362no—
232C22—2362no—
233C22—2362no—
234C22—2362no—
235C22C22×D23611yescharacteristic
236C4—21no—
237C4—21no—
238C4—22no—
239C4—2362no—
240C4—2362no—
241C4C2×D4×D5911yescharacteristic
242C4#1427377311yescharacteristic
243C2—42no—
244C2—4722no—
245C2—2364no—
246C2D4×D23611yescharacteristic
247C2#1683820211yescharacteristic
248C2#1683820711yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#436C2
socleC22×C59C22×D4
hypercenter#436D59
hypocenterC59#3273
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. #16838048C2semidirect
3. #16837786C2semidirect
4. #16837648C2semidirect
5. #16837618C2semidirect
6. #16837566C2semidirect
7. #16837538C2semidirect
8. C4×D472C2semidirect
9. C59×#436C2semidirect
11. C22×D236C22semidirect
13. C2×Dic236C22semidirect
14. C2×#11745660C22semidirect
15. C2×#11745660C22semidirect
19. #14273715C22semidirect
21. #14273706C22semidirect
25. C4×D236C22semidirect
27. #14273661C22semidirect
28. #14273652C22semidirect
29. #14273649C22semidirect
30. #14273649C22semidirect
31. C2×M16×C59C22semidirect
33. C4⋊C8×C59C22semidirect
34. C22⋊C8×C59C22semidirect
35. C4×C8×C59C22semidirect
68. D472D4semidirect
133. #436D59semidirect
134. C59#3273semidirect
144. C2×M16C2×D59semidirect
155. C4⋊C8C2×D59semidirect
159. C22⋊C8C2×D59semidirect
160. C4×C8C2×D59semidirect