Finite Group Databasebeta

← #21435116

Subgroups — #21435116

Order 7552.

490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14273724C211yesmaximal, characteristic, complemented
2#16837936C211yesmaximal, characteristic, complemented
3#16837791C212yesmaximal, complemented
4#16837767C212yesmaximal, complemented
5#16837603C212yesmaximal, complemented
6#16837598C212yesmaximal, complemented
7#16837555C212yesmaximal, complemented
8#16837538C212yesmaximal, complemented
9C59×#432C211yesmaximal, characteristic, complemented
10C22×D236—21no—
11C22×D236—21no—
12C22×D236C2212yes—
13C2×#11745660C2214yescomplemented
14C2×D472C2214yescomplemented
15#14273724—21no—
16#14273724—21no—
17#14273724C2212yes—
18#14273724C2212yes—
19#14273721—21no—
20#14273719C2211yescharacteristic, complemented
21#14273715C2211yescharacteristic, complemented
22#14273710—21no—
23#14273706C2211yescharacteristic
24#14273701C2211yescharacteristic
25C4×Dic118C2211yescharacteristic, complemented
26C4×D236C2211yescharacteristic, complemented
27C4×C22⋊D59—21no—
28#14273684—21no—
29#14273649C2214yescomplemented
30#14273649C2214yescomplemented
31C2×C42×C59C2211yescharacteristic
32C4⋊C8×C59C2212yescomplemented
33C22⋊C8×C59C2212yes—
34#97×C59C2212yescomplemented
35C23×D59—22no—
36C22×C4×C59D411yescharacteristic
37C22×C4×C59D411yescharacteristic
38C22×C4×C59C2311yescharacteristic
39C2×C22⋊D59—21no—
40C2×D236—22no—
41C2×D236—22no—
42C2×D236—22no—
43C2×D236—22no—
44C2×D236—22no—
45C2×D236—44no—
46C2×D236—44no—
47C2×D236—44no—
48C2×D236C2314yes—
49C2×D236C2311yescharacteristic
50C2×C4×D59—21no—
51C2×Dic118C2311yescharacteristic
52C2×C8×C59C2314yes—
53C42×C59D411yescharacteristic
54C42×C59D411yescharacteristic
55C42×C59C2311yescharacteristic
56C42×C59C2311yescharacteristic
57C22⋊Dic59—21no—
58(C2×D59)⋊C4—21no—
59(C2×D59)⋊C4—21no—
60(C2×D59)⋊C4—21no—
61(C2×D59)⋊C4—21no—
62C4⋊Dic59C2311yescharacteristic
63C4⋊Dic59C2311yescharacteristic
64Dic59⋊C4—21no—
65Dic59⋊C4—21no—
66Dic59⋊C4—21no—
67Dic59⋊C4—21no—
68C4×Dic59—21no—
69D472—44no—
70#11745660—44no—
71C23×C59C2×D411yescharacteristic
72C22×D59—21no—
73C22×D59—24no—
74C22×D59—44no—
75C22×D59—44no—
76C22×D59—44no—
77C2×C4×C59—22no—
78C2×C4×C59—22no—
79C2×C4×C59—22no—
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2×D411yescharacteristic
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59C2×D411yescharacteristic
84C2×C4×C59C2×D411yescharacteristic
85C2×C4×C59C2411yescharacteristic
86C22⋊D59—42no—
87C2×Dic59—21no—
88C2×Dic59—21no—
89C2×Dic59—21no—
90D236—24no—
91D236—22no—
92D236—24no—
93D236—44no—
94D236—44no—
95D236—44no—
96D236—44no—
97D236—44no—
98C4×D59—42no—
99Dic118—22no—
100C8×C59—24no—
101C22×C59—21no—
102C22×C59—21no—
103C22×C59AGL(1,ℤ/8)12yes—
104C22×C59C22×D411yescharacteristic
105C2×D59—44no—
106C2×D59—41no—
107C2×D59—41no—
108C2×D59—44no—
109C2×D59—44no—
110C2×D59—41no—
111C2×D59—88no—
112C4×C59—21no—
113C4×C59—21no—
114C4×C59—21no—
115C4×C59—21no—
116C4×C59AGL(1,ℤ/8)12yes—
117C4×C59H(5,𝔽2)12yes—
118Dic59—41no—
119Dic59—41no—
120Dic59—41no—
121#3217—591nomaximal, Sylow
122C2×C59—22no—
123C2×C59#53511yescharacteristic
124C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
125C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
126D59—81no—
127D59—84no—
128C2×#127—591no—
129#529—591no—
130#496—592no—
131#490—592no—
132#460—592no—
133#459—592no—
134#450—592no—
135#447—592no—
136#432D5911yescharacteristic, complemented
137C59#321711yescharacteristic, complemented, Sylow
138C22×D4—592no—
139C22×D4—1181no—
140C22×D4—1181no—
141C2×SD16—594no—
142C2×D8—594no—
143#127—592no—
144#127—592no—
145#127—1181no—
146#127—1181no—
147#126—1181no—
148#125—591no—
149#124—591no—
150#123—1181no—
151C22⋊Q8—591no—
152#121—591no—
153C4×Q8—591no—
154C4×D4—591no—
155C4×D4—1181no—
156#117—1181no—
157C2×C42C2×D5911yescharacteristic
158C4⋊C8C2×D5912yescomplemented
159#102—594no—
160#102—594no—
161C22⋊C8C2×D5912yes—
162#97C2×D5912yescomplemented
163C24—1182no—
164C2×Q8—591no—
165C2×D4—594no—
166C2×D4—591no—
167C2×D4—1181no—
168C2×D4—1182no—
169C2×D4—1182no—
170C2×D4—1182no—
171C2×D4—1182no—
172C2×D4—1182no—
173C2×D4—2364no—
174C2×D4—2364no—
175C2×D4—2364no—
176C22×C4—1181no—
177C22×C4D23611yescharacteristic
178C22×C4D23611yescharacteristic
179C22×C4C22×D5911yescharacteristic
180SD16—2364no—
181D8—2364no—
182C2×C8C22×D5914yes—
183C4⋊C4—591no—
184C4⋊C4—591no—
185C4⋊C4—1181no—
186C4⋊C4—1181no—
187C4⋊C4—1181no—
188C4⋊C4—1181no—
189C22⋊C4—1181no—
190C22⋊C4—1181no—
191C22⋊C4—1181no—
192C22⋊C4—1181no—
193C22⋊C4—1181no—
194C42—1181no—
195C42D23611yescharacteristic
196C42D23611yescharacteristic
197C42C22×D5911yescharacteristic
198C42C22×D5911yescharacteristic
199C23—1181no—
200C23—1184no—
201C23—2364no—
202C23—2364no—
203C23—2364no—
204C23C2×D23611yescharacteristic
205Q8—1182no—
206D4—1182no—
207D4—1184no—
208D4—1184no—
209D4—2364no—
210D4—2364no—
211D4—2364no—
212D4—2364no—
213D4—2362no—
214D4—2364no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—1181no—
219C2×C4—1181no—
220C2×C4—1181no—
221C2×C4—2362no—
222C2×C4C2×D23611yescharacteristic
223C2×C4C2×D23611yescharacteristic
224C2×C4C2×D23611yescharacteristic
225C2×C4C2×D23611yescharacteristic
226C2×C4C2×D23611yescharacteristic
227C2×C4C23×D5911yescharacteristic
228C8—24no—
229C22—21no—
230C22—21no—
231C22—4728no—
232C22—2361no—
233C22—2364no—
234C22—2364no—
235C22—2361no—
236C22—2364no—
237C22—2361no—
238C22#1427375512yes—
239C22C22×D23611yescharacteristic
240C4—21no—
241C4—21no—
242C4—21no—
243C4—21no—
244C4—2361no—
245C4—2361no—
246C4—2361no—
247C4#1427375512yes—
248C4#1427377312yes—
249C2—22no—
250C2—4724no—
251C2—4721no—
252C2#1683797111yescharacteristic
253C2C2×#1427375511yescharacteristic
254C2C2×#1427375511yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#432C2
socleC22×C59C22×D4
hypercenter#432D59
hypocenterC59#3217
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. C2×#14273724C2semidirect
2. #16837936C2semidirect
3. #16837791C2semidirect
4. #16837767C2semidirect
5. #16837603C2semidirect
6. #16837598C2semidirect
7. #16837555C2semidirect
8. #16837538C2semidirect
9. C59×#432C2semidirect
13. C2×#11745660C22semidirect
14. C2×D472C22semidirect
20. #14273719C22semidirect
21. #14273715C22semidirect
25. C4×Dic118C22semidirect
26. C4×D236C22semidirect
29. #14273649C22semidirect
30. #14273649C22semidirect
32. C4⋊C8×C59C22semidirect
34. #97×C59C22semidirect
136. #432D59semidirect
137. C59#3217semidirect
158. C4⋊C8C2×D59semidirect
162. #97C2×D59semidirect