Finite Group Databasebeta

← #21435101

Subgroups — #21435101

Order 7552.

400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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#16837959C211yesmaximal, characteristic, complemented
2C2×#14273715C211yesmaximal, characteristic
3#16837796C212yesmaximal, complemented
4#16837762C212yesmaximal, complemented
5#16837625C214yesmaximal, complemented
6#16837560C212yesmaximal, complemented
7#16837555C212yesmaximal
8C59×#432C211yesmaximal, characteristic, complemented
9C22×Dic118C2211yescharacteristic
10C22×D236C2211yescharacteristic
11C2×Dic236C2214yescomplemented
12C2×#11745660C2214yes—
13#14273727C2211yescharacteristic, complemented
14#14273727C2211yescharacteristic, complemented
15#14273719—21no—
16#14273715—21no—
17#14273715—21no—
18#14273715C2212yes—
19#14273715C2212yes—
20#14273706—21no—
21#14273706C2212yes—
22C4×Dic118—21no—
23C4×Dic118C2212yescomplemented
24#14273686—21no—
25C2×(C2×D59)⋊C4—21no—
26C2×(C2×D59)⋊C4—21no—
27#14273652C2214yescomplemented
28#14273649C2214yes—
29C2×C42×C59C2211yescharacteristic
30C4⋊C8×C59C2212yescomplemented
31C22⋊C8×C59C2212yes—
32#97×C59C2212yescomplemented
33C23×D59—21no—
34C22×C4×C59D411yescharacteristic
35C22×C4×C59D411yescharacteristic
36C22×C4×C59C2311yescharacteristic
37C22×Dic59—21no—
38C2×D236—21no—
39C2×D236—42no—
40C2×D236C2312yes—
41C2×Dic118—21no—
42C2×Dic118—21no—
43C2×Dic118—42no—
44C2×Dic118C2312yes—
45C2×Dic118C2312yes—
46C2×C8×C59C2314yes—
47C42×C59D411yescharacteristic
48C42×C59D411yescharacteristic
49C42×C59C2311yescharacteristic
50C42×C59C2311yescharacteristic
51C22⋊Dic59—22no—
52(C2×D59)⋊C4—22no—
53(C2×D59)⋊C4—22no—
54(C2×D59)⋊C4—22no—
55(C2×D59)⋊C4—22no—
56C4⋊Dic59—21no—
57C4⋊Dic59—21no—
58C4⋊Dic59—21no—
59C4⋊Dic59C2312yes—
60Dic59⋊C4—22no—
61Dic59⋊C4—22no—
62C4×Dic59—22no—
63Dic236—44no—
64#11745660—44no—
65C23×C59C2×D411yescharacteristic
66C22×D59—22no—
67C22×D59—42no—
68C22×D59—42no—
69C22×D59—42no—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59—41no—
73C2×C4×C59C2×D411yescharacteristic
74C2×C4×C59C2×D411yescharacteristic
75C2×C4×C59C2×D411yescharacteristic
76C2×C4×C59C2×D411yescharacteristic
77C2×C4×C59C2×D411yescharacteristic
78C2×C4×C59C2411yescharacteristic
79C2×Dic59—22no—
80C2×Dic59—22no—
81C2×Dic59—22no—
82C2×Dic59—42no—
83D236—24no—
84D236—42no—
85Dic118—24no—
86Dic118—24no—
87Dic118—42no—
88Dic118—42no—
89C8×C59—24no—
90C22×C59—21no—
91C22×C59—21no—
92C22×C59#13712yes—
93C22×C59C22×D411yescharacteristic
94C2×D59—42no—
95C2×D59—42no—
96C2×D59—42no—
97C2×D59—84no—
98C4×C59—21no—
99C4×C59—21no—
100C4×C59—21no—
101C4×C59—21no—
102C4×C59—21no—
103C4×C59H(5,𝔽2)12yes—
104Dic59—42no—
105Dic59—42no—
106Dic59—42no—
107#3215—591nomaximal, Sylow
108C2×C59—22no—
109C2×C59#53511yescharacteristic
110C2×C59C2×#13711yescharacteristic
111C2×C59#57511yescharacteristic
112D59—82no—
113#533—591no—
114C2×#124—591no—
115#497—592no—
116#489—592no—
117#464—594no—
118#451—592no—
119#450—592no—
120#432D5911yescharacteristic, complemented
121C59#321511yescharacteristic, complemented, Sylow
122C22×Q8—591no—
123C22×D4—591no—
124C2×Q16—594no—
125C2×SD16—594no—
126C4⋊Q8—591no—
127C4⋊Q8—591no—
128#125—1181no—
129#124—592no—
130#124—592no—
131#124—1181no—
132#124—1181no—
133C22⋊Q8—592no—
134C22⋊Q8—1181no—
135C4×Q8—592no—
136C4×Q8—1181no—
137#117—1181no—
138C2×C22⋊C4—1181no—
139C2×C22⋊C4—1181no—
140C2×C42C2×D5911yescharacteristic
141C4⋊C8C2×D5912yescomplemented
142#103—594no—
143#102—594no—
144C22⋊C8C2×D5912yes—
145#97C2×D5912yescomplemented
146C24—1181no—
147C2×Q8—592no—
148C2×Q8—592no—
149C2×Q8—1181no—
150C2×Q8—1181no—
151C2×Q8—2362no—
152C2×D4—592no—
153C2×D4—1181no—
154C2×D4—2362no—
155C22×C4—1181no—
156C22×C4D23611yescharacteristic
157C22×C4D23611yescharacteristic
158C22×C4C22×D5911yescharacteristic
159Q16—2364no—
160SD16—2364no—
161C2×C8C22×D5914yes—
162C4⋊C4—592no—
163C4⋊C4—1181no—
164C4⋊C4—1181no—
165C4⋊C4—1182no—
166C4⋊C4—1182no—
167C4⋊C4—1181no—
168C22⋊C4—1182no—
169C22⋊C4—1182no—
170C22⋊C4—1182no—
171C22⋊C4—1182no—
172C22⋊C4—1182no—
173C42—1182no—
174C42D23611yescharacteristic
175C42D23611yescharacteristic
176C42C22×D5911yescharacteristic
177C42C22×D5911yescharacteristic
178C23—1182no—
179C23—2362no—
180C23—2362no—
181C23—2362no—
182C23C2×D23611yescharacteristic
183Q8—1184no—
184Q8—1184no—
185Q8—2362no—
186Q8—2362no—
187D4—1184no—
188D4—2362no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—41no—
192C2×C4—1182no—
193C2×C4—1182no—
194C2×C4—1182no—
195C2×C4—2362no—
196C2×C4C2×D23611yescharacteristic
197C2×C4C2×D23611yescharacteristic
198C2×C4C2×D23611yescharacteristic
199C2×C4C2×D23611yescharacteristic
200C2×C4C2×D23611yescharacteristic
201C2×C4C23×D5911yescharacteristic
202C8—24no—
203C22—21no—
204C22—21no—
205C22—4724no—
206C22—2362no—
207C22—2362no—
208C22—2362no—
209C22#1427376012yes—
210C22C22×D23611yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—21no—
215C4—21no—
216C4—2362no—
217C4—2362no—
218C4—2362no—
219C4#1427377312yes—
220C2—22no—
221C2—4722no—
222C2#1683797111yescharacteristic
223C2C2×#1427376011yescharacteristic
224C2#1683820211yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#432C2
socleC22×C59C22×D4
hypercenter#432D59
hypocenterC59#3215
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. #16837959C2semidirect
3. #16837796C2semidirect
4. #16837762C2semidirect
5. #16837625C2semidirect
6. #16837560C2semidirect
8. C59×#432C2semidirect
11. C2×Dic236C22semidirect
13. #14273727C22semidirect
14. #14273727C22semidirect
23. C4×Dic118C22semidirect
27. #14273652C22semidirect
30. C4⋊C8×C59C22semidirect
32. #97×C59C22semidirect
120. #432D59semidirect
121. C59#3215semidirect
141. C4⋊C8C2×D59semidirect
145. #97C2×D59semidirect