Finite Group Databasebeta

← #21434196

Subgroups — #21434196

Order 7552.

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

normal subgroups only

This group has 444 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
1#16837959C211yesmaximal, characteristic, complemented
2C2×C4×D236C211yesmaximal, characteristic
3#16837738C212yesmaximal, complemented
4#16837683C212yesmaximal, complemented
5#16837608C212yesmaximal, complemented
6#16837555C212yesmaximal
7#16837504C214yesmaximal, complemented
8C59×#432C211yesmaximal, characteristic, complemented
9C22×D236C2211yescharacteristic
10C22×C4×D59—21no—
11C2×#11745660C2214yes—
12#14273727C2211yescharacteristic, complemented
13#14273727C2211yescharacteristic, complemented
14#14273719—21no—
15#14273706—21no—
16#14273706C2212yes—
17C4×Dic118—21no—
18C4×Dic118C2212yescomplemented
19C4×D236—21no—
20C4×D236—21no—
21C4×D236C2212yes—
22C4×D236C2212yes—
23#14273686—21no—
24C2×C4⋊Dic59C2211yescharacteristic
25C2×(C2×D59)⋊C4—21no—
26#14273661C2214yescomplemented
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—24no—
40C2×D236C2312yes—
41C2×C4×D59—22no—
42C2×C4×D59—22no—
43C2×C4×D59—44no—
44C2×Dic118—21no—
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—
54C4⋊Dic59—21no—
55C4⋊Dic59—21no—
56C4⋊Dic59—21no—
57C4⋊Dic59—21no—
58C4⋊Dic59C2312yes—
59C4⋊Dic59C2312yes—
60Dic59⋊C4—22no—
61Dic59⋊C4—22no—
62C4×Dic59—22no—
63#11745660—28no—
64C23×C59C2×D411yescharacteristic
65C22×D59—24no—
66C22×D59—22no—
67C22×D59—42no—
68C22×D59—42no—
69C2×C4×C59—22no—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59C2×D411yescharacteristic
73C2×C4×C59C2×D411yescharacteristic
74C2×C4×C59C2×D411yescharacteristic
75C2×C4×C59C2×D411yescharacteristic
76C2×C4×C59C2×D411yescharacteristic
77C2×C4×C59C2411yescharacteristic
78C2×Dic59—22no—
79C2×Dic59—22no—
80C2×Dic59—22no—
81C2×Dic59—42no—
82D236—24no—
83D236—22no—
84D236#4114yes—
85C4×D59—44no—
86C4×D59—44no—
87Dic118—24no—
88Dic118—42no—
89C8×C59—24no—
90C22×C59—21no—
91C22×C59—21no—
92C22×C59#13712yes—
93C22×C59C22×D411yescharacteristic
94C2×D59—24no—
95C2×D59—48no—
96C2×D59—42no—
97C2×D59—42no—
98C4×C59—21no—
99C4×C59—21no—
100C4×C59—21no—
101C4×C59—21no—
102C4×C59AGL(1,ℤ/8)12yes—
103C4×C59C2×#4112yes—
104Dic59—42no—
105Dic59—42no—
106Dic59—42no—
107#3110—591nomaximal, Sylow
108C2×C59—22no—
109C2×C59#52511yescharacteristic
110C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C59C2×#13711yescharacteristic
112D59—44no—
113#533—591no—
114C2×C4×D4—591no—
115#484—592no—
116#474—592no—
117#461—592no—
118#450—592no—
119#440—594no—
120#432D5911yescharacteristic, complemented
121C59#311011yescharacteristic, complemented, Sylow
122C22×D4—591no—
123C23×C4—1181no—
124C2×SD16—594no—
125C4⋊Q8—591no—
126C4⋊Q8—591no—
127#125—1181no—
128C22⋊Q8—592no—
129C22⋊Q8—1181no—
130C4×Q8—592no—
131C4×Q8—1181no—
132C4×D4—592no—
133C4×D4—592no—
134C4×D4—1181no—
135C4×D4—1181no—
136#117—1181no—
137C2×C4⋊C4—591no—
138C2×C22⋊C4—1181no—
139C2×C42C2×D5911yescharacteristic
140#107—594no—
141C4⋊C8C2×D5912yescomplemented
142#103—594no—
143#102—594no—
144C22⋊C8C2×D5912yes—
145#97C2×D5912yescomplemented
146C24—1181no—
147C2×Q8—592no—
148C2×Q8—1181no—
149C2×D4—592no—
150C2×D4—1184no—
151C2×D4—1181no—
152C22×C4—1181no—
153C22×C4—1182no—
154C22×C4—1182no—
155C22×C4—2364no—
156C22×C4D23611yescharacteristic
157C22×C4D23611yescharacteristic
158C22×C4C22×D5911yescharacteristic
159SD16—1188no—
160C2×C8C22×D5914yes—
161C4⋊C4—592no—
162C4⋊C4—592no—
163C4⋊C4—1181no—
164C4⋊C4—1181no—
165C4⋊C4—1181no—
166C4⋊C4—1182no—
167C4⋊C4—1182no—
168C4⋊C4—1181no—
169C22⋊C4—1182no—
170C22⋊C4—1182no—
171C22⋊C4—1182no—
172C42—1182no—
173C42D23611yescharacteristic
174C42D23611yescharacteristic
175C42C22×D5911yescharacteristic
176C42C22×D5911yescharacteristic
177C23—1184no—
178C23—1182no—
179C23—2362no—
180C23—2362no—
181C23C2×D23611yescharacteristic
182Q8—1184no—
183Q8—2362no—
184D4—594no—
185D4—1184no—
186D4—1182no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—1182no—
191C2×C4—1182no—
192C2×C4—1182no—
193C2×C4—2364no—
194C2×C4—2362no—
195C2×C4—2364no—
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—1184no—
206C22—2368no—
207C22—2362no—
208C22—2362no—
209C22#1427376012yes—
210C22C22×D23611yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—21no—
215C4—2362no—
216C4—2362no—
217C4—2362no—
218C4#1427375512yes—
219C4#41×D5912yes—
220C2—22no—
221C2—2364no—
222C2#1683791411yescharacteristic
223C2C2×#1427375511yescharacteristic
224C2C2×#1427376011yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#432C2
socleC22×C59C22×D4
hypercenter#432D59
hypocenterC59#3110
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. #16837738C2semidirect
4. #16837683C2semidirect
5. #16837608C2semidirect
7. #16837504C2semidirect
8. C59×#432C2semidirect
12. #14273727C22semidirect
13. #14273727C22semidirect
18. C4×Dic118C22semidirect
26. #14273661C22semidirect
27. #14273652C22semidirect
30. C4⋊C8×C59C22semidirect
32. #97×C59C22semidirect
120. #432D59semidirect
121. C59#3110semidirect
141. C4⋊C8C2×D59semidirect
145. #97C2×D59semidirect