Finite Group Databasebeta

← #21434037

Subgroups — #21434037

Order 7552.

462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14273701C211yesmaximal, characteristic
2C2×#14273686C211yesmaximal, characteristic, complemented
3#16837727C214yesmaximal, complemented
4#16837721C212yesmaximal, complemented
5#16837716C212yesmaximal, complemented
6#16837444C212yesmaximal, complemented
7#16837408C212yesmaximal, complemented
8C59×#407C211yesmaximal, characteristic, complemented
9C22×D236C2211yescharacteristic
10C22×C22⋊D59—21no—
11#14273701—21no—
12#14273701—21no—
13#14273701C2212yes—
14#14273701C2212yes—
15#14273686—21no—
16#14273686—21no—
17#14273686C2212yes—
18#14273686C2212yescomplemented
19C2×C4⋊Dic59C2211yescharacteristic
20C2×C4⋊Dic59C2211yescharacteristic, complemented
21C2×C4⋊Dic59C2211yescharacteristic, complemented
22C2×C22⋊Dic59—21no—
23C2×(C2×D59)⋊C4—21no—
24C2×C4×Dic59—21no—
25#14273661C2214yescomplemented
26#14273659C2214yescomplemented
27#14273649C2214yescomplemented
28#14273649C2214yescomplemented
29C23×C4×C59C2211yescharacteristic
30C2×M16×C59C2212yes—
31C22⋊C8×C59C2212yescomplemented
32C22⋊C8×C59C2212yescomplemented
33C24×C59D411yescharacteristic
34C23×D59—21no—
35C22×C4×C59—24no—
36C22×C4×C59D411yescharacteristic
37C22×C4×C59D411yescharacteristic
38C22×C4×C59D411yescharacteristic
39C22×C4×C59C2311yescharacteristic
40C22×C4×C59C2311yescharacteristic
41C22×C4×C59C2311yescharacteristic
42C2×C22⋊D59—22no—
43C2×C22⋊D59—22no—
44C2×C22⋊D59—44no—
45C22×Dic59—21no—
46C22×Dic59—21no—
47C22×Dic59—21no—
48C2×D236—24no—
49C2×D236—21no—
50C2×D236C2312yes—
51M16×C59—24no—
52C2×C8×C59C2314yes—
53C22⋊Dic59—22no—
54C22⋊Dic59—22no—
55(C2×D59)⋊C4—22no—
56(C2×D59)⋊C4—22no—
57C4⋊Dic59—21no—
58C4⋊Dic59—21no—
59C4⋊Dic59—21no—
60C4⋊Dic59C2312yes—
61C4⋊Dic59C2312yes—
62C4⋊Dic59C2312yes—
63C4×Dic59—22no—
64C4×Dic59—22no—
65C23×C59—22no—
66C23×C59—22no—
67C23×C59—41no—
68C23×C59C2×D411yescharacteristic
69C23×C59C2×D411yescharacteristic
70C23×C59C2×D411yescharacteristic
71C22×D59—22no—
72C22×D59—42no—
73C22×D59—42no—
74C22×D59—42no—
75C2×C4×C59—22no—
76C2×C4×C59—22no—
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×C59#4114yes—
84C2×C4×C59C2411yescharacteristic
85C22⋊D59—44no—
86C22⋊D59—44no—
87C2×Dic59—22no—
88C2×Dic59—22no—
89C2×Dic59—22no—
90C2×Dic59—42no—
91C2×Dic59—42no—
92C2×Dic59—42no—
93D236—24no—
94D236—42no—
95C8×C59—24no—
96C22×C59—21no—
97C22×C59—21no—
98C22×C59—21no—
99C22×C59—21no—
100C22×C59—21no—
101C22×C59—21no—
102C22×C59—21no—
103C22×C59—44no—
104C22×C59#12312yes—
105C22×C59AGL(1,ℤ/8)12yes—
106C22×C59C22×D411yescharacteristic
107C2×D59—42no—
108C2×D59—42no—
109C2×D59—42no—
110C2×D59—84no—
111C4×C59—21no—
112C4×C59—21no—
113C4×C59#12312yes—
114C4×C59C2×#4112yes—
115Dic59—42no—
116Dic59—42no—
117Dic59—42no—
118#3094—591nomaximal, Sylow
119C2×C59—22no—
120C2×C59—22no—
121C2×C59—41no—
122C2×C59C2×#12311yescharacteristic
123C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
124C2×C59#57511yescharacteristic
125D59—82no—
126C2×#121—591no—
127C2×#117—591no—
128#482—594no—
129#481—592no—
130#480—592no—
131#428—592no—
132#418—592no—
133#407D5911yescharacteristic, complemented
134C59#309411yescharacteristic, complemented, Sylow
135C22×D4—591no—
136C22×D4—1181no—
137C23×C4C2×D5911yescharacteristic
138C2×M16C2×D5912yes—
139#121—592no—
140#121—592no—
141#121—1181no—
142#121—1181no—
143#117—592no—
144#117—592no—
145#117—1181no—
146#117—1181no—
147C2×C4⋊C4—591no—
148C2×C4⋊C4—591no—
149C2×C4⋊C4—591no—
150C2×C22⋊C4—1181no—
151C2×C22⋊C4—1181no—
152C2×C42—1181no—
153#107—594no—
154#106—594no—
155#102—594no—
156#102—594no—
157C22⋊C8C2×D5912yescomplemented
158C22⋊C8C2×D5912yescomplemented
159C24—1181no—
160C24D23611yescharacteristic
161C2×D4—592no—
162C2×D4—1182no—
163C2×D4—1182no—
164C2×D4—1181no—
165C2×D4—1184no—
166C2×D4—2364no—
167C22×C4—24no—
168C22×C4—1181no—
169C22×C4—1181no—
170C22×C4—1181no—
171C22×C4D23611yescharacteristic
172C22×C4D23611yescharacteristic
173C22×C4D23611yescharacteristic
174C22×C4C22×D5911yescharacteristic
175C22×C4C22×D5911yescharacteristic
176C22×C4C22×D5911yescharacteristic
177M16—24no—
178C2×C8C22×D5914yes—
179C4⋊C4—592no—
180C4⋊C4—592no—
181C4⋊C4—592no—
182C4⋊C4—1181no—
183C4⋊C4—1181no—
184C4⋊C4—1181no—
185C22⋊C4—1182no—
186C22⋊C4—1182no—
187C22⋊C4—1182no—
188C22⋊C4—1182no—
189C42—1182no—
190C42—1182no—
191C23—22no—
192C23—22no—
193C23—41no—
194C23—1182no—
195C23—2362no—
196C23—2362no—
197C23—2362no—
198C23C2×D23611yescharacteristic
199C23C2×D23611yescharacteristic
200C23C2×D23611yescharacteristic
201D4—1184no—
202D4—2364no—
203D4—2364no—
204D4—2362no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—1182no—
211C2×C4—1182no—
212C2×C4—1182no—
213C2×C4—2362no—
214C2×C4—2362no—
215C2×C4—2362no—
216C2×C4C2×D23611yescharacteristic
217C2×C4C2×D23611yescharacteristic
218C2×C4C2×D23611yescharacteristic
219C2×C4#1174568714yes—
220C2×C4C23×D5911yescharacteristic
221C8—24no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—44no—
230C22—4724no—
231C22—2362no—
232C22—2362no—
233C22—2362no—
234C22#1427371112yes—
235C22#1427375512yes—
236C22C22×D23611yescharacteristic
237C4—21no—
238C4—21no—
239C4—2362no—
240C4—2362no—
241C4—2362no—
242C4#1427371112yes—
243C4C2×#1174568712yes—
244C2—22no—
245C2—22no—
246C2—41no—
247C2—4722no—
248C2C2×#1427371111yescharacteristic
249C2C2×#1427375511yescharacteristic
250C2#1683820211yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#407C2
socleC22×C59C22×D4
hypercenter#407D59
hypocenterC59#3094
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#14273686C2semidirect
3. #16837727C2semidirect
4. #16837721C2semidirect
5. #16837716C2semidirect
6. #16837444C2semidirect
7. #16837408C2semidirect
8. C59×#407C2semidirect
18. #14273686C22semidirect
20. C2×C4⋊Dic59C22semidirect
21. C2×C4⋊Dic59C22semidirect
25. #14273661C22semidirect
26. #14273659C22semidirect
27. #14273649C22semidirect
28. #14273649C22semidirect
31. C22⋊C8×C59C22semidirect
32. C22⋊C8×C59C22semidirect
133. #407D59semidirect
134. C59#3094semidirect
157. C22⋊C8C2×D59semidirect
158. C22⋊C8C2×D59semidirect