Finite Group Databasebeta

← #21434467

Subgroups — #21434467

Order 7552.

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

normal subgroups only

This group has 484 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
1#16837957C211yesmaximal, characteristic, complemented
2#127×D59C211yesmaximal, characteristic
3#16837765C214yesmaximal, complemented
4#16837750C211yesmaximal, characteristic, complemented
5#16837749C211yesmaximal, characteristic, complemented
6#16837748C211yesmaximal, characteristic, complemented
7#16837405C214yesmaximal, complemented
8C4×#11745659C211yesmaximal, characteristic, complemented
9C59×#486C211yesmaximal, characteristic, complemented
10C2×D4×D59—21no—
11C2×D4×D59—21no—
12C2×D4×D59C2212yes—
13C2×#11745659C2212yes—
14#14273727C2211yescharacteristic, complemented
15#14273724C2211yescharacteristic
16#14273723—21no—
17#14273723—21no—
18#14273723C2212yes—
19#14273718C2212yescomplemented
20#14273707—21no—
21#14273703—21no—
22Q8×Dic59—21no—
23#14273692—21no—
24#14273685C2212yes—
25C42×D59C2211yescharacteristic
26#14273649C2214yescomplemented
27#14273648C2214yescomplemented
28#14273647C2214yescomplemented
29#14273637C2212yescomplemented
30C4×C59⋊C8C2211yescharacteristic, complemented
31C4⋊Q8×C59C2211yescharacteristic, complemented
32#127×C59C2211yescharacteristic
33#102×C59C2214yescomplemented
34C4×C8×C59C2211yescharacteristic, complemented
35C23×D59—22no—
36C2×Q8×C59—21no—
37C2×D4×C59—21no—
38C2×D4×C59—21no—
39C2×D4×C59C2312yes—
40C2×C22⋊D59—22no—
41C2×C22⋊D59—22no—
42C2×C22⋊D59—22no—
43D4×D59—28no—
44D4×D59—44no—
45D4×D59—44no—
46C2×D236—21no—
47C2×D236—21no—
48C2×D236C2312yes—
49C2×C4×D59D411yescharacteristic
50C2×C4×D59D411yescharacteristic
51C2×C4×D59C2311yescharacteristic
52C2×Dic118—21no—
53C2×C8×C59C2312yes—
54C4⋊C4×C59—21no—
55C4⋊C4×C59C2312yes—
56C42×C59C2311yescharacteristic
57(C2×D59)⋊C4—22no—
58C4⋊Dic59—21no—
59C4⋊Dic59—22no—
60C4⋊Dic59C2312yes—
61Dic59⋊C4—22no—
62C4×Dic59—22no—
63C4×Dic59D411yescharacteristic
64C4×Dic59D411yescharacteristic
65C4×Dic59C2311yescharacteristic
66C2×C59⋊C8C2312yes—
67#11745659—24no—
68C23×C59—22no—
69C22×D59—22no—
70C22×D59—44no—
71C22×D59—44no—
72C22×D59—44no—
73C22×D59C2×D411yescharacteristic
74Q8×C59—42no—
75D4×C59—24no—
76D4×C59—42no—
77D4×C59—42no—
78C2×C4×C59—22no—
79C2×C4×C59C2×D411yescharacteristic
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2411yescharacteristic
82C22⋊D59—44no—
83C22⋊D59—44no—
84C22⋊D59—44no—
85C2×Dic59—22no—
86C2×Dic59C2×D411yescharacteristic
87C2×Dic59C2×D411yescharacteristic
88C2×Dic59C2×D411yescharacteristic
89D236—24no—
90D236—42no—
91D236—42no—
92C4×D59—22no—
93C4×D59—22no—
94C4×D59#4114yes—
95Dic118—42no—
96C8×C59—22no—
97C59⋊C8—22no—
98C22×C59—42no—
99C22×C59—42no—
100C22×C59—42no—
101C22×C59C22×D411yescharacteristic
102C2×D59—21no—
103C2×D59—21no—
104C2×D59—42no—
105C2×D59—42no—
106C2×D59—42no—
107C2×D59—88no—
108C2×D59#12412yes—
109C4×C59—42no—
110C4×C59AGL(1,ℤ/8)12yes—
111C4×C59AGL(1,ℤ/8)12yes—
112C4×C59C2×#4112yes—
113Dic59—21no—
114Dic59—21no—
115Dic59—42no—
116Dic59#12412yes—
117#3138—591nomaximal, Sylow
118C2×C59—82no—
119C2×C59C2×#12411yescharacteristic
120C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
121C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
122D59—22no—
123D59—82no—
124#533—591no—
125C2×#127—591no—
126#490—594no—
127#486—591no—
128#486—591no—
129#486—591no—
130#486D5911yescharacteristic, complemented
131#418—594no—
132C4×M16—591no—
133C59#313811yescharacteristic, complemented, Sylow
134C22×D4—592no—
135C22×D4—1181no—
136C22×D4—1181no—
137C2×M16—592no—
138C4⋊Q8—591no—
139C4⋊Q8C2×D5911yescharacteristic, complemented
140#127—592no—
141#127—591no—
142#127—1181no—
143#127—1181no—
144#127C2×D5911yescharacteristic
145#125—592no—
146C22⋊Q8—1181no—
147C22⋊Q8—1181no—
148C4×Q8—1181no—
149C4×Q8—1181no—
150#117—592no—
151C2×C42—591no—
152#102—594no—
153#102—594no—
154#102—594no—
155#102C2×D5914yescomplemented
156#97—592no—
157C4×C8—591no—
158C4×C8C2×D5911yescharacteristic, complemented
159C24—1182no—
160C2×Q8—21no—
161C2×Q8—1181no—
162C2×D4—21no—
163C2×D4—21no—
164C2×D4—592no—
165C2×D4—1188no—
166C2×D4—1182no—
167C2×D4—1182no—
168C2×D4—1182no—
169C2×D4—1181no—
170C2×D4—1181no—
171C2×D4—2364no—
172C2×D4—2364no—
173C2×D4C22×D5912yes—
174C22×C4—591no—
175C22×C4—591no—
176C22×C4—591no—
177M16—1184no—
178C2×C8—592no—
179C2×C8C22×D5912yes—
180C4⋊C4—21no—
181C4⋊C4—592no—
182C4⋊C4—1182no—
183C4⋊C4—1182no—
184C4⋊C4—1181no—
185C4⋊C4C22×D5912yes—
186C22⋊C4—1182no—
187C42—591no—
188C42—591no—
189C42—591no—
190C42—1182no—
191C42C22×D5911yescharacteristic
192C23—22no—
193C23—591no—
194C23—1182no—
195C23—2364no—
196C23—2364no—
197C23—2364no—
198Q8—42no—
199Q8—2362no—
200D4—24no—
201D4—42no—
202D4—42no—
203D4—1184no—
204D4—2364no—
205D4—2364no—
206D4—2364no—
207D4—2362no—
208D4—2362no—
209C2×C4—22no—
210C2×C4—591no—
211C2×C4—594no—
212C2×C4—591no—
213C2×C4—591no—
214C2×C4—1182no—
215C2×C4—1182no—
216C2×C4—1182no—
217C2×C4D4×D5911yescharacteristic
218C2×C4D4×D5911yescharacteristic
219C2×C4C23×D5911yescharacteristic
220C8—22no—
221C8—1182no—
222C22—42no—
223C22—42no—
224C22—42no—
225C22—592no—
226C22—1181no—
227C22—1181no—
228C22—4728no—
229C22—2362no—
230C22—2362no—
231C22—2362no—
232C22C2×D4×D5911yescharacteristic
233C4—42no—
234C4—592no—
235C4—1181no—
236C4—1181no—
237C4—2362no—
238C4#1427375112yes—
239C4#1427375412yes—
240C4#41×D5912yes—
241C2—82no—
242C2—1182no—
243C2—4722no—
244C2#124×D5911yescharacteristic
245C2C2×#1427375111yescharacteristic
246C2C2×#1427375411yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#486C2
socleC22×C59C22×D4
hypercenter#486D59
hypocenterC59#3138
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #16837957C2semidirect
3. #16837765C2semidirect
4. #16837750C2semidirect
5. #16837749C2semidirect
6. #16837748C2semidirect
7. #16837405C2semidirect
8. C4×#11745659C2semidirect
9. C59×#486C2semidirect
14. #14273727C22semidirect
19. #14273718C22semidirect
26. #14273649C22semidirect
27. #14273648C22semidirect
28. #14273647C22semidirect
29. #14273637C22semidirect
30. C4×C59⋊C8C22semidirect
31. C4⋊Q8×C59C22semidirect
33. #102×C59C22semidirect
34. C4×C8×C59C22semidirect
130. #486D59semidirect
133. C59#3138semidirect
139. C4⋊Q8C2×D59semidirect
155. #102C2×D59semidirect
158. C4×C8C2×D59semidirect