Finite Group Databasebeta

← #21432945

Subgroups — #21432945

Order 7552.

528 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 175 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×D8×D59C211yesmaximal, characteristic
2#16837874C212yesmaximal, complemented
3#16837515C211yesmaximal, characteristic, complemented
4#16837514C211yesmaximal, characteristic, complemented
5#16837513C211yesmaximal, characteristic, complemented
6C4×#11745669C212yesmaximal, complemented
7#16837482C212yesmaximal, complemented
8#16837437C211yesmaximal, characteristic, complemented
9#16837405C212yesmaximal, complemented
10#16837359C211yesmaximal, characteristic, complemented
11C59×#442C211yesmaximal, characteristic, complemented
12C2×D4×D59C2212yes—
13C2×D472C2211yescharacteristic
14C2×#11745669C2212yes—
15D8×D59C418yescomplemented
16C2×#11745659C2211yescharacteristic
17C2×C8×D59C2211yescharacteristic
18C4×D236C2212yescomplemented
19D4×Dic59C2212yescomplemented
20#14273689C2212yescomplemented
21C4×C22⋊D59—22no—
22(C22⋊D59)⋊C4—22no—
23#14273685C2212yes—
24#14273684C2211yescharacteristic
25C2×(C2×D59)⋊C4—22no—
26C22⋊C4×D59—22no—
27#14273660C2212yescomplemented
28#14273659C2211yescharacteristic, complemented
29#14273649C2212yescomplemented
30#14273648C2212yescomplemented
31#14273647C2212yescomplemented
32#14273637C2211yescharacteristic, complemented
33C4×C59⋊C8C2211yescharacteristic, complemented
34C8×Dic59C2211yescharacteristic, complemented
35C2×D8×C59C2211yescharacteristic
36C4×D4×C59C2212yescomplemented
37#106×C59C2211yescharacteristic, complemented
38#102×C59C2212yescomplemented
39#97×C59C2211yescharacteristic, complemented
40C23×D59—22no—
41C2×D4×C59C2312yes—
42C22×C4×C59—22no—
43C2×C22⋊D59—22no—
44C22×Dic59—22no—
45D4×D59—24no—
46D4×D59C2×C418yescomplemented
47C2×D236C2312yes—
48C2×C4×D59—22no—
49C2×C4×D59—22no—
50C2×C4×D59C2311yescharacteristic
51D8×C59C2×C414yescomplemented
52C2×C8×C59C2311yescharacteristic
53C2×C8×C59C2311yescharacteristic
54C4⋊C4×C59C2312yes—
55C22⋊C4×C59—22no—
56C42×C59C2311yescharacteristic
57C22⋊Dic59—22no—
58#11745669C2×C418yescomplemented
59(C2×D59)⋊C4—22no—
60(C2×D59)⋊C4—22no—
61(C2×D59)⋊C4—22no—
62(C2×D59)⋊C4D412yes—
63C4⋊Dic59C2312yes—
64Dic59⋊C4D412yes—
65C4×Dic59—22no—
66C4×Dic59C2311yescharacteristic
67C2×C59⋊C8C2311yescharacteristic
68C2×C59⋊C8C2311yescharacteristic
69D472C2×C414yescomplemented
70#11745659—22no—
71C8×D59C2×C414yescomplemented
72C23×C59—22no—
73C22×D59—22no—
74C22×D59—28no—
75C22×D59—82no—
76C22×D59—82no—
77C22×D59C2×D411yescharacteristic
78D4×C59—22no—
79D4×C59C22×C414yes—
80C2×C4×C59—22no—
81C2×C4×C59—82no—
82C2×C4×C59C2×D412yes—
83C2×C4×C59C2411yescharacteristic
84C22⋊D59—28no—
85C2×Dic59—22no—
86C2×Dic59—82no—
87C2×Dic59C2×D412yes—
88C2×Dic59C2×D411yescharacteristic
89D236—22no—
90D236C22×C414yes—
91C4×D59—82no—
92C4×D59—82no—
93C4×D59C22×C412yes—
94C4×D59#4112yes—
95C8×C59—21no—
96C8×C59C22×C412yes—
97C59⋊C8—21no—
98C59⋊C8C22×C412yes—
99C22×C59—24no—
100C22×C59—42no—
101C22×C59—42no—
102C22×C59C22×D411yescharacteristic
103C2×D59—22no—
104C2×D59—24no—
105C2×D59—42no—
106C2×D59—42no—
107C2×D59—88no—
108C2×D59C4×D412yes—
109C4×C59—22no—
110C4×C59—42no—
111C4×C59C23×C411yescharacteristic
112C4×C59C2×#4111yescharacteristic
113Dic59—22no—
114Dic59—42no—
115Dic59C4×D412yes—
116#2948—591nomaximal, Sylow
117C2×C59—44no—
118C2×C59C2×C4×D411yescharacteristic
119C2×C59#57612yes—
120D59—22no—
121D59—44no—
122C22×D8—591no—
123#518—592no—
124#442—591no—
125#442—591no—
126#442—591no—
127#442D5911yescharacteristic, complemented
128C4×D8—592no—
129C4×D8—592no—
130#427—591no—
131#418—592no—
132#405—591no—
133C59#294811yescharacteristic, complemented, Sylow
134C22×D4—592no—
135C2×D8—592no—
136C2×D8—598no—
137C2×D8—591no—
138C2×D8C2×D5911yescharacteristic
139C2×M16—591no—
140C22×C8—591no—
141C4×D4—592no—
142C4×D4—592no—
143C4×D4—592no—
144C4×D4—1182no—
145C4×D4—1182no—
146C4×D4C2×D5912yescomplemented
147#117—591no—
148#117—592no—
149C2×C22⋊C4—1182no—
150C2×C22⋊C4—1182no—
151#107—592no—
152#106—591no—
153#106C2×D5911yescharacteristic, complemented
154#102—592no—
155#102—592no—
156#102—592no—
157#102C2×D5912yescomplemented
158#97—591no—
159#97C2×D5911yescharacteristic, complemented
160C4×C8—591no—
161C4×C8—591no—
162C24—1182no—
163C2×D4—598no—
164C2×D4—592no—
165C2×D4—1184no—
166C2×D4—1182no—
167C2×D4C22×D5912yes—
168C22×C4—22no—
169C22×C4—591no—
170C22×C4—1182no—
171C22×C4—1182no—
172C22×C4—1182no—
173D8—598no—
174D8—594no—
175D8C4×D5914yescomplemented
176M16—1182no—
177C2×C8—591no—
178C2×C8—594no—
179C2×C8—591no—
180C2×C8C22×D5911yescharacteristic
181C2×C8C22×D5911yescharacteristic
182C4⋊C4—592no—
183C4⋊C4—592no—
184C4⋊C4C22×D5912yes—
185C22⋊C4—22no—
186C22⋊C4—592no—
187C22⋊C4—1182no—
188C22⋊C4—1182no—
189C22⋊C4—1182no—
190C22⋊C4—1182no—
191C42—591no—
192C42—1182no—
193C42C22×D5911yescharacteristic
194C23—22no—
195C23—591no—
196C23—1188no—
197C23—1182no—
198C23—4722no—
199C23—4722no—
200D4—22no—
201D4—594no—
202D4—1188no—
203D4—1182no—
204D4C2×C4×D5914yes—
205C2×C4—22no—
206C2×C4—82no—
207C2×C4—591no—
208C2×C4—592no—
209C2×C4—592no—
210C2×C4—592no—
211C2×C4—1182no—
212C2×C4—4722no—
213C2×C4—4722no—
214C2×C4—4722no—
215C2×C4D4×D5912yes—
216C2×C4C23×D5911yescharacteristic
217C8—21no—
218C8—592no—
219C8—1181no—
220C8C2×C4×D5912yes—
221C22—24no—
222C22—42no—
223C22—42no—
224C22—592no—
225C22—1182no—
226C22—1184no—
227C22—4728no—
228C22—2362no—
229C22—2362no—
230C22C2×D4×D5911yescharacteristic
231C4—22no—
232C4—42no—
233C4—592no—
234C4—1182no—
235C4—2362no—
236C4C22×C4×D5911yescharacteristic
237C4#41×D5911yescharacteristic
238C2—44no—
239C2—1182no—
240C2—2364no—
241C2C4×D4×D5911yescharacteristic
242C2#1683820612yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC4×C59C23×C4
FrattiniC2×C4C23×D59
FittingC59×#442C2
socleC22×C59C22×D4
hypercenter#442D59
hypocenterC59#2948
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #16837874C2semidirect
3. #16837515C2semidirect
4. #16837514C2semidirect
5. #16837513C2semidirect
6. C4×#11745669C2semidirect
7. #16837482C2semidirect
8. #16837437C2semidirect
9. #16837405C2semidirect
10. #16837359C2semidirect
11. C59×#442C2semidirect
15. D8×D59C4semidirect
18. C4×D236C22semidirect
19. D4×Dic59C22semidirect
20. #14273689C22semidirect
27. #14273660C22semidirect
28. #14273659C22semidirect
29. #14273649C22semidirect
30. #14273648C22semidirect
31. #14273647C22semidirect
32. #14273637C22semidirect
33. C4×C59⋊C8C22semidirect
34. C8×Dic59C22semidirect
36. C4×D4×C59C22semidirect
37. #106×C59C22semidirect
38. #102×C59C22semidirect
39. #97×C59C22semidirect
46. D4×D59C2×C4semidirect
51. D8×C59C2×C4semidirect
58. #11745669C2×C4semidirect
69. D472C2×C4semidirect
71. C8×D59C2×C4semidirect
127. #442D59semidirect
133. C59#2948semidirect
146. C4×D4C2×D59semidirect
153. #106C2×D59semidirect
157. #102C2×D59semidirect
159. #97C2×D59semidirect
175. D8C4×D59semidirect