Finite Group Databasebeta

← C22×D16×D59 #29495162

Subgroups — C22×D16×D59 #29495162

Order 15104.

2590 conjugacy classes of subgroups; only the 627 normal subgroups are shown.

normal subgroups only

This group has 2590 conjugacy classes of subgroups — too many to draw. Only its 627 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
1C22×D8×D59C212yesmaximal, complemented
2C22×D944C211yesmaximal, characteristic, complemented
3C22×#14273668C212yesmaximal, complemented
4C2×D16×D59C2124yesmaximal, direct product factor
5C22×C16×D59C211yesmaximal, characteristic, complemented
6C22×D16×C59C211yesmaximal, characteristic, complemented
7C22×D4×D59—22no—
8C22×D472C2212yescomplemented
9C22×#11745669—22no—
10C2×D8×D59—212no—
11C2×D8×D59C22124yescomplemented
12C22×C8×D59C2211yescharacteristic
13C2×D944C22112yescomplemented
14C2×#14273668C22124yescomplemented
15D16×D59C22164yesdirect product factor
16C22×C59⋊C16C2211yescharacteristic, complemented
17C2×C16×D59C22112yescomplemented
18C22×D8×C59C2212yescomplemented
19C2×D16×C59C22112yescomplemented
20C22×C16×C59C2211yescharacteristic, complemented
21C24×D59—42no—
22C22×D236—22no—
23C22×C22⋊D59—42no—
24C2×D4×D59—224no—
25C2×D4×D59—412no—
26C22×C4×D59D411yescharacteristic
27C2×D472—26no—
28C2×D472C23112yescomplemented
29C2×#11745669—224no—
30D8×D59—248no—
31D8×D59C23132yescomplemented
32C22×C59⋊C8D411yescharacteristic
33C2×C8×D59D416yes—
34C2×C8×D59C2316yes—
35D944C23116yescomplemented
36#14273668C23132yescomplemented
37C2×C59⋊C16C2316yescomplemented
38C16×D59C23116yescomplemented
39C22×D4×C59—22no—
40C2×D8×C59—26no—
41C2×D8×C59C23112yescomplemented
42C22×C8×C59C2311yescharacteristic
43D16×C59C23116yescomplemented
44C2×C16×C59C2316yescomplemented
45C24×C59—42no—
46C23×D59—42no—
47C23×D59—424no—
48C23×D59—816no—
49C23×D59D811yescharacteristic
50C2×D4×C59—212no—
51C2×D4×C59—46no—
52C22×C4×C59C2×D411yescharacteristic
53C2×C22⋊D59—424no—
54C22×Dic59D811yescharacteristic
55D4×D59—232no—
56D4×D59—448no—
57C2×D236—212no—
58C2×D236—46no—
59C2×C4×D59D816yes—
60C2×C4×D59C2×D416yes—
61D8×C59—212no—
62D8×C59C2418yescomplemented
63C2×C8×C59C2×D413yes—
64C2×C8×C59C2413yes—
65#11745669—232no—
66C2×C59⋊C8C2×D416yes—
67D472—212no—
68D472C2418yescomplemented
69C8×D59C2×D4112yes—
70C8×D59C2414yes—
71C16×C59C2414yescomplemented
72C59⋊C16C2414yescomplemented
73C23×C59—412no—
74C23×C59—88no—
75C23×C59C2×D811yescharacteristic
76C22×D59—412no—
77C22×D59—432no—
78C22×D59—88no—
79C22×D59—896no—
80C22×D59D1618yesdirect product factor
81C22×D59C2×D816yes—
82D4×C59—28no—
83D4×C59—412no—
84C2×C4×C59C2×D813yes—
85C2×C4×C59C22×D413yes—
86C22⋊D59—432no—
87C2×Dic59C2×D816yes—
88D236—28no—
89D236—412no—
90C4×D59C2×D8112yes—
91C4×D59C22×D414yes—
92C8×C59C22×D413yes—
93C8×C59C2511yescharacteristic
94C59⋊C8C22×D414yes—
95C23×D16—591nomaximal, Sylow
96C22×C59—48no—
97C22×C59—824no—
98C22×C59C2×D1614yescomplemented
99C22×C59C22×D813yes—
100C2×D59—48no—
101C2×D59—824no—
102C2×D59—864no—
103C2×D59C2×D16124yesdirect product factor
104C2×D59C22×D814yes—
105C4×C59C22×D813yes—
106C4×C59C23×D411yescharacteristic
107Dic59C22×D814yes—
108C23×D8—592no—
109C22×D16—5924no—
110C22×D16—591no—
111C22×D16—592no—
112C22×D16D5911yescharacteristic, direct product factor
113C23×C16—591no—
114C2×C59—88no—
115C2×C59C22×D1616yescomplemented
116C2×C59C23×D811yescharacteristic
117D59—88no—
118D59C22×D1618yesdirect product factor
119C23×D4—1182no—
120C22×D8—5924no—
121C22×D8—592no—
122C22×D8—11812no—
123C22×D8—1182no—
124C22×D8C2×D5912yescomplemented
125C23×C8—591no—
126C2×D16—5924no—
127C2×D16—5964no—
128C2×D16—5912no—
129C2×D16C2×D59112yesdirect product factor
130C22×C16—591no—
131C22×C16—5912no—
132C22×C16C2×D5911yescharacteristic, complemented
133C59C23×D1611yescharacteristic, complemented, Sylow
134C25—2362no—
135C22×D4—22no—
136C22×D4—11824no—
137C22×D4—1182no—
138C22×D4—23612no—
139C22×D4—2362no—
140C23×C4—591no—
141C2×D8—26no—
142C2×D8—5932no—
143C2×D8—5912no—
144C2×D8—11848no—
145C2×D8—11824no—
146C2×D8—1186no—
147C2×D8C22×D59112yescomplemented
148C22×C8—591no—
149C22×C8—596no—
150C22×C8—596no—
151C22×C8C22×D5911yescharacteristic
152D16—5932no—
153D16—5916no—
154D16C22×D59116yesdirect product factor
155C2×C16—596no—
156C2×C16—5916no—
157C2×C16C22×D5916yescomplemented
158C24—42no—
159C24—591no—
160C24—47216no—
161C24—23624no—
162C24—2362no—
163C2×D4—212no—
164C2×D4—46no—
165C2×D4—11832no—
166C2×D4—11812no—
167C2×D4—23648no—
168C2×D4—23624no—
169C2×D4—2366no—
170C22×C4—591no—
171C22×C4—596no—
172C22×C4—596no—
173C22×C4D4×D5911yescharacteristic
174D8—212no—
175D8—598no—
176D8—11832no—
177D8—11812no—
178D8C23×D5918yescomplemented
179C2×C8—596no—
180C2×C8—5912no—
181C2×C8—594no—
182C2×C8D4×D5913yes—
183C2×C8C23×D5913yes—
184C16—594no—
185C16C23×D5914yescomplemented
186C23—412no—
187C23—88no—
188C23—596no—
189C23—598no—
190C23—47296no—
191C23—4728no—
192C23—23632no—
193C23—23612no—
194C23D8×D5911yescharacteristic
195D4—28no—
196D4—412no—
197D4—1188no—
198D4—23632no—
199D4—23612no—
200C2×C4—596no—
201C2×C4—5912no—
202C2×C4—594no—
203C2×C4D8×D5913yes—
204C2×C4C2×D4×D5913yes—
205C8—594no—
206C8C2×D4×D5913yes—
207C8C24×D5911yescharacteristic
208C22—48no—
209C22—824no—
210C22—5924no—
211C22—594no—
212C22—47264no—
213C22—47224no—
214C22—2368no—
215C22D16×D5914yesdirect product factor
216C22C2×D8×D5913yes—
217C4—594no—
218C4C2×D8×D5913yes—
219C4C22×D4×D5911yescharacteristic
220C2—88no—
221C2—598no—
222C2—4728no—
223C2C2×D16×D5916yesdirect product factor
224C2C22×D8×D5911yescharacteristic
subgroupG/H
centerC23D8×D59
commutator, cosocleC8×C59C25
FrattiniC8C24×D59
FittingC22×D16×C59C2
socleC23×C59C2×D8
hypercenterC22×D16D59
hypocenterC59C23×D16
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×D16

Complements

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

NH ≅ G/Ntype
1. C22×D8×D59C2semidirect
2. C22×D944C2semidirect
3. C22×#14273668C2semidirect
4. C2×D16×D59C2direct (N × H)
5. C22×C16×D59C2semidirect
6. C22×D16×C59C2semidirect
8. C22×D472C22semidirect
11. C2×D8×D59C22semidirect
13. C2×D944C22semidirect
14. C2×#14273668C22semidirect
15. D16×D59C22direct (N × H)
16. C22×C59⋊C16C22semidirect
17. C2×C16×D59C22semidirect
18. C22×D8×C59C22semidirect
19. C2×D16×C59C22semidirect
20. C22×C16×C59C22semidirect
28. C2×D472C23semidirect
31. D8×D59C23semidirect
35. D944C23semidirect
36. #14273668C23semidirect
37. C2×C59⋊C16C23semidirect
38. C16×D59C23semidirect
41. C2×D8×C59C23semidirect
43. D16×C59C23semidirect
44. C2×C16×C59C23semidirect
62. D8×C59C24semidirect
68. D472C24semidirect
71. C16×C59C24semidirect
72. C59⋊C16C24semidirect
80. C22×D59D16direct (N × H)
98. C22×C59C2×D16semidirect
103. C2×D59C2×D16direct (N × H)
112. C22×D16D59direct (N × H)
115. C2×C59C22×D16semidirect
118. D59C22×D16direct (N × H)
124. C22×D8C2×D59semidirect
129. C2×D16C2×D59direct (N × H)
132. C22×C16C2×D59semidirect
133. C59C23×D16semidirect
147. C2×D8C22×D59semidirect
154. D16C22×D59direct (N × H)
157. C2×C16C22×D59semidirect
178. D8C23×D59semidirect
185. C16C23×D59semidirect
215. C22D16×D59direct (N × H)
223. C2C2×D16×D59direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×D8×D592
C22×D9442
C22×#142736682
C2×D16×D592
C22×C16×D592
C22×D16×C592
C23×D1659