Finite Group Databasebeta

← C22×#10625108 #15686612

Subgroups — C22×#10625108 #15686612

Order 2944.

4544 conjugacy classes of subgroups; only the 725 normal subgroups are shown.

normal subgroups only

This group has 4544 conjugacy classes of subgroups — too many to draw. Only its 725 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
1C25×D23C211yesmaximal, characteristic, complemented
2C23×C22⋊D23C212yesmaximal, complemented
3C2×#10625108C2124yesmaximal, direct product factor
4C22×C22⋊Dic23C211yesmaximal, characteristic, complemented
5C22×(C2×D23)⋊C4C212yesmaximal, complemented
6C23×D4×C23C211yesmaximal, characteristic, complemented
7C25×C23C2211yescharacteristic
8C25×C23C2211yescharacteristic, complemented
9C24×D23—28no—
10C24×D23—216no—
11C24×D23C2212yes—
12C24×D23C22112yescomplemented
13C22×D4×C23—28no—
14C22×D4×C23C22112yescomplemented
15C23×C4×C23C2211yescharacteristic, complemented
16C22×C22⋊D23—216no—
17C22×C22⋊D23C22124yescomplemented
18C23×Dic23C2212yescomplemented
19C2×C22⋊Dic23C22112yescomplemented
20#10625108C22164yesdirect product factor
21C2×(C2×D23)⋊C4C22124yescomplemented
22C24×C23—28no—
23C24×C23—28no—
24C24×C23—24no—
25C24×C23D418yescomplemented
26C24×C23C2316yes—
27C24×C23C2311yescharacteristic
28C24×C23C2316yescomplemented
29C23×D23—2128no—
30C23×D23—28no—
31C23×D23—28no—
32C23×D23—248no—
33C23×D23—296no—
34C23×D23D4116yescomplemented
35C23×D23C23112yes—
36C23×D23C23116yescomplemented
37C2×D4×C23—248no—
38C2×D4×C23C23116yescomplemented
39C22×C4×C23—24no—
40C22×C4×C23C2316yescomplemented
41C2×C22⋊D23—296no—
42C2×C22⋊D23C23132yescomplemented
43C22×Dic23—28no—
44C22×Dic23C23112yescomplemented
45C22⋊Dic23C23116yescomplemented
46(C2×D23)⋊C4C23132yescomplemented
47C23×C23—232no—
48C23×C23—224no—
49C23×C23—224no—
50C23×C23—212no—
51C23×C23—416no—
52C23×C23C2×D418yes—
53C23×C23C2×D414yes—
54C23×C23C2×D4124yescomplemented
55C23×C23C2414yes—
56C23×C23C2413yes—
57C23×C23C2414yescomplemented
58C22×D23—2384no—
59C22×D23—264no—
60C22×D23—224no—
61C22×D23—224no—
62C22×D23—232no—
63C22×D23—264no—
64C22×D23C2×D4148yescomplemented
65C22×D23C2418yes—
66D4×C23—232no—
67C2×C4×C23—212no—
68C2×C4×C23C2414yescomplemented
69C22⋊D23—264no—
70C2×Dic23—224no—
71C2×Dic23C2418yescomplemented
72C22×#120—231nomaximal, Sylow
73C22×C23—248no—
74C22×C23—28no—
75C22×C23—28no—
76C22×C23—24no—
77C22×C23—424no—
78C22×C23#120116yescomplemented
79C22×C23C22×D4112yes—
80C22×C23C22×D416yes—
81C22×C23C22×D418yescomplemented
82C22×C23C2511yescharacteristic
83C2×D23—2128no—
84C2×D23—296no—
85C2×D23—28no—
86C2×D23—28no—
87C2×D23C22×D4116yescomplemented
88C4×C23—24no—
89Dic23—28no—
90C26—231no—
91C23×D4—232no—
92C23×D4D2311yescharacteristic, complemented
93C2×#120—2324no—
94C22×C22⋊C4—231no—
95C22×C22⋊C4—232no—
96C2×C23—28no—
97C2×C23—44no—
98C2×C23C2×#120112yescomplemented
99C2×C23C23×D412yes—
100C2×C23C23×D411yescharacteristic
101D23—216no—
102C25—232no—
103C25—2312no—
104C25—4616no—
105C25—468no—
106C25C2×D2311yescharacteristic
107C25C2×D2311yescharacteristic, complemented
108C22×D4—28no—
109C22×D4—2324no—
110C22×D4—4616no—
111C22×D4C2×D23112yescomplemented
112C23×C4—232no—
113C23×C4C2×D2311yescharacteristic, complemented
114#120—2364no—
115C2×C22⋊C4—2312no—
116C2×C22⋊C4—2324no—
117C23C22×#12011yescharacteristic, complemented, Sylow
118C24—28no—
119C24—28no—
120C24—24no—
121C24—2316no—
122C24—2312no—
123C24—2316no—
124C24—4696no—
125C24—46128no—
126C24—468no—
127C24—468no—
128C24—4648no—
129C24C22⋊D2318yescomplemented
130C24C22×D2316yes—
131C24C22×D2311yescharacteristic
132C24C22×D2316yescomplemented
133C2×D4—248no—
134C2×D4—2332no—
135C2×D4—4696no—
136C2×D4C22×D23116yescomplemented
137C22×C4—24no—
138C22×C4—2312no—
139C22×C4—468no—
140C22×C4C22×D2316yescomplemented
141C22⋊C4—2316no—
142C22⋊C4—2332no—
143C23—232no—
144C23—224no—
145C23—224no—
146C23—212no—
147C23—416no—
148C23—2348no—
149C23—238no—
150C23—4664no—
151C23—46384no—
152C23—4664no—
153C23—4624no—
154C23—4624no—
155C23—4632no—
156C23D4×D2318yes—
157C23C2×C22⋊D2314yes—
158C23C2×C22⋊D23124yescomplemented
159C23C23×D2314yes—
160C23C23×D2313yes—
161C23C23×D2314yescomplemented
162D4—232no—
163D4—4664no—
164C2×C4—212no—
165C2×C4—238no—
166C2×C4—4624no—
167C2×C4C23×D2314yescomplemented
168C22—248no—
169C22—28no—
170C22—28no—
171C22—24no—
172C22—424no—
173C22—2316no—
174C22—46128no—
175C22—4696no—
176C22—468no—
177C22—468no—
178C22#10625108116yesdirect product factor
179C22C2×D4×D23112yes—
180C22C22×C22⋊D2316yes—
181C22C22×C22⋊D2318yescomplemented
182C22C24×D2311yescharacteristic
183C4—24no—
184C4—468no—
185C2—28no—
186C2—44no—
187C2—4616no—
188C2C2×#10625108112yesdirect product factor
189C2C22×D4×D2312yes—
190C2C23×C22⋊D2311yescharacteristic
subgroupG/H
centerC24C22×D23
commutator, cosocleC22×C23C25
FrattiniC22C24×D23
FittingC23×D4×C23C2
socleC24×C23C23
hypercenterC23×D4D23
hypocenterC23C22×#120
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C25×D23C2semidirect
2. C23×C22⋊D23C2semidirect
3. C2×#10625108C2direct (N × H)
4. C22×C22⋊Dic23C2semidirect
5. C22×(C2×D23)⋊C4C2semidirect
6. C23×D4×C23C2semidirect
8. C25×C23C22semidirect
12. C24×D23C22semidirect
14. C22×D4×C23C22semidirect
15. C23×C4×C23C22semidirect
17. C22×C22⋊D23C22semidirect
18. C23×Dic23C22semidirect
19. C2×C22⋊Dic23C22semidirect
20. #10625108C22direct (N × H)
21. C2×(C2×D23)⋊C4C22semidirect
25. C24×C23D4semidirect
28. C24×C23C23semidirect
34. C23×D23D4semidirect
36. C23×D23C23semidirect
38. C2×D4×C23C23semidirect
40. C22×C4×C23C23semidirect
42. C2×C22⋊D23C23semidirect
44. C22×Dic23C23semidirect
45. C22⋊Dic23C23semidirect
46. (C2×D23)⋊C4C23semidirect
54. C23×C23C2×D4semidirect
57. C23×C23C24semidirect
64. C22×D23C2×D4semidirect
68. C2×C4×C23C24semidirect
71. C2×Dic23C24semidirect
78. C22×C23#120semidirect
81. C22×C23C22×D4semidirect
87. C2×D23C22×D4semidirect
92. C23×D4D23semidirect
98. C2×C23C2×#120semidirect
107. C25C2×D23semidirect
111. C22×D4C2×D23semidirect
113. C23×C4C2×D23semidirect
117. C23C22×#120semidirect
129. C24C22⋊D23semidirect
132. C24C22×D23semidirect
136. C2×D4C22×D23semidirect
140. C22×C4C22×D23semidirect
158. C23C2×C22⋊D23semidirect
161. C23C23×D23semidirect
167. C2×C4C23×D23semidirect
178. C22#10625108direct (N × H)
181. C22C22×C22⋊D23semidirect
188. C2C2×#10625108direct (N × H)

Maximal subgroups

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

subgroupindex
C25×D232
C23×C22⋊D232
C2×#106251082
C22×C22⋊Dic232
C22×(C2×D23)⋊C42
C23×D4×C232
C22×#12023