Finite Group Databasebeta

← C22×#10625101 #15686619

Subgroups — C22×#10625101 #15686619

Order 2944.

2528 conjugacy classes of subgroups; only the 725 normal subgroups are shown.

normal subgroups only

This group has 2528 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
1C23×D92C211yesmaximal, characteristic, complemented
2C23×C22⋊D23C212yesmaximal, complemented
3C2×#10625101C2124yesmaximal, direct product factor
4C22×C4⋊Dic23C211yesmaximal, characteristic, complemented
5C22×(C2×D23)⋊C4C212yesmaximal, complemented
6C24×C4×C23C211yesmaximal, characteristic, complemented
7C25×C23C2211yescharacteristic
8C24×D23C2212yes—
9C23×C4×C23—28no—
10C23×C4×C23C2211yescharacteristic
11C23×C4×C23C2211yescharacteristic
12C23×C4×C23C22112yescomplemented
13C22×C22⋊D23—216no—
14C22×C22⋊D23C22124yescomplemented
15C23×Dic23C2212yes—
16C22×D92—28no—
17C22×D92C22112yescomplemented
18#10625101C22164yesdirect product factor
19C2×(C2×D23)⋊C4C22124yescomplemented
20C2×C4⋊Dic23C22112yescomplemented
21C24×C23—24no—
22C24×C23—24no—
23C24×C23D418yescomplemented
24C24×C23C2316yes—
25C24×C23C2311yescharacteristic
26C23×D23—28no—
27C23×D23—28no—
28C23×D23—28no—
29C23×D23C23112yes—
30C22×C4×C23—24no—
31C22×C4×C23—248no—
32C22×C4×C23D418yescomplemented
33C22×C4×C23C2316yes—
34C22×C4×C23C2316yes—
35C22×C4×C23C23116yescomplemented
36C2×C22⋊D23—296no—
37C2×C22⋊D23C23132yescomplemented
38C22×Dic23—28no—
39C22×Dic23C23112yes—
40C2×D92—248no—
41C2×D92C23116yescomplemented
42(C2×D23)⋊C4C23132yescomplemented
43C4⋊Dic23C23116yescomplemented
44C23×C23—232no—
45C23×C23—212no—
46C23×C23—212no—
47C23×C23C2×D414yes—
48C23×C23C2×D414yes—
49C23×C23C2×D4124yescomplemented
50C23×C23#4114yes—
51C23×C23C2414yes—
52C23×C23C2413yes—
53C22×D23—224no—
54C22×D23—224no—
55C22×D23—224no—
56C22×D23—432no—
57C22×D23C2418yes—
58C2×C4×C23—212no—
59C2×C4×C23—232no—
60C2×C4×C23C2×D4124yescomplemented
61C2×C4×C23C2414yes—
62C2×C4×C23C2414yes—
63C22⋊D23—264no—
64C2×Dic23—224no—
65C2×Dic23C2418yes—
66D92—232no—
67C22×#121—231nomaximal, Sylow
68C22×C23—248no—
69C22×C23—24no—
70C22×C23—24no—
71C22×C23#121116yescomplemented
72C22×C23C22×D416yes—
73C22×C23C22×D416yes—
74C22×C23C22×D418yescomplemented
75C22×C23C2×#4116yes—
76C22×C23C2511yescharacteristic
77C2×D23—28no—
78C2×D23—28no—
79C2×D23—28no—
80C2×D23—448no—
81C4×C23—24no—
82C4×C23C22×D418yescomplemented
83Dic23—28no—
84C23×D4—232no—
85C23×D4—231no—
86C24×C4D2311yescharacteristic, complemented
87C2×#121—2324no—
88C22×C4⋊C4—231no—
89C22×C22⋊C4—232no—
90C2×C23—28no—
91C2×C23C2×#121112yescomplemented
92C2×C23C23×D411yescharacteristic
93C2×C23C23×D411yescharacteristic
94C2×C23C22×#4111yescharacteristic
95D23—48no—
96C25—232no—
97C25C2×D2311yescharacteristic
98C22×D4—2324no—
99C22×D4—2312no—
100C22×D4—4616no—
101C22×D4—468no—
102C23×C4—28no—
103C23×C4—232no—
104C23×C4C2×D2311yescharacteristic
105C23×C4C2×D2311yescharacteristic
106C23×C4C2×D23112yescomplemented
107#121—2364no—
108C2×C4⋊C4—2312no—
109C2×C22⋊C4—2324no—
110C23C22×#12111yescharacteristic, complemented, Sylow
111C24—24no—
112C24—24no—
113C24—2312no—
114C24—468no—
115C24—468no—
116C24—468no—
117C24D9218yescomplemented
118C24C22×D2316yes—
119C24C22×D2311yescharacteristic
120C2×D4—2332no—
121C2×D4—2316no—
122C2×D4—4696no—
123C2×D4—4648no—
124C22×C4—24no—
125C22×C4—248no—
126C22×C4—2312no—
127C22×C4—468no—
128C22×C4C22⋊D2318yescomplemented
129C22×C4C22×D2316yes—
130C22×C4C22×D2316yes—
131C22×C4C22×D23116yescomplemented
132C4⋊C4—2316no—
133C22⋊C4—2332no—
134C23—232no—
135C23—212no—
136C23—212no—
137C23—238no—
138C23—4624no—
139C23—4624no—
140C23—4624no—
141C23—9232no—
142C23C2×D9214yes—
143C23C2×D92124yescomplemented
144C23#6728814yes—
145C23C2×C22⋊D2314yes—
146C23C23×D2314yes—
147C23C23×D2313yes—
148D4—4664no—
149D4—4632no—
150C2×C4—212no—
151C2×C4—232no—
152C2×C4—238no—
153C2×C4—4624no—
154C2×C4C2×C22⋊D23124yescomplemented
155C2×C4C23×D2314yes—
156C2×C4C23×D2314yes—
157C22—248no—
158C22—24no—
159C22—24no—
160C22—468no—
161C22—468no—
162C22—468no—
163C22—9248no—
164C22#10625101116yesdirect product factor
165C22C22×D9216yes—
166C22C22×D9218yescomplemented
167C22C2×#6728816yes—
168C22C22×C22⋊D2316yes—
169C22C24×D2311yescharacteristic
170C4—24no—
171C4—468no—
172C4C22×C22⋊D2318yescomplemented
173C2—28no—
174C2—928no—
175C2C2×#10625101112yesdirect product factor
176C2C23×C22⋊D2311yescharacteristic
177C2C23×D9211yescharacteristic
178C2C22×#6728811yescharacteristic
subgroupG/H
centerC24C22×D23
commutator, cosocleC22×C23C25
FrattiniC22C24×D23
FittingC24×C4×C23C2
socleC24×C23C23
hypercenterC24×C4D23
hypocenterC23C22×#121
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C24 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
1. C23×D92C2semidirect
2. C23×C22⋊D23C2semidirect
3. C2×#10625101C2direct (N × H)
4. C22×C4⋊Dic23C2semidirect
5. C22×(C2×D23)⋊C4C2semidirect
6. C24×C4×C23C2semidirect
12. C23×C4×C23C22semidirect
14. C22×C22⋊D23C22semidirect
17. C22×D92C22semidirect
18. #10625101C22direct (N × H)
19. C2×(C2×D23)⋊C4C22semidirect
20. C2×C4⋊Dic23C22semidirect
23. C24×C23D4semidirect
32. C22×C4×C23D4semidirect
35. C22×C4×C23C23semidirect
37. C2×C22⋊D23C23semidirect
41. C2×D92C23semidirect
42. (C2×D23)⋊C4C23semidirect
43. C4⋊Dic23C23semidirect
49. C23×C23C2×D4semidirect
60. C2×C4×C23C2×D4semidirect
71. C22×C23#121semidirect
74. C22×C23C22×D4semidirect
82. C4×C23C22×D4semidirect
86. C24×C4D23semidirect
91. C2×C23C2×#121semidirect
106. C23×C4C2×D23semidirect
110. C23C22×#121semidirect
117. C24D92semidirect
128. C22×C4C22⋊D23semidirect
131. C22×C4C22×D23semidirect
143. C23C2×D92semidirect
154. C2×C4C2×C22⋊D23semidirect
164. C22#10625101direct (N × H)
166. C22C22×D92semidirect
172. C4C22×C22⋊D23semidirect
175. C2C2×#10625101direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D922
C23×C22⋊D232
C2×#106251012
C22×C4⋊Dic232
C22×(C2×D23)⋊C42
C24×C4×C232
C22×#12123