Finite Group Databasebeta

← C22×#10625109 #15686616

Subgroups — C22×#10625109 #15686616

Order 2944.

2528 conjugacy classes of subgroups; only the 685 normal subgroups are shown.

normal subgroups only

This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 685 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×C22⋊D23C212yesmaximal, complemented
2C23×C4×D23C211yesmaximal, characteristic, complemented
3C2×#10625109C2124yesmaximal, direct product factor
4C22×C4⋊Dic23C211yesmaximal, characteristic, complemented
5C22×C22⋊Dic23C212yesmaximal, complemented
6C23×D4×C23C211yesmaximal, characteristic, complemented
7C25×C23C2212yes—
8C24×D23C2211yescharacteristic
9C22×D4×C23—28no—
10C22×D4×C23C22112yescomplemented
11C23×C4×C23C2211yescharacteristic
12C22×C22⋊D23—216no—
13C22×C22⋊D23C22124yescomplemented
14C23×Dic23C2211yescharacteristic
15C23×Dic23C2212yes—
16C22×C4×D23—28no—
17C22×C4×D23C22112yescomplemented
18C2×C22⋊Dic23C22124yescomplemented
19#10625109C22164yesdirect product factor
20C2×C4⋊Dic23C22112yescomplemented
21C24×C23—28no—
22C24×C23—28no—
23C24×C23—28no—
24C24×C23C23112yes—
25C24×C23C2311yescharacteristic
26C23×D23—24no—
27C23×D23—24no—
28C23×D23D418yescomplemented
29C23×D23C2316yes—
30C2×D4×C23—248no—
31C2×D4×C23C23116yescomplemented
32C22×C4×C23D418yescomplemented
33C22×C4×C23C2316yes—
34C2×C22⋊D23—296no—
35C2×C22⋊D23C23132yescomplemented
36C22×Dic23—24no—
37C22×Dic23—28no—
38C22×Dic23C23112yes—
39C22×Dic23C2316yes—
40C2×C4×D23—248no—
41C2×C4×D23C23116yescomplemented
42C22⋊Dic23C23132yescomplemented
43C4⋊Dic23C23116yescomplemented
44C23×C23—224no—
45C23×C23—224no—
46C23×C23—224no—
47C23×C23—432no—
48C23×C23C2×D414yes—
49C23×C23C2×D414yes—
50C23×C23#4114yes—
51C23×C23C2418yes—
52C23×C23C2413yes—
53C22×D23—232no—
54C22×D23—212no—
55C22×D23—212no—
56C22×D23C2×D4124yescomplemented
57C22×D23C2414yes—
58D4×C23—232no—
59C2×C4×C23C2×D4124yescomplemented
60C2×C4×C23C2414yes—
61C22⋊D23—264no—
62C2×Dic23—212no—
63C2×Dic23—224no—
64C2×Dic23C2418yes—
65C2×Dic23C2414yes—
66C4×D23—232no—
67C22×#121—231nomaximal, Sylow
68C22×C23—28no—
69C22×C23—28no—
70C22×C23—28no—
71C22×C23—448no—
72C22×C23#121116yescomplemented
73C22×C23C22×D416yes—
74C22×C23C22×D416yes—
75C22×C23C2×#4116yes—
76C22×C23C2511yescharacteristic
77C2×D23—248no—
78C2×D23—24no—
79C2×D23—24no—
80C2×D23C22×D418yescomplemented
81C4×C23C22×D418yescomplemented
82Dic23—24no—
83Dic23—28no—
84C23×D4—232no—
85C23×D4D2311yescharacteristic, complemented
86C24×C4—231no—
87C2×#121—2324no—
88C22×C4⋊C4—231no—
89C22×C22⋊C4—232no—
90C2×C23—48no—
91C2×C23C2×#121112yescomplemented
92C2×C23C23×D411yescharacteristic
93C2×C23C23×D411yescharacteristic
94C2×C23C22×#4111yescharacteristic
95D23—28no—
96C25—231no—
97C25C2×D2312yes—
98C22×D4—28no—
99C22×D4—2324no—
100C22×D4—4616no—
101C22×D4C2×D23112yescomplemented
102C23×C4—231no—
103C23×C4—232no—
104C23×C4—2312no—
105C23×C4—468no—
106C23×C4C2×D2311yescharacteristic
107#121—2364no—
108C2×C4⋊C4—2312no—
109C2×C22⋊C4—2324no—
110C23C22×#12111yescharacteristic, complemented, Sylow
111C24—28no—
112C24—28no—
113C24—28no—
114C24—238no—
115C24—236no—
116C24—464no—
117C24—464no—
118C24C22×D23112yes—
119C24C22×D2311yescharacteristic
120C2×D4—248no—
121C2×D4—2332no—
122C2×D4—4696no—
123C2×D4C22×D23116yescomplemented
124C22×C4—236no—
125C22×C4—2312no—
126C22×C4—2316no—
127C22×C4—468no—
128C22×C4—464no—
129C22×C4—4648no—
130C22×C4C22⋊D2318yescomplemented
131C22×C4C22×D2316yes—
132C4⋊C4—2316no—
133C22⋊C4—2332no—
134C23—224no—
135C23—224no—
136C23—224no—
137C23—432no—
138C23—2324no—
139C23—234no—
140C23—4632no—
141C23—4612no—
142C23—4612no—
143C23D4×D2314yes—
144C23#6729014yes—
145C23C2×C22⋊D2314yes—
146C23C23×D2318yes—
147C23C23×D2313yes—
148D4—232no—
149D4—4664no—
150C2×C4—234no—
151C2×C4—238no—
152C2×C4—4624no—
153C2×C4—4612no—
154C2×C4—4632no—
155C2×C4C2×C22⋊D23124yescomplemented
156C2×C4C23×D2314yes—
157C22—28no—
158C22—28no—
159C22—28no—
160C22—448no—
161C22—238no—
162C22—4648no—
163C22—464no—
164C22—464no—
165C22#10625109116yesdirect product factor
166C22C2×D4×D2316yes—
167C22C2×#6729016yes—
168C22C22×C22⋊D2316yes—
169C22C24×D2311yescharacteristic
170C4—468no—
171C4—464no—
172C4C22×C22⋊D2318yescomplemented
173C2—48no—
174C2—468no—
175C2C2×#10625109112yesdirect product factor
176C2C22×D4×D2311yescharacteristic
177C2C23×C22⋊D2311yescharacteristic
178C2C22×#6729011yescharacteristic
subgroupG/H
centerC24C22×D23
commutator, cosocleC22×C23C25
FrattiniC22C24×D23
FittingC23×D4×C23C2
socleC24×C23C23
hypercenterC23×D4D23
hypocenterC23C22×#121
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D23C2semidirect
2. C23×C4×D23C2semidirect
3. C2×#10625109C2direct (N × H)
4. C22×C4⋊Dic23C2semidirect
5. C22×C22⋊Dic23C2semidirect
6. C23×D4×C23C2semidirect
10. C22×D4×C23C22semidirect
13. C22×C22⋊D23C22semidirect
17. C22×C4×D23C22semidirect
18. C2×C22⋊Dic23C22semidirect
19. #10625109C22direct (N × H)
20. C2×C4⋊Dic23C22semidirect
28. C23×D23D4semidirect
31. C2×D4×C23C23semidirect
32. C22×C4×C23D4semidirect
35. C2×C22⋊D23C23semidirect
41. C2×C4×D23C23semidirect
42. C22⋊Dic23C23semidirect
43. C4⋊Dic23C23semidirect
56. C22×D23C2×D4semidirect
59. C2×C4×C23C2×D4semidirect
72. C22×C23#121semidirect
80. C2×D23C22×D4semidirect
81. C4×C23C22×D4semidirect
85. C23×D4D23semidirect
91. C2×C23C2×#121semidirect
101. C22×D4C2×D23semidirect
110. C23C22×#121semidirect
123. C2×D4C22×D23semidirect
130. C22×C4C22⋊D23semidirect
155. C2×C4C2×C22⋊D23semidirect
165. C22#10625109direct (N × H)
172. C4C22×C22⋊D23semidirect
175. C2C2×#10625109direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D232
C23×C4×D232
C2×#106251092
C22×C4⋊Dic232
C22×C22⋊Dic232
C23×D4×C232
C22×#12123