Finite Group Databasebeta

← C22×#10625111 #15686668

Subgroups — C22×#10625111 #15686668

Order 2944.

3000 conjugacy classes of subgroups; only the 725 normal subgroups are shown.

normal subgroups only

This group has 3000 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⋊D23C214yesmaximal, complemented
3C2×#10625111C2124yesmaximal, direct product factor
4C22×C4×Dic23C211yesmaximal, characteristic, complemented
5C23×D4×C23C211yesmaximal, characteristic, complemented
6C25×C23C2212yes—
7C24×D23C2212yes—
8C22×D4×C23—28no—
9C22×D4×C23C22112yescomplemented
10C23×C4×C23C2211yescharacteristic
11C22×C22⋊D23—232no—
12C22×C22⋊D23C22148yescomplemented
13C23×Dic23C2212yes—
14C22×D92—28no—
15C22×D92C22112yescomplemented
16#10625111C22164yesdirect product factor
17C2×C4×Dic23C22112yescomplemented
18C24×C23—216no—
19C24×C23—28no—
20C24×C23C23112yes—
21C24×C23C2311yescharacteristic
22C23×D23—28no—
23C23×D23—216no—
24C23×D23C23112yes—
25C2×D4×C23—248no—
26C2×D4×C23C23116yescomplemented
27C22×C4×C23D418yescomplemented
28C22×C4×C23C2316yes—
29C2×C22⋊D23—2192no—
30C2×C22⋊D23C23164yescomplemented
31C22×Dic23D4116yescomplemented
32C22×Dic23C23112yes—
33C2×D92—248no—
34C2×D92C23116yescomplemented
35C4×Dic23C23116yescomplemented
36C23×C23—248no—
37C23×C23—224no—
38C23×C23—432no—
39C23×C23C2×D418yes—
40C23×C23C2×D414yes—
41C23×C23C2418yes—
42C23×C23C2413yes—
43C22×D23—224no—
44C22×D23—248no—
45C22×D23—432no—
46C22×D23C2418yes—
47D4×C23—232no—
48C2×C4×C23C2×D4124yescomplemented
49C2×C4×C23C2414yes—
50C22⋊D23—2128no—
51C2×Dic23C2×D4148yescomplemented
52C2×Dic23C2418yes—
53D92—232no—
54C22×#127—231nomaximal, Sylow
55C22×C23—216no—
56C22×C23—28no—
57C22×C23—448no—
58C22×C23#127116yescomplemented
59C22×C23C22×D4112yes—
60C22×C23C22×D416yes—
61C22×C23C2511yescharacteristic
62C2×D23—28no—
63C2×D23—216no—
64C2×D23—448no—
65C4×C23C22×D418yescomplemented
66Dic23C22×D4116yescomplemented
67C23×D4—234no—
68C23×D4—231no—
69C23×D4D2311yescharacteristic, complemented
70C2×#127—2324no—
71C22×C42—231no—
72C2×C23—48no—
73C2×C23C2×#127112yescomplemented
74C2×C23C23×D412yes—
75C2×C23C23×D411yescharacteristic
76D23—48no—
77C25—232no—
78C25C2×D2312yes—
79C22×D4—28no—
80C22×D4—2348no—
81C22×D4—2312no—
82C22×D4—4632no—
83C22×D4—468no—
84C22×D4C2×D23112yescomplemented
85C23×C4—232no—
86C23×C4C2×D2311yescharacteristic
87#127—2364no—
88C2×C42—2312no—
89C23C22×#12711yescharacteristic, complemented, Sylow
90C24—216no—
91C24—28no—
92C24—2312no—
93C24—4616no—
94C24—468no—
95C24C22×D23112yes—
96C24C22×D2311yescharacteristic
97C2×D4—248no—
98C2×D4—2364no—
99C2×D4—2316no—
100C2×D4—46192no—
101C2×D4—4648no—
102C2×D4C22×D23116yescomplemented
103C22×C4—2316no—
104C22×C4—2312no—
105C22×C4C22⋊D2318yescomplemented
106C22×C4C22×D2316yes—
107C42—2316no—
108C23—248no—
109C23—224no—
110C23—432no—
111C23—238no—
112C23—4648no—
113C23—4624no—
114C23—9232no—
115C23D4×D2318yes—
116C23C2×C22⋊D2314yes—
117C23C23×D2318yes—
118C23C23×D2313yes—
119D4—232no—
120D4—46128no—
121D4—4632no—
122C2×C4—2348no—
123C2×C4—238no—
124C2×C4C2×C22⋊D23124yescomplemented
125C2×C4C23×D2314yes—
126C22—216no—
127C22—28no—
128C22—448no—
129C22—4616no—
130C22—468no—
131C22—9248no—
132C22#10625111116yesdirect product factor
133C22C2×D4×D23112yes—
134C22C22×C22⋊D2316yes—
135C22C24×D2311yescharacteristic
136C4—2316no—
137C4C22×C22⋊D2318yescomplemented
138C2—48no—
139C2—928no—
140C2C2×#10625111112yesdirect product factor
141C2C22×D4×D2312yes—
142C2C23×C22⋊D2311yescharacteristic
subgroupG/H
centerC24C22×D23
commutator, cosocleC22×C23C25
FrattiniC22C24×D23
FittingC23×D4×C23C2
socleC24×C23C23
hypercenterC23×D4D23
hypocenterC23C22×#127
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C23×D92C2semidirect
2. C23×C22⋊D23C2semidirect
3. C2×#10625111C2direct (N × H)
4. C22×C4×Dic23C2semidirect
5. C23×D4×C23C2semidirect
9. C22×D4×C23C22semidirect
12. C22×C22⋊D23C22semidirect
15. C22×D92C22semidirect
16. #10625111C22direct (N × H)
17. C2×C4×Dic23C22semidirect
26. C2×D4×C23C23semidirect
27. C22×C4×C23D4semidirect
30. C2×C22⋊D23C23semidirect
31. C22×Dic23D4semidirect
34. C2×D92C23semidirect
35. C4×Dic23C23semidirect
48. C2×C4×C23C2×D4semidirect
51. C2×Dic23C2×D4semidirect
58. C22×C23#127semidirect
65. C4×C23C22×D4semidirect
66. Dic23C22×D4semidirect
69. C23×D4D23semidirect
73. C2×C23C2×#127semidirect
84. C22×D4C2×D23semidirect
89. C23C22×#127semidirect
102. C2×D4C22×D23semidirect
105. C22×C4C22⋊D23semidirect
124. C2×C4C2×C22⋊D23semidirect
132. C22#10625111direct (N × H)
137. C4C22×C22⋊D23semidirect
140. C2C2×#10625111direct (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×#106251112
C22×C4×Dic232
C23×D4×C232
C22×#12723