Finite Group Databasebeta

← C22×#15693017 #27208415

Subgroups — C22×#15693017 #27208415

Order 13184.

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×D412C211yesmaximal, characteristic, complemented
2C23×C22⋊D103C214yesmaximal, complemented
3C2×#15693017C2124yesmaximal, direct product factor
4C22×C4×Dic103C211yesmaximal, characteristic, complemented
5C23×D4×C103C211yesmaximal, characteristic, complemented
6C24×D103C2212yes—
7C22×D412—28no—
8C22×D412C22112yescomplemented
9C22×C22⋊D103—232no—
10C22×C22⋊D103C22148yescomplemented
11C23×Dic103C2212yes—
12#15693017C22164yesdirect product factor
13C2×C4×Dic103C22112yescomplemented
14C25×C103C2212yes—
15C22×D4×C103—28no—
16C22×D4×C103C22112yescomplemented
17C23×C4×C103C2211yescharacteristic
18C23×D103—216no—
19C23×D103—28no—
20C23×D103C23112yes—
21C2×D412—248no—
22C2×D412C23116yescomplemented
23C2×C22⋊D103—2192no—
24C2×C22⋊D103C23164yescomplemented
25C22×Dic103D4116yescomplemented
26C22×Dic103C23112yes—
27C4×Dic103C23116yescomplemented
28C24×C103—216no—
29C24×C103—28no—
30C24×C103C23112yes—
31C24×C103C2311yescharacteristic
32C2×D4×C103—248no—
33C2×D4×C103C23116yescomplemented
34C22×C4×C103D418yescomplemented
35C22×C4×C103C2316yes—
36C23×C103—224no—
37C23×C103—248no—
38C23×C103—432no—
39C23×C103C2×D418yes—
40C23×C103C2×D414yes—
41C23×C103C2418yes—
42C23×C103C2413yes—
43C22×D103—248no—
44C22×D103—224no—
45C22×D103—432no—
46C22×D103C2418yes—
47D4×C103—232no—
48C2×C4×C103C2×D4124yescomplemented
49C2×C4×C103C2414yes—
50C22⋊D103—2128no—
51C2×Dic103C2×D4148yescomplemented
52C2×Dic103C2418yes—
53D412—232no—
54C22×C103—216no—
55C22×C103—28no—
56C22×C103—448no—
57C22×C103#127116yescomplemented
58C22×C103C22×D4112yes—
59C22×C103C22×D416yes—
60C22×C103C2511yescharacteristic
61C2×D103—28no—
62C2×D103—216no—
63C2×D103—448no—
64C4×C103C22×D418yescomplemented
65Dic103C22×D4116yescomplemented
66C2×C103—48no—
67C2×C103C2×#127112yescomplemented
68C2×C103C23×D412yes—
69C2×C103C23×D411yescharacteristic
70D103—48no—
71C22×#127—1031nomaximal, Sylow
72C103C22×#12711yescharacteristic, complemented, Sylow
73C23×D4—1034no—
74C23×D4—1031no—
75C23×D4D10311yescharacteristic, complemented
76C2×#127—10324no—
77C22×C42—1031no—
78C25—1032no—
79C25C2×D10312yes—
80C22×D4—28no—
81C22×D4—10348no—
82C22×D4—10312no—
83C22×D4—20632no—
84C22×D4—2068no—
85C22×D4C2×D103112yescomplemented
86C23×C4—1032no—
87C23×C4C2×D10311yescharacteristic
88#127—10364no—
89C2×C42—10312no—
90C24—216no—
91C24—28no—
92C24—10312no—
93C24—20616no—
94C24—2068no—
95C24C22×D103112yes—
96C24C22×D10311yescharacteristic
97C2×D4—248no—
98C2×D4—10364no—
99C2×D4—10316no—
100C2×D4—206192no—
101C2×D4—20648no—
102C2×D4C22×D103116yescomplemented
103C22×C4—10316no—
104C22×C4—10312no—
105C22×C4C22⋊D10318yescomplemented
106C22×C4C22×D10316yes—
107C42—10316no—
108C23—248no—
109C23—224no—
110C23—432no—
111C23—1038no—
112C23—41232no—
113C23—20648no—
114C23—20624no—
115C23D4×D10318yes—
116C23C2×C22⋊D10314yes—
117C23C23×D10318yes—
118C23C23×D10313yes—
119D4—232no—
120D4—206128no—
121D4—20632no—
122C2×C4—10348no—
123C2×C4—1038no—
124C2×C4C2×C22⋊D103124yescomplemented
125C2×C4C23×D10314yes—
126C22—216no—
127C22—28no—
128C22—448no—
129C22—41248no—
130C22—20616no—
131C22—2068no—
132C22#15693017116yesdirect product factor
133C22C2×D4×D103112yes—
134C22C22×C22⋊D10316yes—
135C22C24×D10311yescharacteristic
136C4—10316no—
137C4C22×C22⋊D10318yescomplemented
138C2—48no—
139C2—4128no—
140C2C2×#15693017112yesdirect product factor
141C2C22×D4×D10312yes—
142C2C23×C22⋊D10311yescharacteristic
subgroupG/H
centerC24C22×D103
commutator, cosocleC22×C103C25
FrattiniC22C24×D103
FittingC23×D4×C103C2
socleC24×C103C23
hypercenterC23×D4D103
hypocenterC103C22×#127
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C23×D412C2semidirect
2. C23×C22⋊D103C2semidirect
3. C2×#15693017C2direct (N × H)
4. C22×C4×Dic103C2semidirect
5. C23×D4×C103C2semidirect
8. C22×D412C22semidirect
10. C22×C22⋊D103C22semidirect
12. #15693017C22direct (N × H)
13. C2×C4×Dic103C22semidirect
16. C22×D4×C103C22semidirect
22. C2×D412C23semidirect
24. C2×C22⋊D103C23semidirect
25. C22×Dic103D4semidirect
27. C4×Dic103C23semidirect
33. C2×D4×C103C23semidirect
34. C22×C4×C103D4semidirect
48. C2×C4×C103C2×D4semidirect
51. C2×Dic103C2×D4semidirect
57. C22×C103#127semidirect
64. C4×C103C22×D4semidirect
65. Dic103C22×D4semidirect
67. C2×C103C2×#127semidirect
72. C103C22×#127semidirect
75. C23×D4D103semidirect
85. C22×D4C2×D103semidirect
102. C2×D4C22×D103semidirect
105. C22×C4C22⋊D103semidirect
124. C2×C4C2×C22⋊D103semidirect
132. C22#15693017direct (N × H)
137. C4C22×C22⋊D103semidirect
140. C2C2×#15693017direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D4122
C23×C22⋊D1032
C2×#156930172
C22×C4×Dic1032
C23×D4×C1032
C22×#127103