Finite Group Databasebeta

← C2×#127×D103 #27208414

Subgroups — C2×#127×D103 #27208414

Order 13184.

3000 conjugacy classes of subgroups; only the 661 normal subgroups are shown.

normal subgroups only

This group has 3000 conjugacy classes of subgroups — too many to draw. Only its 661 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
1C22×D4×D103C216yesmaximal, complemented
2C2×#15693018C211yesmaximal, characteristic, complemented
3C2×#15693017C216yesmaximal, complemented
4#127×D103C2116yesmaximal, direct product factor
5C2×C42×D103C211yesmaximal, characteristic, complemented
6C2×#127×C103C211yesmaximal, characteristic, complemented
7C24×D103C2214yes—
8C22×D412C2216yescomplemented
9C22×C22⋊D103C22112yescomplemented
10C2×D4×D103—248no—
11C2×D4×D103C22148yescomplemented
12C22×C4×D103C2213yes—
13#15693018C2218yescomplemented
14#15693017C22148yescomplemented
15C2×C4×Dic103C2213yescomplemented
16C42×D103C2218yescomplemented
17C22×D4×C103C2216yescomplemented
18#127×C103C2218yescomplemented
19C2×C42×C103C2211yescharacteristic, complemented
20C23×D103—248no—
21C23×D103C23116yes—
22C23×D103C2314yes—
23C23×D103C2311yescharacteristic
24C2×D412—224no—
25C2×D412C23124yescomplemented
26C2×C22⋊D103—248no—
27C2×C22⋊D103C23148yescomplemented
28D4×D103—2192no—
29C22×Dic103C2313yes—
30C2×C4×D103D4124yescomplemented
31C2×C4×D103C23112yes—
32C4×Dic103C23112yescomplemented
33C24×C103C2314yes—
34C2×D4×C103—224no—
35C2×D4×C103C23124yescomplemented
36C22×C4×C103C2313yes—
37C42×C103C2314yescomplemented
38C23×C103—224no—
39C23×C103C2418yes—
40C23×C103C2411yescharacteristic
41C22×D103—224no—
42C22×D103—296no—
43C22×D103—464no—
44C22×D103C2×D4112yes—
45C22×D103C2418yes—
46C22×D103C2412yes—
47D4×C103—248no—
48C2×C4×C103C2×D4112yescomplemented
49C2×C4×C103C2416yes—
50C22⋊D103—296no—
51C2×Dic103C2×D4112yescomplemented
52C2×Dic103C2416yes—
53D412—248no—
54C4×D103C2×D4148yescomplemented
55C22×C103—224no—
56C22×C103—416no—
57C22×C103C22×D416yes—
58C22×C103C2511yescharacteristic
59C2×D103—224no—
60C2×D103—416no—
61C2×D103—464no—
62C2×D103#127116yesdirect product factor
63C2×D103C22×D4112yes—
64C4×C103C22×D4112yescomplemented
65Dic103C22×D4112yescomplemented
66C2×C103—48no—
67C2×C103C2×#12714yescomplemented
68C2×C103C23×D413yes—
69D103—48no—
70D103C2×#12718yesdirect product factor
71C22×#127—1031nomaximal, Sylow
72C103C22×#12711yescharacteristic, complemented, Sylow
73C23×D4—1036no—
74C2×#127—1036no—
75C2×#127—10316no—
76C2×#127—1031no—
77C2×#127D10311yescharacteristic, direct product factor
78C22×C42—1031no—
79C25—1034no—
80C22×D4—10312no—
81C22×D4—10348no—
82C22×D4—1036no—
83C22×D4—20648no—
84C22×D4C2×D10316yescomplemented
85C23×C4—1033no—
86#127—10348no—
87#127—1038no—
88#127C2×D10318yesdirect product factor
89C2×C42—1033no—
90C2×C42—1038no—
91C2×C42C2×D10311yescharacteristic, complemented
92C24—1031no—
93C24—10316no—
94C24—1034no—
95C24—20648no—
96C24C22×D10314yes—
97C2×D4—224no—
98C2×D4—10348no—
99C2×D4—10324no—
100C2×D4—206192no—
101C2×D4—20648no—
102C2×D4—20624no—
103C2×D4C22×D103124yescomplemented
104C22×C4—1033no—
105C22×C4—10324no—
106C22×C4—10312no—
107C22×C4C22×D10313yes—
108C42—10312no—
109C42C22×D10314yescomplemented
110C23—224no—
111C23—10312no—
112C23—1032no—
113C23—1038no—
114C23—41264no—
115C23—20696no—
116C23—20624no—
117C23C23×D10318yes—
118C23C23×D10311yescharacteristic
119D4—248no—
120D4—20696no—
121D4—20648no—
122C2×C4—10312no—
123C2×C4—1036no—
124C2×C4—10348no—
125C2×C4D4×D103112yescomplemented
126C2×C4C23×D10316yes—
127C22—224no—
128C22—416no—
129C22—10316no—
130C22—10312no—
131C22—41264no—
132C22—41216no—
133C22—20624no—
134C22C2×D4×D10316yes—
135C22C24×D10311yescharacteristic
136C4—10312no—
137C4C2×D4×D103112yescomplemented
138C2—48no—
139C2—1038no—
140C2—4128no—
141C2#127×D10314yesdirect product factor
142C2C22×D4×D10313yes—
subgroupG/H
centerC23C23×D103
commutator, cosocleC22×C103C25
FrattiniC22C24×D103
FittingC2×#127×C103C2
socleC23×C103C24
hypercenterC2×#127D103
hypocenterC103C22×#127
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C22×D4×D103C2semidirect
2. C2×#15693018C2semidirect
3. C2×#15693017C2semidirect
4. #127×D103C2direct (N × H)
5. C2×C42×D103C2semidirect
6. C2×#127×C103C2semidirect
8. C22×D412C22semidirect
9. C22×C22⋊D103C22semidirect
11. C2×D4×D103C22semidirect
13. #15693018C22semidirect
14. #15693017C22semidirect
15. C2×C4×Dic103C22semidirect
16. C42×D103C22semidirect
17. C22×D4×C103C22semidirect
18. #127×C103C22semidirect
19. C2×C42×C103C22semidirect
25. C2×D412C23semidirect
27. C2×C22⋊D103C23semidirect
30. C2×C4×D103D4semidirect
32. C4×Dic103C23semidirect
35. C2×D4×C103C23semidirect
37. C42×C103C23semidirect
48. C2×C4×C103C2×D4semidirect
51. C2×Dic103C2×D4semidirect
54. C4×D103C2×D4semidirect
62. C2×D103#127direct (N × H)
64. C4×C103C22×D4semidirect
65. Dic103C22×D4semidirect
67. C2×C103C2×#127semidirect
70. D103C2×#127direct (N × H)
72. C103C22×#127semidirect
77. C2×#127D103direct (N × H)
84. C22×D4C2×D103semidirect
88. #127C2×D103direct (N × H)
91. C2×C42C2×D103semidirect
103. C2×D4C22×D103semidirect
109. C42C22×D103semidirect
125. C2×C4D4×D103semidirect
137. C4C2×D4×D103semidirect
141. C2#127×D103direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D1032
C2×#156930182
C2×#156930172
#127×D1032
C2×C42×D1032
C2×#127×C1032
C22×#127103