Finite Group Databasebeta

← C2×#126×D103 #27208398

Subgroups — C2×#126×D103 #27208398

Order 13184.

1320 conjugacy classes of subgroups; only the 517 normal subgroups are shown.

normal subgroups only

This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 517 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
1C2×#15693016C213yesmaximal, complemented
2C2×#15693015C211yesmaximal, characteristic, complemented
3C2×#15693014C213yesmaximal, complemented
4#126×D103C2116yesmaximal, direct product factor
5C2×C4⋊C4×D103C213yesmaximal, complemented
6C2×C22⋊C4×D103C213yesmaximal
7C2×C42×D103C211yesmaximal, characteristic, complemented
8C2×#126×C103C211yesmaximal, characteristic, complemented
9C24×D103C2211yescharacteristic
10C22×C4×D103C2213yes—
11C22×C4×D103C2213yes—
12#15693016C22124yescomplemented
13#15693015C2218yescomplemented
14#15693014C22124yescomplemented
15C2×C4⋊Dic103C2213yescomplemented
16C2×Dic103⋊C4C2213yescomplemented
17C2×Dic103⋊C4C2213yescomplemented
18C4⋊C4×D103C22124yescomplemented
19C2×C22⋊Dic103C2213yes—
20C2×(C2×D103)⋊C4C2213yes—
21C2×(C2×D103)⋊C4C2213yes—
22C22⋊C4×D103C22124yes—
23C2×C4×Dic103C2213yescomplemented
24C42×D103C2218yescomplemented
25#126×C103C2218yescomplemented
26C2×C4⋊C4×C103C2213yescomplemented
27C2×C22⋊C4×C103C2213yes—
28C2×C42×C103C2211yescharacteristic, complemented
29C23×D103—212no—
30C23×D103C2314yes—
31C23×D103C2311yescharacteristic
32C23×D103C2311yescharacteristic
33C22×Dic103C2313yes—
34C22×Dic103C2313yes—
35C2×C4×D103—212no—
36C2×C4×D103—212no—
37C2×C4×D103C23112yes—
38C2×C4×D103C23112yes—
39C4⋊Dic103C23112yescomplemented
40Dic103⋊C4C23112yescomplemented
41Dic103⋊C4C23112yescomplemented
42C22⋊Dic103C23112yes—
43(C2×D103)⋊C4C23112yes—
44(C2×D103)⋊C4C23112yes—
45C4×Dic103C23112yescomplemented
46C24×C103C2311yescharacteristic
47C22×C4×C103C2313yes—
48C22×C4×C103C2313yes—
49C4⋊C4×C103C23112yescomplemented
50C22⋊C4×C103C23112yes—
51C42×C103C2314yescomplemented
52C23×C103—26no—
53C23×C103C2412yes—
54C23×C103C2411yescharacteristic
55C22×D103—26no—
56C22×D103—224no—
57C22×D103—416no—
58C22×D103#41112yes—
59C22×D103C2412yes—
60C22×D103C2412yes—
61C2×C4×C103—26no—
62C2×C4×C103—26no—
63C2×C4×C103C2416yes—
64C2×C4×C103C2416yes—
65C2×Dic103—26no—
66C2×Dic103—26no—
67C2×Dic103C2416yes—
68C2×Dic103C2416yes—
69C4×D103—224no—
70C4×D103—224no—
71C22×C103—26no—
72C22×C103—44no—
73C22×C103C2×#4116yes—
74C22×C103C2511yescharacteristic
75C2×D103—26no—
76C2×D103—44no—
77C2×D103—416no—
78C2×D103#126116yesdirect product factor
79C2×D103C2×#41112yes—
80C4×C103—26no—
81C4×C103—26no—
82Dic103—26no—
83Dic103—26no—
84C2×C103—42no—
85C2×C103C2×#12614yescomplemented
86C2×C103C22×#4113yes—
87D103—42no—
88D103C2×#12618yesdirect product factor
89C22×#126—1031nomaximal, Sylow
90C103C22×#12611yescharacteristic, complemented, Sylow
91C2×#126—10316no—
92C2×#126—1033no—
93C2×#126—1033no—
94C2×#126—1031no—
95C2×#126D10311yescharacteristic, direct product factor
96C22×C4⋊C4—1033no—
97C22×C22⋊C4—1033no—
98C22×C42—1031no—
99C25—1031no—
100C23×C4—1033no—
101C23×C4—1033no—
102#126—10324no—
103#126—10324no—
104#126—1038no—
105#126C2×D10318yesdirect product factor
106C2×C4⋊C4—1033no—
107C2×C4⋊C4—1033no—
108C2×C4⋊C4—1033no—
109C2×C4⋊C4—10324no—
110C2×C4⋊C4C2×D10313yescomplemented
111C2×C22⋊C4—1033no—
112C2×C22⋊C4—1033no—
113C2×C22⋊C4—1033no—
114C2×C22⋊C4—10324no—
115C2×C22⋊C4C2×D10313yes—
116C2×C42—1033no—
117C2×C42—1038no—
118C2×C42C2×D10311yescharacteristic, complemented
119C24—1031no—
120C24—1034no—
121C24—1031no—
122C24—20612no—
123C24C22×D10311yescharacteristic
124C22×C4—1033no—
125C22×C4—1033no—
126C22×C4—10312no—
127C22×C4—10312no—
128C22×C4—20612no—
129C22×C4—20612no—
130C22×C4C22×D10313yes—
131C22×C4C22×D10313yes—
132C4⋊C4—10312no—
133C4⋊C4—10312no—
134C4⋊C4—10312no—
135C4⋊C4C22×D103112yescomplemented
136C22⋊C4—10312no—
137C22⋊C4—10312no—
138C22⋊C4—10312no—
139C22⋊C4C22×D103112yes—
140C42—10312no—
141C42C22×D10314yescomplemented
142C23—26no—
143C23—10312no—
144C23—1032no—
145C23—1032no—
146C23—41216no—
147C23—20624no—
148C23—2066no—
149C23C23×D10312yes—
150C23C23×D10311yescharacteristic
151C2×C4—26no—
152C2×C4—26no—
153C2×C4—1036no—
154C2×C4—1036no—
155C2×C4—20624no—
156C2×C4—20624no—
157C2×C4—2066no—
158C2×C4—2066no—
159C2×C4C23×D10316yes—
160C2×C4C23×D10316yes—
161C22—26no—
162C22—44no—
163C22—10316no—
164C22—10312no—
165C22—41216no—
166C22—4124no—
167C22—2066no—
168C22#41×D10316yes—
169C22C24×D10311yescharacteristic
170C4—26no—
171C4—26no—
172C4—2066no—
173C4—2066no—
174C2—42no—
175C2—1038no—
176C2—4122no—
177C2#126×D10314yesdirect product factor
178C2C2×#41×D10313yes—
subgroupG/H
centerC23C23×D103
commutator, cosocleC22×C103C25
FrattiniC22C24×D103
FittingC2×#126×C103C2
socleC23×C103C24
prime radicalC24×D103C22
hypercenterC2×#126D103
hypocenterC103C22×#126
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×#15693016C2semidirect
2. C2×#15693015C2semidirect
3. C2×#15693014C2semidirect
4. #126×D103C2direct (N × H)
5. C2×C4⋊C4×D103C2semidirect
7. C2×C42×D103C2semidirect
8. C2×#126×C103C2semidirect
12. #15693016C22semidirect
13. #15693015C22semidirect
14. #15693014C22semidirect
15. C2×C4⋊Dic103C22semidirect
16. C2×Dic103⋊C4C22semidirect
17. C2×Dic103⋊C4C22semidirect
18. C4⋊C4×D103C22semidirect
23. C2×C4×Dic103C22semidirect
24. C42×D103C22semidirect
25. #126×C103C22semidirect
26. C2×C4⋊C4×C103C22semidirect
28. C2×C42×C103C22semidirect
39. C4⋊Dic103C23semidirect
40. Dic103⋊C4C23semidirect
41. Dic103⋊C4C23semidirect
45. C4×Dic103C23semidirect
49. C4⋊C4×C103C23semidirect
51. C42×C103C23semidirect
78. C2×D103#126direct (N × H)
85. C2×C103C2×#126semidirect
88. D103C2×#126direct (N × H)
90. C103C22×#126semidirect
95. C2×#126D103direct (N × H)
105. #126C2×D103direct (N × H)
110. C2×C4⋊C4C2×D103semidirect
118. C2×C42C2×D103semidirect
135. C4⋊C4C22×D103semidirect
141. C42C22×D103semidirect
177. C2#126×D103direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156930162
C2×#156930152
C2×#156930142
#126×D1032
C2×C4⋊C4×D1032
C2×C22⋊C4×D1032
C2×C42×D1032
C2×#126×C1032
C22×#126103