Finite Group Databasebeta

← C2×#20268532 #27209262

Subgroups — C2×#20268532 #27209262

Order 13184.

1344 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1344 conjugacy classes of subgroups — too many to draw. Only its 469 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
1#20268532C2116yesmaximal, direct product factor
2C2×#15693018C211yesmaximal, characteristic, complemented
3C2×#15693015C211yesmaximal, characteristic, complemented
4C2×#15693006C213yesmaximal, complemented
5C2×#15692996C213yesmaximal, complemented
6C2×#15692994C213yesmaximal, complemented
7C2×#15692991C213yesmaximal, complemented
8C2×#126×C103C211yesmaximal, characteristic, complemented
9C24×D103C2211yescharacteristic
10C22×D412C2213yes—
11C22×D412C2213yes—
12C22×D412C2213yescomplemented
13C22×C22⋊D103C2213yes—
14C22×C4×D103C2213yescomplemented
15#15693018C2218yescomplemented
16#15693015C2218yescomplemented
17#15693006C22124yescomplemented
18#15692996C22124yescomplemented
19#15692994C22124yescomplemented
20#15692991C22124yescomplemented
21C2×Dic103⋊C4C2213yescomplemented
22C2×(C2×D103)⋊C4C2213yes—
23C2×(C2×D103)⋊C4C2213yes—
24C2×(C2×D103)⋊C4C2213yescomplemented
25#126×C103C2218yescomplemented
26C2×C4⋊C4×C103C2213yescomplemented
27C2×C22⋊C4×C103C2213yes—
28C2×C42×C103C2211yescharacteristic, complemented
29C23×D103—46no—
30C23×D103C2313yes—
31C23×D103C2311yescharacteristic
32C23×D103C2311yescharacteristic
33C23×D103C2314yes—
34C2×D412—46no—
35C2×D412—46no—
36C2×D412—46no—
37C2×D412C23112yes—
38C2×D412C23112yes—
39C2×D412C23112yescomplemented
40C2×C22⋊D103—46no—
41C2×C22⋊D103C23112yes—
42C22×Dic103C2313yes—
43C2×C4×D103—46no—
44C2×C4×D103C23112yescomplemented
45Dic103⋊C4C23112yescomplemented
46(C2×D103)⋊C4C23112yes—
47(C2×D103)⋊C4C23112yes—
48(C2×D103)⋊C4C23112yescomplemented
49C24×C103C2311yescharacteristic
50C22×C4×C103C2313yes—
51C22×C4×C103C2313yes—
52C4⋊C4×C103C23112yescomplemented
53C22⋊C4×C103C23112yes—
54C42×C103C2314yescomplemented
55C23×C103—26no—
56C23×C103C2412yes—
57C23×C103C2411yescharacteristic
58C22×D103—26no—
59C22×D103—26no—
60C22×D103—26no—
61C22×D103—26no—
62C22×D103—26no—
63C22×D103—412no—
64C22×D103—416no—
65C22×D103C2412yes—
66C22×D103C2412yes—
67C22×D103C2416yes—
68C2×C4×C103—26no—
69C2×C4×C103—26no—
70C2×C4×C103C2416yes—
71C2×C4×C103C2416yes—
72C22⋊D103—412no—
73C2×Dic103—26no—
74C2×Dic103C2416yes—
75D412—412no—
76D412—412no—
77D412—412no—
78C4×D103—412no—
79C22×C103—26no—
80C22×C103—44no—
81C22×C103H(5,𝔽2)16yes—
82C22×C103C2511yescharacteristic
83C2×D103—26no—
84C2×D103—26no—
85C2×D103—26no—
86C2×D103—26no—
87C2×D103—26no—
88C2×D103—416no—
89C2×D103—412no—
90C2×D103—44no—
91C2×D103—44no—
92C4×C103—26no—
93C4×C103—26no—
94Dic103—26no—
95C2×C103—42no—
96C2×C103#56014yescomplemented
97C2×C103C2×H(5,𝔽2)13yes—
98D103—46no—
99D103—42no—
100D103—42no—
101C2×#560—1031nomaximal, Sylow
102C103C2×#56011yescharacteristic, complemented, Sylow
103#560—10316no—
104C2×#127—1031no—
105C2×#126—1031no—
106C2×#126D10311yescharacteristic, complemented
107C2×#123—1033no—
108C2×#121—1033no—
109C2×#121—1033no—
110C2×#120—1033no—
111C25—1031no—
112C22×D4—1033no—
113C22×D4—1033no—
114C22×D4—1033no—
115C22×D4—1033no—
116C23×C4—1033no—
117#127—1038no—
118#126—1038no—
119#126C2×D10318yescomplemented
120#123—10324no—
121#121—10324no—
122#121—10324no—
123#120—10324no—
124C2×C4⋊C4—1033no—
125C2×C4⋊C4C2×D10313yescomplemented
126C2×C22⋊C4—1033no—
127C2×C22⋊C4—1033no—
128C2×C22⋊C4—1033no—
129C2×C22⋊C4C2×D10313yes—
130C2×C42C2×D10311yescharacteristic, complemented
131C24—1034no—
132C24—1031no—
133C24—1031no—
134C24—1033no—
135C24—4126no—
136C24C22×D10311yescharacteristic
137C2×D4—10312no—
138C2×D4—10312no—
139C2×D4—10312no—
140C2×D4—10312no—
141C2×D4—4126no—
142C2×D4—4126no—
143C2×D4—4126no—
144C2×D4—4126no—
145C22×C4—1033no—
146C22×C4—10312no—
147C22×C4—4126no—
148C22×C4C22×D10313yes—
149C22×C4C22×D10313yes—
150C4⋊C4—10312no—
151C4⋊C4C22×D103112yescomplemented
152C22⋊C4—10312no—
153C22⋊C4—10312no—
154C22⋊C4—10312no—
155C22⋊C4C22×D103112yes—
156C42C22×D10314yescomplemented
157C23—26no—
158C23—1032no—
159C23—1032no—
160C23—1036no—
161C23—41212no—
162C23—41216no—
163C23—2066no—
164C23—2066no—
165C23—2066no—
166C23—2066no—
167C23—2066no—
168C23C23×D10312yes—
169C23C23×D10311yescharacteristic
170D4—41212no—
171D4—41212no—
172D4—41212no—
173D4—41212no—
174C2×C4—26no—
175C2×C4—26no—
176C2×C4—1036no—
177C2×C4—41212no—
178C2×C4—2066no—
179C2×C4C23×D10316yes—
180C2×C4C23×D10316yes—
181C22—26no—
182C22—44no—
183C22—41216no—
184C22—4124no—
185C22—4124no—
186C22—41212no—
187C22—2066no—
188C22—2066no—
189C22—2066no—
190C22—2066no—
191C22—2066no—
192C22#1569306716yes—
193C22C24×D10311yescharacteristic
194C4—26no—
195C4—26no—
196C4—2066no—
197C2—42no—
198C2—4122no—
199C2—4122no—
200C2—4126no—
201C2#2026853214yesdirect product factor
202C2C2×#1569306713yes—
subgroupG/H
centerC23C23×D103
commutator, cosocleC22×C103C25
FrattiniC22C24×D103
FittingC2×#126×C103C2
socleC23×C103C24
hypercenterC2×#126D103
hypocenterC103C2×#560
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #20268532C2direct (N × H)
2. C2×#15693018C2semidirect
3. C2×#15693015C2semidirect
4. C2×#15693006C2semidirect
5. C2×#15692996C2semidirect
6. C2×#15692994C2semidirect
7. C2×#15692991C2semidirect
8. C2×#126×C103C2semidirect
12. C22×D412C22semidirect
14. C22×C4×D103C22semidirect
15. #15693018C22semidirect
16. #15693015C22semidirect
17. #15693006C22semidirect
18. #15692996C22semidirect
19. #15692994C22semidirect
20. #15692991C22semidirect
21. C2×Dic103⋊C4C22semidirect
24. C2×(C2×D103)⋊C4C22semidirect
25. #126×C103C22semidirect
26. C2×C4⋊C4×C103C22semidirect
28. C2×C42×C103C22semidirect
39. C2×D412C23semidirect
44. C2×C4×D103C23semidirect
45. Dic103⋊C4C23semidirect
48. (C2×D103)⋊C4C23semidirect
52. C4⋊C4×C103C23semidirect
54. C42×C103C23semidirect
96. C2×C103#560semidirect
102. C103C2×#560semidirect
106. C2×#126D103semidirect
119. #126C2×D103semidirect
125. C2×C4⋊C4C2×D103semidirect
130. C2×C42C2×D103semidirect
151. C4⋊C4C22×D103semidirect
156. C42C22×D103semidirect
201. C2#20268532direct (N × H)

Maximal subgroups

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

subgroupindex
#202685322
C2×#156930182
C2×#156930152
C2×#156930062
C2×#156929962
C2×#156929942
C2×#156929912
C2×#126×C1032
C2×#560103