Finite Group Databasebeta

← C2×#20299339 #28404692

Subgroups — C2×#20299339 #28404692

Order 14464.

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#20299339C2116yesmaximal, direct product factor
2C2×#16813619C211yesmaximal, characteristic, complemented
3C2×#16813616C211yesmaximal, characteristic, complemented
4C2×#16813607C213yesmaximal, complemented
5C2×#16813597C213yesmaximal, complemented
6C2×#16813595C213yesmaximal, complemented
7C2×#16813592C213yesmaximal, complemented
8C2×#126×C113C211yesmaximal, characteristic, complemented
9C24×D113C2211yescharacteristic
10C22×D452C2213yes—
11C22×D452C2213yes—
12C22×D452C2213yescomplemented
13C22×C22⋊D113C2213yes—
14C22×C4×D113C2213yescomplemented
15#16813619C2218yescomplemented
16#16813616C2218yescomplemented
17#16813607C22124yescomplemented
18#16813597C22124yescomplemented
19#16813595C22124yescomplemented
20#16813592C22124yescomplemented
21C2×#14268626C2213yescomplemented
22C2×#14268624C2213yes—
23C2×#14268624C2213yes—
24C2×#14268624C2213yescomplemented
25#126×C113C2218yescomplemented
26C2×C4⋊C4×C113C2213yescomplemented
27C2×C22⋊C4×C113C2213yes—
28C2×C42×C113C2211yescharacteristic, complemented
29C23×D113—46no—
30C23×D113C2311yescharacteristic
31C23×D113C2311yescharacteristic
32C23×D113C2313yes—
33C23×D113C2314yes—
34C2×D452—46no—
35C2×D452—46no—
36C2×D452—46no—
37C2×D452C23112yes—
38C2×D452C23112yes—
39C2×D452C23112yescomplemented
40C2×C22⋊D113—46no—
41C2×C22⋊D113C23112yes—
42C22×Dic113C2313yes—
43C2×C4×D113—46no—
44C2×C4×D113C23112yescomplemented
45#14268626C23112yescomplemented
46#14268624C23112yes—
47#14268624C23112yes—
48#14268624C23112yescomplemented
49C24×C113C2311yescharacteristic
50C22×C4×C113C2313yes—
51C22×C4×C113C2313yes—
52C4⋊C4×C113C23112yescomplemented
53C22⋊C4×C113C23112yes—
54C42×C113C2314yescomplemented
55C23×C113—26no—
56C23×C113C2412yes—
57C23×C113C2411yescharacteristic
58C22×D113—26no—
59C22×D113—26no—
60C22×D113—26no—
61C22×D113—26no—
62C22×D113—26no—
63C22×D113—412no—
64C22×D113—416no—
65C22×D113C2412yes—
66C22×D113C2412yes—
67C22×D113C2416yes—
68C2×C4×C113—26no—
69C2×C4×C113—26no—
70C2×C4×C113C2416yes—
71C2×C4×C113C2416yes—
72C22⋊D113—412no—
73C2×Dic113—26no—
74C2×Dic113C2416yes—
75D452—412no—
76D452—412no—
77D452—412no—
78C4×D113—412no—
79C22×C113—26no—
80C22×C113—44no—
81C22×C113H(5,𝔽2)16yes—
82C22×C113C2511yescharacteristic
83C2×D113—26no—
84C2×D113—26no—
85C2×D113—26no—
86C2×D113—26no—
87C2×D113—26no—
88C2×D113—416no—
89C2×D113—412no—
90C2×D113—44no—
91C2×D113—44no—
92C4×C113—26no—
93C4×C113—26no—
94Dic113—26no—
95C2×C113—42no—
96C2×C113#56014yescomplemented
97C2×C113C2×H(5,𝔽2)13yes—
98D113—46no—
99D113—42no—
100D113—42no—
101C2×#560—1131nomaximal, Sylow
102C113C2×#56011yescharacteristic, complemented, Sylow
103#560—11316no—
104C2×#127—1131no—
105C2×#126—1131no—
106C2×#126D11311yescharacteristic, complemented
107C2×#123—1133no—
108C2×#121—1133no—
109C2×#121—1133no—
110C2×#120—1133no—
111C25—1131no—
112C22×D4—1133no—
113C22×D4—1133no—
114C22×D4—1133no—
115C22×D4—1133no—
116C23×C4—1133no—
117#127—1138no—
118#126—1138no—
119#126C2×D11318yescomplemented
120#123—11324no—
121#121—11324no—
122#121—11324no—
123#120—11324no—
124C2×C4⋊C4—1133no—
125C2×C4⋊C4C2×D11313yescomplemented
126C2×C22⋊C4—1133no—
127C2×C22⋊C4—1133no—
128C2×C22⋊C4—1133no—
129C2×C22⋊C4C2×D11313yes—
130C2×C42C2×D11311yescharacteristic, complemented
131C24—1134no—
132C24—1131no—
133C24—1131no—
134C24—1133no—
135C24—4526no—
136C24C22×D11311yescharacteristic
137C2×D4—11312no—
138C2×D4—11312no—
139C2×D4—11312no—
140C2×D4—11312no—
141C2×D4—4526no—
142C2×D4—4526no—
143C2×D4—4526no—
144C2×D4—4526no—
145C22×C4—1133no—
146C22×C4—11312no—
147C22×C4—4526no—
148C22×C4C22×D11313yes—
149C22×C4C22×D11313yes—
150C4⋊C4—11312no—
151C4⋊C4C22×D113112yescomplemented
152C22⋊C4—11312no—
153C22⋊C4—11312no—
154C22⋊C4—11312no—
155C22⋊C4C22×D113112yes—
156C42C22×D11314yescomplemented
157C23—26no—
158C23—1132no—
159C23—1132no—
160C23—1136no—
161C23—45212no—
162C23—45216no—
163C23—2266no—
164C23—2266no—
165C23—2266no—
166C23—2266no—
167C23—2266no—
168C23C23×D11312yes—
169C23C23×D11311yescharacteristic
170D4—45212no—
171D4—45212no—
172D4—45212no—
173D4—45212no—
174C2×C4—26no—
175C2×C4—26no—
176C2×C4—1136no—
177C2×C4—45212no—
178C2×C4—2266no—
179C2×C4C23×D11316yes—
180C2×C4C23×D11316yes—
181C22—26no—
182C22—44no—
183C22—45216no—
184C22—4524no—
185C22—4524no—
186C22—45212no—
187C22—2266no—
188C22—2266no—
189C22—2266no—
190C22—2266no—
191C22—2266no—
192C22#1681366816yes—
193C22C24×D11311yescharacteristic
194C4—26no—
195C4—26no—
196C4—2266no—
197C2—42no—
198C2—4522no—
199C2—4522no—
200C2—4526no—
201C2#2029933914yesdirect product factor
202C2C2×#1681366813yes—
subgroupG/H
centerC23C23×D113
commutator, cosocleC22×C113C25
FrattiniC22C24×D113
FittingC2×#126×C113C2
socleC23×C113C24
hypercenterC2×#126D113
hypocenterC113C2×#560
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #20299339C2direct (N × H)
2. C2×#16813619C2semidirect
3. C2×#16813616C2semidirect
4. C2×#16813607C2semidirect
5. C2×#16813597C2semidirect
6. C2×#16813595C2semidirect
7. C2×#16813592C2semidirect
8. C2×#126×C113C2semidirect
12. C22×D452C22semidirect
14. C22×C4×D113C22semidirect
15. #16813619C22semidirect
16. #16813616C22semidirect
17. #16813607C22semidirect
18. #16813597C22semidirect
19. #16813595C22semidirect
20. #16813592C22semidirect
21. C2×#14268626C22semidirect
24. C2×#14268624C22semidirect
25. #126×C113C22semidirect
26. C2×C4⋊C4×C113C22semidirect
28. C2×C42×C113C22semidirect
39. C2×D452C23semidirect
44. C2×C4×D113C23semidirect
45. #14268626C23semidirect
48. #14268624C23semidirect
52. C4⋊C4×C113C23semidirect
54. C42×C113C23semidirect
96. C2×C113#560semidirect
102. C113C2×#560semidirect
106. C2×#126D113semidirect
119. #126C2×D113semidirect
125. C2×C4⋊C4C2×D113semidirect
130. C2×C42C2×D113semidirect
151. C4⋊C4C22×D113semidirect
156. C42C22×D113semidirect
201. C2#20299339direct (N × H)

Maximal subgroups

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

subgroupindex
#202993392
C2×#168136192
C2×#168136162
C2×#168136072
C2×#168135972
C2×#168135952
C2×#168135922
C2×#126×C1132
C2×#560113