Finite Group Databasebeta

← C2×#14583640 #19148713

Subgroups — C2×#14583640 #19148713

Order 5504.

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#14583640C2116yesmaximal, direct product factor
2C2×#13063322C211yesmaximal, characteristic, complemented
3C2×#13063319C211yesmaximal, characteristic, complemented
4C2×#13063310C213yesmaximal, complemented
5C2×#13063300C213yesmaximal, complemented
6C2×#13063298C213yesmaximal, complemented
7C2×#13063295C213yesmaximal, complemented
8C2×#126×C43C211yesmaximal, characteristic, complemented
9C24×D43C2211yescharacteristic
10C22×D172C2213yes—
11C22×D172C2213yes—
12C22×D172C2213yescomplemented
13C22×C22⋊D43C2213yes—
14C22×C4×D43C2213yescomplemented
15#13063322C2218yescomplemented
16#13063319C2218yescomplemented
17#13063310C22124yescomplemented
18#13063300C22124yescomplemented
19#13063298C22124yescomplemented
20#13063295C22124yescomplemented
21C2×Dic43⋊C4C2213yescomplemented
22C2×(C2×D43)⋊C4C2213yes—
23C2×(C2×D43)⋊C4C2213yes—
24C2×(C2×D43)⋊C4C2213yescomplemented
25#126×C43C2218yescomplemented
26C2×C4⋊C4×C43C2213yescomplemented
27C2×C22⋊C4×C43C2213yes—
28C2×C42×C43C2211yescharacteristic, complemented
29C24×C43C2311yescharacteristic
30C23×D43—46no—
31C23×D43C2311yescharacteristic
32C23×D43C2311yescharacteristic
33C23×D43C2313yes—
34C23×D43C2314yes—
35C22×C4×C43C2313yes—
36C22×C4×C43C2313yes—
37C2×C22⋊D43—46no—
38C2×C22⋊D43C23112yes—
39C22×Dic43C2313yes—
40C2×D172—46no—
41C2×D172—46no—
42C2×D172—46no—
43C2×D172C23112yes—
44C2×D172C23112yes—
45C2×D172C23112yescomplemented
46C2×C4×D43—46no—
47C2×C4×D43C23112yescomplemented
48C4⋊C4×C43C23112yescomplemented
49C22⋊C4×C43C23112yes—
50C42×C43C2314yescomplemented
51(C2×D43)⋊C4C23112yes—
52(C2×D43)⋊C4C23112yes—
53(C2×D43)⋊C4C23112yescomplemented
54Dic43⋊C4C23112yescomplemented
55C23×C43—26no—
56C23×C43C2412yes—
57C23×C43C2411yescharacteristic
58C22×D43—26no—
59C22×D43—26no—
60C22×D43—26no—
61C22×D43—26no—
62C22×D43—26no—
63C22×D43—412no—
64C22×D43—416no—
65C22×D43C2412yes—
66C22×D43C2412yes—
67C22×D43C2416yes—
68C2×C4×C43—26no—
69C2×C4×C43—26no—
70C2×C4×C43C2416yes—
71C2×C4×C43C2416yes—
72C22⋊D43—412no—
73C2×Dic43—26no—
74C2×Dic43C2416yes—
75D172—412no—
76D172—412no—
77D172—412no—
78C4×D43—412no—
79C22×C43—26no—
80C22×C43—44no—
81C22×C43H(5,𝔽2)16yes—
82C22×C43C2511yescharacteristic
83C2×D43—26no—
84C2×D43—26no—
85C2×D43—26no—
86C2×D43—26no—
87C2×D43—26no—
88C2×D43—416no—
89C2×D43—412no—
90C2×D43—44no—
91C2×D43—44no—
92C4×C43—26no—
93C4×C43—26no—
94Dic43—26no—
95C2×#560—431nomaximal, Sylow
96C2×C43—42no—
97C2×C43#56014yescomplemented
98C2×C43C2×H(5,𝔽2)13yes—
99D43—46no—
100D43—42no—
101D43—42no—
102#560—4316no—
103C2×#127—431no—
104C2×#126—431no—
105C2×#126D4311yescharacteristic, complemented
106C2×#123—433no—
107C2×#121—433no—
108C2×#121—433no—
109C2×#120—433no—
110C43C2×#56011yescharacteristic, complemented, Sylow
111C25—431no—
112C22×D4—433no—
113C22×D4—433no—
114C22×D4—433no—
115C22×D4—433no—
116C23×C4—433no—
117#127—438no—
118#126—438no—
119#126C2×D4318yescomplemented
120#123—4324no—
121#121—4324no—
122#121—4324no—
123#120—4324no—
124C2×C4⋊C4—433no—
125C2×C4⋊C4C2×D4313yescomplemented
126C2×C22⋊C4—433no—
127C2×C22⋊C4—433no—
128C2×C22⋊C4—433no—
129C2×C22⋊C4C2×D4313yes—
130C2×C42C2×D4311yescharacteristic, complemented
131C24—431no—
132C24—431no—
133C24—433no—
134C24—434no—
135C24—1726no—
136C24C22×D4311yescharacteristic
137C2×D4—4312no—
138C2×D4—4312no—
139C2×D4—4312no—
140C2×D4—4312no—
141C2×D4—1726no—
142C2×D4—1726no—
143C2×D4—1726no—
144C2×D4—1726no—
145C22×C4—433no—
146C22×C4—4312no—
147C22×C4—1726no—
148C22×C4C22×D4313yes—
149C22×C4C22×D4313yes—
150C4⋊C4—4312no—
151C4⋊C4C22×D43112yescomplemented
152C22⋊C4—4312no—
153C22⋊C4—4312no—
154C22⋊C4—4312no—
155C22⋊C4C22×D43112yes—
156C42C22×D4314yescomplemented
157C23—26no—
158C23—432no—
159C23—432no—
160C23—436no—
161C23—866no—
162C23—866no—
163C23—866no—
164C23—866no—
165C23—866no—
166C23—17212no—
167C23—17216no—
168C23C23×D4312yes—
169C23C23×D4311yescharacteristic
170D4—17212no—
171D4—17212no—
172D4—17212no—
173D4—17212no—
174C2×C4—26no—
175C2×C4—26no—
176C2×C4—436no—
177C2×C4—866no—
178C2×C4—17212no—
179C2×C4C23×D4316yes—
180C2×C4C23×D4316yes—
181C22—26no—
182C22—44no—
183C22—866no—
184C22—866no—
185C22—866no—
186C22—866no—
187C22—866no—
188C22—17216no—
189C22—1724no—
190C22—1724no—
191C22—17212no—
192C22#1306337116yes—
193C22C24×D4311yescharacteristic
194C4—26no—
195C4—26no—
196C4—866no—
197C2—42no—
198C2—1722no—
199C2—1722no—
200C2—1726no—
201C2#1458364014yesdirect product factor
202C2C2×#1306337113yes—
subgroupG/H
centerC23C23×D43
commutatorC22×C43C25
FrattiniC22C24×D43
FittingC2×#126×C43C2
socleC23×C43C24
hypercenterC2×#126D43
hypocenterC43C2×#560
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #14583640C2direct (N × H)
2. C2×#13063322C2semidirect
3. C2×#13063319C2semidirect
4. C2×#13063310C2semidirect
5. C2×#13063300C2semidirect
6. C2×#13063298C2semidirect
7. C2×#13063295C2semidirect
8. C2×#126×C43C2semidirect
12. C22×D172C22semidirect
14. C22×C4×D43C22semidirect
15. #13063322C22semidirect
16. #13063319C22semidirect
17. #13063310C22semidirect
18. #13063300C22semidirect
19. #13063298C22semidirect
20. #13063295C22semidirect
21. C2×Dic43⋊C4C22semidirect
24. C2×(C2×D43)⋊C4C22semidirect
25. #126×C43C22semidirect
26. C2×C4⋊C4×C43C22semidirect
28. C2×C42×C43C22semidirect
45. C2×D172C23semidirect
47. C2×C4×D43C23semidirect
48. C4⋊C4×C43C23semidirect
50. C42×C43C23semidirect
53. (C2×D43)⋊C4C23semidirect
54. Dic43⋊C4C23semidirect
97. C2×C43#560semidirect
105. C2×#126D43semidirect
110. C43C2×#560semidirect
119. #126C2×D43semidirect
125. C2×C4⋊C4C2×D43semidirect
130. C2×C42C2×D43semidirect
151. C4⋊C4C22×D43semidirect
156. C42C22×D43semidirect
201. C2#14583640direct (N × H)