Finite Group Databasebeta

← C2×#16840503 #21459937

Subgroups — C2×#16840503 #21459937

Order 7808.

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#16840503C2116yesmaximal, direct product factor
2C2×#14519774C211yesmaximal, characteristic, complemented
3C2×#14519771C211yesmaximal, characteristic, complemented
4C2×#14519762C213yesmaximal, complemented
5C2×#14519752C213yesmaximal, complemented
6C2×#14519750C213yesmaximal, complemented
7C2×#14519747C213yesmaximal, complemented
8C2×#126×C61C211yesmaximal, characteristic, complemented
9C24×D61C2211yescharacteristic
10C22×D244C2213yes—
11C22×D244C2213yes—
12C22×D244C2213yescomplemented
13C22×C22⋊D61C2213yes—
14C22×C4×D61C2213yescomplemented
15#14519774C2218yescomplemented
16#14519771C2218yescomplemented
17#14519762C22124yescomplemented
18#14519752C22124yescomplemented
19#14519750C22124yescomplemented
20#14519747C22124yescomplemented
21C2×#11758196C2213yescomplemented
22C2×#11758198C2213yes—
23C2×#11758198C2213yes—
24C2×#11758198C2213yescomplemented
25#126×C61C2218yescomplemented
26C2×C4⋊C4×C61C2213yescomplemented
27C2×C22⋊C4×C61C2213yes—
28C2×C42×C61C2211yescharacteristic, complemented
29C24×C61C2311yescharacteristic
30C23×D61—46no—
31C23×D61C2313yes—
32C23×D61C2311yescharacteristic
33C23×D61C2311yescharacteristic
34C23×D61C2314yes—
35C22×C4×C61C2313yes—
36C22×C4×C61C2313yes—
37C2×C22⋊D61—46no—
38C2×C22⋊D61C23112yes—
39C22×Dic61C2313yes—
40C2×D244—46no—
41C2×D244—46no—
42C2×D244—46no—
43C2×D244C23112yes—
44C2×D244C23112yes—
45C2×D244C23112yescomplemented
46C2×C4×D61—46no—
47C2×C4×D61C23112yescomplemented
48C4⋊C4×C61C23112yescomplemented
49C22⋊C4×C61C23112yes—
50C42×C61C2314yescomplemented
51#11758198C23112yes—
52#11758198C23112yes—
53#11758198C23112yescomplemented
54#11758196C23112yescomplemented
55C23×C61—26no—
56C23×C61C2412yes—
57C23×C61C2411yescharacteristic
58C22×D61—26no—
59C22×D61—26no—
60C22×D61—26no—
61C22×D61—26no—
62C22×D61—26no—
63C22×D61—412no—
64C22×D61—416no—
65C22×D61C2412yes—
66C22×D61C2412yes—
67C22×D61C2416yes—
68C2×C4×C61—26no—
69C2×C4×C61—26no—
70C2×C4×C61C2416yes—
71C2×C4×C61C2416yes—
72C22⋊D61—412no—
73C2×Dic61—26no—
74C2×Dic61C2416yes—
75D244—412no—
76D244—412no—
77D244—412no—
78C4×D61—412no—
79C22×C61—26no—
80C22×C61—44no—
81C22×C61H(5,𝔽2)16yes—
82C22×C61C2511yescharacteristic
83C2×D61—26no—
84C2×D61—26no—
85C2×D61—26no—
86C2×D61—26no—
87C2×D61—26no—
88C2×D61—416no—
89C2×D61—412no—
90C2×D61—44no—
91C2×D61—44no—
92C4×C61—26no—
93C4×C61—26no—
94Dic61—26no—
95C2×#560—611nomaximal, Sylow
96C2×C61—42no—
97C2×C61#56014yescomplemented
98C2×C61C2×H(5,𝔽2)13yes—
99D61—46no—
100D61—42no—
101D61—42no—
102#560—6116no—
103C2×#127—611no—
104C2×#126—611no—
105C2×#126D6111yescharacteristic, complemented
106C2×#123—613no—
107C2×#121—613no—
108C2×#121—613no—
109C2×#120—613no—
110C61C2×#56011yescharacteristic, complemented, Sylow
111C25—611no—
112C22×D4—613no—
113C22×D4—613no—
114C22×D4—613no—
115C22×D4—613no—
116C23×C4—613no—
117#127—618no—
118#126—618no—
119#126C2×D6118yescomplemented
120#123—6124no—
121#121—6124no—
122#121—6124no—
123#120—6124no—
124C2×C4⋊C4—613no—
125C2×C4⋊C4C2×D6113yescomplemented
126C2×C22⋊C4—613no—
127C2×C22⋊C4—613no—
128C2×C22⋊C4—613no—
129C2×C22⋊C4C2×D6113yes—
130C2×C42C2×D6111yescharacteristic, complemented
131C24—611no—
132C24—611no—
133C24—613no—
134C24—614no—
135C24—2446no—
136C24C22×D6111yescharacteristic
137C2×D4—6112no—
138C2×D4—6112no—
139C2×D4—6112no—
140C2×D4—6112no—
141C2×D4—2446no—
142C2×D4—2446no—
143C2×D4—2446no—
144C2×D4—2446no—
145C22×C4—613no—
146C22×C4—6112no—
147C22×C4—2446no—
148C22×C4C22×D6113yes—
149C22×C4C22×D6113yes—
150C4⋊C4—6112no—
151C4⋊C4C22×D61112yescomplemented
152C22⋊C4—6112no—
153C22⋊C4—6112no—
154C22⋊C4—6112no—
155C22⋊C4C22×D61112yes—
156C42C22×D6114yescomplemented
157C23—26no—
158C23—612no—
159C23—612no—
160C23—616no—
161C23—1226no—
162C23—1226no—
163C23—1226no—
164C23—1226no—
165C23—1226no—
166C23—24412no—
167C23—24416no—
168C23C23×D6112yes—
169C23C23×D6111yescharacteristic
170D4—24412no—
171D4—24412no—
172D4—24412no—
173D4—24412no—
174C2×C4—26no—
175C2×C4—26no—
176C2×C4—616no—
177C2×C4—1226no—
178C2×C4—24412no—
179C2×C4C23×D6116yes—
180C2×C4C23×D6116yes—
181C22—26no—
182C22—44no—
183C22—1226no—
184C22—1226no—
185C22—1226no—
186C22—1226no—
187C22—1226no—
188C22—24416no—
189C22—24412no—
190C22—2444no—
191C22—2444no—
192C22#1451982316yes—
193C22C24×D6111yescharacteristic
194C4—26no—
195C4—26no—
196C4—1226no—
197C2—42no—
198C2—2442no—
199C2—2442no—
200C2—2446no—
201C2#1684050314yesdirect product factor
202C2C2×#1451982313yes—
subgroupG/H
centerC23C23×D61
commutatorC22×C61C25
FrattiniC22C24×D61
FittingC2×#126×C61C2
socleC23×C61C24
hypercenterC2×#126D61
hypocenterC61C2×#560
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #16840503C2direct (N × H)
2. C2×#14519774C2semidirect
3. C2×#14519771C2semidirect
4. C2×#14519762C2semidirect
5. C2×#14519752C2semidirect
6. C2×#14519750C2semidirect
7. C2×#14519747C2semidirect
8. C2×#126×C61C2semidirect
12. C22×D244C22semidirect
14. C22×C4×D61C22semidirect
15. #14519774C22semidirect
16. #14519771C22semidirect
17. #14519762C22semidirect
18. #14519752C22semidirect
19. #14519750C22semidirect
20. #14519747C22semidirect
21. C2×#11758196C22semidirect
24. C2×#11758198C22semidirect
25. #126×C61C22semidirect
26. C2×C4⋊C4×C61C22semidirect
28. C2×C42×C61C22semidirect
45. C2×D244C23semidirect
47. C2×C4×D61C23semidirect
48. C4⋊C4×C61C23semidirect
50. C42×C61C23semidirect
53. #11758198C23semidirect
54. #11758196C23semidirect
97. C2×C61#560semidirect
105. C2×#126D61semidirect
110. C61C2×#560semidirect
119. #126C2×D61semidirect
125. C2×C4⋊C4C2×D61semidirect
130. C2×C42C2×D61semidirect
151. C4⋊C4C22×D61semidirect
156. C42C22×D61semidirect
201. C2#16840503direct (N × H)