Finite Group Databasebeta

← C2×#15689864 #20257506

Subgroups — C2×#15689864 #20257506

Order 6016.

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#15689864C2116yesmaximal, direct product factor
2C2×#13094021C211yesmaximal, characteristic, complemented
3C2×#13094018C211yesmaximal, characteristic, complemented
4C2×#13094009C213yesmaximal, complemented
5C2×#13093999C213yesmaximal, complemented
6C2×#13093997C213yesmaximal, complemented
7C2×#13093994C213yesmaximal, complemented
8C2×#126×C47C211yesmaximal, characteristic, complemented
9C24×D47C2211yescharacteristic
10C22×D188C2213yes—
11C22×D188C2213yes—
12C22×D188C2213yescomplemented
13C22×C22⋊D47C2213yes—
14C22×C4×D47C2213yescomplemented
15#13094021C2218yescomplemented
16#13094018C2218yescomplemented
17#13094009C22124yescomplemented
18#13093999C22124yescomplemented
19#13093997C22124yescomplemented
20#13093994C22124yescomplemented
21C2×Dic47⋊C4C2213yescomplemented
22C2×(C2×D47)⋊C4C2213yes—
23C2×(C2×D47)⋊C4C2213yes—
24C2×(C2×D47)⋊C4C2213yescomplemented
25#126×C47C2218yescomplemented
26C2×C4⋊C4×C47C2213yescomplemented
27C2×C22⋊C4×C47C2213yes—
28C2×C42×C47C2211yescharacteristic, complemented
29C24×C47C2311yescharacteristic
30C23×D47—46no—
31C23×D47C2311yescharacteristic
32C23×D47C2311yescharacteristic
33C23×D47C2313yes—
34C23×D47C2314yes—
35C22×C4×C47C2313yes—
36C22×C4×C47C2313yes—
37C2×C22⋊D47—46no—
38C2×C22⋊D47C23112yes—
39C22×Dic47C2313yes—
40C2×D188—46no—
41C2×D188—46no—
42C2×D188—46no—
43C2×D188C23112yes—
44C2×D188C23112yes—
45C2×D188C23112yescomplemented
46C2×C4×D47—46no—
47C2×C4×D47C23112yescomplemented
48C4⋊C4×C47C23112yescomplemented
49C22⋊C4×C47C23112yes—
50C42×C47C2314yescomplemented
51(C2×D47)⋊C4C23112yes—
52(C2×D47)⋊C4C23112yes—
53(C2×D47)⋊C4C23112yescomplemented
54Dic47⋊C4C23112yescomplemented
55C23×C47—26no—
56C23×C47C2412yes—
57C23×C47C2411yescharacteristic
58C22×D47—26no—
59C22×D47—26no—
60C22×D47—26no—
61C22×D47—26no—
62C22×D47—26no—
63C22×D47—412no—
64C22×D47—416no—
65C22×D47C2412yes—
66C22×D47C2412yes—
67C22×D47C2416yes—
68C2×C4×C47—26no—
69C2×C4×C47—26no—
70C2×C4×C47C2416yes—
71C2×C4×C47C2416yes—
72C22⋊D47—412no—
73C2×Dic47—26no—
74C2×Dic47C2416yes—
75D188—412no—
76D188—412no—
77D188—412no—
78C4×D47—412no—
79C22×C47—26no—
80C22×C47—44no—
81C22×C47H(5,𝔽2)16yes—
82C22×C47C2511yescharacteristic
83C2×D47—26no—
84C2×D47—26no—
85C2×D47—26no—
86C2×D47—26no—
87C2×D47—26no—
88C2×D47—416no—
89C2×D47—412no—
90C2×D47—44no—
91C2×D47—44no—
92C4×C47—26no—
93C4×C47—26no—
94Dic47—26no—
95C2×#560—471nomaximal, Sylow
96C2×C47—42no—
97C2×C47#56014yescomplemented
98C2×C47C2×H(5,𝔽2)13yes—
99D47—46no—
100D47—42no—
101D47—42no—
102#560—4716no—
103C2×#127—471no—
104C2×#126—471no—
105C2×#126D4711yescharacteristic, complemented
106C2×#123—473no—
107C2×#121—473no—
108C2×#121—473no—
109C2×#120—473no—
110C47C2×#56011yescharacteristic, complemented, Sylow
111C25—471no—
112C22×D4—473no—
113C22×D4—473no—
114C22×D4—473no—
115C22×D4—473no—
116C23×C4—473no—
117#127—478no—
118#126—478no—
119#126C2×D4718yescomplemented
120#123—4724no—
121#121—4724no—
122#121—4724no—
123#120—4724no—
124C2×C4⋊C4—473no—
125C2×C4⋊C4C2×D4713yescomplemented
126C2×C22⋊C4—473no—
127C2×C22⋊C4—473no—
128C2×C22⋊C4—473no—
129C2×C22⋊C4C2×D4713yes—
130C2×C42C2×D4711yescharacteristic, complemented
131C24—471no—
132C24—471no—
133C24—473no—
134C24—474no—
135C24—1886no—
136C24C22×D4711yescharacteristic
137C2×D4—4712no—
138C2×D4—4712no—
139C2×D4—4712no—
140C2×D4—4712no—
141C2×D4—1886no—
142C2×D4—1886no—
143C2×D4—1886no—
144C2×D4—1886no—
145C22×C4—473no—
146C22×C4—4712no—
147C22×C4—1886no—
148C22×C4C22×D4713yes—
149C22×C4C22×D4713yes—
150C4⋊C4—4712no—
151C4⋊C4C22×D47112yescomplemented
152C22⋊C4—4712no—
153C22⋊C4—4712no—
154C22⋊C4—4712no—
155C22⋊C4C22×D47112yes—
156C42C22×D4714yescomplemented
157C23—26no—
158C23—472no—
159C23—472no—
160C23—476no—
161C23—946no—
162C23—946no—
163C23—946no—
164C23—946no—
165C23—946no—
166C23—18812no—
167C23—18816no—
168C23C23×D4712yes—
169C23C23×D4711yescharacteristic
170D4—18812no—
171D4—18812no—
172D4—18812no—
173D4—18812no—
174C2×C4—26no—
175C2×C4—26no—
176C2×C4—476no—
177C2×C4—946no—
178C2×C4—18812no—
179C2×C4C23×D4716yes—
180C2×C4C23×D4716yes—
181C22—26no—
182C22—44no—
183C22—946no—
184C22—946no—
185C22—946no—
186C22—946no—
187C22—946no—
188C22—18816no—
189C22—1884no—
190C22—1884no—
191C22—18812no—
192C22#1309407016yes—
193C22C24×D4711yescharacteristic
194C4—26no—
195C4—26no—
196C4—946no—
197C2—42no—
198C2—1882no—
199C2—1882no—
200C2—1886no—
201C2#1568986414yesdirect product factor
202C2C2×#1309407013yes—
subgroupG/H
centerC23C23×D47
commutatorC22×C47C25
FrattiniC22C24×D47
FittingC2×#126×C47C2
socleC23×C47C24
hypercenterC2×#126D47
hypocenterC47C2×#560
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #15689864C2direct (N × H)
2. C2×#13094021C2semidirect
3. C2×#13094018C2semidirect
4. C2×#13094009C2semidirect
5. C2×#13093999C2semidirect
6. C2×#13093997C2semidirect
7. C2×#13093994C2semidirect
8. C2×#126×C47C2semidirect
12. C22×D188C22semidirect
14. C22×C4×D47C22semidirect
15. #13094021C22semidirect
16. #13094018C22semidirect
17. #13094009C22semidirect
18. #13093999C22semidirect
19. #13093997C22semidirect
20. #13093994C22semidirect
21. C2×Dic47⋊C4C22semidirect
24. C2×(C2×D47)⋊C4C22semidirect
25. #126×C47C22semidirect
26. C2×C4⋊C4×C47C22semidirect
28. C2×C42×C47C22semidirect
45. C2×D188C23semidirect
47. C2×C4×D47C23semidirect
48. C4⋊C4×C47C23semidirect
50. C42×C47C23semidirect
53. (C2×D47)⋊C4C23semidirect
54. Dic47⋊C4C23semidirect
97. C2×C47#560semidirect
105. C2×#126D47semidirect
110. C47C2×#560semidirect
119. #126C2×D47semidirect
125. C2×C4⋊C4C2×D47semidirect
130. C2×C42C2×D47semidirect
151. C4⋊C4C22×D47semidirect
156. C42C22×D47semidirect
201. C2#15689864direct (N × H)