Finite Group Databasebeta

← C2×#19099304 #23777518

Subgroups — C2×#19099304 #23777518

Order 10112.

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#19099304C2116yesmaximal, direct product factor
2C2×#14579158C211yesmaximal, characteristic, complemented
3C2×#14579155C211yesmaximal, characteristic, complemented
4C2×#14579146C213yesmaximal, complemented
5C2×#14579136C213yesmaximal, complemented
6C2×#14579134C213yesmaximal, complemented
7C2×#14579131C213yesmaximal, complemented
8C2×#126×C79C211yesmaximal, characteristic, complemented
9C24×D79C2211yescharacteristic
10C22×D316C2213yes—
11C22×D316C2213yes—
12C22×D316C2213yescomplemented
13C22×C22⋊D79C2213yes—
14C22×C4×D79C2213yescomplemented
15#14579158C2218yescomplemented
16#14579155C2218yescomplemented
17#14579146C22124yescomplemented
18#14579136C22124yescomplemented
19#14579134C22124yescomplemented
20#14579131C22124yescomplemented
21C2×Dic79⋊C4C2213yescomplemented
22C2×(C2×D79)⋊C4C2213yes—
23C2×(C2×D79)⋊C4C2213yes—
24C2×(C2×D79)⋊C4C2213yescomplemented
25#126×C79C2218yescomplemented
26C2×C4⋊C4×C79C2213yescomplemented
27C2×C22⋊C4×C79C2213yes—
28C2×C42×C79C2211yescharacteristic, complemented
29C23×D79—46no—
30C23×D79C2311yescharacteristic
31C23×D79C2311yescharacteristic
32C23×D79C2313yes—
33C23×D79C2314yes—
34C2×D316—46no—
35C2×D316—46no—
36C2×D316—46no—
37C2×D316C23112yes—
38C2×D316C23112yes—
39C2×D316C23112yescomplemented
40C2×C22⋊D79—46no—
41C2×C22⋊D79C23112yes—
42C22×Dic79C2313yes—
43C2×C4×D79—46no—
44C2×C4×D79C23112yescomplemented
45Dic79⋊C4C23112yescomplemented
46(C2×D79)⋊C4C23112yes—
47(C2×D79)⋊C4C23112yes—
48(C2×D79)⋊C4C23112yescomplemented
49C24×C79C2311yescharacteristic
50C22×C4×C79C2313yes—
51C22×C4×C79C2313yes—
52C4⋊C4×C79C23112yescomplemented
53C22⋊C4×C79C23112yes—
54C42×C79C2314yescomplemented
55C23×C79—26no—
56C23×C79C2412yes—
57C23×C79C2411yescharacteristic
58C22×D79—26no—
59C22×D79—26no—
60C22×D79—26no—
61C22×D79—26no—
62C22×D79—26no—
63C22×D79—412no—
64C22×D79—416no—
65C22×D79C2412yes—
66C22×D79C2412yes—
67C22×D79C2416yes—
68C2×C4×C79—26no—
69C2×C4×C79—26no—
70C2×C4×C79C2416yes—
71C2×C4×C79C2416yes—
72C22⋊D79—412no—
73C2×Dic79—26no—
74C2×Dic79C2416yes—
75D316—412no—
76D316—412no—
77D316—412no—
78C4×D79—412no—
79C22×C79—26no—
80C22×C79—44no—
81C22×C79H(5,𝔽2)16yes—
82C22×C79C2511yescharacteristic
83C2×D79—26no—
84C2×D79—26no—
85C2×D79—26no—
86C2×D79—26no—
87C2×D79—26no—
88C2×D79—416no—
89C2×D79—412no—
90C2×D79—44no—
91C2×D79—44no—
92C4×C79—26no—
93C4×C79—26no—
94Dic79—26no—
95C2×C79—42no—
96C2×C79#56014yescomplemented
97C2×C79C2×H(5,𝔽2)13yes—
98D79—46no—
99D79—42no—
100D79—42no—
101C2×#560—791nomaximal, Sylow
102C79C2×#56011yescharacteristic, complemented, Sylow
103#560—7916no—
104C2×#127—791no—
105C2×#126—791no—
106C2×#126D7911yescharacteristic, complemented
107C2×#123—793no—
108C2×#121—793no—
109C2×#121—793no—
110C2×#120—793no—
111C25—791no—
112C22×D4—793no—
113C22×D4—793no—
114C22×D4—793no—
115C22×D4—793no—
116C23×C4—793no—
117#127—798no—
118#126—798no—
119#126C2×D7918yescomplemented
120#123—7924no—
121#121—7924no—
122#121—7924no—
123#120—7924no—
124C2×C4⋊C4—793no—
125C2×C4⋊C4C2×D7913yescomplemented
126C2×C22⋊C4—793no—
127C2×C22⋊C4—793no—
128C2×C22⋊C4—793no—
129C2×C22⋊C4C2×D7913yes—
130C2×C42C2×D7911yescharacteristic, complemented
131C24—3166no—
132C24—794no—
133C24—791no—
134C24—791no—
135C24—793no—
136C24C22×D7911yescharacteristic
137C2×D4—3166no—
138C2×D4—3166no—
139C2×D4—3166no—
140C2×D4—3166no—
141C2×D4—7912no—
142C2×D4—7912no—
143C2×D4—7912no—
144C2×D4—7912no—
145C22×C4—3166no—
146C22×C4—7912no—
147C22×C4—793no—
148C22×C4C22×D7913yes—
149C22×C4C22×D7913yes—
150C4⋊C4—7912no—
151C4⋊C4C22×D79112yescomplemented
152C22⋊C4—7912no—
153C22⋊C4—7912no—
154C22⋊C4—7912no—
155C22⋊C4C22×D79112yes—
156C42C22×D7914yescomplemented
157C23—26no—
158C23—31612no—
159C23—31616no—
160C23—792no—
161C23—792no—
162C23—796no—
163C23—1586no—
164C23—1586no—
165C23—1586no—
166C23—1586no—
167C23—1586no—
168C23C23×D7912yes—
169C23C23×D7911yescharacteristic
170D4—31612no—
171D4—31612no—
172D4—31612no—
173D4—31612no—
174C2×C4—26no—
175C2×C4—26no—
176C2×C4—31612no—
177C2×C4—796no—
178C2×C4—1586no—
179C2×C4C23×D7916yes—
180C2×C4C23×D7916yes—
181C22—26no—
182C22—44no—
183C22—31616no—
184C22—3164no—
185C22—3164no—
186C22—31612no—
187C22—1586no—
188C22—1586no—
189C22—1586no—
190C22—1586no—
191C22—1586no—
192C22#1457920716yes—
193C22C24×D7911yescharacteristic
194C4—26no—
195C4—26no—
196C4—1586no—
197C2—42no—
198C2—3162no—
199C2—3162no—
200C2—3166no—
201C2#1909930414yesdirect product factor
202C2C2×#1457920713yes—
subgroupG/H
centerC23C23×D79
commutator, cosocleC22×C79C25
FrattiniC22C24×D79
FittingC2×#126×C79C2
socleC23×C79C24
hypercenterC2×#126D79
hypocenterC79C2×#560
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #19099304C2direct (N × H)
2. C2×#14579158C2semidirect
3. C2×#14579155C2semidirect
4. C2×#14579146C2semidirect
5. C2×#14579136C2semidirect
6. C2×#14579134C2semidirect
7. C2×#14579131C2semidirect
8. C2×#126×C79C2semidirect
12. C22×D316C22semidirect
14. C22×C4×D79C22semidirect
15. #14579158C22semidirect
16. #14579155C22semidirect
17. #14579146C22semidirect
18. #14579136C22semidirect
19. #14579134C22semidirect
20. #14579131C22semidirect
21. C2×Dic79⋊C4C22semidirect
24. C2×(C2×D79)⋊C4C22semidirect
25. #126×C79C22semidirect
26. C2×C4⋊C4×C79C22semidirect
28. C2×C42×C79C22semidirect
39. C2×D316C23semidirect
44. C2×C4×D79C23semidirect
45. Dic79⋊C4C23semidirect
48. (C2×D79)⋊C4C23semidirect
52. C4⋊C4×C79C23semidirect
54. C42×C79C23semidirect
96. C2×C79#560semidirect
102. C79C2×#560semidirect
106. C2×#126D79semidirect
119. #126C2×D79semidirect
125. C2×C4⋊C4C2×D79semidirect
130. C2×C42C2×D79semidirect
151. C4⋊C4C22×D79semidirect
156. C42C22×D79semidirect
201. C2#19099304direct (N × H)