Finite Group Databasebeta

← C2×#19152339 #26034370

Subgroups — C2×#19152339 #26034370

Order 11392.

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#19152339C2116yesmaximal, direct product factor
2C2×#15668009C211yesmaximal, characteristic, complemented
3C2×#15668006C211yesmaximal, characteristic, complemented
4C2×#15667997C213yesmaximal, complemented
5C2×#15667987C213yesmaximal, complemented
6C2×#15667985C213yesmaximal, complemented
7C2×#15667982C213yesmaximal, complemented
8C2×#126×C89C211yesmaximal, characteristic, complemented
9C24×D89C2211yescharacteristic
10C22×D356C2213yes—
11C22×D356C2213yes—
12C22×D356C2213yescomplemented
13C22×C22⋊D89C2213yes—
14C22×C4×D89C2213yescomplemented
15#15668009C2218yescomplemented
16#15668006C2218yescomplemented
17#15667997C22124yescomplemented
18#15667987C22124yescomplemented
19#15667985C22124yescomplemented
20#15667982C22124yescomplemented
21C2×#13083553C2213yescomplemented
22C2×#13083551C2213yes—
23C2×#13083551C2213yes—
24C2×#13083551C2213yescomplemented
25#126×C89C2218yescomplemented
26C2×C4⋊C4×C89C2213yescomplemented
27C2×C22⋊C4×C89C2213yes—
28C2×C42×C89C2211yescharacteristic, complemented
29C23×D89—46no—
30C23×D89C2313yes—
31C23×D89C2311yescharacteristic
32C23×D89C2311yescharacteristic
33C23×D89C2314yes—
34C2×D356—46no—
35C2×D356—46no—
36C2×D356—46no—
37C2×D356C23112yes—
38C2×D356C23112yes—
39C2×D356C23112yescomplemented
40C2×C22⋊D89—46no—
41C2×C22⋊D89C23112yes—
42C22×Dic89C2313yes—
43C2×C4×D89—46no—
44C2×C4×D89C23112yescomplemented
45#13083553C23112yescomplemented
46#13083551C23112yes—
47#13083551C23112yes—
48#13083551C23112yescomplemented
49C24×C89C2311yescharacteristic
50C22×C4×C89C2313yes—
51C22×C4×C89C2313yes—
52C4⋊C4×C89C23112yescomplemented
53C22⋊C4×C89C23112yes—
54C42×C89C2314yescomplemented
55C23×C89—26no—
56C23×C89C2412yes—
57C23×C89C2411yescharacteristic
58C22×D89—26no—
59C22×D89—26no—
60C22×D89—26no—
61C22×D89—26no—
62C22×D89—26no—
63C22×D89—412no—
64C22×D89—416no—
65C22×D89C2412yes—
66C22×D89C2412yes—
67C22×D89C2416yes—
68C2×C4×C89—26no—
69C2×C4×C89—26no—
70C2×C4×C89C2416yes—
71C2×C4×C89C2416yes—
72C22⋊D89—412no—
73C2×Dic89—26no—
74C2×Dic89C2416yes—
75D356—412no—
76D356—412no—
77D356—412no—
78C4×D89—412no—
79C22×C89—26no—
80C22×C89—44no—
81C22×C89H(5,𝔽2)16yes—
82C22×C89C2511yescharacteristic
83C2×D89—26no—
84C2×D89—26no—
85C2×D89—26no—
86C2×D89—26no—
87C2×D89—26no—
88C2×D89—416no—
89C2×D89—412no—
90C2×D89—44no—
91C2×D89—44no—
92C4×C89—26no—
93C4×C89—26no—
94Dic89—26no—
95C2×C89—42no—
96C2×C89#56014yescomplemented
97C2×C89C2×H(5,𝔽2)13yes—
98D89—46no—
99D89—42no—
100D89—42no—
101C2×#560—891nomaximal, Sylow
102C89C2×#56011yescharacteristic, complemented, Sylow
103#560—8916no—
104C2×#127—891no—
105C2×#126—891no—
106C2×#126D8911yescharacteristic, complemented
107C2×#123—893no—
108C2×#121—893no—
109C2×#121—893no—
110C2×#120—893no—
111C25—891no—
112C22×D4—893no—
113C22×D4—893no—
114C22×D4—893no—
115C22×D4—893no—
116C23×C4—893no—
117#127—898no—
118#126—898no—
119#126C2×D8918yescomplemented
120#123—8924no—
121#121—8924no—
122#121—8924no—
123#120—8924no—
124C2×C4⋊C4—893no—
125C2×C4⋊C4C2×D8913yescomplemented
126C2×C22⋊C4—893no—
127C2×C22⋊C4—893no—
128C2×C22⋊C4—893no—
129C2×C22⋊C4C2×D8913yes—
130C2×C42C2×D8911yescharacteristic, complemented
131C24—894no—
132C24—891no—
133C24—891no—
134C24—893no—
135C24—3566no—
136C24C22×D8911yescharacteristic
137C2×D4—8912no—
138C2×D4—8912no—
139C2×D4—8912no—
140C2×D4—8912no—
141C2×D4—3566no—
142C2×D4—3566no—
143C2×D4—3566no—
144C2×D4—3566no—
145C22×C4—893no—
146C22×C4—8912no—
147C22×C4—3566no—
148C22×C4C22×D8913yes—
149C22×C4C22×D8913yes—
150C4⋊C4—8912no—
151C4⋊C4C22×D89112yescomplemented
152C22⋊C4—8912no—
153C22⋊C4—8912no—
154C22⋊C4—8912no—
155C22⋊C4C22×D89112yes—
156C42C22×D8914yescomplemented
157C23—26no—
158C23—892no—
159C23—892no—
160C23—896no—
161C23—35612no—
162C23—35616no—
163C23—1786no—
164C23—1786no—
165C23—1786no—
166C23—1786no—
167C23—1786no—
168C23C23×D8912yes—
169C23C23×D8911yescharacteristic
170D4—35612no—
171D4—35612no—
172D4—35612no—
173D4—35612no—
174C2×C4—26no—
175C2×C4—26no—
176C2×C4—896no—
177C2×C4—35612no—
178C2×C4—1786no—
179C2×C4C23×D8916yes—
180C2×C4C23×D8916yes—
181C22—26no—
182C22—44no—
183C22—35616no—
184C22—3564no—
185C22—3564no—
186C22—35612no—
187C22—1786no—
188C22—1786no—
189C22—1786no—
190C22—1786no—
191C22—1786no—
192C22#1566805816yes—
193C22C24×D8911yescharacteristic
194C4—26no—
195C4—26no—
196C4—1786no—
197C2—42no—
198C2—3562no—
199C2—3562no—
200C2—3566no—
201C2#1915233914yesdirect product factor
202C2C2×#1566805813yes—
subgroupG/H
centerC23C23×D89
commutator, cosocleC22×C89C25
FrattiniC22C24×D89
FittingC2×#126×C89C2
socleC23×C89C24
hypercenterC2×#126D89
hypocenterC89C2×#560
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #19152339C2direct (N × H)
2. C2×#15668009C2semidirect
3. C2×#15668006C2semidirect
4. C2×#15667997C2semidirect
5. C2×#15667987C2semidirect
6. C2×#15667985C2semidirect
7. C2×#15667982C2semidirect
8. C2×#126×C89C2semidirect
12. C22×D356C22semidirect
14. C22×C4×D89C22semidirect
15. #15668009C22semidirect
16. #15668006C22semidirect
17. #15667997C22semidirect
18. #15667987C22semidirect
19. #15667985C22semidirect
20. #15667982C22semidirect
21. C2×#13083553C22semidirect
24. C2×#13083551C22semidirect
25. #126×C89C22semidirect
26. C2×C4⋊C4×C89C22semidirect
28. C2×C42×C89C22semidirect
39. C2×D356C23semidirect
44. C2×C4×D89C23semidirect
45. #13083553C23semidirect
48. #13083551C23semidirect
52. C4⋊C4×C89C23semidirect
54. C42×C89C23semidirect
96. C2×C89#560semidirect
102. C89C2×#560semidirect
106. C2×#126D89semidirect
119. #126C2×D89semidirect
125. C2×C4⋊C4C2×D89semidirect
130. C2×C42C2×D89semidirect
151. C4⋊C4C22×D89semidirect
156. C42C22×D89semidirect
201. C2#19152339direct (N × H)

Maximal subgroups

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

subgroupindex
#191523392
C2×#156680092
C2×#156680062
C2×#156679972
C2×#156679872
C2×#156679852
C2×#156679822
C2×#126×C892
C2×#56089