Finite Group Databasebeta

← C2×#127×D89 #26033522

Subgroups — C2×#127×D89 #26033522

Order 11392.

3000 conjugacy classes of subgroups; only the 661 normal subgroups are shown.

normal subgroups only

This group has 3000 conjugacy classes of subgroups — too many to draw. Only its 661 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
1C22×D4×D89C216yesmaximal, complemented
2C2×#15668009C211yesmaximal, characteristic, complemented
3C2×#15668008C216yesmaximal, complemented
4#127×D89C2116yesmaximal, direct product factor
5C2×C42×D89C211yesmaximal, characteristic, complemented
6C2×#127×C89C211yesmaximal, characteristic, complemented
7C24×D89C2214yes—
8C22×D356C2216yescomplemented
9C22×C22⋊D89C22112yescomplemented
10C2×D4×D89—248no—
11C2×D4×D89C22148yescomplemented
12C22×C4×D89C2213yes—
13#15668009C2218yescomplemented
14#15668008C22148yescomplemented
15C2×C4×Dic89C2213yescomplemented
16C42×D89C2218yescomplemented
17C22×D4×C89C2216yescomplemented
18#127×C89C2218yescomplemented
19C2×C42×C89C2211yescharacteristic, complemented
20C23×D89—248no—
21C23×D89C23116yes—
22C23×D89C2314yes—
23C23×D89C2311yescharacteristic
24C2×D356—224no—
25C2×D356C23124yescomplemented
26C2×C22⋊D89—248no—
27C2×C22⋊D89C23148yescomplemented
28D4×D89—2192no—
29C22×Dic89C2313yes—
30C2×C4×D89D4124yescomplemented
31C2×C4×D89C23112yes—
32C4×Dic89C23112yescomplemented
33C24×C89C2314yes—
34C2×D4×C89—224no—
35C2×D4×C89C23124yescomplemented
36C22×C4×C89C2313yes—
37C42×C89C2314yescomplemented
38C23×C89—224no—
39C23×C89C2418yes—
40C23×C89C2411yescharacteristic
41C22×D89—224no—
42C22×D89—296no—
43C22×D89—464no—
44C22×D89C2×D4112yes—
45C22×D89C2418yes—
46C22×D89C2412yes—
47D4×C89—248no—
48C2×C4×C89C2×D4112yescomplemented
49C2×C4×C89C2416yes—
50C22⋊D89—296no—
51C2×Dic89C2×D4112yescomplemented
52C2×Dic89C2416yes—
53D356—248no—
54C4×D89C2×D4148yescomplemented
55C22×C89—224no—
56C22×C89—416no—
57C22×C89C22×D416yes—
58C22×C89C2511yescharacteristic
59C2×D89—224no—
60C2×D89—416no—
61C2×D89—464no—
62C2×D89#127116yesdirect product factor
63C2×D89C22×D4112yes—
64C4×C89C22×D4112yescomplemented
65Dic89C22×D4112yescomplemented
66C2×C89—48no—
67C2×C89C2×#12714yescomplemented
68C2×C89C23×D413yes—
69D89—48no—
70D89C2×#12718yesdirect product factor
71C22×#127—891nomaximal, Sylow
72C89C22×#12711yescharacteristic, complemented, Sylow
73C23×D4—896no—
74C2×#127—896no—
75C2×#127—8916no—
76C2×#127—891no—
77C2×#127D8911yescharacteristic, direct product factor
78C22×C42—891no—
79C25—894no—
80C22×D4—8912no—
81C22×D4—8948no—
82C22×D4—896no—
83C22×D4—17848no—
84C22×D4C2×D8916yescomplemented
85C23×C4—893no—
86#127—8948no—
87#127—898no—
88#127C2×D8918yesdirect product factor
89C2×C42—893no—
90C2×C42—898no—
91C2×C42C2×D8911yescharacteristic, complemented
92C24—891no—
93C24—8916no—
94C24—894no—
95C24—17848no—
96C24C22×D8914yes—
97C2×D4—224no—
98C2×D4—8948no—
99C2×D4—8924no—
100C2×D4—178192no—
101C2×D4—17848no—
102C2×D4—17824no—
103C2×D4C22×D89124yescomplemented
104C22×C4—893no—
105C22×C4—8924no—
106C22×C4—8912no—
107C22×C4C22×D8913yes—
108C42—8912no—
109C42C22×D8914yescomplemented
110C23—224no—
111C23—8912no—
112C23—892no—
113C23—898no—
114C23—35664no—
115C23—17896no—
116C23—17824no—
117C23C23×D8918yes—
118C23C23×D8911yescharacteristic
119D4—248no—
120D4—17896no—
121D4—17848no—
122C2×C4—8912no—
123C2×C4—896no—
124C2×C4—8948no—
125C2×C4D4×D89112yescomplemented
126C2×C4C23×D8916yes—
127C22—224no—
128C22—416no—
129C22—8916no—
130C22—8912no—
131C22—35664no—
132C22—35616no—
133C22—17824no—
134C22C2×D4×D8916yes—
135C22C24×D8911yescharacteristic
136C4—8912no—
137C4C2×D4×D89112yescomplemented
138C2—48no—
139C2—898no—
140C2—3568no—
141C2#127×D8914yesdirect product factor
142C2C22×D4×D8913yes—
subgroupG/H
centerC23C23×D89
commutator, cosocleC22×C89C25
FrattiniC22C24×D89
FittingC2×#127×C89C2
socleC23×C89C24
hypercenterC2×#127D89
hypocenterC89C22×#127
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C22×D4×D89C2semidirect
2. C2×#15668009C2semidirect
3. C2×#15668008C2semidirect
4. #127×D89C2direct (N × H)
5. C2×C42×D89C2semidirect
6. C2×#127×C89C2semidirect
8. C22×D356C22semidirect
9. C22×C22⋊D89C22semidirect
11. C2×D4×D89C22semidirect
13. #15668009C22semidirect
14. #15668008C22semidirect
15. C2×C4×Dic89C22semidirect
16. C42×D89C22semidirect
17. C22×D4×C89C22semidirect
18. #127×C89C22semidirect
19. C2×C42×C89C22semidirect
25. C2×D356C23semidirect
27. C2×C22⋊D89C23semidirect
30. C2×C4×D89D4semidirect
32. C4×Dic89C23semidirect
35. C2×D4×C89C23semidirect
37. C42×C89C23semidirect
48. C2×C4×C89C2×D4semidirect
51. C2×Dic89C2×D4semidirect
54. C4×D89C2×D4semidirect
62. C2×D89#127direct (N × H)
64. C4×C89C22×D4semidirect
65. Dic89C22×D4semidirect
67. C2×C89C2×#127semidirect
70. D89C2×#127direct (N × H)
72. C89C22×#127semidirect
77. C2×#127D89direct (N × H)
84. C22×D4C2×D89semidirect
88. #127C2×D89direct (N × H)
91. C2×C42C2×D89semidirect
103. C2×D4C22×D89semidirect
109. C42C22×D89semidirect
125. C2×C4D4×D89semidirect
137. C4C2×D4×D89semidirect
141. C2#127×D89direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D892
C2×#156680092
C2×#156680082
#127×D892
C2×C42×D892
C2×#127×C892
C22×#12789