Finite Group Databasebeta

← C2×#127×D83 #24920733

Subgroups — C2×#127×D83 #24920733

Order 10624.

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×D83C216yesmaximal, complemented
2C2×#14581789C211yesmaximal, characteristic, complemented
3C2×#14581788C216yesmaximal, complemented
4#127×D83C2116yesmaximal, direct product factor
5C2×C42×D83C211yesmaximal, characteristic, complemented
6C2×#127×C83C211yesmaximal, characteristic, complemented
7C24×D83C2214yes—
8C22×D332C2216yescomplemented
9C22×C22⋊D83C22112yescomplemented
10C2×D4×D83—248no—
11C2×D4×D83C22148yescomplemented
12C22×C4×D83C2213yes—
13#14581789C2218yescomplemented
14#14581788C22148yescomplemented
15C2×C4×Dic83C2213yescomplemented
16C42×D83C2218yescomplemented
17C22×D4×C83C2216yescomplemented
18#127×C83C2218yescomplemented
19C2×C42×C83C2211yescharacteristic, complemented
20C23×D83—248no—
21C23×D83C23116yes—
22C23×D83C2314yes—
23C23×D83C2311yescharacteristic
24C2×D332—224no—
25C2×D332C23124yescomplemented
26C2×C22⋊D83—248no—
27C2×C22⋊D83C23148yescomplemented
28D4×D83—2192no—
29C22×Dic83C2313yes—
30C2×C4×D83D4124yescomplemented
31C2×C4×D83C23112yes—
32C4×Dic83C23112yescomplemented
33C24×C83C2314yes—
34C2×D4×C83—224no—
35C2×D4×C83C23124yescomplemented
36C22×C4×C83C2313yes—
37C42×C83C2314yescomplemented
38C23×C83—224no—
39C23×C83C2418yes—
40C23×C83C2411yescharacteristic
41C22×D83—224no—
42C22×D83—296no—
43C22×D83—464no—
44C22×D83C2×D4112yes—
45C22×D83C2418yes—
46C22×D83C2412yes—
47D4×C83—248no—
48C2×C4×C83C2×D4112yescomplemented
49C2×C4×C83C2416yes—
50C22⋊D83—296no—
51C2×Dic83C2×D4112yescomplemented
52C2×Dic83C2416yes—
53D332—248no—
54C4×D83C2×D4148yescomplemented
55C22×C83—224no—
56C22×C83—416no—
57C22×C83C22×D416yes—
58C22×C83C2511yescharacteristic
59C2×D83—224no—
60C2×D83—416no—
61C2×D83—464no—
62C2×D83#127116yesdirect product factor
63C2×D83C22×D4112yes—
64C4×C83C22×D4112yescomplemented
65Dic83C22×D4112yescomplemented
66C2×C83—48no—
67C2×C83C2×#12714yescomplemented
68C2×C83C23×D413yes—
69D83—48no—
70D83C2×#12718yesdirect product factor
71C22×#127—831nomaximal, Sylow
72C83C22×#12711yescharacteristic, complemented, Sylow
73C23×D4—836no—
74C2×#127—836no—
75C2×#127—8316no—
76C2×#127—831no—
77C2×#127D8311yescharacteristic, direct product factor
78C22×C42—831no—
79C25—834no—
80C22×D4—8312no—
81C22×D4—8348no—
82C22×D4—836no—
83C22×D4—16648no—
84C22×D4C2×D8316yescomplemented
85C23×C4—833no—
86#127—8348no—
87#127—838no—
88#127C2×D8318yesdirect product factor
89C2×C42—833no—
90C2×C42—838no—
91C2×C42C2×D8311yescharacteristic, complemented
92C24—831no—
93C24—8316no—
94C24—834no—
95C24—16648no—
96C24C22×D8314yes—
97C2×D4—224no—
98C2×D4—8348no—
99C2×D4—8324no—
100C2×D4—166192no—
101C2×D4—16648no—
102C2×D4—16624no—
103C2×D4C22×D83124yescomplemented
104C22×C4—833no—
105C22×C4—8324no—
106C22×C4—8312no—
107C22×C4C22×D8313yes—
108C42—8312no—
109C42C22×D8314yescomplemented
110C23—224no—
111C23—33264no—
112C23—8312no—
113C23—832no—
114C23—838no—
115C23—16696no—
116C23—16624no—
117C23C23×D8318yes—
118C23C23×D8311yescharacteristic
119D4—248no—
120D4—16696no—
121D4—16648no—
122C2×C4—8312no—
123C2×C4—836no—
124C2×C4—8348no—
125C2×C4D4×D83112yescomplemented
126C2×C4C23×D8316yes—
127C22—224no—
128C22—416no—
129C22—33264no—
130C22—33216no—
131C22—8316no—
132C22—8312no—
133C22—16624no—
134C22C2×D4×D8316yes—
135C22C24×D8311yescharacteristic
136C4—8312no—
137C4C2×D4×D83112yescomplemented
138C2—48no—
139C2—3328no—
140C2—838no—
141C2#127×D8314yesdirect product factor
142C2C22×D4×D8313yes—
subgroupG/H
centerC23C23×D83
commutator, cosocleC22×C83C25
FrattiniC22C24×D83
FittingC2×#127×C83C2
socleC23×C83C24
hypercenterC2×#127D83
hypocenterC83C22×#127
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C22×D4×D83C2semidirect
2. C2×#14581789C2semidirect
3. C2×#14581788C2semidirect
4. #127×D83C2direct (N × H)
5. C2×C42×D83C2semidirect
6. C2×#127×C83C2semidirect
8. C22×D332C22semidirect
9. C22×C22⋊D83C22semidirect
11. C2×D4×D83C22semidirect
13. #14581789C22semidirect
14. #14581788C22semidirect
15. C2×C4×Dic83C22semidirect
16. C42×D83C22semidirect
17. C22×D4×C83C22semidirect
18. #127×C83C22semidirect
19. C2×C42×C83C22semidirect
25. C2×D332C23semidirect
27. C2×C22⋊D83C23semidirect
30. C2×C4×D83D4semidirect
32. C4×Dic83C23semidirect
35. C2×D4×C83C23semidirect
37. C42×C83C23semidirect
48. C2×C4×C83C2×D4semidirect
51. C2×Dic83C2×D4semidirect
54. C4×D83C2×D4semidirect
62. C2×D83#127direct (N × H)
64. C4×C83C22×D4semidirect
65. Dic83C22×D4semidirect
67. C2×C83C2×#127semidirect
70. D83C2×#127direct (N × H)
72. C83C22×#127semidirect
77. C2×#127D83direct (N × H)
84. C22×D4C2×D83semidirect
88. #127C2×D83direct (N × H)
91. C2×C42C2×D83semidirect
103. C2×D4C22×D83semidirect
109. C42C22×D83semidirect
125. C2×C4D4×D83semidirect
137. C4C2×D4×D83semidirect
141. C2#127×D83direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D832
C2×#145817892
C2×#145817882
#127×D832
C2×C42×D832
C2×#127×C832
C22×#12783