Finite Group Databasebeta

← C2×#19128336 #24920902

Subgroups — C2×#19128336 #24920902

Order 10624.

2536 conjugacy classes of subgroups; only the 581 normal subgroups are shown.

normal subgroups only

This group has 2536 conjugacy classes of subgroups — too many to draw. Only its 581 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×D83C214yesmaximal, complemented
2#19128336C2116yesmaximal, direct product factor
3C2×#14581763C214yesmaximal, complemented
4C2×#14581760C214yesmaximal, complemented
5C2×C4×D332C212yesmaximal, complemented
6C2×#127×C83C211yesmaximal, characteristic, complemented
7C24×D83C2214yescomplemented
8C22×D332C2212yes—
9C22×C22⋊D83C2218yescomplemented
10C2×D4×D83—232no—
11C2×D4×D83C22132yescomplemented
12C22×C4×D83C2214yescomplemented
13#14581763C22132yescomplemented
14#14581760C22132yescomplemented
15C4×D332C22116yescomplemented
16C2×C4⋊Dic83C2212yescomplemented
17C2×C22⋊Dic83C2214yescomplemented
18C2×(C2×D83)⋊C4C2214yescomplemented
19C22×D4×C83C2214yescomplemented
20C22×D4×C83C2212yescomplemented
21#127×C83C2218yescomplemented
22C2×C42×C83C2211yescharacteristic, complemented
23C23×D83—232no—
24C23×D83—48no—
25C23×D83C2314yes—
26C23×D83C23116yescomplemented
27C2×D332D4116yescomplemented
28C2×D332C2318yes—
29C2×C22⋊D83—232no—
30C2×C22⋊D83C23132yescomplemented
31D4×D83—2128no—
32C22×Dic83C2314yes—
33C2×C4×D83—216no—
34C2×C4×D83C23116yescomplemented
35C4⋊Dic83C2318yescomplemented
36C22⋊Dic83C23116yescomplemented
37(C2×D83)⋊C4C23116yescomplemented
38C24×C83C2314yes—
39C2×D4×C83—216no—
40C2×D4×C83—44no—
41C2×D4×C83C23116yescomplemented
42C2×D4×C83C2318yescomplemented
43C22×C4×C83C2311yescharacteristic
44C22×C4×C83C2312yes—
45C42×C83C2314yescomplemented
46C23×C83—216no—
47C23×C83—28no—
48C23×C83C2418yes—
49C23×C83C2411yescharacteristic
50C22×D83—28no—
51C22×D83—28no—
52C22×D83—264no—
53C22×D83—416no—
54C22×D83—464no—
55C22×D83C2×D4116yescomplemented
56C22×D83C2418yes—
57D4×C83—232no—
58D4×C83—48no—
59C2×C4×C83—22no—
60C2×C4×C83C2×D418yescomplemented
61C2×C4×C83C2412yes—
62C2×C4×C83C2414yes—
63C22⋊D83—264no—
64C2×Dic83—28no—
65C2×Dic83C2418yes—
66D332C2×D4132yescomplemented
67C4×D83—232no—
68C22×C83—216no—
69C22×C83—28no—
70C22×C83—416no—
71C22×C83C22×D414yes—
72C22×C83H(5,𝔽2)12yes—
73C22×C83C2511yescharacteristic
74C2×D83—232no—
75C2×D83—28no—
76C2×D83—28no—
77C2×D83—464no—
78C2×D83C22×D4116yescomplemented
79C4×C83—22no—
80C4×C83C22×D418yescomplemented
81Dic83—28no—
82C2×C83—48no—
83C2×C83D4214yescomplemented
84C2×C83C23×D412yes—
85C2×C83C2×H(5,𝔽2)11yescharacteristic
86D83—216no—
87C2×D42—831nomaximal, Sylow
88C83C2×D4211yescharacteristic, complemented, Sylow
89C23×D4—834no—
90D42—8316no—
91C2×#127D8311yescharacteristic, complemented
92C2×#121—834no—
93C2×#120—834no—
94C2×C4×D4—832no—
95C25—834no—
96C22×D4—838no—
97C22×D4—8332no—
98C22×D4—832no—
99C22×D4—16632no—
100C22×D4C2×D8314yescomplemented
101C22×D4C2×D8312yescomplemented
102C23×C4—834no—
103#127C2×D8318yescomplemented
104#121—8332no—
105#120—8332no—
106C4×D4—8316no—
107C2×C4⋊C4—832no—
108C2×C22⋊C4—834no—
109C2×C22⋊C4—834no—
110C2×C42C2×D8311yescharacteristic, complemented
111C24—3328no—
112C24—8316no—
113C24—834no—
114C24—16632no—
115C24C22×D8314yes—
116C2×D4—216no—
117C2×D4—44no—
118C2×D4—8332no—
119C2×D4—8316no—
120C2×D4—838no—
121C2×D4—166128no—
122C2×D4—16632no—
123C2×D4C22×D83116yescomplemented
124C2×D4C22×D8318yescomplemented
125C22×C4—834no—
126C22×C4—8316no—
127C22×C4—16616no—
128C22×C4C22×D8311yescharacteristic
129C22×C4C22×D8312yes—
130C4⋊C4—838no—
131C22⋊C4—8316no—
132C22⋊C4—8316no—
133C42C22×D8314yescomplemented
134C23—216no—
135C23—28no—
136C23—33216no—
137C23—33264no—
138C23—8316no—
139C23—838no—
140C23—16664no—
141C23—1668no—
142C23—1668no—
143C23C23×D8318yes—
144C23C23×D8311yescharacteristic
145D4—232no—
146D4—48no—
147D4—8332no—
148D4—16664no—
149C2×C4—22no—
150C2×C4—838no—
151C2×C4—1668no—
152C2×C4—16632no—
153C2×C4D4×D8318yescomplemented
154C2×C4C23×D8312yes—
155C2×C4C23×D8314yes—
156C22—216no—
157C22—28no—
158C22—416no—
159C22—33264no—
160C22—8316no—
161C22—16632no—
162C22—1668no—
163C22—1668no—
164C22C2×D4×D8314yes—
165C22#1458183712yes—
166C22C24×D8311yescharacteristic
167C4—22no—
168C4—1668no—
169C4C2×D4×D8318yescomplemented
170C2—48no—
171C2—16616no—
172C2#1912833614yesdirect product factor
173C2C22×D4×D8312yes—
174C2C2×#1458183711yescharacteristic
subgroupG/H
centerC23C23×D83
commutator, cosocleC22×C83C25
FrattiniC22C24×D83
FittingC2×#127×C83C2
socleC23×C83C24
hypercenterC2×#127D83
hypocenterC83C2×D42
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. #19128336C2direct (N × H)
3. C2×#14581763C2semidirect
4. C2×#14581760C2semidirect
5. C2×C4×D332C2semidirect
6. C2×#127×C83C2semidirect
7. C24×D83C22semidirect
9. C22×C22⋊D83C22semidirect
11. C2×D4×D83C22semidirect
12. C22×C4×D83C22semidirect
13. #14581763C22semidirect
14. #14581760C22semidirect
15. C4×D332C22semidirect
16. C2×C4⋊Dic83C22semidirect
17. C2×C22⋊Dic83C22semidirect
18. C2×(C2×D83)⋊C4C22semidirect
19. C22×D4×C83C22semidirect
20. C22×D4×C83C22semidirect
21. #127×C83C22semidirect
22. C2×C42×C83C22semidirect
26. C23×D83C23semidirect
27. C2×D332D4semidirect
30. C2×C22⋊D83C23semidirect
34. C2×C4×D83C23semidirect
35. C4⋊Dic83C23semidirect
36. C22⋊Dic83C23semidirect
37. (C2×D83)⋊C4C23semidirect
41. C2×D4×C83C23semidirect
42. C2×D4×C83C23semidirect
45. C42×C83C23semidirect
55. C22×D83C2×D4semidirect
60. C2×C4×C83C2×D4semidirect
66. D332C2×D4semidirect
78. C2×D83C22×D4semidirect
80. C4×C83C22×D4semidirect
83. C2×C83D42semidirect
88. C83C2×D42semidirect
91. C2×#127D83semidirect
100. C22×D4C2×D83semidirect
101. C22×D4C2×D83semidirect
103. #127C2×D83semidirect
110. C2×C42C2×D83semidirect
123. C2×D4C22×D83semidirect
124. C2×D4C22×D83semidirect
133. C42C22×D83semidirect
153. C2×C4D4×D83semidirect
169. C4C2×D4×D83semidirect
172. C2#19128336direct (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
#191283362
C2×#145817632
C2×#145817602
C2×C4×D3322
C2×#127×C832
C2×D4283