Finite Group Databasebeta

← C2×#19128263 #24920766

Subgroups — C2×#19128263 #24920766

Order 10624.

1984 conjugacy classes of subgroups; only the 565 normal subgroups are shown.

normal subgroups only

This group has 1984 conjugacy classes of subgroups — too many to draw. Only its 565 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
1C23×C22⋊D83C212yesmaximal, complemented
2#19128263C2116yesmaximal, direct product factor
3C2×#14581776C214yesmaximal, complemented
4C2×#14581766C214yesmaximal, complemented
5C2×#14581762C214yesmaximal, complemented
6C22×C22⋊C4×C83C211yesmaximal, characteristic, complemented
7C24×D83C2212yescomplemented
8C22×D332C2214yescomplemented
9C22×C22⋊D83—216no—
10C22×C22⋊D83C2214yes—
11C22×C22⋊D83C2214yescomplemented
12C22×C22⋊D83C22116yescomplemented
13C23×Dic83C2212yescomplemented
14#14581776C22132yescomplemented
15#14581766C22132yescomplemented
16#14581762C22132yescomplemented
17C2×C4⋊Dic83C2214yescomplemented
18C2×(C2×D83)⋊C4C2218yescomplemented
19C25×C83C2211yescharacteristic
20C23×C4×C83C2212yescomplemented
21C2×C22⋊C4×C83C2214yescomplemented
22C2×C22⋊C4×C83C2218yescomplemented
23C23×D83—28no—
24C23×D83—48no—
25C23×D83C2314yes—
26C23×D83C2318yescomplemented
27C2×D332—48no—
28C2×D332C23116yescomplemented
29C2×C22⋊D83—216no—
30C2×C22⋊D83—216no—
31C2×C22⋊D83—264no—
32C2×C22⋊D83C23116yes—
33C2×C22⋊D83C23116yescomplemented
34C22×Dic83—28no—
35C22×Dic83C2314yes—
36C22×Dic83C2318yescomplemented
37C4⋊Dic83C23116yescomplemented
38(C2×D83)⋊C4C23132yescomplemented
39C24×C83—44no—
40C24×C83D418yescomplemented
41C24×C83C2312yes—
42C24×C83C2311yescharacteristic
43C24×C83C2314yes—
44C22×C4×C83—44no—
45C22×C4×C83C2314yes—
46C22×C4×C83C2318yescomplemented
47C22⋊C4×C83C23116yescomplemented
48C23×C83—24no—
49C23×C83—28no—
50C23×C83—416no—
51C23×C83—48no—
52C23×C83C2×D418yes—
53C23×C83C2×D414yes—
54C23×C83C2×D4116yescomplemented
55C23×C83C2414yes—
56C23×C83C2412yes—
57C23×C83C2411yescharacteristic
58C22×D83—28no—
59C22×D83—216no—
60C22×D83—216no—
61C22×D83—416no—
62C22×D83—432no—
63C22×D83C2418yes—
64C2×C4×C83—28no—
65C2×C4×C83—48no—
66C2×C4×C83C2418yes—
67C22⋊D83—232no—
68C22⋊D83—232no—
69C2×Dic83—28no—
70C2×Dic83—216no—
71C2×Dic83C2418yes—
72D332—416no—
73C22×C83—216no—
74C22×C83—28no—
75C22×C83—24no—
76C22×C83—28no—
77C22×C83—416no—
78C22×C83C22×D418yes—
79C22×C83C22×D414yes—
80C22×C83C22×D412yes—
81C22×C83H(5,𝔽2)14yes—
82C22×C83C2511yescharacteristic
83C2×D83—28no—
84C2×D83—216no—
85C2×D83—432no—
86C2×D83—416no—
87C4×C83—28no—
88Dic83—28no—
89C2×C83—28no—
90C2×C83—24no—
91C2×C83#53414yescomplemented
92C2×C83C23×D411yescharacteristic
93C2×C83C2×H(5,𝔽2)12yes—
94D83—48no—
95C2×#534—831nomaximal, Sylow
96C83C2×#53411yescharacteristic, complemented, Sylow
97C23×D4—832no—
98#534—8316no—
99C2×#123—834no—
100C2×#121—834no—
101C2×#120—834no—
102C22×C22⋊C4D8311yescharacteristic, complemented
103C25—832no—
104C25C2×D8311yescharacteristic
105C22×D4—834no—
106C22×D4—834no—
107C22×D4—8316no—
108C22×D4—834no—
109C22×D4—16616no—
110C23×C4—832no—
111C23×C4C2×D8312yescomplemented
112#123—8332no—
113#121—8332no—
114#120—8332no—
115C2×C4⋊C4—834no—
116C2×C22⋊C4—838no—
117C2×C22⋊C4C2×D8314yescomplemented
118C2×C22⋊C4C2×D8318yescomplemented
119C24—44no—
120C24—3328no—
121C24—838no—
122C24—834no—
123C24—1668no—
124C24D33218yescomplemented
125C24C22×D8312yes—
126C24C22×D8311yescharacteristic
127C24C22×D8314yes—
128C2×D4—3328no—
129C2×D4—8316no—
130C2×D4—8316no—
131C2×D4—8316no—
132C2×D4—16616no—
133C2×D4—16616no—
134C2×D4—16664no—
135C22×C4—44no—
136C22×C4—838no—
137C22×C4—834no—
138C22×C4—1668no—
139C22×C4C22×D8314yes—
140C22×C4C22×D8318yescomplemented
141C4⋊C4—8316no—
142C22⋊C4—8332no—
143C22⋊C4C22×D83116yescomplemented
144C23—24no—
145C23—28no—
146C23—416no—
147C23—48no—
148C23—33232no—
149C23—33216no—
150C23—838no—
151C23—16616no—
152C23—1668no—
153C23—16616no—
154C23C2×D33218yes—
155C23C2×D33214yes—
156C23C2×D332116yescomplemented
157C23C23×D8314yes—
158C23C23×D8312yes—
159C23C23×D8311yescharacteristic
160D4—33216no—
161D4—16632no—
162D4—16632no—
163C2×C4—28no—
164C2×C4—48no—
165C2×C4—838no—
166C2×C4—16616no—
167C2×C4—1668no—
168C2×C4C23×D8318yes—
169C22—216no—
170C22—28no—
171C22—24no—
172C22—28no—
173C22—416no—
174C22—33232no—
175C22—33216no—
176C22—1668no—
177C22—16616no—
178C22C22×D33218yes—
179C22C22×D33214yes—
180C22C22×D33212yes—
181C22#1458183714yes—
182C22C24×D8311yescharacteristic
183C4—28no—
184C4—1668no—
185C2—28no—
186C2—24no—
187C2—3328no—
188C2#1912826314yesdirect product factor
189C2C23×D33211yescharacteristic
190C2C2×#1458183712yes—
subgroupG/H
centerC23C23×D83
commutator, cosocleC22×C83C25
FrattiniC22C24×D83
FittingC22×C22⋊C4×C83C2
socleC23×C83C24
hypercenterC22×C22⋊C4D83
hypocenterC83C2×#534
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D83C2semidirect
2. #19128263C2direct (N × H)
3. C2×#14581776C2semidirect
4. C2×#14581766C2semidirect
5. C2×#14581762C2semidirect
6. C22×C22⋊C4×C83C2semidirect
7. C24×D83C22semidirect
8. C22×D332C22semidirect
11. C22×C22⋊D83C22semidirect
12. C22×C22⋊D83C22semidirect
13. C23×Dic83C22semidirect
14. #14581776C22semidirect
15. #14581766C22semidirect
16. #14581762C22semidirect
17. C2×C4⋊Dic83C22semidirect
18. C2×(C2×D83)⋊C4C22semidirect
20. C23×C4×C83C22semidirect
21. C2×C22⋊C4×C83C22semidirect
22. C2×C22⋊C4×C83C22semidirect
26. C23×D83C23semidirect
28. C2×D332C23semidirect
33. C2×C22⋊D83C23semidirect
36. C22×Dic83C23semidirect
37. C4⋊Dic83C23semidirect
38. (C2×D83)⋊C4C23semidirect
40. C24×C83D4semidirect
46. C22×C4×C83C23semidirect
47. C22⋊C4×C83C23semidirect
54. C23×C83C2×D4semidirect
91. C2×C83#534semidirect
96. C83C2×#534semidirect
102. C22×C22⋊C4D83semidirect
111. C23×C4C2×D83semidirect
117. C2×C22⋊C4C2×D83semidirect
118. C2×C22⋊C4C2×D83semidirect
124. C24D332semidirect
140. C22×C4C22×D83semidirect
143. C22⋊C4C22×D83semidirect
156. C23C2×D332semidirect
188. C2#19128263direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D832
#191282632
C2×#145817762
C2×#145817662
C2×#145817622
C22×C22⋊C4×C832
C2×#53483