Finite Group Databasebeta

← C2×#14521611 #16859014

Subgroups — C2×#14521611 #16859014

Order 3968.

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⋊D31C212yesmaximal, complemented
2#14521611C2116yesmaximal, direct product factor
3C2×#11758463C214yesmaximal, complemented
4C2×#11758507C214yesmaximal, complemented
5C2×#11758459C214yesmaximal, complemented
6C22×C22⋊C4×C31C211yesmaximal, characteristic, complemented
7C25×C31C2211yescharacteristic
8C24×D31C2212yescomplemented
9C23×C4×C31C2212yescomplemented
10C22×C22⋊D31—216no—
11C22×C22⋊D31C2214yes—
12C22×C22⋊D31C2214yescomplemented
13C22×C22⋊D31C22116yescomplemented
14C23×Dic31C2212yescomplemented
15C22×D124C2214yescomplemented
16C2×C22⋊C4×C31C2214yescomplemented
17C2×C22⋊C4×C31C2218yescomplemented
18#11758507C22132yescomplemented
19C2×(C2×D31)⋊C4C2218yescomplemented
20C2×C4⋊Dic31C2214yescomplemented
21#11758463C22132yescomplemented
22#11758459C22132yescomplemented
23C24×C31—44no—
24C24×C31D418yescomplemented
25C24×C31C2312yes—
26C24×C31C2311yescharacteristic
27C24×C31C2314yes—
28C23×D31—28no—
29C23×D31—48no—
30C23×D31C2314yes—
31C23×D31C2318yescomplemented
32C22×C4×C31—44no—
33C22×C4×C31C2314yes—
34C22×C4×C31C2318yescomplemented
35C2×C22⋊D31—216no—
36C2×C22⋊D31—216no—
37C2×C22⋊D31—264no—
38C2×C22⋊D31C23116yes—
39C2×C22⋊D31C23116yescomplemented
40C22×Dic31—28no—
41C22×Dic31C2314yes—
42C22×Dic31C2318yescomplemented
43C2×D124—48no—
44C2×D124C23116yescomplemented
45C22⋊C4×C31C23116yescomplemented
46(C2×D31)⋊C4C23132yescomplemented
47C4⋊Dic31C23116yescomplemented
48C23×C31—24no—
49C23×C31—28no—
50C23×C31—416no—
51C23×C31—48no—
52C23×C31C2×D418yes—
53C23×C31C2×D414yes—
54C23×C31C2×D4116yescomplemented
55C23×C31C2414yes—
56C23×C31C2412yes—
57C23×C31C2411yescharacteristic
58C22×D31—28no—
59C22×D31—216no—
60C22×D31—216no—
61C22×D31—416no—
62C22×D31—432no—
63C22×D31C2418yes—
64C2×C4×C31—28no—
65C2×C4×C31—48no—
66C2×C4×C31C2418yes—
67C22⋊D31—232no—
68C22⋊D31—232no—
69C2×Dic31—28no—
70C2×Dic31—216no—
71C2×Dic31C2418yes—
72D124—416no—
73C2×#534—311nomaximal, Sylow
74C22×C31—216no—
75C22×C31—28no—
76C22×C31—24no—
77C22×C31—28no—
78C22×C31—416no—
79C22×C31C22×D418yes—
80C22×C31C22×D414yes—
81C22×C31C22×D412yes—
82C22×C31H(5,𝔽2)14yes—
83C22×C31C2511yescharacteristic
84C2×D31—28no—
85C2×D31—216no—
86C2×D31—432no—
87C2×D31—416no—
88C4×C31—28no—
89Dic31—28no—
90C23×D4—312no—
91#534—3116no—
92C2×#123—314no—
93C2×#121—314no—
94C2×#120—314no—
95C22×C22⋊C4D3111yescharacteristic, complemented
96C2×C31—28no—
97C2×C31—24no—
98C2×C31#53414yescomplemented
99C2×C31C23×D411yescharacteristic
100C2×C31C2×H(5,𝔽2)12yes—
101D31—48no—
102C25—312no—
103C25C2×D3111yescharacteristic
104C22×D4—314no—
105C22×D4—314no—
106C22×D4—3116no—
107C22×D4—314no—
108C22×D4—6216no—
109C23×C4—312no—
110C23×C4C2×D3112yescomplemented
111#123—3132no—
112#121—3132no—
113#120—3132no—
114C2×C4⋊C4—314no—
115C2×C22⋊C4—318no—
116C2×C22⋊C4C2×D3114yescomplemented
117C2×C22⋊C4C2×D3118yescomplemented
118C31C2×#53411yescharacteristic, complemented, Sylow
119C24—44no—
120C24—314no—
121C24—318no—
122C24—628no—
123C24—1248no—
124C24D12418yescomplemented
125C24C22×D3112yes—
126C24C22×D3111yescharacteristic
127C24C22×D3114yes—
128C2×D4—3116no—
129C2×D4—3116no—
130C2×D4—3116no—
131C2×D4—6216no—
132C2×D4—6216no—
133C2×D4—6264no—
134C2×D4—1248no—
135C22×C4—44no—
136C22×C4—318no—
137C22×C4—314no—
138C22×C4—628no—
139C22×C4C22×D3114yes—
140C22×C4C22×D3118yescomplemented
141C4⋊C4—3116no—
142C22⋊C4—3132no—
143C22⋊C4C22×D31116yescomplemented
144C23—24no—
145C23—28no—
146C23—416no—
147C23—48no—
148C23—318no—
149C23—6216no—
150C23—628no—
151C23—6216no—
152C23—12416no—
153C23—12432no—
154C23C2×D12418yes—
155C23C2×D12414yes—
156C23C2×D124116yescomplemented
157C23C23×D3114yes—
158C23C23×D3112yes—
159C23C23×D3111yescharacteristic
160D4—6232no—
161D4—6232no—
162D4—12416no—
163C2×C4—28no—
164C2×C4—48no—
165C2×C4—318no—
166C2×C4—6216no—
167C2×C4—628no—
168C2×C4C23×D3118yes—
169C22—216no—
170C22—28no—
171C22—24no—
172C22—28no—
173C22—416no—
174C22—628no—
175C22—6216no—
176C22—12432no—
177C22—12416no—
178C22C22×D12418yes—
179C22C22×D12414yes—
180C22C22×D12412yes—
181C22#1175856114yes—
182C22C24×D3111yescharacteristic
183C4—28no—
184C4—628no—
185C2—28no—
186C2—24no—
187C2—1248no—
188C2#1452161114yesdirect product factor
189C2C23×D12411yescharacteristic
190C2C2×#1175856112yes—
subgroupG/H
centerC23C23×D31
commutator, cosocleC22×C31C25
FrattiniC22C24×D31
FittingC22×C22⋊C4×C31C2
socleC23×C31C24
hypercenterC22×C22⋊C4D31
hypocenterC31C2×#534
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D31C2semidirect
2. #14521611C2direct (N × H)
3. C2×#11758463C2semidirect
4. C2×#11758507C2semidirect
5. C2×#11758459C2semidirect
6. C22×C22⋊C4×C31C2semidirect
8. C24×D31C22semidirect
9. C23×C4×C31C22semidirect
12. C22×C22⋊D31C22semidirect
13. C22×C22⋊D31C22semidirect
14. C23×Dic31C22semidirect
15. C22×D124C22semidirect
16. C2×C22⋊C4×C31C22semidirect
17. C2×C22⋊C4×C31C22semidirect
18. #11758507C22semidirect
19. C2×(C2×D31)⋊C4C22semidirect
20. C2×C4⋊Dic31C22semidirect
21. #11758463C22semidirect
22. #11758459C22semidirect
24. C24×C31D4semidirect
31. C23×D31C23semidirect
34. C22×C4×C31C23semidirect
39. C2×C22⋊D31C23semidirect
42. C22×Dic31C23semidirect
44. C2×D124C23semidirect
45. C22⋊C4×C31C23semidirect
46. (C2×D31)⋊C4C23semidirect
47. C4⋊Dic31C23semidirect
54. C23×C31C2×D4semidirect
95. C22×C22⋊C4D31semidirect
98. C2×C31#534semidirect
110. C23×C4C2×D31semidirect
116. C2×C22⋊C4C2×D31semidirect
117. C2×C22⋊C4C2×D31semidirect
118. C31C2×#534semidirect
124. C24D124semidirect
140. C22×C4C22×D31semidirect
143. C22⋊C4C22×D31semidirect
156. C23C2×D124semidirect
188. C2#14521611direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D312
#145216112
C2×#117584632
C2×#117585072
C2×#117584592
C22×C22⋊C4×C312
C2×#53431