Finite Group Databasebeta

← C2×#14521786 #16859825

Subgroups — C2×#14521786 #16859825

Order 3968.

1344 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1344 conjugacy classes of subgroups — too many to draw. Only its 469 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
1#14521786C2116yesmaximal, direct product factor
2C2×#11758453C212yesmaximal, complemented
3C2×#11758512C213yesmaximal, complemented
4C2×#11758516C216yesmaximal, complemented
5C2×#11758514C213yesmaximal, complemented
6C2×C31×#127C211yesmaximal, characteristic, complemented
7C24×D31C2211yescharacteristic
8C22×D4×C31C2213yes—
9C22×D4×C31C2213yescomplemented
10C22×C22⋊D31C2216yes—
11C23×Dic31C2213yescomplemented
12C31×#127C2218yescomplemented
13C2×C42×C31C2211yescharacteristic, complemented
14C2×C22⋊Dic31C2213yes—
15C2×C22⋊Dic31C2213yescomplemented
16#11758516C22148yescomplemented
17#11758514C22124yescomplemented
18#11758512C22124yescomplemented
19C2×(C2×D31)⋊C4C2216yes—
20C2×Dic31⋊C4C2216yescomplemented
21#11758453C22116yescomplemented
22C24×C31C2311yescharacteristic
23C24×C31C2313yes—
24C23×D31—46no—
25C23×D31C2312yes—
26C23×D31C2314yes—
27C2×D4×C31—46no—
28C2×D4×C31—46no—
29C2×D4×C31C23112yes—
30C2×D4×C31C23112yescomplemented
31C22×C4×C31C2313yes—
32C2×C22⋊D31—412no—
33C2×C22⋊D31C23124yes—
34C22×Dic31—46no—
35C22×Dic31C2316yes—
36C22×Dic31C23112yescomplemented
37C42×C31C2314yescomplemented
38C22⋊Dic31C23112yes—
39C22⋊Dic31C23112yescomplemented
40(C2×D31)⋊C4C23124yes—
41Dic31⋊C4C23124yescomplemented
42C23×C31—26no—
43C23×C31—212no—
44C23×C31—26no—
45C23×C31C2412yes—
46C23×C31C2416yes—
47C23×C31C2411yescharacteristic
48C22×D31—212no—
49C22×D31—412no—
50C22×D31—416no—
51C22×D31C2414yes—
52D4×C31—412no—
53D4×C31—412no—
54C2×C4×C31—26no—
55C2×C4×C31C2416yes—
56C22⋊D31—424no—
57C2×Dic31—212no—
58C2×Dic31—412no—
59C2×Dic31C24112yes—
60C2×#560—311nomaximal, Sylow
61C22×C31—26no—
62C22×C31—212no—
63C22×C31—26no—
64C22×C31—44no—
65C22×C31—412no—
66C22×C31H(5,𝔽2)16yes—
67C22×C31C2511yescharacteristic
68C2×D31—212no—
69C2×D31—416no—
70C2×D31—48no—
71C4×C31—26no—
72Dic31—212no—
73#560—3116no—
74C2×#127D3111yescharacteristic, complemented
75C2×#126—312no—
76C2×#123—313no—
77C2×#121—316no—
78C2×#120—313no—
79C2×C31—42no—
80C2×C31—46no—
81C2×C31#56014yescomplemented
82C2×C31C2×H(5,𝔽2)13yes—
83D31—44no—
84C25—311no—
85C22×D4—316no—
86C22×D4C2×D3113yes—
87C22×D4C2×D3113yescomplemented
88C23×C4—313no—
89#127C2×D3118yescomplemented
90#126—3116no—
91#123—3124no—
92#121—3148no—
93#120—3124no—
94C2×C4⋊C4—316no—
95C2×C22⋊C4—313no—
96C2×C22⋊C4—313no—
97C2×C22⋊C4—316no—
98C2×C42C2×D3111yescharacteristic, complemented
99C31C2×#56011yescharacteristic, complemented, Sylow
100C24—312no—
101C24—314no—
102C24—1246no—
103C24C22×D3111yescharacteristic
104C24C22×D3113yes—
105C2×D4—46no—
106C2×D4—46no—
107C2×D4—3124no—
108C2×D4—12412no—
109C2×D4C22×D31112yes—
110C2×D4C22×D31112yescomplemented
111C22×C4—316no—
112C22×C4—3112no—
113C22×C4—1246no—
114C22×C4C22×D3113yes—
115C4⋊C4—3124no—
116C22⋊C4—3112no—
117C22⋊C4—3112no—
118C22⋊C4—3124no—
119C42C22×D3114yescomplemented
120C23—26no—
121C23—212no—
122C23—26no—
123C23—314no—
124C23—6212no—
125C23—12412no—
126C23—12416no—
127C23C23×D3112yes—
128C23C23×D3116yes—
129C23C23×D3111yescharacteristic
130D4—412no—
131D4—412no—
132D4—12424no—
133C2×C4—26no—
134C2×C4—3112no—
135C2×C4—6212no—
136C2×C4—12412no—
137C2×C4C23×D3116yes—
138C22—26no—
139C22—212no—
140C22—26no—
141C22—44no—
142C22—412no—
143C22—6212no—
144C22—12416no—
145C22—1248no—
146C22#1175856116yes—
147C22C24×D3111yescharacteristic
148C4—26no—
149C4—6212no—
150C2—42no—
151C2—46no—
152C2—1244no—
153C2#1452178614yesdirect product factor
154C2C2×#1175856113yes—
subgroupG/H
centerC23C23×D31
commutator, cosocleC22×C31C25
FrattiniC22C24×D31
FittingC2×C31×#127C2
socleC23×C31C24
hypercenterC2×#127D31
hypocenterC31C2×#560
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #14521786C2direct (N × H)
2. C2×#11758453C2semidirect
3. C2×#11758512C2semidirect
4. C2×#11758516C2semidirect
5. C2×#11758514C2semidirect
6. C2×C31×#127C2semidirect
9. C22×D4×C31C22semidirect
11. C23×Dic31C22semidirect
12. C31×#127C22semidirect
13. C2×C42×C31C22semidirect
15. C2×C22⋊Dic31C22semidirect
16. #11758516C22semidirect
17. #11758514C22semidirect
18. #11758512C22semidirect
20. C2×Dic31⋊C4C22semidirect
21. #11758453C22semidirect
30. C2×D4×C31C23semidirect
36. C22×Dic31C23semidirect
37. C42×C31C23semidirect
39. C22⋊Dic31C23semidirect
41. Dic31⋊C4C23semidirect
74. C2×#127D31semidirect
81. C2×C31#560semidirect
87. C22×D4C2×D31semidirect
89. #127C2×D31semidirect
98. C2×C42C2×D31semidirect
99. C31C2×#560semidirect
110. C2×D4C22×D31semidirect
119. C42C22×D31semidirect
153. C2#14521786direct (N × H)

Maximal subgroups

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

subgroupindex
#145217862
C2×#117584532
C2×#117585122
C2×#117585162
C2×#117585142
C2×C31×#1272
C2×#56031