Finite Group Databasebeta

← C2×#14521792 #16859832

Subgroups — C2×#14521792 #16859832

Order 3968.

1408 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1408 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#14521792C2116yesmaximal, direct product factor
2C2×#11758513C213yesmaximal, complemented
3C2×#11758462C216yesmaximal, complemented
4C2×#11758530C212yesmaximal, complemented
5C2×#11758514C213yesmaximal, complemented
6C2×C31×#120C211yesmaximal, characteristic, complemented
7C25×C31C2211yescharacteristic, complemented
8C24×D31C2211yescharacteristic, complemented
9C22×D4×C31C2213yes—
10C22×C22⋊D31C2216yes—
11C22×Dic62C2213yescomplemented
12C31×#120C2218yescomplemented
13C2×C22⋊C4×C31C2213yescomplemented
14#11758530C22116yescomplemented
15C2×C22⋊Dic31C2213yescomplemented
16C2×C22⋊Dic31C2216yescomplemented
17#11758514C22124yescomplemented
18#11758513C22124yescomplemented
19C2×(C2×D31)⋊C4C2216yescomplemented
20C2×C4×Dic31C2213yescomplemented
21#11758462C22148yescomplemented
22C24×C31—46no—
23C24×C31C2311yescharacteristic
24C24×C31C2313yes—
25C24×C31C2314yescomplemented
26C23×D31—46no—
27C23×D31C2312yes—
28C23×D31C2314yescomplemented
29C2×D4×C31—46no—
30C2×D4×C31C23112yes—
31C22×C4×C31C2313yes—
32C2×C22⋊D31—412no—
33C2×C22⋊D31C23124yes—
34C22×Dic31C2316yes—
35C2×Dic62—46no—
36C2×Dic62C23112yescomplemented
37C22⋊C4×C31C23112yescomplemented
38C22⋊Dic31C23124yescomplemented
39C22⋊Dic31C23112yescomplemented
40(C2×D31)⋊C4C23124yescomplemented
41C4×Dic31C23112yescomplemented
42C23×C31—212no—
43C23×C31—26no—
44C23×C31—26no—
45C23×C31—412no—
46C23×C31—416no—
47C23×C31C2412yes—
48C23×C31C2416yes—
49C23×C31C2411yescharacteristic
50C22×D31—212no—
51C22×D31—412no—
52C22×D31—416no—
53C22×D31C2414yes—
54D4×C31—412no—
55C2×C4×C31—26no—
56C2×C4×C31C2416yes—
57C22⋊D31—424no—
58C2×Dic31—212no—
59C2×Dic31C24112yes—
60Dic62—412no—
61C2×H(3,𝔽4)—311nomaximal, Sylow
62C22×C31—212no—
63C22×C31—26no—
64C22×C31—26no—
65C22×C31—416no—
66C22×C31—44no—
67C22×C31—412no—
68C22×C31H(5,𝔽2)16yes—
69C22×C31C2511yescharacteristic
70C2×D31—212no—
71C2×D31—416no—
72C2×D31—48no—
73C4×C31—26no—
74Dic31—212no—
75H(3,𝔽4)—3116no—
76C2×#124—313no—
77C2×#124—316no—
78C2×#120—312no—
79C2×#120—313no—
80C2×#120D3111yescharacteristic, complemented
81C2×C31—42no—
82C2×C31—46no—
83C2×C31H(3,𝔽4)14yescomplemented
84C2×C31C2×H(5,𝔽2)13yes—
85D31—44no—
86C25—311no—
87C25C2×D3111yescharacteristic, complemented
88C22×Q8—313no—
89C22×D4—316no—
90C22×D4C2×D3113yes—
91#124—3124no—
92#124—3148no—
93#120—3116no—
94#120—3124no—
95#120C2×D3118yescomplemented
96C2×C22⋊C4—313no—
97C2×C22⋊C4—316no—
98C2×C22⋊C4—316no—
99C2×C22⋊C4C2×D3113yescomplemented
100C2×C42—313no—
101C31C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
102C24—46no—
103C24—312no—
104C24—314no—
105C24—1246no—
106C24C22×D3111yescharacteristic
107C24C22×D3113yes—
108C24C22×D3114yescomplemented
109C2×Q8—3112no—
110C2×Q8—1246no—
111C2×D4—46no—
112C2×D4—3124no—
113C2×D4—12412no—
114C2×D4C22×D31112yes—
115C22×C4—316no—
116C22×C4C22×D3113yes—
117C22⋊C4—3112no—
118C22⋊C4—3124no—
119C22⋊C4—3124no—
120C22⋊C4C22×D31112yescomplemented
121C42—3112no—
122C23—26no—
123C23—26no—
124C23—212no—
125C23—412no—
126C23—416no—
127C23—314no—
128C23—6212no—
129C23—12412no—
130C23—12416no—
131C23C23×D3112yes—
132C23C23×D3116yes—
133C23C23×D3111yescharacteristic
134Q8—12412no—
135D4—412no—
136D4—12424no—
137C2×C4—26no—
138C2×C4—3112no—
139C2×C4—6212no—
140C2×C4C23×D3116yes—
141C22—26no—
142C22—26no—
143C22—212no—
144C22—416no—
145C22—412no—
146C22—44no—
147C22—6212no—
148C22—12416no—
149C22—1248no—
150C22#1175856116yes—
151C22C24×D3111yescharacteristic
152C4—26no—
153C4—6212no—
154C2—46no—
155C2—42no—
156C2—1244no—
157C2#1452179214yesdirect product factor
158C2C2×#1175856113yes—
subgroupG/H
centerC23C23×D31
commutator, cosocleC22×C31C25
FrattiniC22C24×D31
FittingC2×C31×#120C2
socleC23×C31C24
hypercenterC2×#120D31
hypocenterC31C2×H(3,𝔽4)
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #14521792C2direct (N × H)
2. C2×#11758513C2semidirect
3. C2×#11758462C2semidirect
4. C2×#11758530C2semidirect
5. C2×#11758514C2semidirect
6. C2×C31×#120C2semidirect
7. C25×C31C22semidirect
8. C24×D31C22semidirect
11. C22×Dic62C22semidirect
12. C31×#120C22semidirect
13. C2×C22⋊C4×C31C22semidirect
14. #11758530C22semidirect
15. C2×C22⋊Dic31C22semidirect
16. C2×C22⋊Dic31C22semidirect
17. #11758514C22semidirect
18. #11758513C22semidirect
19. C2×(C2×D31)⋊C4C22semidirect
20. C2×C4×Dic31C22semidirect
21. #11758462C22semidirect
25. C24×C31C23semidirect
28. C23×D31C23semidirect
36. C2×Dic62C23semidirect
37. C22⋊C4×C31C23semidirect
38. C22⋊Dic31C23semidirect
39. C22⋊Dic31C23semidirect
40. (C2×D31)⋊C4C23semidirect
41. C4×Dic31C23semidirect
80. C2×#120D31semidirect
83. C2×C31H(3,𝔽4)semidirect
87. C25C2×D31semidirect
95. #120C2×D31semidirect
99. C2×C22⋊C4C2×D31semidirect
101. C31C2×H(3,𝔽4)semidirect
108. C24C22×D31semidirect
120. C22⋊C4C22×D31semidirect
157. C2#14521792direct (N × H)

Maximal subgroups

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

subgroupindex
#145217922
C2×#117585132
C2×#117584622
C2×#117585302
C2×#117585142
C2×C31×#1202
C2×H(3,𝔽4)31