Finite Group Databasebeta

← C2×#14521239 #16855099

Subgroups — C2×#14521239 #16855099

Order 3968.

794 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 794 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C2×#11758512C213yesmaximal, complemented
2#14521239C218yesmaximal, direct product factor
3C2×#11758422C213yesmaximal, complemented
4C2×C31×H(5,𝔽2)C211yesmaximal, characteristic
5C31×H(5,𝔽2)—26no—
6C31×H(5,𝔽2)C2214yes—
7C2×#41×C31—23no—
8C22×D4×C31—23no—
9C22×D4×C31C2213yes—
10C23×Dic31C2211yescharacteristic, complemented
11C2×C22⋊Dic31—23no—
12C2×C22⋊Dic31C2213yescomplemented
13#11758512—26no—
14#11758512C22112yescomplemented
15C2×Dic31⋊C4—23no—
16#11758422C22112yescomplemented
17C24×C31—21no—
18C24×C31D413yes—
19C24×C31C2311yescharacteristic
20#41×C31—212no—
21#41×C31—212no—
22C2×Q8×C31—21no—
23C2×D4×C31—23no—
24C2×D4×C31—212no—
25C2×D4×C31—26no—
26C2×D4×C31—212no—
27C2×D4×C31—26no—
28C2×D4×C31D416yes—
29C2×D4×C31C2316yes—
30C22×C4×C31—23no—
31C22×C4×C31D413yes—
32C22×Dic31—23no—
33C22×Dic31—23no—
34C22×Dic31—23no—
35C22×Dic31C2312yescomplemented
36C22⋊Dic31—23no—
37C22⋊Dic31—212no—
38C22⋊Dic31C2316yescomplemented
39Dic31⋊C4—212no—
40C23×C31—24no—
41C23×C31—23no—
42C23×C31—23no—
43C23×C31—42no—
44C23×C31—46no—
45C23×C31—82no—
46C23×C31C2×D413yes—
47C23×C31C2×D416yes—
48C23×C31C2×D413yes—
49C23×C31C2411yescharacteristic
50Q8×C31—24no—
51D4×C31—212no—
52D4×C31—212no—
53D4×C31—212no—
54C2×C4×C31—212no—
55C2×C4×C31—23no—
56C2×C4×C31—23no—
57C2×C4×C31C2×D416yes—
58C2×Dic31—26no—
59C2×Dic31—26no—
60C2×Dic31—46no—
61C2×Dic31—43no—
62C2×Dic31—41no—
63C2×#458—311nomaximal, Sylow
64C22×C31—26no—
65C22×C31—26no—
66C22×C31—43no—
67C22×C31—41no—
68C22×C31—46no—
69C22×C31—46no—
70C22×C31—83no—
71C22×C31—84no—
72C22×C31#12013yes—
73C22×C31#12011yescharacteristic
74C22×C31C22×D413yes—
75C4×C31—26no—
76Dic31—46no—
77Dic31—42no—
78C2×H(5,𝔽2)D3111yescharacteristic
79C2×#123—313no—
80#458—318no—
81C2×#99—313no—
82C2×C31—23no—
83C2×C31—23no—
84C2×C31—46no—
85C2×C31#45812yescomplemented
86C2×C31C2×#12011yescharacteristic
87H(5,𝔽2)—26no—
88H(5,𝔽2)C2×D3114yes—
89C2×#41—23no—
90C22×D4—23no—
91C22×D4C2×D3113yes—
92C23×C4—311no—
93#123—3112no—
94#123—626no—
95C2×C4⋊C4—623no—
96C2×C22⋊C4—313no—
97C2×C22⋊C4—623no—
98#99—3112no—
99C31C2×#45811yescharacteristic, complemented, Sylow
100C24—21no—
101C24C22⋊D3113yes—
102C24C22×D3111yescharacteristic
103#41—212no—
104#41—212no—
105C2×Q8—21no—
106C2×D4—23no—
107C2×D4—212no—
108C2×D4—26no—
109C2×D4—212no—
110C2×D4—26no—
111C2×D4C22⋊D3116yes—
112C2×D4C22×D3116yes—
113C22×C4—23no—
114C22×C4—312no—
115C22×C4—623no—
116C22×C4—623no—
117C22×C4—623no—
118C22×C4C22⋊D3113yes—
119C4⋊C4—6212no—
120C22⋊C4—316no—
121C22⋊C4—623no—
122C22⋊C4—6212no—
123C23—24no—
124C23—23no—
125C23—23no—
126C23—42no—
127C23—46no—
128C23—82no—
129C23C2×C22⋊D3113yes—
130C23C2×C22⋊D3116yes—
131C23C2×C22⋊D3113yes—
132C23C23×D3111yescharacteristic
133Q8—24no—
134D4—212no—
135D4—212no—
136D4—212no—
137C2×C4—212no—
138C2×C4—23no—
139C2×C4—23no—
140C2×C4—626no—
141C2×C4—626no—
142C2×C4—1246no—
143C2×C4—1243no—
144C2×C4—1241no—
145C2×C4C2×C22⋊D3116yes—
146C22—26no—
147C22—26no—
148C22—43no—
149C22—41no—
150C22—46no—
151C22—46no—
152C22—83no—
153C22—84no—
154C22#1175853013yes—
155C22#1175853011yescharacteristic
156C22C22×C22⋊D3113yes—
157C4—26no—
158C4—1246no—
159C4—1242no—
160C2—23no—
161C2—23no—
162C2—46no—
163C2#1452123912yesdirect product factor
164C2C2×#1175853011yescharacteristic
subgroupG/H
centerC22#11758530
commutator, cosocleC23×C31C24
FrattiniC23C23×D31
Fitting, prime radicalC2×C31×H(5,𝔽2)C2
socleC22×C31#120
hypercenterC2×H(5,𝔽2)D31
hypocenterC31C2×#458
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C24 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C2×#11758512C2semidirect
2. #14521239C2direct (N × H)
3. C2×#11758422C2semidirect
10. C23×Dic31C22semidirect
12. C2×C22⋊Dic31C22semidirect
14. #11758512C22semidirect
16. #11758422C22semidirect
35. C22×Dic31C23semidirect
38. C22⋊Dic31C23semidirect
85. C2×C31#458semidirect
99. C31C2×#458semidirect
163. C2#14521239direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117585122
#145212392
C2×#117584222
C2×C31×H(5,𝔽2)2
C2×#45831