Finite Group Databasebeta

← C2×#14521854 #16860464

Subgroups — C2×#14521854 #16860464

Order 3968.

1512 conjugacy classes of subgroups; only the 549 normal subgroups are shown.

normal subgroups only

This group has 1512 conjugacy classes of subgroups — too many to draw. Only its 549 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×#11758566C212yesmaximal, complemented
2#14521854C2116yesmaximal, direct product factor
3C2×#11758485C216yesmaximal, complemented
4C2×#11758481C213yesmaximal, complemented
5C22×D248C213yesmaximal, complemented
6C2×C31×#131C211yesmaximal, characteristic, complemented
7C2×#41×C31C2211yescharacteristic
8#11758566—28no—
9#11758566C22116yescomplemented
10C2×#92499—22no—
11C2×D4×D31—26no—
12C2×#92495C2216yescomplemented
13C22×D124C2216yescomplemented
14C31×#131C2218yescomplemented
15C2×M16×C31C2213yescomplemented
16C22×C8×C31C2213yescomplemented
17#11758485C22148yescomplemented
18C2×Dic124C2211yescharacteristic, complemented
19#11758481C22124yescomplemented
20C2×D248C2213yescomplemented
21C2×D248C2216yescomplemented
22C2×D248C22124yescomplemented
23C2×#92470C2216yescomplemented
24C23×D31—26no—
25#41×C31D414yes—
26#41×C31C2314yes—
27C2×Q8×C31D411yescharacteristic
28C2×D4×C31D413yes—
29C22×C4×C31C2313yes—
30C2×C22⋊D31—26no—
31#92499—216no—
32D4×D31—248no—
33#92495—212no—
34#92495C23124yescomplemented
35C2×D124—26no—
36C2×D124—212no—
37C2×D124C2316yes—
38C2×D124C23124yescomplemented
39C2×C4×D31—26no—
40C2×Dic62C2312yes—
41M16×C31C23112yescomplemented
42C2×C8×C31C2313yes—
43C2×C8×C31C2311yescharacteristic
44C2×C8×C31C23112yescomplemented
45Dic124C2314yescomplemented
46D248C23112yescomplemented
47D248C23124yescomplemented
48#92470C23124yescomplemented
49C23×C31C2×D413yes—
50C22×D31—26no—
51C22×D31—224no—
52C22×D31—812no—
53Q8×C31C2×D414yes—
54D4×C31C2×D4112yes—
55C2×C4×C31C2×D413yes—
56C2×C4×C31C2×D416yes—
57C2×C4×C31C2411yescharacteristic
58C2×C4×C31C2416yes—
59C22⋊D31—224no—
60C2×Dic31—22no—
61D124—26no—
62D124—224no—
63D124C24112yes—
64C4×D31—224no—
65Dic62—22no—
66Dic62C2414yes—
67C8×C31C2416yes—
68C8×C31C2412yes—
69C2×#576—311nomaximal, Sylow
70C22×C31—26no—
71C22×C31C22×D416yes—
72C22×C31C22×D411yescharacteristic
73C2×D31—212no—
74C2×D31—412no—
75C2×D31—824no—
76C4×C31C22×D411yescharacteristic
77C4×C31C22×D416yes—
78C4×C31C2511yescharacteristic
79Dic31—24no—
80C2×H(5,𝔽2)—312no—
81#576—3116no—
82C2×AGL(1,ℤ/8)—316no—
83C2×#135—313no—
84C22×D8—313no—
85C2×#131D3111yescharacteristic, complemented
86C2×C31—26no—
87C2×C31#57612yescomplemented
88C2×C31C23×D411yescharacteristic
89D31—412no—
90H(5,𝔽2)—3116no—
91H(5,𝔽2)—628no—
92C2×#41—316no—
93C2×#41—622no—
94C2×#41C2×D3111yescharacteristic
95C22×D4—316no—
96C22×D4—626no—
97AGL(1,ℤ/8)—3148no—
98#135—3124no—
99C2×Q16—311no—
100C2×SD16—316no—
101C2×D8—313no—
102C2×D8—316no—
103C2×D8—3124no—
104#131C2×D3118yescomplemented
105C2×M16C2×D3113yescomplemented
106C22×C8C2×D3113yescomplemented
107C31C2×#57611yescharacteristic, complemented, Sylow
108C24—626no—
109#41—3124no—
110#41—6216no—
111#41—6212no—
112#41D12414yes—
113#41C22×D3114yes—
114C2×Q8—312no—
115C2×Q8D12411yescharacteristic
116C2×D4—316no—
117C2×D4—3124no—
118C2×D4—626no—
119C2×D4—6248no—
120C2×D4—626no—
121C2×D4—6212no—
122C2×D4D12413yes—
123C22×C4—626no—
124C22×C4C22×D3113yes—
125Q16—314no—
126SD16—3124no—
127D8—3112no—
128D8—3124no—
129M16C22×D31112yescomplemented
130C2×C8C22×D3111yescharacteristic
131C2×C8C22×D3113yes—
132C2×C8C22×D31112yescomplemented
133C23—626no—
134C23—6224no—
135C23—24812no—
136C23C2×D12413yes—
137Q8—314no—
138Q8—622no—
139Q8C2×D12414yes—
140D4—3112no—
141D4—6224no—
142D4—6224no—
143D4—626no—
144D4C2×D124112yes—
145C2×C4—622no—
146C2×C4—6224no—
147C2×C4C2×D12416yes—
148C2×C4C2×D12413yes—
149C2×C4C23×D3116yes—
150C2×C4C23×D3111yescharacteristic
151C8C23×D3112yes—
152C8C23×D3116yes—
153C22—26no—
154C22—6212no—
155C22—12412no—
156C22—24824no—
157C22C22×D12416yes—
158C22C22×D12411yescharacteristic
159C4—624no—
160C4C22×D12416yes—
161C4C22×D12411yescharacteristic
162C4C24×D3111yescharacteristic
163C2—26no—
164C2—12412no—
165C2#1452185412yesdirect product factor
166C2C23×D12411yescharacteristic
subgroupG/H
centerC22C22×D124
commutator, cosocleC4×C31C25
FrattiniC4C24×D31
FittingC2×C31×#131C2
socleC22×C31C22×D4
hypercenterC2×#131D31
hypocenterC31C2×#576
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. C2×#11758566C2semidirect
2. #14521854C2direct (N × H)
3. C2×#11758485C2semidirect
4. C2×#11758481C2semidirect
5. C22×D248C2semidirect
6. C2×C31×#131C2semidirect
9. #11758566C22semidirect
12. C2×#92495C22semidirect
13. C22×D124C22semidirect
14. C31×#131C22semidirect
15. C2×M16×C31C22semidirect
16. C22×C8×C31C22semidirect
17. #11758485C22semidirect
18. C2×Dic124C22semidirect
19. #11758481C22semidirect
20. C2×D248C22semidirect
21. C2×D248C22semidirect
22. C2×D248C22semidirect
23. C2×#92470C22semidirect
34. #92495C23semidirect
38. C2×D124C23semidirect
41. M16×C31C23semidirect
44. C2×C8×C31C23semidirect
45. Dic124C23semidirect
46. D248C23semidirect
47. D248C23semidirect
48. #92470C23semidirect
85. C2×#131D31semidirect
87. C2×C31#576semidirect
104. #131C2×D31semidirect
105. C2×M16C2×D31semidirect
106. C22×C8C2×D31semidirect
107. C31C2×#576semidirect
129. M16C22×D31semidirect
132. C2×C8C22×D31semidirect
165. C2#14521854direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117585662
#145218542
C2×#117584852
C2×#117584812
C22×D2482
C2×C31×#1312
C2×#57631