Finite Group Databasebeta

← C22×D8×D31 #16860425

Subgroups — C22×D8×D31 #16860425

Order 3968.

1976 conjugacy classes of subgroups; only the 565 normal subgroups are shown.

normal subgroups only

This group has 1976 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
1C22×D4×D31C212yesmaximal, complemented
2C22×D248C211yesmaximal, characteristic, complemented
3C22×#92479C212yesmaximal, complemented
4C2×D8×D31C2124yesmaximal, direct product factor
5C22×C8×D31C211yesmaximal, characteristic, complemented
6C22×D8×C31C211yesmaximal, characteristic, complemented
7C24×D31—22no—
8C22×D4×C31C2212yescomplemented
9C22×C22⋊D31—22no—
10C2×D4×D31—212no—
11C2×D4×D31C22124yescomplemented
12C22×D124C2212yescomplemented
13C22×C4×D31C2211yescharacteristic
14C2×D8×C31C22112yescomplemented
15C22×C8×C31C2211yescharacteristic, complemented
16C2×#92479C22124yescomplemented
17C22×C31⋊C8C2211yescharacteristic, complemented
18D8×D31C22164yesdirect product factor
19C2×D248C22112yescomplemented
20C2×C8×D31C22112yescomplemented
21C24×C31—22no—
22C23×D31—22no—
23C23×D31—224no—
24C23×D31—416no—
25C23×D31D411yescharacteristic
26C2×D4×C31—26no—
27C2×D4×C31C23112yescomplemented
28C22×C4×C31C2311yescharacteristic
29C2×C22⋊D31—224no—
30C22×Dic31D411yescharacteristic
31D4×D31—248no—
32D4×D31C23132yescomplemented
33C2×D124—26no—
34C2×D124C23112yescomplemented
35C2×C4×D31D416yes—
36C2×C4×D31C2316yes—
37D8×C31C23116yescomplemented
38C2×C8×C31C2316yescomplemented
39#92479C23132yescomplemented
40C2×C31⋊C8C2316yescomplemented
41D248C23116yescomplemented
42C8×D31C23116yescomplemented
43C23×C31—212no—
44C23×C31—48no—
45C23×C31C2×D411yescharacteristic
46C22×D31—212no—
47C22×D31—232no—
48C22×D31—48no—
49C22×D31—496no—
50C22×D31D818yesdirect product factor
51C22×D31C2×D416yes—
52D4×C31—212no—
53D4×C31C2418yescomplemented
54C2×C4×C31C2×D413yes—
55C2×C4×C31C2413yes—
56C22⋊D31—232no—
57C2×Dic31C2×D416yes—
58D124—212no—
59D124C2418yescomplemented
60C4×D31C2×D4112yes—
61C4×D31C2414yes—
62C8×C31C2414yescomplemented
63C31⋊C8C2414yescomplemented
64C23×D8—311nomaximal, Sylow
65C22×C31—28no—
66C22×C31—424no—
67C22×C31C2×D814yescomplemented
68C22×C31C22×D413yes—
69C2×D31—28no—
70C2×D31—424no—
71C2×D31—464no—
72C2×D31C2×D8124yesdirect product factor
73C2×D31C22×D414yes—
74C4×C31C22×D413yes—
75C4×C31C2511yescharacteristic
76Dic31C22×D414yes—
77C23×D4—312no—
78C22×D8—312no—
79C22×D8—3124no—
80C22×D8—311no—
81C22×D8D3111yescharacteristic, direct product factor
82C23×C8—311no—
83C2×C31—48no—
84C2×C31C22×D816yescomplemented
85C2×C31C23×D411yescharacteristic
86D31—48no—
87D31C22×D818yesdirect product factor
88C25—622no—
89C22×D4—3124no—
90C22×D4—312no—
91C22×D4—6212no—
92C22×D4—622no—
93C22×D4C2×D3112yescomplemented
94C23×C4—311no—
95C2×D8—3124no—
96C2×D8—3164no—
97C2×D8—3112no—
98C2×D8C2×D31112yesdirect product factor
99C22×C8—311no—
100C22×C8—3112no—
101C22×C8C2×D3111yescharacteristic, complemented
102C31C23×D811yescharacteristic, complemented, Sylow
103C24—22no—
104C24—311no—
105C24—6224no—
106C24—622no—
107C24—12416no—
108C2×D4—26no—
109C2×D4—3132no—
110C2×D4—3112no—
111C2×D4—6248no—
112C2×D4—6224no—
113C2×D4—626no—
114C2×D4C22×D31112yescomplemented
115C22×C4—311no—
116C22×C4—316no—
117C22×C4—316no—
118C22×C4C22×D3111yescharacteristic
119D8—3132no—
120D8—3116no—
121D8C22×D31116yesdirect product factor
122C2×C8—316no—
123C2×C8—3116no—
124C2×C8C22×D3116yescomplemented
125C23—212no—
126C23—48no—
127C23—318no—
128C23—316no—
129C23—6232no—
130C23—6212no—
131C23—12496no—
132C23—1248no—
133C23D4×D3111yescharacteristic
134D4—212no—
135D4—318no—
136D4—6232no—
137D4—6212no—
138D4C23×D3118yescomplemented
139C2×C4—316no—
140C2×C4—3112no—
141C2×C4—314no—
142C2×C4D4×D3113yes—
143C2×C4C23×D3113yes—
144C8—314no—
145C8C23×D3114yescomplemented
146C22—28no—
147C22—424no—
148C22—314no—
149C22—3124no—
150C22—628no—
151C22—12464no—
152C22—12424no—
153C22D8×D3114yesdirect product factor
154C22C2×D4×D3113yes—
155C4—314no—
156C4C2×D4×D3113yes—
157C4C24×D3111yescharacteristic
158C2—48no—
159C2—318no—
160C2—1248no—
161C2C2×D8×D3116yesdirect product factor
162C2C22×D4×D3111yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC4×C31C25
FrattiniC4C24×D31
FittingC22×D8×C31C2
socleC23×C31C2×D4
hypercenterC22×D8D31
hypocenterC31C23×D8
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×D4×D31C2semidirect
2. C22×D248C2semidirect
3. C22×#92479C2semidirect
4. C2×D8×D31C2direct (N × H)
5. C22×C8×D31C2semidirect
6. C22×D8×C31C2semidirect
8. C22×D4×C31C22semidirect
11. C2×D4×D31C22semidirect
12. C22×D124C22semidirect
14. C2×D8×C31C22semidirect
15. C22×C8×C31C22semidirect
16. C2×#92479C22semidirect
17. C22×C31⋊C8C22semidirect
18. D8×D31C22direct (N × H)
19. C2×D248C22semidirect
20. C2×C8×D31C22semidirect
27. C2×D4×C31C23semidirect
32. D4×D31C23semidirect
34. C2×D124C23semidirect
37. D8×C31C23semidirect
38. C2×C8×C31C23semidirect
39. #92479C23semidirect
40. C2×C31⋊C8C23semidirect
41. D248C23semidirect
42. C8×D31C23semidirect
50. C22×D31D8direct (N × H)
53. D4×C31C24semidirect
59. D124C24semidirect
62. C8×C31C24semidirect
63. C31⋊C8C24semidirect
67. C22×C31C2×D8semidirect
72. C2×D31C2×D8direct (N × H)
81. C22×D8D31direct (N × H)
84. C2×C31C22×D8semidirect
87. D31C22×D8direct (N × H)
93. C22×D4C2×D31semidirect
98. C2×D8C2×D31direct (N × H)
101. C22×C8C2×D31semidirect
102. C31C23×D8semidirect
114. C2×D4C22×D31semidirect
121. D8C22×D31direct (N × H)
124. C2×C8C22×D31semidirect
138. D4C23×D31semidirect
145. C8C23×D31semidirect
153. C22D8×D31direct (N × H)
161. C2C2×D8×D31direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D312
C22×D2482
C22×#924792
C2×D8×D312
C22×C8×D312
C22×D8×C312
C23×D831