Finite Group Databasebeta

← C4×D4×D281 #31823920

Subgroups — C4×D4×D281 #31823920

Order 17984.

426 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 169 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×D4×D281C211yesmaximal, characteristic
2C22×C4×D281C212yesmaximal, complemented
3C4×D1124C211yesmaximal, characteristic, complemented
4D4×Dic281C211yesmaximal, characteristic, complemented
5#22582841C211yesmaximal, characteristic, complemented
6C4×C22⋊D281C212yesmaximal, complemented
7#22582839C212yesmaximal, complemented
8C4⋊C4×D281C211yesmaximal, characteristic, complemented
9C22⋊C4×D281C212yesmaximal, complemented
10C42×D281C211yesmaximal, characteristic, complemented
11C4×D4×C281C211yesmaximal, characteristic, complemented
12C23×D281C2212yes—
13C2×D1124C2211yescharacteristic
14C2×C22⋊D281C2212yes—
15D4×D281C418yesdirect product factor
16C22×Dic281C2212yescomplemented
17C2×C4×D281—28no—
18C2×C4×D281C2211yescharacteristic
19C2×C4×D281C2212yes—
20C2×C4×D281C2211yescharacteristic
21C2×C4×D281C2211yescharacteristic
22C2×C4×D281C2212yescomplemented
23C2×C4×D281C2212yescomplemented
24C4⋊Dic281C2211yescharacteristic, complemented
25#17985117C2212yescomplemented
26C22⋊Dic281C2212yescomplemented
27#17985115C2212yescomplemented
28#17985115C2212yescomplemented
29C4×Dic281C2211yescharacteristic, complemented
30C4×Dic281C2211yescharacteristic, complemented
31C4×Dic281C2211yescharacteristic, complemented
32C2×D4×C281C2211yescharacteristic
33C22×C4×C281C2212yescomplemented
34C4⋊C4×C281C2211yescharacteristic, complemented
35C22⋊C4×C281C2212yescomplemented
36C42×C281C2211yescharacteristic, complemented
37C22×D281—24no—
38C22×D281—24no—
39C22×D281C2×C418yescomplemented
40C22×D281C2312yes—
41C22×D281C2311yescharacteristic
42D1124C2×C414yescomplemented
43C22⋊D281C2×C418yescomplemented
44C2×Dic281—24no—
45C2×Dic281C2311yescharacteristic
46C2×Dic281C2312yes—
47C2×Dic281C2311yescharacteristic
48C2×Dic281C2311yescharacteristic
49C4×D281—24no—
50C4×D281—22no—
51C4×D281—24no—
52C4×D281—24no—
53C4×D281C2×C414yescomplemented
54C4×D281D414yesdirect product factor
55C23×C281C2312yes—
56D4×C281C2×C414yescomplemented
57C2×C4×C281—24no—
58C2×C4×C281C2311yescharacteristic
59C2×C4×C281C2312yes—
60C2×C4×C281C2311yescharacteristic
61C2×C4×C281C2311yescharacteristic
62C22×C281—22no—
63C22×C281—22no—
64C22×C281C22×C414yescomplemented
65C22×C281C2411yescharacteristic
66C2×D281—22no—
67C2×D281—22no—
68C2×D281—216no—
69C2×D281C22×C412yes—
70C2×D281C22×C414yescomplemented
71C2×D281C2×D412yes—
72C2×D281#4112yes—
73C4×C281—22no—
74C4×C281—21no—
75C4×C281C22×C412yescomplemented
76C4×C281C2×D412yescomplemented
77Dic281—22no—
78Dic281—21no—
79Dic281C22×C412yescomplemented
80Dic281C2×D412yescomplemented
81C2×C281—24no—
82C2×C281C23×C411yescharacteristic
83C2×C281C22×D411yescharacteristic
84C2×C281C2×#4111yescharacteristic
85D281—24no—
86D281C4×D414yesdirect product factor
87C281C2×C4×D411yescharacteristic, complemented, Sylow
88C2×C4×D4—2811nomaximal, Sylow
89C22×D4—2811no—
90C23×C4—2812no—
91C4×D4—2811no—
92C4×D4—2812no—
93C4×D4—2811no—
94C4×D4—2812no—
95C4×D4—2811no—
96C4×D4D28111yescharacteristic, direct product factor
97C2×C4⋊C4—2811no—
98C2×C22⋊C4—2812no—
99C2×C42—2811no—
100C24—2812no—
101C2×D4—2812no—
102C2×D4—2818no—
103C2×D4—2811no—
104C2×D4C2×D28111yescharacteristic
105C22×C4—2811no—
106C22×C4—2811no—
107C22×C4—2812no—
108C22×C4—2811no—
109C22×C4—2812no—
110C22×C4—2812no—
111C22×C4—2812no—
112C22×C4—5628no—
113C22×C4C2×D28112yescomplemented
114C4⋊C4—2812no—
115C4⋊C4—2811no—
116C4⋊C4C2×D28111yescharacteristic, complemented
117C22⋊C4—2812no—
118C22⋊C4—2812no—
119C22⋊C4—2812no—
120C22⋊C4C2×D28112yescomplemented
121C42—2811no—
122C42—2811no—
123C42—2811no—
124C42C2×D28111yescharacteristic, complemented
125C23—2811no—
126C23—2818no—
127C23—2812no—
128C23—5624no—
129C23—5624no—
130C23C22×D28112yes—
131D4—2818no—
132D4—2814no—
133D4C4×D28114yesdirect product factor
134C2×C4—24no—
135C2×C4—2811no—
136C2×C4—2811no—
137C2×C4—2814no—
138C2×C4—2814no—
139C2×C4—2811no—
140C2×C4—2812no—
141C2×C4—5624no—
142C2×C4—5624no—
143C2×C4—5622no—
144C2×C4—5624no—
145C2×C4—5624no—
146C2×C4C22×D28111yescharacteristic
147C2×C4C22×D28112yes—
148C2×C4C22×D28111yescharacteristic
149C2×C4C22×D28111yescharacteristic
150C22—22no—
151C22—22no—
152C22—2812no—
153C22—2812no—
154C22—2812no—
155C22—2814no—
156C22—56216no—
157C22—5622no—
158C22—5622no—
159C22C2×C4×D28114yescomplemented
160C22C23×D28111yescharacteristic
161C4—22no—
162C4—21no—
163C4—2812no—
164C4—2812no—
165C4—5622no—
166C4—5621no—
167C4C2×C4×D28112yescomplemented
168C4D4×D28112yesdirect product factor
169C2—24no—
170C2—2814no—
171C2—5624no—
172C2C22×C4×D28111yescharacteristic
173C2C2×D4×D28111yescharacteristic
174C2#41×D28111yescharacteristic
subgroupG/H
centerC2×C4C22×D281
commutatorC2×C281C23×C4
FrattiniC22C23×D281
FittingC4×D4×C281C2
socle, cosocleC22×C281C24
prime radicalC2×D4×D281C2
hypercenterC4×D4D281
hypocenterC281C2×C4×D4
LCSG ▷ C2×C281 ▷ C281
UCSC1 ◁ C2×C4 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×C4×D281C2semidirect
3. C4×D1124C2semidirect
4. D4×Dic281C2semidirect
5. #22582841C2semidirect
6. C4×C22⋊D281C2semidirect
7. #22582839C2semidirect
8. C4⋊C4×D281C2semidirect
9. C22⋊C4×D281C2semidirect
10. C42×D281C2semidirect
11. C4×D4×C281C2semidirect
15. D4×D281C4direct (N × H)
16. C22×Dic281C22semidirect
22. C2×C4×D281C22semidirect
23. C2×C4×D281C22semidirect
24. C4⋊Dic281C22semidirect
25. #17985117C22semidirect
26. C22⋊Dic281C22semidirect
27. #17985115C22semidirect
28. #17985115C22semidirect
29. C4×Dic281C22semidirect
30. C4×Dic281C22semidirect
31. C4×Dic281C22semidirect
33. C22×C4×C281C22semidirect
34. C4⋊C4×C281C22semidirect
35. C22⋊C4×C281C22semidirect
36. C42×C281C22semidirect
39. C22×D281C2×C4semidirect
42. D1124C2×C4semidirect
43. C22⋊D281C2×C4semidirect
53. C4×D281C2×C4semidirect
54. C4×D281D4direct (N × H)
56. D4×C281C2×C4semidirect
64. C22×C281C22×C4semidirect
70. C2×D281C22×C4semidirect
75. C4×C281C22×C4semidirect
76. C4×C281C2×D4semidirect
79. Dic281C22×C4semidirect
80. Dic281C2×D4semidirect
86. D281C4×D4direct (N × H)
87. C281C2×C4×D4semidirect
96. C4×D4D281direct (N × H)
113. C22×C4C2×D281semidirect
116. C4⋊C4C2×D281semidirect
120. C22⋊C4C2×D281semidirect
124. C42C2×D281semidirect
133. D4C4×D281direct (N × H)
159. C22C2×C4×D281semidirect
167. C4C2×C4×D281semidirect
168. C4D4×D281direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×D2812
C22×C4×D2812
C4×D11242
D4×Dic2812
#225828412
C4×C22⋊D2812
#225828392
C4⋊C4×D2812
C22⋊C4×D2812
C42×D2812
C4×D4×C2812
C2×C4×D4281