Finite Group Databasebeta

← #31823935

Subgroups — #31823935

Order 17984.

338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 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
2C4×D1124C211yesmaximal, characteristic, complemented
3D4×Dic281C211yesmaximal, characteristic, complemented
4#22582841C211yesmaximal, characteristic, complemented
5C4×C22⋊D281C212yesmaximal, complemented
6#22582839C212yesmaximal, complemented
7#22582837C211yesmaximal, characteristic, complemented
8#22582836C211yesmaximal, characteristic, complemented
9C2×#17985115C212yesmaximal, complemented
10C22⋊C4×D281C212yesmaximal, complemented
11C4×D4×C281C211yesmaximal, characteristic, complemented
12C23×D281C2212yes—
13C2×D1124C2211yescharacteristic
14C2×C22⋊D281C2212yes—
15D4×D281C418yescomplemented
16C22×Dic281C2212yescomplemented
17C2×C4×D281C2211yescharacteristic
18C2×C4×D281C2212yescomplemented
19C2×C4×D281C2212yescomplemented
20C4⋊Dic281C2211yescharacteristic, complemented
21#17985117C2211yescharacteristic, complemented
22#17985117C2211yescharacteristic, complemented
23C22⋊Dic281C2212yescomplemented
24#17985115C2211yescharacteristic
25#17985115C2212yes—
26#17985115C2211yescharacteristic
27#17985115C2212yescomplemented
28#17985115C2212yescomplemented
29C4×Dic281C2211yescharacteristic, complemented
30C4×Dic281C2212yescomplemented
31C2×D4×C281C2211yescharacteristic
32C22×C4×C281C2212yescomplemented
33C4⋊C4×C281C2211yescharacteristic, complemented
34C22⋊C4×C281C2212yescomplemented
35C42×C281C2211yescharacteristic, complemented
36C22×D281—42no—
37C22×D281—42no—
38C22×D281C2×C418yescomplemented
39C22×D281C2311yescharacteristic
40C22×D281C2312yes—
41D1124C2×C414yescomplemented
42C22⋊D281C2×C418yescomplemented
43C2×Dic281—42no—
44C2×Dic281C2311yescharacteristic
45C2×Dic281C2312yes—
46C2×Dic281C2311yescharacteristic
47C2×Dic281C2311yescharacteristic
48C4×D281—42no—
49C4×D281—42no—
50C4×D281C2×C414yescomplemented
51C23×C281C2312yes—
52D4×C281C2×C414yescomplemented
53C2×C4×C281—42no—
54C2×C4×C281C2311yescharacteristic
55C2×C4×C281C2311yescharacteristic
56C2×C4×C281C2312yes—
57C2×C4×C281C2311yescharacteristic
58C22×C281—22no—
59C22×C281—22no—
60C22×C281C22×C414yes—
61C22×C281C2411yescharacteristic
62C2×D281—22no—
63C2×D281—22no—
64C2×D281—21no—
65C2×D281—21no—
66C2×D281—48no—
67C2×D281C22×C412yes—
68C2×D281C22×C414yes—
69C4×C281—21no—
70C4×C281—22no—
71C4×C281—21no—
72C4×C281C22×C412yes—
73Dic281—21no—
74Dic281—22no—
75Dic281—21no—
76Dic281C22×C412yes—
77C2×C281—24no—
78C2×C281C23×C411yescharacteristic
79C2×C281H(5,𝔽2)11yescharacteristic
80C2×C281H(5,𝔽2)11yescharacteristic
81D281—22no—
82D281—24no—
83C281#51811yescharacteristic, complemented, Sylow
84#518—2811nomaximal, Sylow
85C22×D4—2811no—
86C4×D4—2811no—
87C4×D4—2812no—
88C4×D4—2811no—
89C4×D4—2812no—
90C4×D4—2811no—
91C4×D4D28111yescharacteristic, complemented
92#117—2811no—
93#117—2811no—
94C2×C22⋊C4—2812no—
95C2×C22⋊C4—2812no—
96C24—2812no—
97C2×D4—2812no—
98C2×D4—2818no—
99C2×D4—2811no—
100C2×D4C2×D28111yescharacteristic
101C22×C4—2811no—
102C22×C4—2812no—
103C22×C4—2812no—
104C22×C4—2812no—
105C22×C4C2×D28112yescomplemented
106C4⋊C4—2811no—
107C4⋊C4—2811no—
108C4⋊C4—2811no—
109C4⋊C4C2×D28111yescharacteristic, complemented
110C22⋊C4—2812no—
111C22⋊C4—2812no—
112C22⋊C4—2811no—
113C22⋊C4—2811no—
114C22⋊C4—2812no—
115C22⋊C4—2812no—
116C22⋊C4C2×D28112yescomplemented
117C42—2812no—
118C42—2811no—
119C42C2×D28111yescharacteristic, complemented
120C23—2811no—
121C23—2812no—
122C23—2818no—
123C23—11242no—
124C23—11242no—
125C23C22×D28112yes—
126D4—2818no—
127D4—2814no—
128D4C4×D28114yescomplemented
129C2×C4—42no—
130C2×C4—2811no—
131C2×C4—2814no—
132C2×C4—2811no—
133C2×C4—2812no—
134C2×C4—2811no—
135C2×C4—11242no—
136C2×C4—11242no—
137C2×C4—11242no—
138C2×C4C22×D28112yes—
139C2×C4C22×D28111yescharacteristic
140C2×C4C22×D28111yescharacteristic
141C2×C4C22×D28111yescharacteristic
142C22—22no—
143C22—22no—
144C22—2812no—
145C22—2814no—
146C22—5622no—
147C22—5621no—
148C22—5622no—
149C22—5621no—
150C22—11248no—
151C22C2×C4×D28114yes—
152C22C23×D28111yescharacteristic
153C4—21no—
154C4—22no—
155C4—21no—
156C4—2812no—
157C4—5621no—
158C4—5622no—
159C4—5621no—
160C4C2×C4×D28112yes—
161C2—24no—
162C2—5622no—
163C2—5624no—
164C2C22×C4×D28111yescharacteristic
165C2#2258292411yescharacteristic
166C2#2258292511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D281
commutatorC2×C281C23×C4
FittingC4×D4×C281C2
socle, cosocleC22×C281C24
prime radicalC2×D4×D281C2
hypercenterC4×D4D281
hypocenterC281#518
LCSG ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×D1124C2semidirect
3. D4×Dic281C2semidirect
4. #22582841C2semidirect
5. C4×C22⋊D281C2semidirect
6. #22582839C2semidirect
7. #22582837C2semidirect
8. #22582836C2semidirect
9. C2×#17985115C2semidirect
10. C22⋊C4×D281C2semidirect
11. C4×D4×C281C2semidirect
15. D4×D281C4semidirect
16. C22×Dic281C22semidirect
18. C2×C4×D281C22semidirect
19. C2×C4×D281C22semidirect
20. C4⋊Dic281C22semidirect
21. #17985117C22semidirect
22. #17985117C22semidirect
23. C22⋊Dic281C22semidirect
27. #17985115C22semidirect
28. #17985115C22semidirect
29. C4×Dic281C22semidirect
30. C4×Dic281C22semidirect
32. C22×C4×C281C22semidirect
33. C4⋊C4×C281C22semidirect
34. C22⋊C4×C281C22semidirect
35. C42×C281C22semidirect
38. C22×D281C2×C4semidirect
41. D1124C2×C4semidirect
42. C22⋊D281C2×C4semidirect
50. C4×D281C2×C4semidirect
52. D4×C281C2×C4semidirect
83. C281#518semidirect
91. C4×D4D281semidirect
105. C22×C4C2×D281semidirect
109. C4⋊C4C2×D281semidirect
116. C22⋊C4C2×D281semidirect
119. C42C2×D281semidirect
128. D4C4×D281semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D2812
C4×D11242
D4×Dic2812
#225828412
C4×C22⋊D2812
#225828392
#225828372
#225828362
C2×#179851152
C22⋊C4×D2812
C4×D4×C2812
#518281