Finite Group Databasebeta

← #31824095

Subgroups — #31824095

Order 17984.

428 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 115 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×C22⋊D281C212yesmaximal, complemented
2C2×D4×D281C212yesmaximal, complemented
3#22582875C211yesmaximal, characteristic, complemented
4#22582852C212yesmaximal, complemented
5#22582851C212yesmaximal, complemented
6#22582849C212yesmaximal, complemented
7#22582847C211yesmaximal, characteristic, complemented
8#22582839C212yesmaximal, complemented
9#120×C281C211yesmaximal, characteristic, complemented
10C23×D281C2211yescharacteristic, complemented
11C23×D281C2212yescomplemented
12C2×D1124C2212yescomplemented
13C2×D1124C2211yescharacteristic, complemented
14C2×C22⋊D281—28no—
15C2×C22⋊D281C2212yes—
16C2×C22⋊D281C2212yescomplemented
17C2×C22⋊D281C2212yescomplemented
18C2×C22⋊D281C2212yescomplemented
19C2×C22⋊D281C2212yescomplemented
20D4×D281—28no—
21C22×Dic281C2212yescomplemented
22C2×C4×D281C2212yescomplemented
23#17985117C2212yescomplemented
24C22⋊Dic281C2211yescharacteristic, complemented
25#17985115C2212yescomplemented
26#17985115C2212yescomplemented
27C4×Dic281C2211yescharacteristic, complemented
28C24×C281C2211yescharacteristic, complemented
29C2×D4×C281C2212yescomplemented
30C2×D4×C281C2211yescharacteristic, complemented
31C22⋊C4×C281C2212yescomplemented
32C22⋊C4×C281C2211yescharacteristic, complemented
33C22×D281—24no—
34C22×D281—24no—
35C22×D281—24no—
36C22×D281—41no—
37C22×D281—42no—
38C22×D281C2312yes—
39C22×D281C2312yes—
40D1124—24no—
41D1124—41no—
42C22⋊D281—24no—
43C22⋊D281—24no—
44C22⋊D281—24no—
45C22⋊D281—24no—
46C22⋊D281D418yescomplemented
47C2×Dic281—24no—
48C2×Dic281C2312yes—
49C2×Dic281C2312yes—
50C4×D281—24no—
51C23×C281—24no—
52C23×C281—41no—
53C23×C281C2311yescharacteristic
54C23×C281C2311yescharacteristic
55C23×C281C2312yes—
56D4×C281—24no—
57D4×C281—41no—
58C2×C4×C281C2311yescharacteristic
59C2×C4×C281C2312yes—
60C22×C281—22no—
61C22×C281—22no—
62C22×C281—22no—
63C22×C281—22no—
64C22×C281—21no—
65C22×C281—21no—
66C22×C281—44no—
67C22×C281C2×D414yescomplemented
68C22×C281C2411yescharacteristic
69C2×D281—22no—
70C2×D281—22no—
71C2×D281—22no—
72C2×D281—22no—
73C2×D281—22no—
74C2×D281—44no—
75C2×D281—48no—
76C2×D281C2×D414yescomplemented
77C4×C281—22no—
78C4×C281—21no—
79Dic281—22no—
80Dic281C2×D414yescomplemented
81C2×C281—24no—
82C2×C281—41no—
83C2×C281—41no—
84C2×C281C22×D412yes—
85C2×C281H(5,𝔽2)11yescharacteristic
86D281—24no—
87D281—42no—
88C281D4211yescharacteristic, complemented, Sylow
89D42—2811nomaximal, Sylow
90C22×D4—2812no—
91C22×D4—2812no—
92#127—2811no—
93#121—2812no—
94#121—2812no—
95#120—2811no—
96#120—2812no—
97#120D28111yescharacteristic, complemented
98C4×D4—2812no—
99C24—2811no—
100C24—2812no—
101C24C2×D28111yescharacteristic, complemented
102C2×D4—2812no—
103C2×D4—2812no—
104C2×D4—2812no—
105C2×D4—2812no—
106C2×D4—2812no—
107C2×D4—2812no—
108C2×D4—2811no—
109C2×D4—5628no—
110C2×D4—5628no—
111C2×D4C2×D28112yescomplemented
112C2×D4C2×D28111yescharacteristic, complemented
113C22×C4—2812no—
114C22×C4—2812no—
115C4⋊C4—2812no—
116C22⋊C4—2811no—
117C22⋊C4—2812no—
118C22⋊C4—2812no—
119C22⋊C4C2×D28112yescomplemented
120C22⋊C4C2×D28111yescharacteristic, complemented
121C42—2811no—
122C23—24no—
123C23—41no—
124C23—2812no—
125C23—2812no—
126C23—5624no—
127C23—5624no—
128C23—5624no—
129C23—11242no—
130C23—11241no—
131C23C22×D28111yescharacteristic
132C23C22×D28111yescharacteristic
133C23C22×D28112yes—
134D4—24no—
135D4—41no—
136D4—2818no—
137D4—5624no—
138D4—5624no—
139D4—5624no—
140D4—5624no—
141D4—5624no—
142D4—11241no—
143C2×C4—2812no—
144C2×C4—2812no—
145C2×C4—5624no—
146C2×C4—5624no—
147C2×C4C22×D28111yescharacteristic
148C2×C4C22×D28112yes—
149C22—22no—
150C22—22no—
151C22—22no—
152C22—22no—
153C22—21no—
154C22—21no—
155C22—44no—
156C22—2814no—
157C22—5622no—
158C22—5622no—
159C22—5622no—
160C22—5622no—
161C22—5622no—
162C22—11248no—
163C22—11244no—
164C22D4×D28114yescomplemented
165C22C23×D28111yescharacteristic
166C4—22no—
167C4—21no—
168C4—2814no—
169C4—5622no—
170C2—24no—
171C2—41no—
172C2—41no—
173C2—5624no—
174C2—11242no—
175C2C2×D4×D28112yes—
176C2#2258292411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D281
commutator, socle, cosocleC22×C281C24
Fitting#120×C281C2
hypercenter#120D281
hypocenterC281D42
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D281C2semidirect
2. C2×D4×D281C2semidirect
3. #22582875C2semidirect
4. #22582852C2semidirect
5. #22582851C2semidirect
6. #22582849C2semidirect
7. #22582847C2semidirect
8. #22582839C2semidirect
9. #120×C281C2semidirect
10. C23×D281C22semidirect
11. C23×D281C22semidirect
12. C2×D1124C22semidirect
13. C2×D1124C22semidirect
16. C2×C22⋊D281C22semidirect
17. C2×C22⋊D281C22semidirect
18. C2×C22⋊D281C22semidirect
19. C2×C22⋊D281C22semidirect
21. C22×Dic281C22semidirect
22. C2×C4×D281C22semidirect
23. #17985117C22semidirect
24. C22⋊Dic281C22semidirect
25. #17985115C22semidirect
26. #17985115C22semidirect
27. C4×Dic281C22semidirect
28. C24×C281C22semidirect
29. C2×D4×C281C22semidirect
30. C2×D4×C281C22semidirect
31. C22⋊C4×C281C22semidirect
32. C22⋊C4×C281C22semidirect
46. C22⋊D281D4semidirect
67. C22×C281C2×D4semidirect
76. C2×D281C2×D4semidirect
80. Dic281C2×D4semidirect
88. C281D42semidirect
97. #120D281semidirect
101. C24C2×D281semidirect
111. C2×D4C2×D281semidirect
112. C2×D4C2×D281semidirect
119. C22⋊C4C2×D281semidirect
120. C22⋊C4C2×D281semidirect
164. C22D4×D281semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D2812
C2×D4×D2812
#225828752
#225828522
#225828512
#225828492
#225828472
#225828392
#120×C2812
D42281