Finite Group Databasebeta

← #31824108

Subgroups — #31824108

Order 17984.

334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 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×#17985137C211yesmaximal, characteristic, complemented
2C2×D4×D281C211yesmaximal, characteristic, complemented
3#22582867C211yesmaximal, characteristic, complemented
4#22582863C212yesmaximal, complemented
5#22582859C211yesmaximal, characteristic, complemented
6#22582854C211yesmaximal, characteristic, complemented
7#22582853C212yesmaximal, complemented
8#22582849C212yesmaximal, complemented
9C4×D1124C211yesmaximal, characteristic, complemented
10C2×#17985115C212yesmaximal, complemented
11C4×D4×C281C211yesmaximal, characteristic, complemented
12C23×D281C2212yes—
13#17985137—24no—
14C2×Dic562C2211yescharacteristic, complemented
15C2×D1124C2211yescharacteristic
16C2×D1124C2211yescharacteristic
17C2×D1124C2212yescomplemented
18C2×C22⋊D281C2212yes—
19C2×C22⋊D281C2212yescomplemented
20D4×D281—24no—
21C22×Dic281C2212yescomplemented
22C2×C4×D281C2211yescharacteristic
23C2×C4×D281C2211yescharacteristic, complemented
24C4⋊Dic281C2211yescharacteristic, complemented
25C4⋊Dic281C2212yescomplemented
26#17985115C2211yescharacteristic
27#17985115C2212yes—
28#17985115C2212yescomplemented
29#17985115C2212yescomplemented
30#17985115C2211yescharacteristic, complemented
31#17985115C2212yescomplemented
32C2×D4×C281C2211yescharacteristic
33C22×C4×C281C2212yescomplemented
34C4⋊C4×C281C2211yescharacteristic, complemented
35C22⋊C4×C281C2212yescomplemented
36C42×C281C2211yescharacteristic, complemented
37C22×D281—24no—
38C22×D281—24no—
39C22×D281—42no—
40C22×D281C2312yes—
41C22×D281C2311yescharacteristic
42C22×D281C2311yescharacteristic
43Dic562—22no—
44D1124—22no—
45D1124—22no—
46D1124—42no—
47C22⋊D281—24no—
48C22⋊D281—24no—
49C2×Dic281—24no—
50C2×Dic281C2311yescharacteristic
51C2×Dic281C2312yes—
52C2×Dic281C2311yescharacteristic
53C4×D281—22no—
54C4×D281—22no—
55C23×C281C2312yes—
56D4×C281D414yescomplemented
57C2×C4×C281—42no—
58C2×C4×C281C2311yescharacteristic
59C2×C4×C281C2311yescharacteristic
60C2×C4×C281C2312yes—
61C2×C4×C281C2311yescharacteristic
62C22×C281—22no—
63C22×C281—22no—
64C22×C281C2×D414yes—
65C22×C281C2411yescharacteristic
66C2×D281—21no—
67C2×D281—21no—
68C2×D281—21no—
69C2×D281—22no—
70C2×D281—21no—
71C2×D281—22no—
72C2×D281—21no—
73C2×D281—22no—
74C2×D281—48no—
75C2×D281#4112yescomplemented
76C4×C281—21no—
77C4×C281—21no—
78C4×C281—22no—
79C4×C281C2×D412yes—
80Dic281—21no—
81Dic281—21no—
82Dic281—22no—
83C2×C281—24no—
84C2×C281C22×D411yescharacteristic
85C2×C281C2×#4111yescharacteristic
86C2×C281H(5,𝔽2)11yescharacteristic
87D281—22no—
88D281—41no—
89D281—42no—
90C281#54611yescharacteristic, complemented, Sylow
91#546—2811nomaximal, Sylow
92C2×#41—2811no—
93C22×D4—2811no—
94#124—2811no—
95#123—2812no—
96C22⋊Q8—2811no—
97#121—2812no—
98#121—2811no—
99#120—2812no—
100C4×D4—2811no—
101C4×D4D28111yescharacteristic, complemented
102C2×C22⋊C4—2812no—
103C24—2812no—
104#41—5624no—
105C2×Q8—2811no—
106C2×D4—2812no—
107C2×D4—2812no—
108C2×D4—2811no—
109C2×D4—2811no—
110C2×D4—2812no—
111C2×D4—5624no—
112C2×D4C2×D28111yescharacteristic
113C22×C4—2812no—
114C22×C4—2811no—
115C22×C4—2811no—
116C22×C4C2×D28112yescomplemented
117C4⋊C4—2811no—
118C4⋊C4—2812no—
119C4⋊C4C2×D28111yescharacteristic, complemented
120C22⋊C4—2811no—
121C22⋊C4—2812no—
122C22⋊C4—2812no—
123C22⋊C4—2812no—
124C22⋊C4—2811no—
125C22⋊C4—2812no—
126C22⋊C4C2×D28112yescomplemented
127C42C2×D28111yescharacteristic, complemented
128C23—2811no—
129C23—2812no—
130C23—2811no—
131C23—5624no—
132C23—5624no—
133C23—11242no—
134C23C22×D28112yes—
135Q8—5622no—
136D4—5622no—
137D4—5624no—
138D4—5624no—
139D4—5622no—
140D4—11242no—
141D4D112414yescomplemented
142C2×C4—42no—
143C2×C4—2811no—
144C2×C4—2812no—
145C2×C4—2811no—
146C2×C4—5624no—
147C2×C4—5622no—
148C2×C4—5622no—
149C2×C4C22×D28111yescharacteristic
150C2×C4C22×D28111yescharacteristic
151C2×C4C22×D28112yes—
152C2×C4C22×D28111yescharacteristic
153C22—22no—
154C22—22no—
155C22—2812no—
156C22—5621no—
157C22—5621no—
158C22—5621no—
159C22—5622no—
160C22—5621no—
161C22—5622no—
162C22—5621no—
163C22—5622no—
164C22—11248no—
165C22C2×D112414yes—
166C22C23×D28111yescharacteristic
167C4—21no—
168C4—21no—
169C4—22no—
170C4—5621no—
171C4—5621no—
172C4—5622no—
173C4C2×D112412yes—
174C2—24no—
175C2—5622no—
176C2—11242no—
177C2—11241no—
178C2C22×D112411yescharacteristic
179C2#41×D28111yescharacteristic
180C2#2258292411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D281
commutator, socle, cosocleC22×C281C24
FittingC4×D4×C281C2
hypercenterC4×D4D281
hypocenterC281#546
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#17985137C2semidirect
2. C2×D4×D281C2semidirect
3. #22582867C2semidirect
4. #22582863C2semidirect
5. #22582859C2semidirect
6. #22582854C2semidirect
7. #22582853C2semidirect
8. #22582849C2semidirect
9. C4×D1124C2semidirect
10. C2×#17985115C2semidirect
11. C4×D4×C281C2semidirect
14. C2×Dic562C22semidirect
17. C2×D1124C22semidirect
19. C2×C22⋊D281C22semidirect
21. C22×Dic281C22semidirect
23. C2×C4×D281C22semidirect
24. C4⋊Dic281C22semidirect
25. C4⋊Dic281C22semidirect
28. #17985115C22semidirect
29. #17985115C22semidirect
30. #17985115C22semidirect
31. #17985115C22semidirect
33. C22×C4×C281C22semidirect
34. C4⋊C4×C281C22semidirect
35. C22⋊C4×C281C22semidirect
36. C42×C281C22semidirect
56. D4×C281D4semidirect
75. C2×D281#41semidirect
90. C281#546semidirect
101. C4×D4D281semidirect
116. C22×C4C2×D281semidirect
119. C4⋊C4C2×D281semidirect
126. C22⋊C4C2×D281semidirect
127. C42C2×D281semidirect
141. D4D1124semidirect

Maximal subgroups

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

subgroupindex
C2×#179851372
C2×D4×D2812
#225828672
#225828632
#225828592
#225828542
#225828532
#225828492
C4×D11242
C2×#179851152
C4×D4×C2812
#546281