Finite Group Databasebeta

← #31824270

Subgroups — #31824270

Order 17984.

258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 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
1#22582926C211yesmaximal, characteristic, complemented
2#22582925C211yesmaximal, characteristic, complemented
3#22582911C212yesmaximal, complemented
4#22582909C211yesmaximal, characteristic, complemented
5#22582904C211yesmaximal, characteristic, complemented
6#22582903C212yesmaximal, complemented
7#22582900C212yesmaximal, complemented
8C2×#17985127C211yesmaximal, characteristic, complemented
9SD16×D281C212yesmaximal, complemented
10#22582885C211yesmaximal, characteristic, complemented
11#135×C281C211yesmaximal, characteristic, complemented
12#17985139C2212yes—
13#17985138—21no—
14#17985138—21no—
15#17985138C2211yescharacteristic
16#17985137—22no—
17#17985137C2212yescomplemented
18C2×Dic562—21no—
19C2×Dic562C2211yescharacteristic, complemented
20Q8×D281C2212yescomplemented
21C2×D1124—21no—
22C2×D1124C2211yescharacteristic
23D4×D281—22no—
24D4×D281C2212yes—
25#17985128C2212yescomplemented
26#17985127C2212yescomplemented
27#17985127C2212yescomplemented
28#17985126C2212yescomplemented
29#17985125C2212yescomplemented
30#17985123C2212yescomplemented
31#17985122C2211yescharacteristic, complemented
32#17985121C2212yescomplemented
33C8×D281C2212yescomplemented
34#41×C281C2211yescharacteristic
35#41×C281C2211yescharacteristic, complemented
36Q16×C281C2211yescharacteristic, complemented
37SD16×C281C2211yescharacteristic, complemented
38SD16×C281C2211yescharacteristic, complemented
39D8×C281C2211yescharacteristic, complemented
40C2×C8×C281C2211yescharacteristic, complemented
41C22×D281—21no—
42C22×D281—22no—
43Dic562—21no—
44Dic562—22no—
45Dic562D411yescharacteristic
46Dic562C2312yes—
47D1124—22no—
48D1124—21no—
49D1124D411yescharacteristic
50D1124C2312yes—
51C22⋊D281—22no—
52C22⋊D281—22no—
53C22⋊D281D412yes—
54C2×Dic281—21no—
55C2×Dic281—22no—
56C4×D281—22no—
57C4×D281—22no—
58C4×D281C2312yes—
59#14555886C2312yes—
60Q8×C281C2311yescharacteristic
61Q8×C281C2311yescharacteristic
62D4×C281—21no—
63D4×C281—21no—
64D4×C281C2311yescharacteristic
65D4×C281C2311yescharacteristic
66C2×C4×C281—21no—
67C2×C4×C281—21no—
68C2×C4×C281C2311yescharacteristic
69C8×C281C2311yescharacteristic
70C8×C281C2311yescharacteristic
71C22×C281—21no—
72C22×C281—21no—
73C22×C281C2×D411yescharacteristic
74C2×D281—22no—
75C2×D281—82no—
76C2×D281—81no—
77C2×D281C2×D412yes—
78C4×C281—21no—
79C4×C281—21no—
80C4×C281C2×D411yescharacteristic
81C4×C281C2411yescharacteristic
82Dic281—22no—
83Dic281C2×D412yes—
84C2×C281—21no—
85C2×C281—41no—
86C2×C281—41no—
87C2×C281C22×D411yescharacteristic
88D281—22no—
89D281—42no—
90C281#57711yescharacteristic, complemented, Sylow
91#577—2811nomaximal, Sylow
922−1+4—2811no—
93H(5,𝔽2)—2811no—
94#137—2811no—
95#137—2812no—
96AGL(1,ℤ/8)—2811no—
97AGL(1,ℤ/8)—2812no—
98#135—2812no—
99#135D28111yescharacteristic, complemented
100C2×SD16—2812no—
101C2×SD16—2811no—
102#131—2811no—
103#41—2811no—
104#41—2812no—
105#41—2812no—
106#41—5621no—
107#41—5621no—
108#41—5622no—
109#41C2×D28111yescharacteristic
110#41C2×D28111yescharacteristic, complemented
111C2×Q8—2812no—
112C2×Q8—2811no—
113C2×Q8—5621no—
114C2×D4—2812no—
115C2×D4—2811no—
116C2×D4—5621no—
117C2×D4—5622no—
118Q16—2812no—
119Q16C2×D28111yescharacteristic, complemented
120SD16—2812no—
121SD16—2812no—
122SD16—2812no—
123SD16—2812no—
124SD16C2×D28111yescharacteristic, complemented
125SD16C2×D28111yescharacteristic, complemented
126D8—2812no—
127D8C2×D28111yescharacteristic, complemented
128M16—2811no—
129M16—2812no—
130C2×C8—2812no—
131C2×C8C2×D28111yescharacteristic, complemented
132C23—5622no—
133C23—5621no—
134Q8—2811no—
135Q8—2812no—
136Q8—5622no—
137Q8—5621no—
138Q8C22×D28111yescharacteristic
139Q8C22×D28111yescharacteristic
140D4—21no—
141D4—21no—
142D4—2812no—
143D4—2811no—
144D4—2812no—
145D4—5622no—
146D4—5622no—
147D4—5622no—
148D4—5621no—
149D4C22×D28111yescharacteristic
150D4C22×D28111yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—2812no—
154C2×C4—5622no—
155C2×C4—5622no—
156C2×C4—5622no—
157C2×C4—5621no—
158C2×C4C22×D28111yescharacteristic
159C8—2812no—
160C8C22×D28111yescharacteristic
161C8C22×D28111yescharacteristic
162C22—21no—
163C22—21no—
164C22—2812no—
165C22—5622no—
166C22—22481no—
167C22—22482no—
168C22D4×D28111yescharacteristic
169C4—21no—
170C4—21no—
171C4—2812no—
172C4—5622no—
173C4D4×D28111yescharacteristic
174C4C23×D28111yescharacteristic
175C2—21no—
176C2—41no—
177C2—41no—
178C2—5622no—
179C2—11242no—
180C2C2×D4×D28111yescharacteristic
subgroupG/H
centerC2C2×D4×D281
commutator, cosocleC4×C281C24
FrattiniC4C23×D281
Fitting#135×C281C2
socleC2×C281C22×D4
hypercenter#135D281
hypocenterC281#577
LCSG ▷ C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #22582926C2semidirect
2. #22582925C2semidirect
3. #22582911C2semidirect
4. #22582909C2semidirect
5. #22582904C2semidirect
6. #22582903C2semidirect
7. #22582900C2semidirect
8. C2×#17985127C2semidirect
9. SD16×D281C2semidirect
10. #22582885C2semidirect
11. #135×C281C2semidirect
17. #17985137C22semidirect
19. C2×Dic562C22semidirect
20. Q8×D281C22semidirect
25. #17985128C22semidirect
26. #17985127C22semidirect
27. #17985127C22semidirect
28. #17985126C22semidirect
29. #17985125C22semidirect
30. #17985123C22semidirect
31. #17985122C22semidirect
32. #17985121C22semidirect
33. C8×D281C22semidirect
35. #41×C281C22semidirect
36. Q16×C281C22semidirect
37. SD16×C281C22semidirect
38. SD16×C281C22semidirect
39. D8×C281C22semidirect
40. C2×C8×C281C22semidirect
90. C281#577semidirect
99. #135D281semidirect
110. #41C2×D281semidirect
119. Q16C2×D281semidirect
124. SD16C2×D281semidirect
125. SD16C2×D281semidirect
127. D8C2×D281semidirect
131. C2×C8C2×D281semidirect

Maximal subgroups

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

subgroupindex
#225829262
#225829252
#225829112
#225829092
#225829042
#225829032
#225829002
C2×#179851272
SD16×D2812
#225828852
#135×C2812
#577281