Finite Group Databasebeta

← #31824259

Subgroups — #31824259

Order 17984.

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

normal subgroups only

This group has 262 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
1C2×#17985137C211yesmaximal, characteristic, complemented
2#41×D281C211yesmaximal, characteristic, complemented
3#22582912C211yesmaximal, characteristic, complemented
4#22582909C211yesmaximal, characteristic, complemented
5#22582908C212yesmaximal, complemented
6#22582905C211yesmaximal, characteristic, complemented
7#22582903C212yesmaximal, complemented
8#22582900C212yesmaximal, complemented
9#22582898C212yesmaximal, complemented
10M16×D281C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C281C211yesmaximal, characteristic, complemented
12#17985139C2211yescharacteristic, complemented
13#17985138—21no—
14#17985138C2211yescharacteristic
15#17985137—21no—
16#17985137—21no—
17#17985137—21no—
18#17985137C2212yes—
19#17985137C2211yescharacteristic, complemented
20#17985137C2212yescomplemented
21C2×Dic562C2211yescharacteristic, complemented
22Q8×D281C2211yescharacteristic, complemented
23C2×C22⋊D281—21no—
24D4×D281—21no—
25D4×D281C2211yescharacteristic, complemented
26C22×Dic281—21no—
27C2×C4×D281—21no—
28C2×C4×D281C2211yescharacteristic
29Dic1124C2212yescomplemented
30#17985128C2212yescomplemented
31#17985127C2212yescomplemented
32#17985126C2212yescomplemented
33#17985126C2212yescomplemented
34#17985123C2212yescomplemented
35#17985122C2211yescharacteristic, complemented
36#17985121C2212yescomplemented
37C8×D281C2212yescomplemented
38#41×C281C2211yescharacteristic
39C2×D4×C281C2211yescharacteristic, complemented
40SD16×C281C2212yescomplemented
41D8×C281C2212yescomplemented
42M16×C281C2211yescharacteristic, complemented
43C22×D281—21no—
44C22×D281D411yescharacteristic
45Dic562—21no—
46Dic562—21no—
47Dic562C2311yescharacteristic
48Dic562C2312yes—
49D1124—21no—
50D1124C2311yescharacteristic
51C22⋊D281—21no—
52C22⋊D281—21no—
53C22⋊D281—22no—
54C22⋊D281—22no—
55C22⋊D281—21no—
56C2×Dic281—21no—
57C2×Dic281—21no—
58C2×Dic281—22no—
59C2×Dic281—22no—
60C2×Dic281D411yescharacteristic
61C4×D281—21no—
62C4×D281—21no—
63C4×D281—21no—
64C4×D281D411yescharacteristic
65C4×D281D411yescharacteristic
66C4×D281C2311yescharacteristic
67C4×D281C2311yescharacteristic
68#14555886C2312yes—
69C23×C281—21no—
70Q8×C281C2311yescharacteristic
71D4×C281—21no—
72D4×C281—21no—
73D4×C281C2311yescharacteristic
74D4×C281C2312yes—
75C2×C4×C281—21no—
76C2×C4×C281C2311yescharacteristic
77C8×C281C2312yes—
78C22×C281—21no—
79C22×C281—22no—
80C22×C281—42no—
81C22×C281C2×D411yescharacteristic
82C2×D281—21no—
83C2×D281—41no—
84C2×D281—42no—
85C2×D281C2×D411yescharacteristic
86C2×D281C2×D411yescharacteristic
87C4×C281—21no—
88C4×C281C2×D411yescharacteristic
89C4×C281C2411yescharacteristic
90Dic281—21no—
91Dic281—22no—
92Dic281C2×D411yescharacteristic
93Dic281C2×D411yescharacteristic
94C2×C281—21no—
95C2×C281—41no—
96C2×C281—42no—
97C2×C281C22×D411yescharacteristic
98D281—21no—
99D281—21no—
100D281—41no—
101C281#57511yescharacteristic, complemented, Sylow
102#575—2811nomaximal, Sylow
103C2×#41—2811no—
104C2×#41—2811no—
105#137—2811no—
106#137—2812no—
107#137—2811no—
108AGL(1,ℤ/8)—2811no—
109AGL(1,ℤ/8)—2812no—
110AGL(1,ℤ/8)D28111yescharacteristic, complemented
111#135—2812no—
112#135—2812no—
113C2×M16—2811no—
114#41—2811no—
115#41—2812no—
116#41—2812no—
117#41—2811no—
118#41—2811no—
119#41—5621no—
120#41—5621no—
121#41—5621no—
122#41—5621no—
123#41C2×D28111yescharacteristic
124C2×Q8—2811no—
125C2×Q8—2811no—
126C2×D4—2811no—
127C2×D4—5621no—
128C2×D4—5621no—
129C2×D4C2×D28111yescharacteristic, complemented
130C22×C4—2811no—
131C22×C4—5621no—
132C22×C4—5621no—
133Q16—2812no—
134Q16—2812no—
135SD16—2812no—
136SD16—2812no—
137SD16—2812no—
138SD16C2×D28112yescomplemented
139D8—2812no—
140D8C2×D28112yescomplemented
141M16—2811no—
142M16—2812no—
143M16C2×D28111yescharacteristic, complemented
144C2×C8—2812no—
145C23—21no—
146C23—2811no—
147C23—5621no—
148Q8—2811no—
149Q8—2812no—
150Q8—5621no—
151Q8—5621no—
152Q8C22×D28111yescharacteristic
153D4—21no—
154D4—21no—
155D4—2811no—
156D4—5621no—
157D4—5621no—
158D4—5621no—
159D4—5622no—
160D4—5622no—
161D4—5621no—
162D4C22×D28112yes—
163D4C22×D28111yescharacteristic
164C2×C4—21no—
165C2×C4—2811no—
166C2×C4—2811no—
167C2×C4—2811no—
168C2×C4—2811no—
169C2×C4—2811no—
170C2×C4—5621no—
171C2×C4—5621no—
172C2×C4—5621no—
173C2×C4—5622no—
174C2×C4—5622no—
175C2×C4—5621no—
176C2×C4—5621no—
177C2×C4C22×D28111yescharacteristic
178C8—2812no—
179C8C22×D28112yes—
180C22—21no—
181C22—22no—
182C22—42no—
183C22—2811no—
184C22—2811no—
185C22—5621no—
186C22—11241no—
187C22—11242no—
188C22D4×D28111yescharacteristic
189C4—21no—
190C4—2811no—
191C4—2811no—
192C4—5621no—
193C4—5622no—
194C4D4×D28111yescharacteristic
195C4C23×D28111yescharacteristic
196C2—21no—
197C2—42no—
198C2—41no—
199C2—5621no—
200C2—5621no—
201C2—11241no—
202C2C2×D4×D28111yescharacteristic
subgroupG/H
centerC2C2×D4×D281
commutator, cosocleC4×C281C24
FrattiniC4C23×D281
FittingAGL(1,ℤ/8)×C281C2
socleC2×C281C22×D4
hypercenterAGL(1,ℤ/8)D281
hypocenterC281#575
LCSG ▷ C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#17985137C2semidirect
2. #41×D281C2semidirect
3. #22582912C2semidirect
4. #22582909C2semidirect
5. #22582908C2semidirect
6. #22582905C2semidirect
7. #22582903C2semidirect
8. #22582900C2semidirect
9. #22582898C2semidirect
10. M16×D281C2semidirect
11. AGL(1,ℤ/8)×C281C2semidirect
12. #17985139C22semidirect
19. #17985137C22semidirect
20. #17985137C22semidirect
21. C2×Dic562C22semidirect
22. Q8×D281C22semidirect
25. D4×D281C22semidirect
29. Dic1124C22semidirect
30. #17985128C22semidirect
31. #17985127C22semidirect
32. #17985126C22semidirect
33. #17985126C22semidirect
34. #17985123C22semidirect
35. #17985122C22semidirect
36. #17985121C22semidirect
37. C8×D281C22semidirect
39. C2×D4×C281C22semidirect
40. SD16×C281C22semidirect
41. D8×C281C22semidirect
42. M16×C281C22semidirect
101. C281#575semidirect
110. AGL(1,ℤ/8)D281semidirect
129. C2×D4C2×D281semidirect
138. SD16C2×D281semidirect
140. D8C2×D281semidirect
143. M16C2×D281semidirect

Maximal subgroups

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

subgroupindex
C2×#179851372
#41×D2812
#225829122
#225829092
#225829082
#225829052
#225829032
#225829002
#225828982
M16×D2812
AGL(1,ℤ/8)×C2812
#575281