Finite Group Databasebeta

← #31827269

Subgroups — #31827269

Order 18112.

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

normal subgroups only

This group has 268 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#22583656C211yesmaximal, characteristic, complemented
2#22583655C211yesmaximal, characteristic, complemented
3#22583638C211yesmaximal, characteristic, complemented
4#22583637C212yesmaximal, complemented
5#22583634C212yesmaximal, complemented
6#22583631C212yesmaximal, complemented
7#22583630C211yesmaximal, characteristic, complemented
8C2×#17985377C211yesmaximal, characteristic, complemented
9D8×D283C212yesmaximal, complemented
10#22583618C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C283C211yesmaximal, characteristic, complemented
12#17985393C2212yescomplemented
13#17985392—21no—
14#17985392C2211yescharacteristic
15#17985392C2211yescharacteristic, complemented
16#17985391—21no—
17#17985391C2212yescomplemented
18C2×D1132—21no—
19C2×D1132C2211yescharacteristic, complemented
20C2×C22⋊D283—22no—
21D4×D283—21no—
22D4×D283—22no—
23D4×D283C2212yescomplemented
24D4×D283C2212yescomplemented
25#17985382C2211yescharacteristic, complemented
26#17985381C2212yescomplemented
27#17985380C2211yescharacteristic, complemented
28#17985379C2211yescharacteristic, complemented
29D2264C2212yescomplemented
30#17985377C2211yescharacteristic, complemented
31#17985377C2212yescomplemented
32#17985377C2212yescomplemented
33#17985375C2212yescomplemented
34C2×C283⋊C8C2211yescharacteristic, complemented
35C8×D283C2212yescomplemented
36#41×C283C2211yescharacteristic, complemented
37C2×D4×C283C2211yescharacteristic, complemented
38SD16×C283C2212yescomplemented
39D8×C283C2212yescomplemented
40M16×C283C2211yescharacteristic, complemented
41C22×D283—21no—
42C22×D283—22no—
43C22×D283—22no—
44Dic566D411yescharacteristic
45Dic566C2311yescharacteristic
46D1132—22no—
47D1132—21no—
48D1132D411yescharacteristic
49D1132C2312yes—
50D1132C2311yescharacteristic
51C22⋊D283—21no—
52C22⋊D283—22no—
53C22⋊D283—22no—
54C22⋊D283—22no—
55C22⋊D283D412yes—
56C2×Dic283—22no—
57C4×D283—21no—
58C4×D283—22no—
59C4×D283C2312yes—
60C283⋊C8C2311yescharacteristic
61C283⋊C8C2311yescharacteristic
62C23×C283—21no—
63Q8×C283C2311yescharacteristic
64D4×C283—21no—
65D4×C283—21no—
66D4×C283C2311yescharacteristic
67D4×C283C2312yes—
68C2×C4×C283—21no—
69C2×C4×C283C2311yescharacteristic
70C8×C283C2312yes—
71C22×C283—21no—
72C22×C283—22no—
73C22×C283—81no—
74C22×C283C2×D411yescharacteristic
75C2×D283—21no—
76C2×D283—22no—
77C2×D283—82no—
78C2×D283—82no—
79C2×D283—81no—
80C2×D283C2×D412yes—
81C4×C283—21no—
82C4×C283C2×D411yescharacteristic
83C4×C283C2411yescharacteristic
84Dic283—21no—
85Dic283C2×D412yes—
86C2×C283—21no—
87C2×C283—41no—
88C2×C283—42no—
89C2×C283C22×D411yescharacteristic
90D283—22no—
91D283—41no—
92D283—42no—
93C283#57611yescharacteristic, complemented, Sylow
94#576—2831nomaximal, Sylow
95H(5,𝔽2)—2831no—
96H(5,𝔽2)—2831no—
97AGL(1,ℤ/8)—2832no—
98AGL(1,ℤ/8)—2832no—
99AGL(1,ℤ/8)—2831no—
100AGL(1,ℤ/8)D28311yescharacteristic, complemented
101#135—2831no—
102#135—2832no—
103C2×D8—2831no—
104C2×D8—2832no—
105#131—2831no—
106#41—2831no—
107#41—2832no—
108#41—2832no—
109#41—2831no—
110#41—5661no—
111#41—5661no—
112#41C2×D28311yescharacteristic, complemented
113C2×D4—2832no—
114C2×D4—2832no—
115C2×D4—2831no—
116C2×D4—5661no—
117C2×D4—5662no—
118C2×D4—5661no—
119C2×D4—5662no—
120C2×D4C2×D28311yescharacteristic, complemented
121Q16—2831no—
122SD16—2831no—
123SD16—2831no—
124SD16—2832no—
125SD16C2×D28312yescomplemented
126D8—2832no—
127D8—2831no—
128D8—2832no—
129D8—2832no—
130D8C2×D28312yescomplemented
131M16—2832no—
132M16C2×D28311yescharacteristic, complemented
133C2×C8—2831no—
134C2×C8—2832no—
135C23—21no—
136C23—5662no—
137C23—5662no—
138C23—5661no—
139Q8—2831no—
140Q8—2831no—
141Q8C22×D28311yescharacteristic
142D4—21no—
143D4—21no—
144D4—2832no—
145D4—2831no—
146D4—2832no—
147D4—2831no—
148D4—5662no—
149D4—5662no—
150D4—5662no—
151D4—5662no—
152D4—5661no—
153D4—5661no—
154D4C22×D28312yes—
155D4C22×D28311yescharacteristic
156C2×C4—21no—
157C2×C4—2832no—
158C2×C4—5662no—
159C2×C4—5662no—
160C2×C4—5661no—
161C2×C4C22×D28311yescharacteristic
162C8—2831no—
163C8—2831no—
164C8C22×D28312yes—
165C22—21no—
166C22—22no—
167C22—81no—
168C22—2832no—
169C22—5662no—
170C22—5661no—
171C22—22641no—
172C22—22642no—
173C22—22642no—
174C22D4×D28311yescharacteristic
175C4—21no—
176C4—2832no—
177C4—5661no—
178C4D4×D28311yescharacteristic
179C4C23×D28311yescharacteristic
180C2—21no—
181C2—42no—
182C2—41no—
183C2—5662no—
184C2—11322no—
185C2—11321no—
186C2C2×D4×D28311yescharacteristic
subgroupG/H
centerC2C2×D4×D283
commutator, cosocleC4×C283C24
FrattiniC4C23×D283
FittingAGL(1,ℤ/8)×C283C2
socleC2×C283C22×D4
hypercenterAGL(1,ℤ/8)D283
hypocenterC283#576
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #22583656C2semidirect
2. #22583655C2semidirect
3. #22583638C2semidirect
4. #22583637C2semidirect
5. #22583634C2semidirect
6. #22583631C2semidirect
7. #22583630C2semidirect
8. C2×#17985377C2semidirect
9. D8×D283C2semidirect
10. #22583618C2semidirect
11. AGL(1,ℤ/8)×C283C2semidirect
12. #17985393C22semidirect
15. #17985392C22semidirect
17. #17985391C22semidirect
19. C2×D1132C22semidirect
23. D4×D283C22semidirect
24. D4×D283C22semidirect
25. #17985382C22semidirect
26. #17985381C22semidirect
27. #17985380C22semidirect
28. #17985379C22semidirect
29. D2264C22semidirect
30. #17985377C22semidirect
31. #17985377C22semidirect
32. #17985377C22semidirect
33. #17985375C22semidirect
34. C2×C283⋊C8C22semidirect
35. C8×D283C22semidirect
36. #41×C283C22semidirect
37. C2×D4×C283C22semidirect
38. SD16×C283C22semidirect
39. D8×C283C22semidirect
40. M16×C283C22semidirect
93. C283#576semidirect
100. AGL(1,ℤ/8)D283semidirect
112. #41C2×D283semidirect
120. C2×D4C2×D283semidirect
125. SD16C2×D283semidirect
130. D8C2×D283semidirect
132. M16C2×D283semidirect

Maximal subgroups

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

subgroupindex
#225836562
#225836552
#225836382
#225836372
#225836342
#225836312
#225836302
C2×#179853772
D8×D2832
#225836182
AGL(1,ℤ/8)×C2832
#576283