Finite Group Databasebeta

← #31827274

Subgroups — #31827274

Order 18112.

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#22583658C211yesmaximal, characteristic, complemented
2#22583656C211yesmaximal, characteristic, complemented
3#22583642C212yesmaximal, complemented
4#22583638C211yesmaximal, characteristic, complemented
5#22583637C212yesmaximal, complemented
6#22583633C212yesmaximal, complemented
7#22583630C211yesmaximal, characteristic, complemented
8C2×#17985379C211yesmaximal, characteristic, complemented
9SD16×D283C212yesmaximal, complemented
10#22583618C211yesmaximal, characteristic, complemented
11#137×C283C211yesmaximal, characteristic, complemented
12#17985393—21no—
13#17985393C2212yes—
14#17985393C2212yescomplemented
15#17985392—21no—
16#17985392—22no—
17#17985392C2211yescharacteristic
18#17985392C2211yescharacteristic, complemented
19Q8×D283—21no—
20Q8×D283C2212yescomplemented
21C2×D1132—21no—
22C2×D1132C2211yescharacteristic
23D4×D283—22no—
24D4×D283C2212yes—
25#17985382C2211yescharacteristic, complemented
26#17985381C2212yescomplemented
27#17985380C2211yescharacteristic, complemented
28#17985379C2212yescomplemented
29#17985379C2212yescomplemented
30#17985379C2211yescharacteristic, complemented
31D2264C2212yescomplemented
32#17985377C2211yescharacteristic, complemented
33#17985375C2212yescomplemented
34C2×C283⋊C8C2211yescharacteristic, complemented
35C8×D283C2212yescomplemented
36#41×C283C2211yescharacteristic
37C2×Q8×C283C2211yescharacteristic, complemented
38Q16×C283C2212yescomplemented
39SD16×C283C2212yescomplemented
40M16×C283C2211yescharacteristic, complemented
41C22×D283—21no—
42C22×D283—22no—
43Dic566—22no—
44Dic566D411yescharacteristic
45Dic566C2311yescharacteristic
46D1132—22no—
47D1132—22no—
48D1132—21no—
49D1132D411yescharacteristic
50D1132C2311yescharacteristic
51D1132C2312yes—
52C22⋊D283—21no—
53C22⋊D283—22no—
54C22⋊D283D412yes—
55C4×D283—22no—
56C4×D283—21no—
57C4×D283—22no—
58C4×D283—22no—
59C4×D283C2312yes—
60C283⋊C8C2311yescharacteristic
61C283⋊C8C2311yescharacteristic
62Q8×C283—21no—
63Q8×C283C2312yes—
64Q8×C283C2311yescharacteristic
65D4×C283—21no—
66D4×C283C2311yescharacteristic
67C2×C4×C283—21no—
68C2×C4×C283—21no—
69C2×C4×C283C2311yescharacteristic
70C8×C283C2312yes—
71C22×C283—21no—
72C22×C283C2×D411yescharacteristic
73C2×D283—21no—
74C2×D283—22no—
75C2×D283—82no—
76C2×D283—81no—
77C2×D283C2×D412yes—
78C4×C283—21no—
79C4×C283—22no—
80C4×C283C2×D411yescharacteristic
81C4×C283C2411yescharacteristic
82Dic283—21no—
83Dic283C2×D412yes—
84C2×C283—21no—
85C2×C283—41no—
86C2×C283C22×D411yescharacteristic
87D283—22no—
88D283—41no—
89D283—42no—
90C283#57711yescharacteristic, complemented, Sylow
91#577—2831nomaximal, Sylow
922−1+4—2831no—
93H(5,𝔽2)—2831no—
94#137—2832no—
95#137D28311yescharacteristic, complemented
96AGL(1,ℤ/8)—2832no—
97AGL(1,ℤ/8)—2831no—
98#135—2831no—
99#135—2832no—
100C2×SD16—2831no—
101C2×SD16—2832no—
102#131—2831no—
103#41—2831no—
104#41—2832no—
105#41—2832no—
106#41—2831no—
107#41—5662no—
108#41—5661no—
109#41—5661no—
110#41C2×D28311yescharacteristic
111C2×Q8—2832no—
112C2×Q8—5661no—
113C2×Q8C2×D28311yescharacteristic, complemented
114C2×D4—2832no—
115C2×D4—2831no—
116C2×D4—5661no—
117C2×D4—5662no—
118Q16—2831no—
119Q16C2×D28312yescomplemented
120SD16—2832no—
121SD16—2832no—
122SD16—2831no—
123SD16—2831no—
124SD16—2832no—
125SD16C2×D28312yescomplemented
126D8—2831no—
127D8—2832no—
128M16—2832no—
129M16C2×D28311yescharacteristic, complemented
130C2×C8—2831no—
131C2×C8—2832no—
132C23—5662no—
133C23—5661no—
134Q8—21no—
135Q8—2831no—
136Q8—2831no—
137Q8—5662no—
138Q8C22×D28312yes—
139Q8C22×D28311yescharacteristic
140D4—21no—
141D4—2832no—
142D4—2831no—
143D4—2831no—
144D4—2832no—
145D4—5662no—
146D4—5662no—
147D4—5662no—
148D4—5661no—
149D4—5661no—
150D4C22×D28311yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—2832no—
154C2×C4—5662no—
155C2×C4—5662no—
156C2×C4—5662no—
157C2×C4—5661no—
158C2×C4C22×D28311yescharacteristic
159C8—2831no—
160C8—2831no—
161C8C22×D28312yes—
162C22—21no—
163C22—2832no—
164C22—5661no—
165C22—5662no—
166C22—22641no—
167C22—22642no—
168C22D4×D28311yescharacteristic
169C4—21no—
170C4—22no—
171C4—2832no—
172C4—5661no—
173C4D4×D28311yescharacteristic
174C4C23×D28311yescharacteristic
175C2—21no—
176C2—41no—
177C2—5662no—
178C2—11322no—
179C2—11321no—
180C2C2×D4×D28311yescharacteristic
subgroupG/H
centerC2C2×D4×D283
commutator, cosocleC4×C283C24
FrattiniC4C23×D283
Fitting#137×C283C2
socleC2×C283C22×D4
hypercenter#137D283
hypocenterC283#577
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. #22583658C2semidirect
2. #22583656C2semidirect
3. #22583642C2semidirect
4. #22583638C2semidirect
5. #22583637C2semidirect
6. #22583633C2semidirect
7. #22583630C2semidirect
8. C2×#17985379C2semidirect
9. SD16×D283C2semidirect
10. #22583618C2semidirect
11. #137×C283C2semidirect
14. #17985393C22semidirect
18. #17985392C22semidirect
20. Q8×D283C22semidirect
25. #17985382C22semidirect
26. #17985381C22semidirect
27. #17985380C22semidirect
28. #17985379C22semidirect
29. #17985379C22semidirect
30. #17985379C22semidirect
31. D2264C22semidirect
32. #17985377C22semidirect
33. #17985375C22semidirect
34. C2×C283⋊C8C22semidirect
35. C8×D283C22semidirect
37. C2×Q8×C283C22semidirect
38. Q16×C283C22semidirect
39. SD16×C283C22semidirect
40. M16×C283C22semidirect
90. C283#577semidirect
95. #137D283semidirect
113. C2×Q8C2×D283semidirect
119. Q16C2×D283semidirect
125. SD16C2×D283semidirect
129. M16C2×D283semidirect

Maximal subgroups

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

subgroupindex
#225836582
#225836562
#225836422
#225836382
#225836372
#225836332
#225836302
C2×#179853792
SD16×D2832
#225836182
#137×C2832
#577283