Finite Group Databasebeta

← #31827272

Subgroups — #31827272

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#22583657C211yesmaximal, characteristic, complemented
2#22583656C211yesmaximal, characteristic, complemented
3#22583642C212yesmaximal, complemented
4#22583640C211yesmaximal, characteristic, complemented
5#22583635C211yesmaximal, characteristic, complemented
6#22583634C212yesmaximal, complemented
7#22583631C212yesmaximal, complemented
8C2×#17985381C211yesmaximal, characteristic, complemented
9SD16×D283C212yesmaximal, complemented
10#22583616C211yesmaximal, characteristic, complemented
11#135×C283C211yesmaximal, characteristic, complemented
12#17985393C2212yes—
13#17985392—21no—
14#17985392—21no—
15#17985392C2211yescharacteristic
16#17985391—22no—
17#17985391C2212yescomplemented
18C2×Dic566—21no—
19C2×Dic566C2211yescharacteristic, complemented
20Q8×D283C2212yescomplemented
21C2×D1132—21no—
22C2×D1132C2211yescharacteristic
23D4×D283—22no—
24D4×D283C2212yes—
25#17985382C2212yescomplemented
26#17985381C2212yescomplemented
27#17985381C2212yescomplemented
28#17985380C2212yescomplemented
29#17985379C2212yescomplemented
30#17985377C2212yescomplemented
31#17985376C2211yescharacteristic, complemented
32#17985375C2212yescomplemented
33C8×D283C2212yescomplemented
34#41×C283C2211yescharacteristic
35#41×C283C2211yescharacteristic, complemented
36Q16×C283C2211yescharacteristic, complemented
37SD16×C283C2211yescharacteristic, complemented
38SD16×C283C2211yescharacteristic, complemented
39D8×C283C2211yescharacteristic, complemented
40C2×C8×C283C2211yescharacteristic, complemented
41C22×D283—21no—
42C22×D283—22no—
43Dic566—21no—
44Dic566—22no—
45Dic566D411yescharacteristic
46Dic566C2312yes—
47D1132—22no—
48D1132—21no—
49D1132D411yescharacteristic
50D1132C2312yes—
51C22⋊D283—22no—
52C22⋊D283—22no—
53C22⋊D283D412yes—
54C2×Dic283—21no—
55C2×Dic283—22no—
56C4×D283—22no—
57C4×D283—22no—
58C4×D283C2312yes—
59C283⋊C8C2312yes—
60Q8×C283C2311yescharacteristic
61Q8×C283C2311yescharacteristic
62D4×C283—21no—
63D4×C283—21no—
64D4×C283C2311yescharacteristic
65D4×C283C2311yescharacteristic
66C2×C4×C283—21no—
67C2×C4×C283—21no—
68C2×C4×C283C2311yescharacteristic
69C8×C283C2311yescharacteristic
70C8×C283C2311yescharacteristic
71C22×C283—21no—
72C22×C283—21no—
73C22×C283C2×D411yescharacteristic
74C2×D283—22no—
75C2×D283—82no—
76C2×D283—81no—
77C2×D283C2×D412yes—
78C4×C283—21no—
79C4×C283—21no—
80C4×C283C2×D411yescharacteristic
81C4×C283C2411yescharacteristic
82Dic283—22no—
83Dic283C2×D412yes—
84C2×C283—21no—
85C2×C283—41no—
86C2×C283—41no—
87C2×C283C22×D411yescharacteristic
88D283—22no—
89D283—42no—
90C283#57711yescharacteristic, complemented, Sylow
91#577—2831nomaximal, Sylow
922−1+4—2831no—
93H(5,𝔽2)—2831no—
94#137—2831no—
95#137—2832no—
96AGL(1,ℤ/8)—2831no—
97AGL(1,ℤ/8)—2832no—
98#135—2832no—
99#135D28311yescharacteristic, complemented
100C2×SD16—2832no—
101C2×SD16—2831no—
102#131—2831no—
103#41—2831no—
104#41—2832no—
105#41—2832no—
106#41—5661no—
107#41—5661no—
108#41—5662no—
109#41C2×D28311yescharacteristic
110#41C2×D28311yescharacteristic, complemented
111C2×Q8—2832no—
112C2×Q8—2831no—
113C2×Q8—5661no—
114C2×D4—2832no—
115C2×D4—2831no—
116C2×D4—5661no—
117C2×D4—5662no—
118Q16—2832no—
119Q16C2×D28311yescharacteristic, complemented
120SD16—2832no—
121SD16—2832no—
122SD16—2832no—
123SD16—2832no—
124SD16C2×D28311yescharacteristic, complemented
125SD16C2×D28311yescharacteristic, complemented
126D8—2832no—
127D8C2×D28311yescharacteristic, complemented
128M16—2831no—
129M16—2832no—
130C2×C8—2832no—
131C2×C8C2×D28311yescharacteristic, complemented
132C23—5662no—
133C23—5661no—
134Q8—2831no—
135Q8—2832no—
136Q8—5662no—
137Q8—5661no—
138Q8C22×D28311yescharacteristic
139Q8C22×D28311yescharacteristic
140D4—21no—
141D4—21no—
142D4—2832no—
143D4—2831no—
144D4—2832no—
145D4—5662no—
146D4—5662no—
147D4—5662no—
148D4—5661no—
149D4C22×D28311yescharacteristic
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—2832no—
160C8C22×D28311yescharacteristic
161C8C22×D28311yescharacteristic
162C22—21no—
163C22—21no—
164C22—2832no—
165C22—5662no—
166C22—22641no—
167C22—22642no—
168C22D4×D28311yescharacteristic
169C4—21no—
170C4—21no—
171C4—2832no—
172C4—5662no—
173C4D4×D28311yescharacteristic
174C4C23×D28311yescharacteristic
175C2—21no—
176C2—41no—
177C2—41no—
178C2—5662no—
179C2—11322no—
180C2C2×D4×D28311yescharacteristic
subgroupG/H
centerC2C2×D4×D283
commutator, cosocleC4×C283C24
FrattiniC4C23×D283
Fitting#135×C283C2
socleC2×C283C22×D4
hypercenter#135D283
hypocenterC283#577
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #22583657C2semidirect
2. #22583656C2semidirect
3. #22583642C2semidirect
4. #22583640C2semidirect
5. #22583635C2semidirect
6. #22583634C2semidirect
7. #22583631C2semidirect
8. C2×#17985381C2semidirect
9. SD16×D283C2semidirect
10. #22583616C2semidirect
11. #135×C283C2semidirect
17. #17985391C22semidirect
19. C2×Dic566C22semidirect
20. Q8×D283C22semidirect
25. #17985382C22semidirect
26. #17985381C22semidirect
27. #17985381C22semidirect
28. #17985380C22semidirect
29. #17985379C22semidirect
30. #17985377C22semidirect
31. #17985376C22semidirect
32. #17985375C22semidirect
33. C8×D283C22semidirect
35. #41×C283C22semidirect
36. Q16×C283C22semidirect
37. SD16×C283C22semidirect
38. SD16×C283C22semidirect
39. D8×C283C22semidirect
40. C2×C8×C283C22semidirect
90. C283#577semidirect
99. #135D283semidirect
110. #41C2×D283semidirect
119. Q16C2×D283semidirect
124. SD16C2×D283semidirect
125. SD16C2×D283semidirect
127. D8C2×D283semidirect
131. C2×C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#225836572
#225836562
#225836422
#225836402
#225836352
#225836342
#225836312
C2×#179853812
SD16×D2832
#225836162
#135×C2832
#577283