Finite Group Databasebeta

← #31827110

Subgroups — #31827110

Order 18112.

334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 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×#17985391C211yesmaximal, characteristic, complemented
2C2×D4×D283C211yesmaximal, characteristic, complemented
3#22583598C211yesmaximal, characteristic, complemented
4#22583594C212yesmaximal, complemented
5#22583590C211yesmaximal, characteristic, complemented
6#22583585C211yesmaximal, characteristic, complemented
7#22583584C212yesmaximal, complemented
8#22583580C212yesmaximal, complemented
9C4×D1132C211yesmaximal, characteristic, complemented
10C2×(C2×D283)⋊C4C212yesmaximal, complemented
11C4×D4×C283C211yesmaximal, characteristic, complemented
12C23×D283C2212yes—
13#17985391—24no—
14C2×Dic566C2211yescharacteristic, complemented
15C2×D1132C2211yescharacteristic
16C2×D1132C2211yescharacteristic
17C2×D1132C2212yescomplemented
18C2×C22⋊D283C2212yes—
19C2×C22⋊D283C2212yescomplemented
20D4×D283—24no—
21C22×Dic283C2212yescomplemented
22C2×C4×D283C2211yescharacteristic
23C2×C4×D283C2211yescharacteristic, complemented
24C4⋊Dic283C2211yescharacteristic, complemented
25C4⋊Dic283C2212yescomplemented
26(C2×D283)⋊C4C2211yescharacteristic
27(C2×D283)⋊C4C2212yes—
28(C2×D283)⋊C4C2212yescomplemented
29(C2×D283)⋊C4C2212yescomplemented
30(C2×D283)⋊C4C2211yescharacteristic, complemented
31(C2×D283)⋊C4C2212yescomplemented
32C2×D4×C283C2211yescharacteristic
33C22×C4×C283C2212yescomplemented
34C4⋊C4×C283C2211yescharacteristic, complemented
35C22⋊C4×C283C2212yescomplemented
36C42×C283C2211yescharacteristic, complemented
37C22×D283—24no—
38C22×D283—24no—
39C22×D283—42no—
40C22×D283C2312yes—
41C22×D283C2311yescharacteristic
42C22×D283C2311yescharacteristic
43Dic566—22no—
44D1132—22no—
45D1132—22no—
46D1132—42no—
47C22⋊D283—24no—
48C22⋊D283—24no—
49C2×Dic283—24no—
50C2×Dic283C2311yescharacteristic
51C2×Dic283C2312yes—
52C2×Dic283C2311yescharacteristic
53C4×D283—22no—
54C4×D283—22no—
55C23×C283C2312yes—
56D4×C283D414yescomplemented
57C2×C4×C283—42no—
58C2×C4×C283C2311yescharacteristic
59C2×C4×C283C2311yescharacteristic
60C2×C4×C283C2312yes—
61C2×C4×C283C2311yescharacteristic
62C22×C283—22no—
63C22×C283—22no—
64C22×C283C2×D414yes—
65C22×C283C2411yescharacteristic
66C2×D283—21no—
67C2×D283—21no—
68C2×D283—21no—
69C2×D283—22no—
70C2×D283—21no—
71C2×D283—22no—
72C2×D283—21no—
73C2×D283—22no—
74C2×D283—48no—
75C2×D283#4112yescomplemented
76C4×C283—21no—
77C4×C283—21no—
78C4×C283—22no—
79C4×C283C2×D412yes—
80Dic283—21no—
81Dic283—21no—
82Dic283—22no—
83C2×C283—24no—
84C2×C283C22×D411yescharacteristic
85C2×C283C2×#4111yescharacteristic
86C2×C283H(5,𝔽2)11yescharacteristic
87D283—22no—
88D283—41no—
89D283—42no—
90C283#54611yescharacteristic, complemented, Sylow
91#546—2831nomaximal, Sylow
92C2×#41—2831no—
93C22×D4—2831no—
94#124—2831no—
95#123—2832no—
96C22⋊Q8—2831no—
97#121—2832no—
98#121—2831no—
99#120—2832no—
100C4×D4—2831no—
101C4×D4D28311yescharacteristic, complemented
102C2×C22⋊C4—2832no—
103C24—2832no—
104#41—5664no—
105C2×Q8—2831no—
106C2×D4—2832no—
107C2×D4—2832no—
108C2×D4—2831no—
109C2×D4—2831no—
110C2×D4—2832no—
111C2×D4—5664no—
112C2×D4C2×D28311yescharacteristic
113C22×C4—2832no—
114C22×C4—2831no—
115C22×C4—2831no—
116C22×C4C2×D28312yescomplemented
117C4⋊C4—2831no—
118C4⋊C4—2832no—
119C4⋊C4C2×D28311yescharacteristic, complemented
120C22⋊C4—2831no—
121C22⋊C4—2832no—
122C22⋊C4—2832no—
123C22⋊C4—2832no—
124C22⋊C4—2831no—
125C22⋊C4—2832no—
126C22⋊C4C2×D28312yescomplemented
127C42C2×D28311yescharacteristic, complemented
128C23—2831no—
129C23—2832no—
130C23—2831no—
131C23—5664no—
132C23—5664no—
133C23—11322no—
134C23C22×D28312yes—
135Q8—5662no—
136D4—5662no—
137D4—5664no—
138D4—5664no—
139D4—5662no—
140D4—11322no—
141D4D113214yescomplemented
142C2×C4—42no—
143C2×C4—2831no—
144C2×C4—2832no—
145C2×C4—2831no—
146C2×C4—5664no—
147C2×C4—5662no—
148C2×C4—5662no—
149C2×C4C22×D28311yescharacteristic
150C2×C4C22×D28311yescharacteristic
151C2×C4C22×D28312yes—
152C2×C4C22×D28311yescharacteristic
153C22—22no—
154C22—22no—
155C22—2832no—
156C22—5661no—
157C22—5661no—
158C22—5661no—
159C22—5662no—
160C22—5661no—
161C22—5662no—
162C22—5661no—
163C22—5662no—
164C22—11328no—
165C22C2×D113214yes—
166C22C23×D28311yescharacteristic
167C4—21no—
168C4—21no—
169C4—22no—
170C4—5661no—
171C4—5661no—
172C4—5662no—
173C4C2×D113212yes—
174C2—24no—
175C2—5662no—
176C2—11322no—
177C2—11321no—
178C2C22×D113211yescharacteristic
179C2#41×D28311yescharacteristic
180C2#2258365511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D283
commutator, socle, cosocleC22×C283C24
FittingC4×D4×C283C2
hypercenterC4×D4D283
hypocenterC283#546
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#17985391C2semidirect
2. C2×D4×D283C2semidirect
3. #22583598C2semidirect
4. #22583594C2semidirect
5. #22583590C2semidirect
6. #22583585C2semidirect
7. #22583584C2semidirect
8. #22583580C2semidirect
9. C4×D1132C2semidirect
10. C2×(C2×D283)⋊C4C2semidirect
11. C4×D4×C283C2semidirect
14. C2×Dic566C22semidirect
17. C2×D1132C22semidirect
19. C2×C22⋊D283C22semidirect
21. C22×Dic283C22semidirect
23. C2×C4×D283C22semidirect
24. C4⋊Dic283C22semidirect
25. C4⋊Dic283C22semidirect
28. (C2×D283)⋊C4C22semidirect
29. (C2×D283)⋊C4C22semidirect
30. (C2×D283)⋊C4C22semidirect
31. (C2×D283)⋊C4C22semidirect
33. C22×C4×C283C22semidirect
34. C4⋊C4×C283C22semidirect
35. C22⋊C4×C283C22semidirect
36. C42×C283C22semidirect
56. D4×C283D4semidirect
75. C2×D283#41semidirect
90. C283#546semidirect
101. C4×D4D283semidirect
116. C22×C4C2×D283semidirect
119. C4⋊C4C2×D283semidirect
126. C22⋊C4C2×D283semidirect
127. C42C2×D283semidirect
141. D4D1132semidirect

Maximal subgroups

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

subgroupindex
C2×#179853912
C2×D4×D2832
#225835982
#225835942
#225835902
#225835852
#225835842
#225835802
C4×D11322
C2×(C2×D283)⋊C42
C4×D4×C2832
#546283