Finite Group Databasebeta

← #31827109

Subgroups — #31827109

Order 18112.

334 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 115 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
2#22583597C211yesmaximal, characteristic, complemented
3#22583591C212yesmaximal, complemented
4#22583589C211yesmaximal, characteristic, complemented
5#22583582C212yesmaximal, complemented
6#22583581C211yesmaximal, characteristic, complemented
7#22583579C212yesmaximal, complemented
8D4×Dic283C211yesmaximal, characteristic, complemented
9C4×C22⋊D283C211yesmaximal, characteristic, complemented
10C2×C22⋊Dic283C212yesmaximal, complemented
11C22×D4×C283C211yesmaximal, characteristic, complemented
12#17985391—24no—
13C2×Dic566C2211yescharacteristic, complemented
14C2×C22⋊D283C2211yescharacteristic
15C2×C22⋊D283C2212yescomplemented
16C2×C22⋊D283C2212yescomplemented
17C22×Dic283C2212yescomplemented
18C22×Dic283C2212yescomplemented
19C2×C4×D283C2211yescharacteristic, complemented
20C4⋊Dic283C2211yescharacteristic, complemented
21Dic283⋊C4C2211yescharacteristic, complemented
22Dic283⋊C4C2212yescomplemented
23C22⋊Dic283C2211yescharacteristic
24C22⋊Dic283C2212yes—
25C22⋊Dic283C2212yescomplemented
26C22⋊Dic283C2212yescomplemented
27C22⋊Dic283C2212yescomplemented
28C22⋊Dic283C2212yescomplemented
29(C2×D283)⋊C4C2211yescharacteristic, complemented
30C4×Dic283C2211yescharacteristic, complemented
31C24×C283C2212yes—
32C2×D4×C283—24no—
33C2×D4×C283C2211yescharacteristic
34C2×D4×C283C2212yes—
35C2×D4×C283C2211yescharacteristic
36C22×C4×C283C2211yescharacteristic
37C22×D283C2311yescharacteristic
38Dic566—22no—
39C22⋊D283—24no—
40C22⋊D283—22no—
41C22⋊D283—42no—
42C2×Dic283—24no—
43C2×Dic283—42no—
44C2×Dic283C2311yescharacteristic
45C2×Dic283C2311yescharacteristic
46C2×Dic283C2312yes—
47C2×Dic283C2311yescharacteristic
48C2×Dic283C2312yes—
49C4×D283—22no—
50C23×C283—24no—
51C23×C283—24no—
52C23×C283—42no—
53C23×C283C2312yes—
54C23×C283C2312yes—
55C23×C283C2311yescharacteristic
56D4×C283—24no—
57D4×C283—22no—
58D4×C283D414yescomplemented
59C2×C4×C283—22no—
60C2×C4×C283C2311yescharacteristic
61C2×C4×C283C2311yescharacteristic
62C22×C283—21no—
63C22×C283—22no—
64C22×C283—21no—
65C22×C283—22no—
66C22×C283—22no—
67C22×C283—22no—
68C22×C283—22no—
69C22×C283—48no—
70C22×C283C2×D414yes—
71C22×C283#4112yescomplemented
72C22×C283C2411yescharacteristic
73C2×D283—21no—
74C2×D283—21no—
75C2×D283—21no—
76C4×C283—21no—
77C4×C283C2×D412yes—
78Dic283—21no—
79Dic283—22no—
80Dic283—21no—
81Dic283—21no—
82Dic283—22no—
83C2×C283—22no—
84C2×C283—24no—
85C2×C283—42no—
86C2×C283C22×D411yescharacteristic
87C2×C283C2×#4111yescharacteristic
88C2×C283H(5,𝔽2)11yescharacteristic
89D283—41no—
90C283#54611yescharacteristic, complemented, Sylow
91#546—2831nomaximal, Sylow
92C2×#41—2831no—
93C22×D4D28311yescharacteristic, complemented
94#124—2831no—
95#123—2832no—
96C22⋊Q8—2831no—
97#121—2831no—
98#121—2832no—
99#120—2832no—
100C4×D4—2831no—
101C4×D4—2831no—
102C2×C22⋊C4—2832no—
103C24C2×D28312yes—
104#41—5664no—
105C2×Q8—2831no—
106C2×D4—24no—
107C2×D4—2831no—
108C2×D4—2832no—
109C2×D4—2832no—
110C2×D4C2×D28312yes—
111C2×D4C2×D28311yescharacteristic
112C2×D4C2×D28311yescharacteristic
113C22×C4—2832no—
114C22×C4—2832no—
115C22×C4—2831no—
116C22×C4C2×D28311yescharacteristic
117C4⋊C4—2831no—
118C4⋊C4—2832no—
119C4⋊C4—2831no—
120C22⋊C4—2831no—
121C22⋊C4—2832no—
122C22⋊C4—2832no—
123C22⋊C4—2832no—
124C22⋊C4—2832no—
125C22⋊C4—2832no—
126C22⋊C4—2831no—
127C42—2831no—
128C23—24no—
129C23—24no—
130C23—42no—
131C23—2831no—
132C23C22×D28312yes—
133C23C22×D28312yes—
134C23C22×D28311yescharacteristic
135Q8—5662no—
136D4—24no—
137D4—22no—
138D4—5664no—
139D4—5662no—
140D4—11322no—
141D4C22⋊D28314yescomplemented
142C2×C4—22no—
143C2×C4—2831no—
144C2×C4—2831no—
145C2×C4—2832no—
146C2×C4—2831no—
147C2×C4—2832no—
148C2×C4—5664no—
149C2×C4—5662no—
150C2×C4—11322no—
151C2×C4C22×D28311yescharacteristic
152C2×C4C22×D28311yescharacteristic
153C22—21no—
154C22—22no—
155C22—22no—
156C22—21no—
157C22—22no—
158C22—22no—
159C22—22no—
160C22—48no—
161C22—5661no—
162C22—5661no—
163C22—5661no—
164C22C2×C22⋊D28314yes—
165C22#1798539112yescomplemented
166C22C23×D28311yescharacteristic
167C4—21no—
168C4—5661no—
169C4—5662no—
170C4—5661no—
171C4—5661no—
172C4—5662no—
173C4C2×C22⋊D28312yes—
174C2—22no—
175C2—24no—
176C2—42no—
177C2—11321no—
178C2C22×C22⋊D28311yescharacteristic
179C2C2×#1798539111yescharacteristic
180C2#2258365511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D283
commutator, socle, cosocleC22×C283C24
FittingC22×D4×C283C2
hypercenterC22×D4D283
hypocenterC283#546
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#17985391C2semidirect
2. #22583597C2semidirect
3. #22583591C2semidirect
4. #22583589C2semidirect
5. #22583582C2semidirect
6. #22583581C2semidirect
7. #22583579C2semidirect
8. D4×Dic283C2semidirect
9. C4×C22⋊D283C2semidirect
10. C2×C22⋊Dic283C2semidirect
11. C22×D4×C283C2semidirect
13. C2×Dic566C22semidirect
15. C2×C22⋊D283C22semidirect
16. C2×C22⋊D283C22semidirect
17. C22×Dic283C22semidirect
18. C22×Dic283C22semidirect
19. C2×C4×D283C22semidirect
20. C4⋊Dic283C22semidirect
21. Dic283⋊C4C22semidirect
22. Dic283⋊C4C22semidirect
25. C22⋊Dic283C22semidirect
26. C22⋊Dic283C22semidirect
27. C22⋊Dic283C22semidirect
28. C22⋊Dic283C22semidirect
29. (C2×D283)⋊C4C22semidirect
30. C4×Dic283C22semidirect
58. D4×C283D4semidirect
71. C22×C283#41semidirect
90. C283#546semidirect
93. C22×D4D283semidirect
141. D4C22⋊D283semidirect
165. C22#17985391semidirect

Maximal subgroups

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

subgroupindex
C2×#179853912
#225835972
#225835912
#225835892
#225835822
#225835812
#225835792
D4×Dic2832
C4×C22⋊D2832
C2×C22⋊Dic2832
C22×D4×C2832
#546283