Finite Group Databasebeta

← #31827112

Subgroups — #31827112

Order 18112.

334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 105 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×#17985392C211yesmaximal, characteristic, complemented
2C2×D4×D283C211yesmaximal, characteristic, complemented
3#22583597C211yesmaximal, characteristic, complemented
4#22583592C212yesmaximal, complemented
5#22583590C211yesmaximal, characteristic, complemented
6#22583581C212yesmaximal, complemented
7#22583578C212yesmaximal, complemented
8#22583572C211yesmaximal, characteristic, complemented
9C4×C22⋊D283C211yesmaximal, characteristic, complemented
10C22⋊C4×D283C212yesmaximal, complemented
11#121×C283C211yesmaximal, characteristic, complemented
12C23×D283C2212yes—
13#17985392—24no—
14C2×Dic566C2211yescharacteristic, complemented
15C2×D1132C2211yescharacteristic
16C2×C22⋊D283C2211yescharacteristic
17C2×C22⋊D283C2212yes—
18C2×C22⋊D283C2212yescomplemented
19D4×D283—24no—
20C2×C4×D283C2211yescharacteristic
21C2×C4×D283C2212yescomplemented
22C2×C4×D283C2212yescomplemented
23C4⋊Dic283C2212yescomplemented
24Dic283⋊C4C2211yescharacteristic, complemented
25C22⋊Dic283C2212yescomplemented
26C22⋊Dic283C2211yescharacteristic, complemented
27C22⋊Dic283C2212yescomplemented
28(C2×D283)⋊C4C2211yescharacteristic
29(C2×D283)⋊C4C2212yes—
30(C2×D283)⋊C4C2212yescomplemented
31C4×Dic283C2211yescharacteristic, complemented
32C2×D4×C283C2211yescharacteristic
33C2×D4×C283C2212yescomplemented
34C22×C4×C283C2211yescharacteristic, complemented
35C4⋊C4×C283C2211yescharacteristic, complemented
36C22⋊C4×C283C2212yescomplemented
37C22×D283—24no—
38C22×D283—24no—
39C22×D283—42no—
40C22×D283C2312yes—
41C22×D283C2311yescharacteristic
42Dic566—22no—
43D1132D414yescomplemented
44C22⋊D283—24no—
45C22⋊D283—24no—
46C22⋊D283—22no—
47C2×Dic283C2311yescharacteristic
48C2×Dic283C2311yescharacteristic
49C2×Dic283C2312yes—
50C2×Dic283C2311yescharacteristic
51C4×D283—24no—
52C4×D283—22no—
53C4×D283—42no—
54C23×C283C2312yes—
55C23×C283C2311yescharacteristic
56D4×C283—22no—
57D4×C283—42no—
58C2×C4×C283—22no—
59C2×C4×C283C2311yescharacteristic
60C2×C4×C283C2312yes—
61C2×C4×C283C2311yescharacteristic
62C22×C283—21no—
63C22×C283—22no—
64C22×C283—21no—
65C22×C283—22no—
66C22×C283—21no—
67C22×C283—22no—
68C22×C283C2411yescharacteristic
69C2×D283—21no—
70C2×D283—22no—
71C2×D283—22no—
72C2×D283—21no—
73C2×D283—48no—
74C2×D283C2×D414yes—
75C2×D283#4112yescomplemented
76C4×C283—21no—
77C4×C283—22no—
78C4×C283C2×D412yes—
79Dic283—21no—
80Dic283—22no—
81Dic283—21no—
82Dic283—21no—
83C2×C283—42no—
84C2×C283—41no—
85C2×C283C22×D411yescharacteristic
86C2×C283C2×#4111yescharacteristic
87C2×C283H(5,𝔽2)11yescharacteristic
88D283—22no—
89D283—24no—
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#121D28311yescharacteristic, complemented
99#120—2832no—
100C4×D4—2831no—
101C4×D4—2831no—
102C2×C22⋊C4—2832no—
103C24—2832no—
104#41—5664no—
105C2×Q8—2831no—
106C2×D4—2831no—
107C2×D4—2832no—
108C2×D4—2832no—
109C2×D4—2831no—
110C2×D4—5664no—
111C2×D4C2×D28311yescharacteristic
112C2×D4C2×D28312yescomplemented
113C22×C4—2831no—
114C22×C4—2832no—
115C22×C4—2832no—
116C22×C4C2×D28311yescharacteristic, complemented
117C4⋊C4—2831no—
118C4⋊C4—2832no—
119C4⋊C4C2×D28311yescharacteristic, complemented
120C22⋊C4—2832no—
121C22⋊C4—2831no—
122C22⋊C4—2832no—
123C22⋊C4—2831no—
124C22⋊C4—2832no—
125C22⋊C4—2832no—
126C22⋊C4C2×D28312yescomplemented
127C42—2831no—
128C23—2831no—
129C23—2832no—
130C23—5664no—
131C23—5664no—
132C23—11322no—
133C23C22×D28312yes—
134C23C22×D28311yescharacteristic
135Q8—5662no—
136D4—22no—
137D4—42no—
138D4—2834no—
139D4—5664no—
140D4—5664no—
141D4—5662no—
142C2×C4—22no—
143C2×C4—2831no—
144C2×C4—2831no—
145C2×C4—2832no—
146C2×C4—2831no—
147C2×C4—5664no—
148C2×C4—5662no—
149C2×C4—11322no—
150C2×C4C22×D28312yes—
151C2×C4C22×D28311yescharacteristic
152C2×C4C22×D28311yescharacteristic
153C22—21no—
154C22—22no—
155C22—21no—
156C22—22no—
157C22—21no—
158C22—22no—
159C22—2834no—
160C22—2832no—
161C22—5661no—
162C22—5662no—
163C22—5662no—
164C22—5661no—
165C22—11328no—
166C22C23×D28311yescharacteristic
167C4—21no—
168C4—22no—
169C4—5661no—
170C4—5662no—
171C4—5661no—
172C4—5661no—
173C4D4×D28312yes—
174C2—42no—
175C2—41no—
176C2—5662no—
177C2—5664no—
178C2C2×D4×D28311yescharacteristic
179C2#41×D28311yescharacteristic
180C2#2258365511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D283
commutator, socle, cosocleC22×C283C24
Fitting#121×C283C2
hypercenter#121D283
hypocenterC283#546
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#17985392C2semidirect
2. C2×D4×D283C2semidirect
3. #22583597C2semidirect
4. #22583592C2semidirect
5. #22583590C2semidirect
6. #22583581C2semidirect
7. #22583578C2semidirect
8. #22583572C2semidirect
9. C4×C22⋊D283C2semidirect
10. C22⋊C4×D283C2semidirect
11. #121×C283C2semidirect
14. C2×Dic566C22semidirect
18. C2×C22⋊D283C22semidirect
21. C2×C4×D283C22semidirect
22. C2×C4×D283C22semidirect
23. C4⋊Dic283C22semidirect
24. Dic283⋊C4C22semidirect
25. C22⋊Dic283C22semidirect
26. C22⋊Dic283C22semidirect
27. C22⋊Dic283C22semidirect
30. (C2×D283)⋊C4C22semidirect
31. C4×Dic283C22semidirect
33. C2×D4×C283C22semidirect
34. C22×C4×C283C22semidirect
35. C4⋊C4×C283C22semidirect
36. C22⋊C4×C283C22semidirect
43. D1132D4semidirect
75. C2×D283#41semidirect
90. C283#546semidirect
98. #121D283semidirect
112. C2×D4C2×D283semidirect
116. C22×C4C2×D283semidirect
119. C4⋊C4C2×D283semidirect
126. C22⋊C4C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#179853922
C2×D4×D2832
#225835972
#225835922
#225835902
#225835812
#225835782
#225835722
C4×C22⋊D2832
C22⋊C4×D2832
#121×C2832
#546283