Finite Group Databasebeta

← #31827111

Subgroups — #31827111

Order 18112.

334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 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
2C22×D1132C211yesmaximal, characteristic, complemented
3#22583598C211yesmaximal, characteristic, complemented
4#22583595C212yesmaximal, complemented
5#22583589C211yesmaximal, characteristic, complemented
6#22583584C211yesmaximal, characteristic, complemented
7#22583583C212yesmaximal, complemented
8#22583578C212yesmaximal, complemented
9C4×D1132C211yesmaximal, characteristic, complemented
10C22⋊C4×D283C212yesmaximal, complemented
11C4×D4×C283C211yesmaximal, characteristic, complemented
12C23×D283C2212yes—
13#17985392—24no—
14C2×Dic566C2211yescharacteristic, complemented
15C2×D1132—24no—
16C2×D1132C2212yes—
17C2×D1132C2211yescharacteristic
18C2×D1132C2211yescharacteristic
19C2×C22⋊D283C2212yescomplemented
20C2×C22⋊D283C2212yescomplemented
21C2×C4×D283C2212yescomplemented
22C2×C4×D283C2212yescomplemented
23C4⋊Dic283C2211yescharacteristic, complemented
24Dic283⋊C4C2212yescomplemented
25C22⋊Dic283C2212yes—
26(C2×D283)⋊C4C2212yescomplemented
27(C2×D283)⋊C4C2212yescomplemented
28(C2×D283)⋊C4C2212yescomplemented
29(C2×D283)⋊C4C2212yescomplemented
30C2×D4×C283C2211yescharacteristic
31C22×C4×C283C2211yescharacteristic
32C22×C4×C283C2211yescharacteristic, complemented
33C4⋊C4×C283C2211yescharacteristic, complemented
34C22⋊C4×C283C2211yescharacteristic
35C22⋊C4×C283C2211yescharacteristic, complemented
36C42×C283C2211yescharacteristic, complemented
37C22×D283—24no—
38C22×D283—24no—
39C22×D283—42no—
40C22×D283C2312yes—
41C22×D283C2312yes—
42Dic566—22no—
43D1132—24no—
44D1132—22no—
45D1132D414yescomplemented
46C22⋊D283—24no—
47C22⋊D283—42no—
48C2×Dic283C2312yes—
49C2×Dic283C2312yes—
50C4×D283—24no—
51C4×D283—42no—
52C23×C283C2311yescharacteristic
53C23×C283C2311yescharacteristic
54D4×C283—22no—
55C2×C4×C283—22no—
56C2×C4×C283—22no—
57C2×C4×C283C2311yescharacteristic
58C2×C4×C283C2311yescharacteristic
59C2×C4×C283C2311yescharacteristic
60C2×C4×C283C2311yescharacteristic
61C2×C4×C283C2311yescharacteristic
62C22×C283—21no—
63C22×C283—21no—
64C22×C283—21no—
65C22×C283—21no—
66C22×C283—21no—
67C22×C283#4112yescomplemented
68C22×C283C2411yescharacteristic
69C2×D283—22no—
70C2×D283—22no—
71C2×D283—22no—
72C2×D283—22no—
73C2×D283—22no—
74C2×D283—48no—
75C2×D283C2×D414yes—
76C4×C283—21no—
77C4×C283—21no—
78C4×C283—21no—
79C4×C283—21no—
80C4×C283C2×D412yes—
81Dic283—22no—
82Dic283—22no—
83C2×C283—22no—
84C2×C283—41no—
85C2×C283C22×D411yescharacteristic
86C2×C283C2×#4111yescharacteristic
87C2×C283H(5,𝔽2)11yescharacteristic
88D283—24no—
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—2831no—
98#121—2832no—
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—2832no—
110C2×D4—2831no—
111C2×D4—5664no—
112C2×D4C2×D28311yescharacteristic
113C22×C4—2832no—
114C22×C4—2832no—
115C22×C4C2×D28311yescharacteristic
116C22×C4C2×D28311yescharacteristic, complemented
117C4⋊C4—2832no—
118C4⋊C4—2831no—
119C4⋊C4C2×D28311yescharacteristic, complemented
120C22⋊C4—2832no—
121C22⋊C4—2832no—
122C22⋊C4—2832no—
123C22⋊C4—2832no—
124C22⋊C4—2832no—
125C22⋊C4C2×D28311yescharacteristic
126C22⋊C4C2×D28311yescharacteristic, complemented
127C42C2×D28311yescharacteristic, complemented
128C23—2832no—
129C23—2832no—
130C23—5664no—
131C23—5664no—
132C23—11322no—
133C23C22×D28311yescharacteristic
134C23C22×D28311yescharacteristic
135Q8—5662no—
136D4—22no—
137D4—2834no—
138D4—5664no—
139D4—5664no—
140D4—5662no—
141D4—11322no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—2832no—
145C2×C4—2832no—
146C2×C4—5664no—
147C2×C4—11322no—
148C2×C4C22×D28311yescharacteristic
149C2×C4C22×D28311yescharacteristic
150C2×C4C22×D28311yescharacteristic
151C2×C4C22×D28311yescharacteristic
152C2×C4C22×D28311yescharacteristic
153C22—21no—
154C22—21no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22—2834no—
159C22—5662no—
160C22—5662no—
161C22—5662no—
162C22—5662no—
163C22—5662no—
164C22—11328no—
165C22#1798539212yescomplemented
166C22C23×D28311yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—5662no—
172C4—5662no—
173C4D4×D28312yes—
174C2—22no—
175C2—41no—
176C2—5664no—
177C2—11322no—
178C2C2×D4×D28311yescharacteristic
179C2C2×#1798539211yescharacteristic
180C2#2258365611yescharacteristic
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×#17985392C2semidirect
2. C22×D1132C2semidirect
3. #22583598C2semidirect
4. #22583595C2semidirect
5. #22583589C2semidirect
6. #22583584C2semidirect
7. #22583583C2semidirect
8. #22583578C2semidirect
9. C4×D1132C2semidirect
10. C22⋊C4×D283C2semidirect
11. C4×D4×C283C2semidirect
14. C2×Dic566C22semidirect
19. C2×C22⋊D283C22semidirect
20. C2×C22⋊D283C22semidirect
21. C2×C4×D283C22semidirect
22. C2×C4×D283C22semidirect
23. C4⋊Dic283C22semidirect
24. Dic283⋊C4C22semidirect
26. (C2×D283)⋊C4C22semidirect
27. (C2×D283)⋊C4C22semidirect
28. (C2×D283)⋊C4C22semidirect
29. (C2×D283)⋊C4C22semidirect
32. C22×C4×C283C22semidirect
33. C4⋊C4×C283C22semidirect
35. C22⋊C4×C283C22semidirect
36. C42×C283C22semidirect
45. D1132D4semidirect
67. C22×C283#41semidirect
90. C283#546semidirect
101. C4×D4D283semidirect
116. C22×C4C2×D283semidirect
119. C4⋊C4C2×D283semidirect
126. C22⋊C4C2×D283semidirect
127. C42C2×D283semidirect
165. C22#17985392semidirect

Maximal subgroups

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

subgroupindex
C2×#179853922
C22×D11322
#225835982
#225835952
#225835892
#225835842
#225835832
#225835782
C4×D11322
C22⋊C4×D2832
C4×D4×C2832
#546283