Finite Group Databasebeta

← C2×#16811185 #20288018

Subgroups — C2×#16811185 #20288018

Order 6784.

1984 conjugacy classes of subgroups; only the 565 normal subgroups are shown.

normal subgroups only

This group has 1984 conjugacy classes of subgroups — too many to draw. Only its 565 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
1C23×C22⋊D53C212yesmaximal, complemented
2#16811185C2116yesmaximal, direct product factor
3C2×#13133201C214yesmaximal, complemented
4C2×#13133191C214yesmaximal, complemented
5C2×#13133187C214yesmaximal, complemented
6C22×C22⋊C4×C53C211yesmaximal, characteristic, complemented
7C24×D53C2212yescomplemented
8C22×D212C2214yescomplemented
9C22×C22⋊D53—216no—
10C22×C22⋊D53C2214yes—
11C22×C22⋊D53C2214yescomplemented
12C22×C22⋊D53C22116yescomplemented
13C23×Dic53C2212yescomplemented
14#13133201C22132yescomplemented
15#13133191C22132yescomplemented
16#13133187C22132yescomplemented
17C2×C4⋊Dic53C2214yescomplemented
18C2×#11719921C2218yescomplemented
19C25×C53C2211yescharacteristic
20C23×C4×C53C2212yescomplemented
21C2×C22⋊C4×C53C2214yescomplemented
22C2×C22⋊C4×C53C2218yescomplemented
23C24×C53—44no—
24C24×C53D418yescomplemented
25C24×C53C2312yes—
26C24×C53C2311yescharacteristic
27C24×C53C2314yes—
28C23×D53—28no—
29C23×D53—48no—
30C23×D53C2314yes—
31C23×D53C2318yescomplemented
32C22×C4×C53—44no—
33C22×C4×C53C2314yes—
34C22×C4×C53C2318yescomplemented
35C2×C22⋊D53—216no—
36C2×C22⋊D53—216no—
37C2×C22⋊D53—264no—
38C2×C22⋊D53C23116yes—
39C2×C22⋊D53C23116yescomplemented
40C22×Dic53—28no—
41C22×Dic53C2314yes—
42C22×Dic53C2318yescomplemented
43C2×D212—48no—
44C2×D212C23116yescomplemented
45C22⋊C4×C53C23116yescomplemented
46#11719921C23132yescomplemented
47C4⋊Dic53C23116yescomplemented
48C23×C53—24no—
49C23×C53—28no—
50C23×C53—416no—
51C23×C53—48no—
52C23×C53C2×D418yes—
53C23×C53C2×D414yes—
54C23×C53C2×D4116yescomplemented
55C23×C53C2414yes—
56C23×C53C2412yes—
57C23×C53C2411yescharacteristic
58C22×D53—28no—
59C22×D53—216no—
60C22×D53—216no—
61C22×D53—416no—
62C22×D53—432no—
63C22×D53C2418yes—
64C2×C4×C53—28no—
65C2×C4×C53—48no—
66C2×C4×C53C2418yes—
67C22⋊D53—232no—
68C22⋊D53—232no—
69C2×Dic53—28no—
70C2×Dic53—216no—
71C2×Dic53C2418yes—
72D212—416no—
73C22×C53—216no—
74C22×C53—28no—
75C22×C53—24no—
76C22×C53—28no—
77C22×C53—416no—
78C22×C53C22×D418yes—
79C22×C53C22×D414yes—
80C22×C53C22×D412yes—
81C22×C53H(5,𝔽2)14yes—
82C22×C53C2511yescharacteristic
83C2×D53—28no—
84C2×D53—216no—
85C2×D53—432no—
86C2×D53—416no—
87C4×C53—28no—
88Dic53—28no—
89C2×#534—531nomaximal, Sylow
90C2×C53—28no—
91C2×C53—24no—
92C2×C53#53414yescomplemented
93C2×C53C23×D411yescharacteristic
94C2×C53C2×H(5,𝔽2)12yes—
95D53—48no—
96C23×D4—532no—
97#534—5316no—
98C2×#123—534no—
99C2×#121—534no—
100C2×#120—534no—
101C22×C22⋊C4D5311yescharacteristic, complemented
102C53C2×#53411yescharacteristic, complemented, Sylow
103C25—532no—
104C25C2×D5311yescharacteristic
105C22×D4—534no—
106C22×D4—534no—
107C22×D4—5316no—
108C22×D4—534no—
109C22×D4—10616no—
110C23×C4—532no—
111C23×C4C2×D5312yescomplemented
112#123—5332no—
113#121—5332no—
114#120—5332no—
115C2×C4⋊C4—534no—
116C2×C22⋊C4—538no—
117C2×C22⋊C4C2×D5314yescomplemented
118C2×C22⋊C4C2×D5318yescomplemented
119C24—44no—
120C24—534no—
121C24—538no—
122C24—1068no—
123C24—2128no—
124C24D21218yescomplemented
125C24C22×D5312yes—
126C24C22×D5311yescharacteristic
127C24C22×D5314yes—
128C2×D4—5316no—
129C2×D4—5316no—
130C2×D4—5316no—
131C2×D4—10616no—
132C2×D4—10616no—
133C2×D4—10664no—
134C2×D4—2128no—
135C22×C4—44no—
136C22×C4—538no—
137C22×C4—534no—
138C22×C4—1068no—
139C22×C4C22×D5314yes—
140C22×C4C22×D5318yescomplemented
141C4⋊C4—5316no—
142C22⋊C4—5332no—
143C22⋊C4C22×D53116yescomplemented
144C23—24no—
145C23—28no—
146C23—416no—
147C23—48no—
148C23—538no—
149C23—10616no—
150C23—1068no—
151C23—10616no—
152C23—21216no—
153C23—21232no—
154C23C2×D21218yes—
155C23C2×D21214yes—
156C23C2×D212116yescomplemented
157C23C23×D5314yes—
158C23C23×D5312yes—
159C23C23×D5311yescharacteristic
160D4—10632no—
161D4—10632no—
162D4—21216no—
163C2×C4—28no—
164C2×C4—48no—
165C2×C4—538no—
166C2×C4—10616no—
167C2×C4—1068no—
168C2×C4C23×D5318yes—
169C22—216no—
170C22—28no—
171C22—24no—
172C22—28no—
173C22—416no—
174C22—1068no—
175C22—10616no—
176C22—21232no—
177C22—21216no—
178C22C22×D21218yes—
179C22C22×D21214yes—
180C22C22×D21212yes—
181C22#1313326214yes—
182C22C24×D5311yescharacteristic
183C4—28no—
184C4—1068no—
185C2—28no—
186C2—24no—
187C2—2128no—
188C2#1681118514yesdirect product factor
189C2C23×D21211yescharacteristic
190C2C2×#1313326212yes—
subgroupG/H
centerC23C23×D53
commutatorC22×C53C25
FrattiniC22C24×D53
FittingC22×C22⋊C4×C53C2
socleC23×C53C24
hypercenterC22×C22⋊C4D53
hypocenterC53C2×#534
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D53C2semidirect
2. #16811185C2direct (N × H)
3. C2×#13133201C2semidirect
4. C2×#13133191C2semidirect
5. C2×#13133187C2semidirect
6. C22×C22⋊C4×C53C2semidirect
7. C24×D53C22semidirect
8. C22×D212C22semidirect
11. C22×C22⋊D53C22semidirect
12. C22×C22⋊D53C22semidirect
13. C23×Dic53C22semidirect
14. #13133201C22semidirect
15. #13133191C22semidirect
16. #13133187C22semidirect
17. C2×C4⋊Dic53C22semidirect
18. C2×#11719921C22semidirect
20. C23×C4×C53C22semidirect
21. C2×C22⋊C4×C53C22semidirect
22. C2×C22⋊C4×C53C22semidirect
24. C24×C53D4semidirect
31. C23×D53C23semidirect
34. C22×C4×C53C23semidirect
39. C2×C22⋊D53C23semidirect
42. C22×Dic53C23semidirect
44. C2×D212C23semidirect
45. C22⋊C4×C53C23semidirect
46. #11719921C23semidirect
47. C4⋊Dic53C23semidirect
54. C23×C53C2×D4semidirect
92. C2×C53#534semidirect
101. C22×C22⋊C4D53semidirect
102. C53C2×#534semidirect
111. C23×C4C2×D53semidirect
117. C2×C22⋊C4C2×D53semidirect
118. C2×C22⋊C4C2×D53semidirect
124. C24D212semidirect
140. C22×C4C22×D53semidirect
143. C22⋊C4C22×D53semidirect
156. C23C2×D212semidirect
188. C2#16811185direct (N × H)