Finite Group Databasebeta

← C2×#15689685 #20256691

Subgroups — C2×#15689685 #20256691

Order 6016.

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⋊D47C212yesmaximal, complemented
2#15689685C2116yesmaximal, direct product factor
3C2×#13094008C214yesmaximal, complemented
4C2×#13093998C214yesmaximal, complemented
5C2×#13093994C214yesmaximal, complemented
6C22×C22⋊C4×C47C211yesmaximal, characteristic, complemented
7C24×D47C2212yescomplemented
8C22×D188C2214yescomplemented
9C22×C22⋊D47—216no—
10C22×C22⋊D47C2214yes—
11C22×C22⋊D47C2214yescomplemented
12C22×C22⋊D47C22116yescomplemented
13C23×Dic47C2212yescomplemented
14#13094008C22132yescomplemented
15#13093998C22132yescomplemented
16#13093994C22132yescomplemented
17C2×C4⋊Dic47C2214yescomplemented
18C2×(C2×D47)⋊C4C2218yescomplemented
19C25×C47C2211yescharacteristic
20C23×C4×C47C2212yescomplemented
21C2×C22⋊C4×C47C2214yescomplemented
22C2×C22⋊C4×C47C2218yescomplemented
23C24×C47—44no—
24C24×C47D418yescomplemented
25C24×C47C2312yes—
26C24×C47C2311yescharacteristic
27C24×C47C2314yes—
28C23×D47—28no—
29C23×D47—48no—
30C23×D47C2314yes—
31C23×D47C2318yescomplemented
32C22×C4×C47—44no—
33C22×C4×C47C2314yes—
34C22×C4×C47C2318yescomplemented
35C2×C22⋊D47—216no—
36C2×C22⋊D47—216no—
37C2×C22⋊D47—264no—
38C2×C22⋊D47C23116yes—
39C2×C22⋊D47C23116yescomplemented
40C22×Dic47—28no—
41C22×Dic47C2314yes—
42C22×Dic47C2318yescomplemented
43C2×D188—48no—
44C2×D188C23116yescomplemented
45C22⋊C4×C47C23116yescomplemented
46(C2×D47)⋊C4C23132yescomplemented
47C4⋊Dic47C23116yescomplemented
48C23×C47—24no—
49C23×C47—28no—
50C23×C47—416no—
51C23×C47—48no—
52C23×C47C2×D418yes—
53C23×C47C2×D414yes—
54C23×C47C2×D4116yescomplemented
55C23×C47C2414yes—
56C23×C47C2412yes—
57C23×C47C2411yescharacteristic
58C22×D47—28no—
59C22×D47—216no—
60C22×D47—216no—
61C22×D47—416no—
62C22×D47—432no—
63C22×D47C2418yes—
64C2×C4×C47—28no—
65C2×C4×C47—48no—
66C2×C4×C47C2418yes—
67C22⋊D47—232no—
68C22⋊D47—232no—
69C2×Dic47—28no—
70C2×Dic47—216no—
71C2×Dic47C2418yes—
72D188—416no—
73C22×C47—216no—
74C22×C47—28no—
75C22×C47—24no—
76C22×C47—28no—
77C22×C47—416no—
78C22×C47C22×D418yes—
79C22×C47C22×D414yes—
80C22×C47C22×D412yes—
81C22×C47H(5,𝔽2)14yes—
82C22×C47C2511yescharacteristic
83C2×D47—28no—
84C2×D47—216no—
85C2×D47—432no—
86C2×D47—416no—
87C4×C47—28no—
88Dic47—28no—
89C2×#534—471nomaximal, Sylow
90C2×C47—28no—
91C2×C47—24no—
92C2×C47#53414yescomplemented
93C2×C47C23×D411yescharacteristic
94C2×C47C2×H(5,𝔽2)12yes—
95D47—48no—
96C23×D4—472no—
97#534—4716no—
98C2×#123—474no—
99C2×#121—474no—
100C2×#120—474no—
101C22×C22⋊C4D4711yescharacteristic, complemented
102C47C2×#53411yescharacteristic, complemented, Sylow
103C25—472no—
104C25C2×D4711yescharacteristic
105C22×D4—474no—
106C22×D4—474no—
107C22×D4—4716no—
108C22×D4—474no—
109C22×D4—9416no—
110C23×C4—472no—
111C23×C4C2×D4712yescomplemented
112#123—4732no—
113#121—4732no—
114#120—4732no—
115C2×C4⋊C4—474no—
116C2×C22⋊C4—478no—
117C2×C22⋊C4C2×D4714yescomplemented
118C2×C22⋊C4C2×D4718yescomplemented
119C24—44no—
120C24—474no—
121C24—478no—
122C24—948no—
123C24—1888no—
124C24D18818yescomplemented
125C24C22×D4712yes—
126C24C22×D4711yescharacteristic
127C24C22×D4714yes—
128C2×D4—4716no—
129C2×D4—4716no—
130C2×D4—4716no—
131C2×D4—9416no—
132C2×D4—9416no—
133C2×D4—9464no—
134C2×D4—1888no—
135C22×C4—44no—
136C22×C4—478no—
137C22×C4—474no—
138C22×C4—948no—
139C22×C4C22×D4714yes—
140C22×C4C22×D4718yescomplemented
141C4⋊C4—4716no—
142C22⋊C4—4732no—
143C22⋊C4C22×D47116yescomplemented
144C23—24no—
145C23—28no—
146C23—416no—
147C23—48no—
148C23—478no—
149C23—9416no—
150C23—948no—
151C23—9416no—
152C23—18816no—
153C23—18832no—
154C23C2×D18818yes—
155C23C2×D18814yes—
156C23C2×D188116yescomplemented
157C23C23×D4714yes—
158C23C23×D4712yes—
159C23C23×D4711yescharacteristic
160D4—9432no—
161D4—9432no—
162D4—18816no—
163C2×C4—28no—
164C2×C4—48no—
165C2×C4—478no—
166C2×C4—9416no—
167C2×C4—948no—
168C2×C4C23×D4718yes—
169C22—216no—
170C22—28no—
171C22—24no—
172C22—28no—
173C22—416no—
174C22—948no—
175C22—9416no—
176C22—18832no—
177C22—18816no—
178C22C22×D18818yes—
179C22C22×D18814yes—
180C22C22×D18812yes—
181C22#1309406914yes—
182C22C24×D4711yescharacteristic
183C4—28no—
184C4—948no—
185C2—28no—
186C2—24no—
187C2—1888no—
188C2#1568968514yesdirect product factor
189C2C23×D18811yescharacteristic
190C2C2×#1309406912yes—
subgroupG/H
centerC23C23×D47
commutatorC22×C47C25
FrattiniC22C24×D47
FittingC22×C22⋊C4×C47C2
socleC23×C47C24
hypercenterC22×C22⋊C4D47
hypocenterC47C2×#534
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D47C2semidirect
2. #15689685C2direct (N × H)
3. C2×#13094008C2semidirect
4. C2×#13093998C2semidirect
5. C2×#13093994C2semidirect
6. C22×C22⋊C4×C47C2semidirect
7. C24×D47C22semidirect
8. C22×D188C22semidirect
11. C22×C22⋊D47C22semidirect
12. C22×C22⋊D47C22semidirect
13. C23×Dic47C22semidirect
14. #13094008C22semidirect
15. #13093998C22semidirect
16. #13093994C22semidirect
17. C2×C4⋊Dic47C22semidirect
18. C2×(C2×D47)⋊C4C22semidirect
20. C23×C4×C47C22semidirect
21. C2×C22⋊C4×C47C22semidirect
22. C2×C22⋊C4×C47C22semidirect
24. C24×C47D4semidirect
31. C23×D47C23semidirect
34. C22×C4×C47C23semidirect
39. C2×C22⋊D47C23semidirect
42. C22×Dic47C23semidirect
44. C2×D188C23semidirect
45. C22⋊C4×C47C23semidirect
46. (C2×D47)⋊C4C23semidirect
47. C4⋊Dic47C23semidirect
54. C23×C47C2×D4semidirect
92. C2×C47#534semidirect
101. C22×C22⋊C4D47semidirect
102. C47C2×#534semidirect
111. C23×C4C2×D47semidirect
117. C2×C22⋊C4C2×D47semidirect
118. C2×C22⋊C4C2×D47semidirect
124. C24D188semidirect
140. C22×C4C22×D47semidirect
143. C22⋊C4C22×D47semidirect
156. C23C2×D188semidirect
188. C2#15689685direct (N × H)