Finite Group Databasebeta

← C2×#20268353 #27208447

Subgroups — C2×#20268353 #27208447

Order 13184.

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⋊D103C212yesmaximal, complemented
2#20268353C2116yesmaximal, direct product factor
3C2×#15693005C214yesmaximal, complemented
4C2×#15692995C214yesmaximal, complemented
5C2×#15692991C214yesmaximal, complemented
6C22×C22⋊C4×C103C211yesmaximal, characteristic, complemented
7C24×D103C2212yescomplemented
8C22×D412C2214yescomplemented
9C22×C22⋊D103—216no—
10C22×C22⋊D103C2214yes—
11C22×C22⋊D103C2214yescomplemented
12C22×C22⋊D103C22116yescomplemented
13C23×Dic103C2212yescomplemented
14#15693005C22132yescomplemented
15#15692995C22132yescomplemented
16#15692991C22132yescomplemented
17C2×C4⋊Dic103C2214yescomplemented
18C2×(C2×D103)⋊C4C2218yescomplemented
19C25×C103C2211yescharacteristic
20C23×C4×C103C2212yescomplemented
21C2×C22⋊C4×C103C2214yescomplemented
22C2×C22⋊C4×C103C2218yescomplemented
23C23×D103—28no—
24C23×D103—48no—
25C23×D103C2314yes—
26C23×D103C2318yescomplemented
27C2×D412—48no—
28C2×D412C23116yescomplemented
29C2×C22⋊D103—216no—
30C2×C22⋊D103—216no—
31C2×C22⋊D103—264no—
32C2×C22⋊D103C23116yes—
33C2×C22⋊D103C23116yescomplemented
34C22×Dic103—28no—
35C22×Dic103C2314yes—
36C22×Dic103C2318yescomplemented
37C4⋊Dic103C23116yescomplemented
38(C2×D103)⋊C4C23132yescomplemented
39C24×C103—44no—
40C24×C103D418yescomplemented
41C24×C103C2312yes—
42C24×C103C2311yescharacteristic
43C24×C103C2314yes—
44C22×C4×C103—44no—
45C22×C4×C103C2314yes—
46C22×C4×C103C2318yescomplemented
47C22⋊C4×C103C23116yescomplemented
48C23×C103—24no—
49C23×C103—28no—
50C23×C103—416no—
51C23×C103—48no—
52C23×C103C2×D418yes—
53C23×C103C2×D414yes—
54C23×C103C2×D4116yescomplemented
55C23×C103C2414yes—
56C23×C103C2412yes—
57C23×C103C2411yescharacteristic
58C22×D103—28no—
59C22×D103—216no—
60C22×D103—216no—
61C22×D103—416no—
62C22×D103—432no—
63C22×D103C2418yes—
64C2×C4×C103—28no—
65C2×C4×C103—48no—
66C2×C4×C103C2418yes—
67C22⋊D103—232no—
68C22⋊D103—232no—
69C2×Dic103—28no—
70C2×Dic103—216no—
71C2×Dic103C2418yes—
72D412—416no—
73C22×C103—216no—
74C22×C103—28no—
75C22×C103—24no—
76C22×C103—28no—
77C22×C103—416no—
78C22×C103C22×D418yes—
79C22×C103C22×D414yes—
80C22×C103C22×D412yes—
81C22×C103H(5,𝔽2)14yes—
82C22×C103C2511yescharacteristic
83C2×D103—28no—
84C2×D103—216no—
85C2×D103—432no—
86C2×D103—416no—
87C4×C103—28no—
88Dic103—28no—
89C2×C103—28no—
90C2×C103—24no—
91C2×C103#53414yescomplemented
92C2×C103C23×D411yescharacteristic
93C2×C103C2×H(5,𝔽2)12yes—
94D103—48no—
95C2×#534—1031nomaximal, Sylow
96C103C2×#53411yescharacteristic, complemented, Sylow
97C23×D4—1032no—
98#534—10316no—
99C2×#123—1034no—
100C2×#121—1034no—
101C2×#120—1034no—
102C22×C22⋊C4D10311yescharacteristic, complemented
103C25—1032no—
104C25C2×D10311yescharacteristic
105C22×D4—1034no—
106C22×D4—1034no—
107C22×D4—10316no—
108C22×D4—1034no—
109C22×D4—20616no—
110C23×C4—1032no—
111C23×C4C2×D10312yescomplemented
112#123—10332no—
113#121—10332no—
114#120—10332no—
115C2×C4⋊C4—1034no—
116C2×C22⋊C4—1038no—
117C2×C22⋊C4C2×D10314yescomplemented
118C2×C22⋊C4C2×D10318yescomplemented
119C24—44no—
120C24—1038no—
121C24—1034no—
122C24—4128no—
123C24—2068no—
124C24D41218yescomplemented
125C24C22×D10312yes—
126C24C22×D10311yescharacteristic
127C24C22×D10314yes—
128C2×D4—10316no—
129C2×D4—10316no—
130C2×D4—10316no—
131C2×D4—4128no—
132C2×D4—20616no—
133C2×D4—20616no—
134C2×D4—20664no—
135C22×C4—44no—
136C22×C4—1038no—
137C22×C4—1034no—
138C22×C4—2068no—
139C22×C4C22×D10314yes—
140C22×C4C22×D10318yescomplemented
141C4⋊C4—10316no—
142C22⋊C4—10332no—
143C22⋊C4C22×D103116yescomplemented
144C23—24no—
145C23—28no—
146C23—416no—
147C23—48no—
148C23—1038no—
149C23—41232no—
150C23—41216no—
151C23—20616no—
152C23—2068no—
153C23—20616no—
154C23C2×D41218yes—
155C23C2×D41214yes—
156C23C2×D412116yescomplemented
157C23C23×D10314yes—
158C23C23×D10312yes—
159C23C23×D10311yescharacteristic
160D4—41216no—
161D4—20632no—
162D4—20632no—
163C2×C4—28no—
164C2×C4—48no—
165C2×C4—1038no—
166C2×C4—20616no—
167C2×C4—2068no—
168C2×C4C23×D10318yes—
169C22—216no—
170C22—28no—
171C22—24no—
172C22—28no—
173C22—416no—
174C22—41232no—
175C22—41216no—
176C22—2068no—
177C22—20616no—
178C22C22×D41218yes—
179C22C22×D41214yes—
180C22C22×D41212yes—
181C22#1569306614yes—
182C22C24×D10311yescharacteristic
183C4—28no—
184C4—2068no—
185C2—28no—
186C2—24no—
187C2—4128no—
188C2#2026835314yesdirect product factor
189C2C23×D41211yescharacteristic
190C2C2×#1569306612yes—
subgroupG/H
centerC23C23×D103
commutator, cosocleC22×C103C25
FrattiniC22C24×D103
FittingC22×C22⋊C4×C103C2
socleC23×C103C24
hypercenterC22×C22⋊C4D103
hypocenterC103C2×#534
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D103C2semidirect
2. #20268353C2direct (N × H)
3. C2×#15693005C2semidirect
4. C2×#15692995C2semidirect
5. C2×#15692991C2semidirect
6. C22×C22⋊C4×C103C2semidirect
7. C24×D103C22semidirect
8. C22×D412C22semidirect
11. C22×C22⋊D103C22semidirect
12. C22×C22⋊D103C22semidirect
13. C23×Dic103C22semidirect
14. #15693005C22semidirect
15. #15692995C22semidirect
16. #15692991C22semidirect
17. C2×C4⋊Dic103C22semidirect
18. C2×(C2×D103)⋊C4C22semidirect
20. C23×C4×C103C22semidirect
21. C2×C22⋊C4×C103C22semidirect
22. C2×C22⋊C4×C103C22semidirect
26. C23×D103C23semidirect
28. C2×D412C23semidirect
33. C2×C22⋊D103C23semidirect
36. C22×Dic103C23semidirect
37. C4⋊Dic103C23semidirect
38. (C2×D103)⋊C4C23semidirect
40. C24×C103D4semidirect
46. C22×C4×C103C23semidirect
47. C22⋊C4×C103C23semidirect
54. C23×C103C2×D4semidirect
91. C2×C103#534semidirect
96. C103C2×#534semidirect
102. C22×C22⋊C4D103semidirect
111. C23×C4C2×D103semidirect
117. C2×C22⋊C4C2×D103semidirect
118. C2×C22⋊C4C2×D103semidirect
124. C24D412semidirect
140. C22×C4C22×D103semidirect
143. C22⋊C4C22×D103semidirect
156. C23C2×D412semidirect
188. C2#20268353direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D1032
#202683532
C2×#156930052
C2×#156929952
C2×#156929912
C22×C22⋊C4×C1032
C2×#534103