Finite Group Databasebeta

← C2×#13092979 #15686700

Subgroups — C2×#13092979 #15686700

Order 2944.

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⋊D23C212yesmaximal, complemented
2#13092979C2116yesmaximal, direct product factor
3C2×#10625057C214yesmaximal, complemented
4C2×#10625101C214yesmaximal, complemented
5C2×#10625053C214yesmaximal, complemented
6C22×C22⋊C4×C23C211yesmaximal, characteristic, complemented
7C25×C23C2211yescharacteristic
8C24×D23C2212yescomplemented
9C23×C4×C23C2212yescomplemented
10C22×C22⋊D23—216no—
11C22×C22⋊D23C2214yes—
12C22×C22⋊D23C2214yescomplemented
13C22×C22⋊D23C22116yescomplemented
14C23×Dic23C2212yescomplemented
15C22×D92C2214yescomplemented
16C2×C22⋊C4×C23C2214yescomplemented
17C2×C22⋊C4×C23C2218yescomplemented
18#10625101C22132yescomplemented
19C2×(C2×D23)⋊C4C2218yescomplemented
20C2×C4⋊Dic23C2214yescomplemented
21#10625057C22132yescomplemented
22#10625053C22132yescomplemented
23C24×C23—44no—
24C24×C23D418yescomplemented
25C24×C23C2312yes—
26C24×C23C2311yescharacteristic
27C24×C23C2314yes—
28C23×D23—28no—
29C23×D23—48no—
30C23×D23C2314yes—
31C23×D23C2318yescomplemented
32C22×C4×C23—44no—
33C22×C4×C23C2314yes—
34C22×C4×C23C2318yescomplemented
35C2×C22⋊D23—216no—
36C2×C22⋊D23—216no—
37C2×C22⋊D23—264no—
38C2×C22⋊D23C23116yes—
39C2×C22⋊D23C23116yescomplemented
40C22×Dic23—28no—
41C22×Dic23C2314yes—
42C22×Dic23C2318yescomplemented
43C2×D92—48no—
44C2×D92C23116yescomplemented
45C22⋊C4×C23C23116yescomplemented
46(C2×D23)⋊C4C23132yescomplemented
47C4⋊Dic23C23116yescomplemented
48C23×C23—24no—
49C23×C23—28no—
50C23×C23—416no—
51C23×C23—48no—
52C23×C23C2×D418yes—
53C23×C23C2×D414yes—
54C23×C23C2×D4116yescomplemented
55C23×C23C2414yes—
56C23×C23C2412yes—
57C23×C23C2411yescharacteristic
58C22×D23—28no—
59C22×D23—216no—
60C22×D23—216no—
61C22×D23—416no—
62C22×D23—432no—
63C22×D23C2418yes—
64C2×C4×C23—28no—
65C2×C4×C23—48no—
66C2×C4×C23C2418yes—
67C22⋊D23—232no—
68C22⋊D23—232no—
69C2×Dic23—28no—
70C2×Dic23—216no—
71C2×Dic23C2418yes—
72D92—416no—
73C2×#534—231nomaximal, Sylow
74C22×C23—216no—
75C22×C23—28no—
76C22×C23—24no—
77C22×C23—28no—
78C22×C23—416no—
79C22×C23C22×D418yes—
80C22×C23C22×D414yes—
81C22×C23C22×D412yes—
82C22×C23H(5,𝔽2)14yes—
83C22×C23C2511yescharacteristic
84C2×D23—28no—
85C2×D23—216no—
86C2×D23—432no—
87C2×D23—416no—
88C4×C23—28no—
89Dic23—28no—
90C23×D4—232no—
91#534—2316no—
92C2×#123—234no—
93C2×#121—234no—
94C2×#120—234no—
95C22×C22⋊C4D2311yescharacteristic, complemented
96C2×C23—28no—
97C2×C23—24no—
98C2×C23#53414yescomplemented
99C2×C23C23×D411yescharacteristic
100C2×C23C2×H(5,𝔽2)12yes—
101D23—48no—
102C25—232no—
103C25C2×D2311yescharacteristic
104C22×D4—234no—
105C22×D4—234no—
106C22×D4—2316no—
107C22×D4—234no—
108C22×D4—4616no—
109C23×C4—232no—
110C23×C4C2×D2312yescomplemented
111#123—2332no—
112#121—2332no—
113#120—2332no—
114C2×C4⋊C4—234no—
115C2×C22⋊C4—238no—
116C2×C22⋊C4C2×D2314yescomplemented
117C2×C22⋊C4C2×D2318yescomplemented
118C23C2×#53411yescharacteristic, complemented, Sylow
119C24—44no—
120C24—234no—
121C24—238no—
122C24—468no—
123C24—928no—
124C24D9218yescomplemented
125C24C22×D2312yes—
126C24C22×D2311yescharacteristic
127C24C22×D2314yes—
128C2×D4—2316no—
129C2×D4—2316no—
130C2×D4—2316no—
131C2×D4—4616no—
132C2×D4—4616no—
133C2×D4—4664no—
134C2×D4—928no—
135C22×C4—44no—
136C22×C4—238no—
137C22×C4—234no—
138C22×C4—468no—
139C22×C4C22×D2314yes—
140C22×C4C22×D2318yescomplemented
141C4⋊C4—2316no—
142C22⋊C4—2332no—
143C22⋊C4C22×D23116yescomplemented
144C23—24no—
145C23—28no—
146C23—416no—
147C23—48no—
148C23—238no—
149C23—4616no—
150C23—468no—
151C23—4616no—
152C23—9216no—
153C23—9232no—
154C23C2×D9218yes—
155C23C2×D9214yes—
156C23C2×D92116yescomplemented
157C23C23×D2314yes—
158C23C23×D2312yes—
159C23C23×D2311yescharacteristic
160D4—4632no—
161D4—4632no—
162D4—9216no—
163C2×C4—28no—
164C2×C4—48no—
165C2×C4—238no—
166C2×C4—4616no—
167C2×C4—468no—
168C2×C4C23×D2318yes—
169C22—216no—
170C22—28no—
171C22—24no—
172C22—28no—
173C22—416no—
174C22—468no—
175C22—4616no—
176C22—9232no—
177C22—9216no—
178C22C22×D9218yes—
179C22C22×D9214yes—
180C22C22×D9212yes—
181C22#1062515514yes—
182C22C24×D2311yescharacteristic
183C4—28no—
184C4—468no—
185C2—28no—
186C2—24no—
187C2—928no—
188C2#1309297914yesdirect product factor
189C2C23×D9211yescharacteristic
190C2C2×#1062515512yes—
subgroupG/H
centerC23C23×D23
commutator, cosocleC22×C23C25
FrattiniC22C24×D23
FittingC22×C22⋊C4×C23C2
socleC23×C23C24
hypercenterC22×C22⋊C4D23
hypocenterC23C2×#534
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D23C2semidirect
2. #13092979C2direct (N × H)
3. C2×#10625057C2semidirect
4. C2×#10625101C2semidirect
5. C2×#10625053C2semidirect
6. C22×C22⋊C4×C23C2semidirect
8. C24×D23C22semidirect
9. C23×C4×C23C22semidirect
12. C22×C22⋊D23C22semidirect
13. C22×C22⋊D23C22semidirect
14. C23×Dic23C22semidirect
15. C22×D92C22semidirect
16. C2×C22⋊C4×C23C22semidirect
17. C2×C22⋊C4×C23C22semidirect
18. #10625101C22semidirect
19. C2×(C2×D23)⋊C4C22semidirect
20. C2×C4⋊Dic23C22semidirect
21. #10625057C22semidirect
22. #10625053C22semidirect
24. C24×C23D4semidirect
31. C23×D23C23semidirect
34. C22×C4×C23C23semidirect
39. C2×C22⋊D23C23semidirect
42. C22×Dic23C23semidirect
44. C2×D92C23semidirect
45. C22⋊C4×C23C23semidirect
46. (C2×D23)⋊C4C23semidirect
47. C4⋊Dic23C23semidirect
54. C23×C23C2×D4semidirect
95. C22×C22⋊C4D23semidirect
98. C2×C23#534semidirect
110. C23×C4C2×D23semidirect
116. C2×C22⋊C4C2×D23semidirect
117. C2×C22⋊C4C2×D23semidirect
118. C23C2×#534semidirect
124. C24D92semidirect
140. C22×C4C22×D23semidirect
143. C22⋊C4C22×D23semidirect
156. C23C2×D92semidirect
188. C2#13092979direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D232
#130929792
C2×#106250572
C2×#106251012
C2×#106250532
C22×C22⋊C4×C232
C2×#53423