Finite Group Databasebeta

← C2×#14558095 #18007899

Subgroups — C2×#14558095 #18007899

Order 4736.

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⋊D37C212yesmaximal, complemented
2#14558095C2116yesmaximal, direct product factor
3C2×#11924520C214yesmaximal, complemented
4C2×#11924510C214yesmaximal, complemented
5C2×#11924506C214yesmaximal, complemented
6C22×C22⋊C4×C37C211yesmaximal, characteristic, complemented
7C24×D37C2212yescomplemented
8C22×D148C2214yescomplemented
9C22×C22⋊D37—216no—
10C22×C22⋊D37C2214yes—
11C22×C22⋊D37C2214yescomplemented
12C22×C22⋊D37C22116yescomplemented
13C23×Dic37C2212yescomplemented
14#11924520C22132yescomplemented
15#11924510C22132yescomplemented
16#11924506C22132yescomplemented
17C2×C4⋊Dic37C2214yescomplemented
18C2×#10596938C2218yescomplemented
19C25×C37C2211yescharacteristic
20C23×C4×C37C2212yescomplemented
21C2×C22⋊C4×C37C2214yescomplemented
22C2×C22⋊C4×C37C2218yescomplemented
23C24×C37—44no—
24C24×C37D418yescomplemented
25C24×C37C2312yes—
26C24×C37C2311yescharacteristic
27C24×C37C2314yes—
28C23×D37—28no—
29C23×D37—48no—
30C23×D37C2314yes—
31C23×D37C2318yescomplemented
32C22×C4×C37—44no—
33C22×C4×C37C2314yes—
34C22×C4×C37C2318yescomplemented
35C2×C22⋊D37—216no—
36C2×C22⋊D37—216no—
37C2×C22⋊D37—264no—
38C2×C22⋊D37C23116yes—
39C2×C22⋊D37C23116yescomplemented
40C22×Dic37—28no—
41C22×Dic37C2314yes—
42C22×Dic37C2318yescomplemented
43C2×D148—48no—
44C2×D148C23116yescomplemented
45C22⋊C4×C37C23116yescomplemented
46#10596938C23132yescomplemented
47C4⋊Dic37C23116yescomplemented
48C23×C37—24no—
49C23×C37—28no—
50C23×C37—416no—
51C23×C37—48no—
52C23×C37C2×D418yes—
53C23×C37C2×D414yes—
54C23×C37C2×D4116yescomplemented
55C23×C37C2414yes—
56C23×C37C2412yes—
57C23×C37C2411yescharacteristic
58C22×D37—28no—
59C22×D37—216no—
60C22×D37—216no—
61C22×D37—416no—
62C22×D37—432no—
63C22×D37C2418yes—
64C2×C4×C37—28no—
65C2×C4×C37—48no—
66C2×C4×C37C2418yes—
67C22⋊D37—232no—
68C22⋊D37—232no—
69C2×Dic37—28no—
70C2×Dic37—216no—
71C2×Dic37C2418yes—
72D148—416no—
73C22×C37—216no—
74C22×C37—28no—
75C22×C37—24no—
76C22×C37—28no—
77C22×C37—416no—
78C22×C37C22×D418yes—
79C22×C37C22×D414yes—
80C22×C37C22×D412yes—
81C22×C37H(5,𝔽2)14yes—
82C22×C37C2511yescharacteristic
83C2×D37—28no—
84C2×D37—216no—
85C2×D37—432no—
86C2×D37—416no—
87C4×C37—28no—
88Dic37—28no—
89C2×#534—371nomaximal, Sylow
90C2×C37—28no—
91C2×C37—24no—
92C2×C37#53414yescomplemented
93C2×C37C23×D411yescharacteristic
94C2×C37C2×H(5,𝔽2)12yes—
95D37—48no—
96C23×D4—372no—
97#534—3716no—
98C2×#123—374no—
99C2×#121—374no—
100C2×#120—374no—
101C22×C22⋊C4D3711yescharacteristic, complemented
102C37C2×#53411yescharacteristic, complemented, Sylow
103C25—372no—
104C25C2×D3711yescharacteristic
105C22×D4—374no—
106C22×D4—374no—
107C22×D4—3716no—
108C22×D4—374no—
109C22×D4—7416no—
110C23×C4—372no—
111C23×C4C2×D3712yescomplemented
112#123—3732no—
113#121—3732no—
114#120—3732no—
115C2×C4⋊C4—374no—
116C2×C22⋊C4—378no—
117C2×C22⋊C4C2×D3714yescomplemented
118C2×C22⋊C4C2×D3718yescomplemented
119C24—44no—
120C24—374no—
121C24—378no—
122C24—748no—
123C24—1488no—
124C24D14818yescomplemented
125C24C22×D3712yes—
126C24C22×D3711yescharacteristic
127C24C22×D3714yes—
128C2×D4—3716no—
129C2×D4—3716no—
130C2×D4—3716no—
131C2×D4—7416no—
132C2×D4—7416no—
133C2×D4—7464no—
134C2×D4—1488no—
135C22×C4—44no—
136C22×C4—378no—
137C22×C4—374no—
138C22×C4—748no—
139C22×C4C22×D3714yes—
140C22×C4C22×D3718yescomplemented
141C4⋊C4—3716no—
142C22⋊C4—3732no—
143C22⋊C4C22×D37116yescomplemented
144C23—24no—
145C23—28no—
146C23—416no—
147C23—48no—
148C23—378no—
149C23—7416no—
150C23—748no—
151C23—7416no—
152C23—14816no—
153C23—14832no—
154C23C2×D14818yes—
155C23C2×D14814yes—
156C23C2×D148116yescomplemented
157C23C23×D3714yes—
158C23C23×D3712yes—
159C23C23×D3711yescharacteristic
160D4—7432no—
161D4—7432no—
162D4—14816no—
163C2×C4—28no—
164C2×C4—48no—
165C2×C4—378no—
166C2×C4—7416no—
167C2×C4—748no—
168C2×C4C23×D3718yes—
169C22—216no—
170C22—28no—
171C22—24no—
172C22—28no—
173C22—416no—
174C22—748no—
175C22—7416no—
176C22—14832no—
177C22—14816no—
178C22C22×D14818yes—
179C22C22×D14814yes—
180C22C22×D14812yes—
181C22#1192458114yes—
182C22C24×D3711yescharacteristic
183C4—28no—
184C4—748no—
185C2—28no—
186C2—24no—
187C2—1488no—
188C2#1455809514yesdirect product factor
189C2C23×D14811yescharacteristic
190C2C2×#1192458112yes—
subgroupG/H
centerC23C23×D37
commutator, cosocleC22×C37C25
FrattiniC22C24×D37
FittingC22×C22⋊C4×C37C2
socleC23×C37C24
hypercenterC22×C22⋊C4D37
hypocenterC37C2×#534
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D37C2semidirect
2. #14558095C2direct (N × H)
3. C2×#11924520C2semidirect
4. C2×#11924510C2semidirect
5. C2×#11924506C2semidirect
6. C22×C22⋊C4×C37C2semidirect
7. C24×D37C22semidirect
8. C22×D148C22semidirect
11. C22×C22⋊D37C22semidirect
12. C22×C22⋊D37C22semidirect
13. C23×Dic37C22semidirect
14. #11924520C22semidirect
15. #11924510C22semidirect
16. #11924506C22semidirect
17. C2×C4⋊Dic37C22semidirect
18. C2×#10596938C22semidirect
20. C23×C4×C37C22semidirect
21. C2×C22⋊C4×C37C22semidirect
22. C2×C22⋊C4×C37C22semidirect
24. C24×C37D4semidirect
31. C23×D37C23semidirect
34. C22×C4×C37C23semidirect
39. C2×C22⋊D37C23semidirect
42. C22×Dic37C23semidirect
44. C2×D148C23semidirect
45. C22⋊C4×C37C23semidirect
46. #10596938C23semidirect
47. C4⋊Dic37C23semidirect
54. C23×C37C2×D4semidirect
92. C2×C37#534semidirect
101. C22×C22⋊C4D37semidirect
102. C37C2×#534semidirect
111. C23×C4C2×D37semidirect
117. C2×C22⋊C4C2×D37semidirect
118. C2×C22⋊C4C2×D37semidirect
124. C24D148semidirect
140. C22×C4C22×D37semidirect
143. C22⋊C4C22×D37semidirect
156. C23C2×D148semidirect
188. C2#14558095direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D372
#145580952
C2×#119245202
C2×#119245102
C2×#119245062
C22×C22⋊C4×C372
C2×#53437