Finite Group Databasebeta

← C2×#14558275 #18008716

Subgroups — C2×#14558275 #18008716

Order 4736.

1408 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 469 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
1#14558275C2116yesmaximal, direct product factor
2C2×#11924525C212yesmaximal, complemented
3C2×#11924524C212yesmaximal, complemented
4C2×#11924522C214yesmaximal, complemented
5C2×#11924506C214yesmaximal, complemented
6C2×#11924504C212yesmaximal, complemented
7C2×#124×C37C211yesmaximal, characteristic, complemented
8C24×D37C2212yescomplemented
9C22×Dic74C2212yescomplemented
10C22×D148C2212yes—
11C22×D148C2212yes—
12C22×C22⋊D37C2214yes—
13#11924525C22116yescomplemented
14#11924524C22116yescomplemented
15#11924522C22132yescomplemented
16#11924506C22132yescomplemented
17#11924504C22116yescomplemented
18C2×C22⋊Dic37C2212yescomplemented
19C2×#10596938C2214yescomplemented
20C2×#10596938C2214yescomplemented
21C2×#10596938C2214yescomplemented
22C2×C4×Dic37C2212yescomplemented
23C22×Q8×C37C2211yescharacteristic, complemented
24C22×D4×C37C2211yescharacteristic
25#124×C37C2218yescomplemented
26C2×C22⋊C4×C37C2214yescomplemented
27C2×C42×C37C2211yescharacteristic, complemented
28C24×C37C2312yes—
29C23×D37—44no—
30C23×D37—48no—
31C23×D37C2314yes—
32C23×D37C2318yescomplemented
33C2×Q8×C37—42no—
34C2×Q8×C37C2314yescomplemented
35C2×D4×C37—42no—
36C2×D4×C37C2314yes—
37C22×C4×C37C2312yes—
38C22×C4×C37C2311yescharacteristic
39C22×C4×C37C2312yes—
40C2×C22⋊D37—48no—
41C2×C22⋊D37C23116yes—
42C22×Dic37C2314yes—
43C2×D148—44no—
44C2×D148—44no—
45C2×D148C2318yes—
46C2×D148C2318yes—
47C2×Dic74—44no—
48C2×Dic74C2318yescomplemented
49C22⋊C4×C37C23116yescomplemented
50C42×C37C2314yescomplemented
51C22⋊Dic37C2318yescomplemented
52#10596938C23116yescomplemented
53#10596938C23116yescomplemented
54#10596938C23116yescomplemented
55C4×Dic37C2318yescomplemented
56C23×C37—28no—
57C23×C37—24no—
58C23×C37C2414yes—
59C23×C37C2411yescharacteristic
60C22×D37—28no—
61C22×D37—28no—
62C22×D37—28no—
63C22×D37—48no—
64C22×D37—416no—
65C22×D37—432no—
66C22×D37C2418yes—
67Q8×C37—44no—
68D4×C37—44no—
69C2×C4×C37—24no—
70C2×C4×C37—24no—
71C2×C4×C37—22no—
72C2×C4×C37C2414yes—
73C2×C4×C37C2412yes—
74C2×C4×C37C2414yes—
75C22⋊D37—416no—
76C2×Dic37—28no—
77C2×Dic37C2418yes—
78D148—48no—
79D148—48no—
80Dic74—48no—
81C22×C37—28no—
82C22×C37—24no—
83C22×C37—48no—
84C22×C37H(5,𝔽2)12yes—
85C22×C37H(5,𝔽2)14yes—
86C22×C37C2511yescharacteristic
87C2×D37—28no—
88C2×D37—28no—
89C2×D37—28no—
90C2×D37—432no—
91C2×D37—416no—
92C4×C37—24no—
93C4×C37—24no—
94C4×C37—22no—
95Dic37—28no—
96C2×H(3,𝔽4)—371nomaximal, Sylow
97C2×C37—44no—
98C2×C37H(3,𝔽4)14yescomplemented
99C2×C37C2×H(5,𝔽2)11yescharacteristic
100C2×C37C2×H(5,𝔽2)12yes—
101D37—48no—
102H(3,𝔽4)—3716no—
103C2×#124—372no—
104C2×#124—374no—
105C2×#124—372no—
106C2×#124D3711yescharacteristic, complemented
107C2×#120—372no—
108C2×#120—374no—
109C37C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
110C25—372no—
111C22×Q8—372no—
112C22×Q8C2×D3711yescharacteristic, complemented
113C22×D4—374no—
114C22×D4—372no—
115C22×D4—372no—
116C22×D4C2×D3711yescharacteristic
117#124—3716no—
118#124—3732no—
119#124—3716no—
120#124C2×D3718yescomplemented
121#120—3716no—
122#120—3732no—
123C2×C22⋊C4—372no—
124C2×C22⋊C4—374no—
125C2×C22⋊C4—374no—
126C2×C22⋊C4—374no—
127C2×C22⋊C4C2×D3714yescomplemented
128C2×C42—372no—
129C2×C42C2×D3711yescharacteristic, complemented
130C24—374no—
131C24—378no—
132C24—1484no—
133C24—1488no—
134C24C22×D3712yes—
135C2×Q8—42no—
136C2×Q8—378no—
137C2×Q8—1484no—
138C2×Q8C22×D3714yescomplemented
139C2×D4—42no—
140C2×D4—3716no—
141C2×D4—378no—
142C2×D4—378no—
143C2×D4—1484no—
144C2×D4—1484no—
145C2×D4—1488no—
146C2×D4C22×D3714yes—
147C22×C4—374no—
148C22×C4C22×D3712yes—
149C22×C4C22×D3711yescharacteristic
150C22×C4C22×D3712yes—
151C22⋊C4—378no—
152C22⋊C4—3716no—
153C22⋊C4—3716no—
154C22⋊C4—3716no—
155C22⋊C4C22×D37116yescomplemented
156C42—378no—
157C42C22×D3714yescomplemented
158C23—24no—
159C23—28no—
160C23—378no—
161C23—748no—
162C23—748no—
163C23—748no—
164C23—1488no—
165C23—14816no—
166C23—14832no—
167C23C23×D3714yes—
168C23C23×D3711yescharacteristic
169Q8—44no—
170Q8—1488no—
171D4—44no—
172D4—1488no—
173D4—1488no—
174D4—14816no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—378no—
179C2×C4—748no—
180C2×C4C23×D3714yes—
181C2×C4C23×D3712yes—
182C2×C4C23×D3714yes—
183C22—24no—
184C22—28no—
185C22—48no—
186C22—748no—
187C22—748no—
188C22—748no—
189C22—14832no—
190C22—14816no—
191C22#1192458112yes—
192C22#1192458214yes—
193C22C24×D3711yescharacteristic
194C4—22no—
195C4—24no—
196C4—24no—
197C4—748no—
198C2—44no—
199C2—1488no—
200C2#1455827514yesdirect product factor
201C2C2×#1192458111yescharacteristic
202C2C2×#1192458212yes—
subgroupG/H
centerC23C23×D37
commutator, cosocleC22×C37C25
FrattiniC22C24×D37
FittingC2×#124×C37C2
socleC23×C37C24
hypercenterC2×#124D37
hypocenterC37C2×H(3,𝔽4)
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #14558275C2direct (N × H)
2. C2×#11924525C2semidirect
3. C2×#11924524C2semidirect
4. C2×#11924522C2semidirect
5. C2×#11924506C2semidirect
6. C2×#11924504C2semidirect
7. C2×#124×C37C2semidirect
8. C24×D37C22semidirect
9. C22×Dic74C22semidirect
13. #11924525C22semidirect
14. #11924524C22semidirect
15. #11924522C22semidirect
16. #11924506C22semidirect
17. #11924504C22semidirect
18. C2×C22⋊Dic37C22semidirect
19. C2×#10596938C22semidirect
20. C2×#10596938C22semidirect
21. C2×#10596938C22semidirect
22. C2×C4×Dic37C22semidirect
23. C22×Q8×C37C22semidirect
25. #124×C37C22semidirect
26. C2×C22⋊C4×C37C22semidirect
27. C2×C42×C37C22semidirect
32. C23×D37C23semidirect
34. C2×Q8×C37C23semidirect
48. C2×Dic74C23semidirect
49. C22⋊C4×C37C23semidirect
50. C42×C37C23semidirect
51. C22⋊Dic37C23semidirect
52. #10596938C23semidirect
53. #10596938C23semidirect
54. #10596938C23semidirect
55. C4×Dic37C23semidirect
98. C2×C37H(3,𝔽4)semidirect
106. C2×#124D37semidirect
109. C37C2×H(3,𝔽4)semidirect
112. C22×Q8C2×D37semidirect
120. #124C2×D37semidirect
127. C2×C22⋊C4C2×D37semidirect
129. C2×C42C2×D37semidirect
138. C2×Q8C22×D37semidirect
155. C22⋊C4C22×D37semidirect
157. C42C22×D37semidirect
200. C2#14558275direct (N × H)

Maximal subgroups

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

subgroupindex
#145582752
C2×#119245252
C2×#119245242
C2×#119245222
C2×#119245062
C2×#119245042
C2×#124×C372
C2×H(3,𝔽4)37