Finite Group Databasebeta

← C23×#10587639 #17940955

Subgroups — C23×#10587639 #17940955

Order 4352.

42862 conjugacy classes of subgroups; only the 5451 normal subgroups are shown.

normal subgroups only

This group has 42862 conjugacy classes of subgroups — too many to draw. Only its 5451 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
1C24×C22⋊D17C213yesmaximal, complemented
2C22×#10587639C2156yesmaximal, direct product factor
3C23×C22⋊Dic17C213yesmaximal, complemented
4C27×C17C211yesmaximal, characteristic, complemented
5C25×D17C2211yescharacteristic, complemented
6C23×C22⋊D17—248no—
7C23×C22⋊D17C22184yescomplemented
8C24×Dic17C2213yescomplemented
9C2×#10587639C221448yesdirect product factor
10C22×C22⋊Dic17C22184yescomplemented
11C26×C17—248no—
12C26×C17C2213yes—
13C26×C17C22128yescomplemented
14C25×C17—2512no—
15C25×C17—248no—
16C25×C17—2672no—
17C25×C17D4148yescomplemented
18C25×C17C23142yes—
19C25×C17C2311yescharacteristic
20C25×C17C231112yescomplemented
21C24×D17—224no—
22C24×D17C23114yescomplemented
23C22×C22⋊D17—2672no—
24C22×C22⋊D17C231336yescomplemented
25C23×Dic17—224no—
26C23×Dic17C23142yescomplemented
27#10587639C231512yesdirect product factor
28C2×C22⋊Dic17C231336yescomplemented
29C24×C17—23584no—
30C24×C17—2384no—
31C24×C17—2336no—
32C24×C17—21344no—
33C24×C17C2×D4124yes—
34C24×C17C2×D41336yescomplemented
35C24×C17C24184yes—
36C24×C17C2417yes—
37C24×C17C24164yescomplemented
38C23×D17—2168no—
39C23×D17—464no—
40C23×D17C24128yescomplemented
41C2×C22⋊D17—21344no—
42C2×C22⋊D17C241192yescomplemented
43C22×Dic17—2168no—
44C22×Dic17C24184yescomplemented
45C22⋊Dic17C241192yescomplemented
46C23×#120—171nomaximal, Sylow
47C23×C17—23584no—
48C23×C17—21344no—
49C23×C17—2336no—
50C23×C17—2384no—
51C23×C17#120164yescomplemented
52C23×C17C22×D4184yes—
53C23×C17C22×D41336yescomplemented
54C23×C17C25124yes—
55C23×C17C2517yes—
56C22×D17—2168no—
57C22×D17—4224no—
58C22×D17C2518yescomplemented
59C22⋊D17—2384no—
60C2×Dic17—2168no—
61C2×Dic17C25124yescomplemented
62C27D1711yescharacteristic, complemented
63C24×D4—173no—
64C22×#120—1756no—
65C23×C22⋊C4—173no—
66C22×C17—2512no—
67C22×C17—248no—
68C22×C17—2672no—
69C22×C17C2×#1201112yescomplemented
70C22×C17C23×D4142yes—
71C22×C17C23×D4148yescomplemented
72C22×C17C2611yescharacteristic
73C2×D17—224no—
74C2×D17—4112no—
75Dic17—224no—
76C26—248no—
77C26—171no—
78C26C2×D1713yes—
79C26C2×D17128yescomplemented
80C23×D4—1784no—
81C23×D4—3448no—
82C24×C4—173no—
83C2×#120—17448no—
84C22×C22⋊C4—1784no—
85C2×C17—248no—
86C2×C17C22×#120128yescomplemented
87C2×C17C24×D413yes—
88D17—48no—
89C25—2512no—
90C25—248no—
91C25—2672no—
92C25—1714no—
93C25—3424no—
94C25C22⋊D17148yescomplemented
95C25C22×D17142yes—
96C25C22×D1711yescharacteristic
97C25C22×D171112yescomplemented
98C22×D4—17336no—
99C22×D4—34672no—
100C23×C4—1742no—
101C23×C4—3424no—
102#120—17512no—
103C2×C22⋊C4—17336no—
104C17C23×#12011yescharacteristic, complemented, Sylow
105C24—23584no—
106C24—2336no—
107C24—21344no—
108C24—2384no—
109C24—1728no—
110C24—34168no—
111C24—6864no—
112C24C2×C22⋊D17124yes—
113C24C2×C22⋊D171336yescomplemented
114C24C23×D17184yes—
115C24C23×D1717yes—
116C24C23×D17164yescomplemented
117C2×D4—17192no—
118C2×D4—341344no—
119C22×C4—1784no—
120C22×C4—34168no—
121C22⋊C4—17192no—
122C23—23584no—
123C23—21344no—
124C23—2336no—
125C23—2384no—
126C23—178no—
127C23—34168no—
128C23—68224no—
129C23#10587639164yesdirect product factor
130C23C22×C22⋊D17184yes—
131C23C22×C22⋊D171336yescomplemented
132C23C24×D17124yes—
133C23C24×D1717yes—
134D4—34384no—
135C2×C4—1724no—
136C2×C4—34168no—
137C22—2512no—
138C22—2672no—
139C22—248no—
140C22—3424no—
141C22—68112no—
142C22C2×#105876391112yesdirect product factor
143C22C23×C22⋊D17142yes—
144C22C23×C22⋊D17148yescomplemented
145C22C25×D1711yescharacteristic
146C4—3424no—
147C2—248no—
148C2—688no—
149C2C22×#10587639128yesdirect product factor
150C2C24×C22⋊D1713yes—
subgroupG/H
centerC25C22×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC27×C17C2
socleC25×C17C23
hypercenterC27D17
hypocenterC17C23×#120
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C25 ◁ C27

Complements

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

NH ≅ G/Ntype
1. C24×C22⋊D17C2semidirect
2. C22×#10587639C2direct (N × H)
3. C23×C22⋊Dic17C2semidirect
4. C27×C17C2semidirect
5. C25×D17C22semidirect
7. C23×C22⋊D17C22semidirect
8. C24×Dic17C22semidirect
9. C2×#10587639C22direct (N × H)
10. C22×C22⋊Dic17C22semidirect
13. C26×C17C22semidirect
17. C25×C17D4semidirect
20. C25×C17C23semidirect
22. C24×D17C23semidirect
24. C22×C22⋊D17C23semidirect
26. C23×Dic17C23semidirect
27. #10587639C23direct (N × H)
28. C2×C22⋊Dic17C23semidirect
34. C24×C17C2×D4semidirect
37. C24×C17C24semidirect
40. C23×D17C24semidirect
42. C2×C22⋊D17C24semidirect
44. C22×Dic17C24semidirect
45. C22⋊Dic17C24semidirect
51. C23×C17#120semidirect
53. C23×C17C22×D4semidirect
58. C22×D17C25semidirect
61. C2×Dic17C25semidirect
62. C27D17semidirect
69. C22×C17C2×#120semidirect
71. C22×C17C23×D4semidirect
79. C26C2×D17semidirect
86. C2×C17C22×#120semidirect
94. C25C22⋊D17semidirect
97. C25C22×D17semidirect
104. C17C23×#120semidirect
113. C24C2×C22⋊D17semidirect
116. C24C23×D17semidirect
129. C23#10587639direct (N × H)
131. C23C22×C22⋊D17semidirect
142. C22C2×#10587639direct (N × H)
144. C22C23×C22⋊D17semidirect
149. C2C22×#10587639direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C22⋊D172
C22×#105876392
C23×C22⋊Dic172
C27×C172
C23×#12017