Finite Group Databasebeta

← #17186890

Subgroups — #17186890

Order 4352.

1006 conjugacy classes of subgroups; only the 459 normal subgroups are shown.

normal subgroups only

This group has 1006 conjugacy classes of subgroups — too many to draw. Only its 459 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
1C2×#11763207C214yesmaximal
2#14537182C212yesmaximal
3#14528941C218yesmaximal
4C42×C8×C17C211yesmaximal, characteristic
5C2×#10587555—24no—
6C2×#10587555C2214yes—
7#11763207—216no—
8C2×#10587488C22116yes—
9#11762679—24no—
10#11762679C2218yes—
11C2×C4×C8×C17C2212yes—
12C2×C4×C8×C17C2214yes—
13C43×C17C2211yescharacteristic
14C22×Dic34—24no—
15C22×C8×C17C2314yes—
16C2×C42×C17D414yes—
17C2×C42×C17C2311yescharacteristic
18C2×C42×C17C2312yes—
19C2×C4⋊Dic17—216no—
20C2×C4⋊Dic17—24no—
21C2×C4⋊Dic17C2318yes—
22#10587555—216no—
23#10587555—416no—
24C4×C8×C17D418yes—
25C4×C8×C17Q8116yescomplemented
26#10587488—232no—
27C22×C4×C17C2×D412yes—
28C22×C4×C17C2×D414yes—
29C22×C4×C17C2411yescharacteristic
30C22×Dic17—28no—
31C2×Dic34—48no—
32C2×Dic34—416no—
33C2×C8×C17C2×D418yes—
34C2×C8×C17C2×Q8116yes—
35C42×C17SD16116yes—
36C42×C17C2×D414yes—
37C42×C17C2×Q818yes—
38C4⋊Dic17—216no—
39C4⋊Dic17—48no—
40C4⋊Dic17—432no—
41#33310—171nomaximal, Sylow
42C23×C17C22×D411yescharacteristic
43C2×C4×C17#12714yes—
44C2×C4×C17C4⋊Q818yes—
45C2×C4×C17C2×SD1618yes—
46C2×C4×C17C2×SD16116yes—
47C2×C4×C17C22×D412yes—
48C2×C4×C17C22×Q814yes—
49C2×Dic17—48no—
50C2×Dic17—416no—
51Dic34—816no—
52C8×C17C4⋊Q8116yescomplemented
53C2×#498—174no—
54#2868—172no—
55#1844—178no—
56C42×C8D1711yescharacteristic
57C22×C17C2×#12711yescharacteristic
58C22×C17C2×C4⋊Q812yes—
59C22×C17C22×SD1614yes—
60C4×C17#49218yes—
61C4×C17#498116yescomplemented
62C4×C17C2×C4⋊Q814yes—
63Dic17—88no—
64C2×C4⋊Q8—174no—
65C2×C4⋊Q8—344no—
66#498—3416no—
67C2×#106—1716no—
68C2×C4×C8C2×D1714yes—
69C2×C4×C8C2×D1712yes—
70#384—178no—
71#384—344no—
72C43C2×D1711yescharacteristic
73C2×C17#286811yescharacteristic
74C2×C17C2×#49212yes—
75C2×C17C2×#49814yes—
76C22×Q8—344no—
77C22×C8C22×D1714yes—
78C4⋊Q8—3416no—
79C4⋊Q8—6816no—
80C2×C4⋊C4—178no—
81C2×C4⋊C4—344no—
82C2×C4⋊C4—3416no—
83C2×C42D6814yes—
84C2×C42C22×D1712yes—
85C2×C42C22×D1711yescharacteristic
86#106—3432no—
87C4×C8Dic34116yescomplemented
88C4×C8D6818yes—
89C17#3331011yescharacteristic, complemented, Sylow
90C2×Q8—688no—
91C2×Q8—6816no—
92C22×C4—348no—
93C22×C4C2×D6814yes—
94C22×C4C2×D6812yes—
95C22×C4C23×D1711yescharacteristic
96C2×C8C2×Dic34116yes—
97C2×C8C2×D6818yes—
98C4⋊C4—3416no—
99C4⋊C4—688no—
100C4⋊C4—6832no—
101C42#63219116yes—
102C42C2×Dic3418yes—
103C42C2×D6814yes—
104C23C22×D6811yescharacteristic
105Q8—13616no—
106C2×C4—6816no—
107C2×C4—688no—
108C2×C4#1058755518yes—
109C2×C4#1058756014yes—
110C2×C4C2×#63219116yes—
111C2×C4C2×#6321918yes—
112C2×C4C22×Dic3414yes—
113C2×C4C22×D6812yes—
114C8#10587555116yescomplemented
115C22C2×#1058756011yescharacteristic
116C22C2×#1058755512yes—
117C22C22×#6321914yes—
118C4—1368no—
119C4#1176318218yes—
120C4#11763207116yescomplemented
121C4C2×#1058755514yes—
122C2#1453718211yescharacteristic
123C2C2×#1176318212yes—
124C2C2×#1176320714yes—
subgroupG/H
centerC23C22×D68
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC42×C8×C17C2
socle, prime radicalC23×C17C22×D4
hypercenterC42×C8D17
hypocenterC17#33310
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C43 ◁ C42×C8

Complements

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

NH ≅ G/Ntype
25. C4×C8×C17Q8semidirect
52. C8×C17C4⋊Q8semidirect
61. C4×C17#498semidirect
87. C4×C8Dic34semidirect
89. C17#33310semidirect
114. C8#10587555semidirect
120. C4#11763207semidirect

Maximal subgroups

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

subgroupindex
C2×#117632072
#145371822
#145289412
C42×C8×C172
#3331017