Finite Group Databasebeta

← #17953086

Subgroups — #17953086

Order 4352.

910 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 910 conjugacy classes of subgroups — too many to draw. Only its 100 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#14544679C216yesmaximal
2C22×#10587562C211yesmaximal, characteristic
3#11763750C2214yes—
4#11763687—212no—
5C2×#10587562—212no—
6C22×#63225C413yescomplemented
7C22×#63227C2213yes—
8C22×C42×C17C411yescharacteristic, complemented
9C24×D17C2311yescharacteristic
10C23×C4×C17C2×C413yes—
11C23×Dic17C2×C413yes—
12C2×C22⋊#595—212no—
13C2×C42×C17—26no—
14C2×#63227—26no—
15C2×#63227—26no—
16C2×#63227D4112yes—
17C2×#63225—26no—
18C2×#63225—26no—
19C2×#63225—26no—
20#10587562—232no—
21C24×C17C22×C411yescharacteristic
22C23×D17—46no—
23C23×D17C2×D416yes—
24C22×#595—44no—
25C22×C4×C17—23no—
26C22×C4×C17—23no—
27C22×C4×C17—46no—
28C22×C4×C17C22⋊C416yes—
29C22×Dic17—23no—
30C22×Dic17—23no—
31C22×Dic17—46no—
32C22×Dic17C22⋊C416yes—
33C22⋊#595—424no—
34C42×C17—28no—
35#63227—224no—
36#63225—224no—
37#8545—171nomaximal, Sylow
38C23×C17—26no—
39C23×C17C2×C22⋊C413yes—
40C22×D17—212no—
41C22×D17—46no—
42C22×D17—46no—
43C22×D17—88no—
44C22×D17#12014yes—
45C2×#595—812no—
46C2×C4×C17—26no—
47C2×C4×C17—46no—
48C2×C4×C17—46no—
49C2×C4×C17—46no—
50C2×Dic17—26no—
51C2×Dic17—46no—
52C2×Dic17—46no—
53C2×Dic17—46no—
54C22×#126—171no—
55#1819—176no—
56C22×C17—28no—
57C22×C17—23no—
58C22×C17—23no—
59C22×C17#37911yescharacteristic
60C22×C17#41016yes—
61C2×D17—212no—
62C2×D17—812no—
63#595—164no—
64C4×C17—46no—
65Dic17—46no—
66C2×#126—3412no—
67C22×C4⋊C4—173no—
68C22×C22⋊C4—173no—
69C22×C42#59511yescharacteristic, complemented
70#379—174no—
71#342—3412no—
72C2×C17—26no—
73C2×C17#178213yes—
74D17—44no—
75C25—171no—
76C23×C4—173no—
77C23×C4C2×#59513yes—
78#126—3432no—
79C2×C4⋊C4—346no—
80C2×C4⋊C4—346no—
81C2×C4⋊C4—346no—
82C2×C22⋊C4—1712no—
83C2×C22⋊C4—346no—
84C2×C22⋊C4—346no—
85C2×C22⋊C4—3412no—
86C2×C42—26no—
87C17#854511yescharacteristic, complemented, Sylow
88C24—176no—
89C24—686no—
90C24C22×#59511yescharacteristic
91C22×C4—23no—
92C22×C4—23no—
93C22×C4—46no—
94C22×C4—176no—
95C22×C4—343no—
96C22×C4—343no—
97C22×C4—686no—
98C22×C4—684no—
99C22×C4C22⋊#59516yes—
100C4⋊C4—3424no—
101C22⋊C4—3424no—
102C22⋊C4—6824no—
103C42—28no—
104C23—26no—
105C23—174no—
106C23—3412no—
107C23—686no—
108C23—686no—
109C23—1368no—
110C23C2×C22⋊#59513yes—
111C2×C4—26no—
112C2×C4—46no—
113C2×C4—46no—
114C2×C4—46no—
115C2×C4—346no—
116C2×C4—686no—
117C2×C4—686no—
118C2×C4—686no—
119C2×C4—13612no—
120C22—28no—
121C22—23no—
122C22—23no—
123C22—3412no—
124C22—13612no—
125C22#1176375011yescharacteristic
126C22#1176378816yes—
127C4—46no—
128C4—2724no—
129C4—686no—
130C2—26no—
131C2—684no—
132C2#1454461313yes—
subgroupG/H
centerC22#11763750
commutatorC24×C17C22×C4
FrattiniC24C22×#595
FittingC22×C42×C17C4
socleC22×C17#379
prime radical, cosocleC24×D17C23
hypercenterC22×C42#595
hypocenterC17#8545
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
6. C22×#63225C4semidirect
8. C22×C42×C17C4semidirect
69. C22×C42#595semidirect
87. C17#8545semidirect

Maximal subgroups

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

subgroupindex
#145446792
C22×#105875622
#854517