Finite Group Databasebeta

← #28405567

Subgroups — #28405567

Order 14464.

104 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 30 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#20299493C211yesmaximal, characteristic
2#20299474C211yesmaximal, characteristic
3#20298840C211yesmaximal, characteristic
4C2×#14268657—21no—
5C2×#14268650—21no—
6C2×Dic452C411yescharacteristic
7C2×C8×D113C2211yescharacteristic
8#16813602—21no—
9#16813545—21no—
10#107×C113C411yescharacteristic
11#14268657—22no—
12#14268657—41no—
13C2×#11744753—41no—
14#14268650—41no—
15C2×Dic226—21no—
16C2×C4×D113D411yescharacteristic
17Dic452—41no—
18C2×#11744751D411yescharacteristic
19C8×D113—41no—
20C4⋊Dic113—41no—
21#14268624—41no—
22C2×C8×C113C2×C411yescharacteristic
23C4⋊C4×C113—21no—
24C22×D113SD1611yescharacteristic
25C2×C4×C113—41no—
26C2×C4×C113C22⋊C411yescharacteristic
27C2×Dic113—41no—
28C2×Dic113D811yescharacteristic
29C4×D113—21no—
30C4×D113—21no—
31Dic226—41no—
32Dic226—41no—
33#11744753—42no—
34C8×C113—21no—
35#11744751—21no—
36C22×C113#10211yescharacteristic
37C2×D113—21no—
38C2×D113—21no—
39C2×D113—21no—
40C4×C113—81no—
41C4×C113#9911yescharacteristic
42C4×C113#10411yescharacteristic
43Dic113—21no—
44Dic113—81no—
45C2×C113#32711yescharacteristic
46C2×C113#35911yescharacteristic
47C2×C113#36211yescharacteristic
48D113—41no—
49#1350—1131nomaximal, Sylow
50C113#135011yescharacteristic, complemented, Sylow
51#467—1131no—
52C22⋊C16—1131no—
53#341—1131no—
54C2×Q16—1131no—
55C2×M16—2261no—
56C22×C8—1131no—
57C22⋊Q8—2261no—
58C2×C16—2261no—
59#107#9067311yescharacteristic
60#103—2261no—
61C2×Q8—2261no—
62C22×C4—1131no—
63Q16—4521no—
64M16—4521no—
65M16—2262no—
66C2×C8—1131no—
67C2×C8—4521no—
68C2×C8—4521no—
69C2×C8C2×#9067311yescharacteristic
70C4⋊C4—21no—
71C4⋊C4—4521no—
72C22⋊C4—4521no—
73C16—4521no—
74C23—1131no—
75Q8—4521no—
76Q8—4521no—
77C2×C4—41no—
78C2×C4—1131no—
79C2×C4—4521no—
80C2×C4—2261no—
81C2×C4—2261no—
82C2×C4C22⋊#9067311yescharacteristic
83C8—21no—
84C8—4522no—
85C8—2261no—
86C22—2261no—
87C22—2261no—
88C22—2261no—
89C22#1681368411yescharacteristic
90C4—81no—
91C4—9041no—
92C4—2261no—
93C4#1681368111yescharacteristic
94C4#1681368711yescharacteristic
95C2—4521no—
96C2#2029945011yescharacteristic
97C2#2029951211yescharacteristic
98C2#2029951711yescharacteristic
subgroupG/H
centerC22#16813684
commutatorC2×C8×C113C2×C4
FrattiniC2×C8C2×#90673
Fitting#107×C113C4
socleC22×C113#102
prime radicalC22×D113SD16
cosocleC2×C8×D113C22
hypercenter#107#90673
hypocenterC113#1350
LCSG ▷ C2×C8×C113 ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
50. C113#1350semidirect

Maximal subgroups

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

subgroupindex
#202994932
#202994742
#202988402
#1350113