Finite Group Databasebeta

← #28405697

Subgroups — #28405697

Order 14464.

112 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 20 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#20299504C211yesmaximal, characteristic, complemented
2#20299454C211yesmaximal, characteristic, complemented
3#20298771C211yesmaximal, characteristic
4#16813681—21no—
5#16813677—21no—
6#16813647—21no—
7#16813611C2211yescharacteristic
8#16813549—21no—
9#16813541C411yescharacteristic, complemented
102−1+4×C113C411yescharacteristic, complemented
11C2×#11744753—41no—
12C22⋊#90673—41no—
13C2×D452D411yescharacteristic
14#14268634—41no—
15#14268632—41no—
16#14268631—21no—
17#14268624—41no—
18C4×Dic113D411yescharacteristic
19#41×C113—21no—
20#41×C113—41no—
21#41×C113—41no—
22C2×Q8×C113—41no—
23C2×Q8×C113C2×C411yescharacteristic
24C22×D113—21no—
25C2×#90673—81no—
26Q8×C113—21no—
27Q8×C113—41no—
28Q8×C113—41no—
29D4×C113—21no—
30D4×C113—41no—
31D4×C113—41no—
32C2×C4×C113—21no—
33C2×C4×C113—41no—
34C2×C4×C113—42no—
35C2×C4×C113C22⋊C411yescharacteristic
36C2×Dic113—21no—
37D452—41no—
38#11744753—42no—
39#11744751—41no—
40C22×C113—41no—
41C22×C113#9911yescharacteristic
42C2×D113—41no—
43C2×D113—81no—
44#90673—161no—
45C4×C113—21no—
46C4×C113—41no—
47C4×C113—41no—
48Dic113—41no—
49C2×C113—21no—
50C2×C113—81no—
51C2×C113AΣL(1,𝔽16)11yescharacteristic
52D113—81no—
53#1404—1131nomaximal, Sylow
54C113#140411yescharacteristic, complemented, Sylow
55#454—1131no—
56#354—1131no—
57#329—1131no—
582−1+4#9067311yescharacteristic, complemented
59AGL(1,ℤ/8)—2261no—
60#124—1131no—
61#104—2261no—
62#101—1131no—
63#99—2261no—
64#97—2261no—
65#41—21no—
66#41—41no—
67#41—41no—
68C2×Q8—41no—
69C2×Q8C2×#9067311yescharacteristic
70C2×D4—1131no—
71SD16—4521no—
72D8—4521no—
73M16—2261no—
74C2×C8—4521no—
75C22⋊C4—4521no—
76C22⋊C4—4521no—
77C42—1131no—
78C23—2261no—
79Q8—21no—
80Q8—41no—
81Q8—41no—
82D4—21no—
83D4—41no—
84D4—41no—
85D4—4521no—
86C2×C4—21no—
87C2×C4—41no—
88C2×C4—42no—
89C2×C4—9041no—
90C2×C4—2261no—
91C2×C4C22⋊#9067311yescharacteristic
92C8—4521no—
93C8—4522no—
94C22—41no—
95C22—9041no—
96C22—4521no—
97C22#1681368011yescharacteristic
98C4—21no—
99C4—41no—
100C4—41no—
101C4—18081no—
102C4—4521no—
103C2—21no—
104C2—81no—
105C2—9041no—
106C2#2029949811yescharacteristic
subgroupG/H
centerC2#20299498
commutatorC2×Q8×C113C2×C4
FrattiniC2×Q8C2×#90673
Fitting2−1+4×C113C4
socleC2×C113AΣL(1,𝔽16)
prime radical#20298771C2
cosocle#16813611C22
hypercenter2−1+4#90673
hypocenterC113#1404
LCSG ▷ C2×Q8×C113 ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. #20299504C2semidirect
2. #20299454C2semidirect
9. #16813541C4semidirect
10. 2−1+4×C113C4semidirect
54. C113#1404semidirect
58. 2−1+4#90673semidirect

Maximal subgroups

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

subgroupindex
#202995042
#202994542
#202987712
#1404113