Finite Group Databasebeta

← #28405698

Subgroups — #28405698

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#20298773C211yesmaximal, characteristic
4#16813681—21no—
5#16813677—21no—
6#16813670C411yescharacteristic, complemented
7#16813650—21no—
8#16813611C2211yescharacteristic
9#16813548—21no—
10#101×C113C411yescharacteristic, complemented
11C2×#11744753—41no—
12C22⋊#90673—41no—
13#14268648—41no—
14#14268647—21no—
15#14268647—41no—
16Q8×D113—41no—
17C2×D452D411yescharacteristic
18#14268636—41no—
19D904—41no—
20#14268624—41no—
21C4×Dic113D411yescharacteristic
22C2×Q8×C113C2×C411yescharacteristic
23M16×C113—21no—
24C22×D113—21no—
25C2×#90673—81no—
26Q8×C113—41no—
27C2×C4×C113—21no—
28C2×C4×C113C22⋊C411yescharacteristic
29C22⋊D113—41no—
30C2×Dic113—21no—
31D452—21no—
32D452—41no—
33D452—41no—
34C4×D113—41no—
35C4×D113—42no—
36Dic226—21no—
37Dic226—41no—
38#11744753—42no—
39C8×C113—41no—
40C22×C113#9911yescharacteristic
41C2×D113—41no—
42C2×D113—41no—
43C2×D113—81no—
44#90673—161no—
45C4×C113—21no—
46C4×C113—41no—
47Dic113—41no—
48Dic113—41no—
49C2×C113—21no—
50C2×C113AΣL(1,𝔽16)11yescharacteristic
51D113—81no—
52D113—81no—
53#1404—1131nomaximal, Sylow
54C113#140411yescharacteristic, complemented, Sylow
55#454—1131no—
56#354—1131no—
57#329—1131no—
582−1+4—1131no—
59AGL(1,ℤ/8)—2261no—
60#124—1131no—
61#104—2261no—
62#101#9067311yescharacteristic, complemented
63#99—2261no—
64#97—2261no—
65#41—4521no—
66#41—4521no—
67#41—2261no—
68C2×Q8—4521no—
69C2×Q8C2×#9067311yescharacteristic
70C2×D4—1131no—
71SD16—4521no—
72D8—4521no—
73M16—21no—
74C2×C8—4521no—
75C22⋊C4—4521no—
76C22⋊C4—4521no—
77C42—1131no—
78C23—2261no—
79Q8—41no—
80Q8—4521no—
81Q8—2261no—
82D4—4521no—
83D4—4521no—
84D4—4521no—
85D4—2261no—
86C2×C4—21no—
87C2×C4—9041no—
88C2×C4—4521no—
89C2×C4—4522no—
90C2×C4—2261no—
91C2×C4C22⋊#9067311yescharacteristic
92C8—41no—
93C8—4522no—
94C22—9041no—
95C22—4521no—
96C22—4521no—
97C22#1681368111yescharacteristic
98C4—21no—
99C4—41no—
100C4—18081no—
101C4—4521no—
102C4—4521no—
103C2—21no—
104C2—9041no—
105C2—9041no—
106C2#2029949911yescharacteristic
subgroupG/H
centerC2#20299499
commutatorC2×Q8×C113C2×C4
FrattiniC2×Q8C2×#90673
Fitting#101×C113C4
socleC2×C113AΣL(1,𝔽16)
prime radical#20298773C2
cosocle#16813611C22
hypercenter#101#90673
hypocenterC113#1404
LCSG ▷ C2×Q8×C113 ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8 ◁ #101

Complements

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

NH ≅ G/Ntype
1. #20299504C2semidirect
2. #20299454C2semidirect
6. #16813670C4semidirect
10. #101×C113C4semidirect
54. C113#1404semidirect
62. #101#90673semidirect

Maximal subgroups

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

subgroupindex
#202995042
#202994542
#202987732
#1404113