Finite Group Databasebeta

← #23781926

Subgroups — #23781926

Order 10432.

104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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#19104765C211yesmaximal, characteristic, complemented
2C2×#14579687C211yesmaximal, characteristic, complemented
3#19104742C211yesmaximal, characteristic, complemented
4#19104670C211yesmaximal, characteristic, complemented
5#19104653C211yesmaximal, characteristic, complemented
6#19104652C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C163C211yesmaximal, characteristic
8C2×Dic326C2211yescharacteristic
9#14579689—21no—
10#14579687—21no—
11#14579687—21no—
12#14579687—21no—
13#14579683—21no—
14#14579683C2211yescharacteristic
15#14579683C2211yescharacteristic
16C2×C163⋊C8—21no—
17C2×C163⋊C8C2211yescharacteristic
18#41×C163C2211yescharacteristic
19C2×D4×C163C2211yescharacteristic
20SD16×C163—21no—
21D8×C163—21no—
22M16×C163C2211yescharacteristic
23Dic326—21no—
24Dic326—21no—
25C2×Dic163—21no—
26C163⋊C8—21no—
27C163⋊C8—21no—
28C163⋊C8D411yescharacteristic
29C163⋊C8D411yescharacteristic
30C23×C163—21no—
31Q8×C163D411yescharacteristic
32D4×C163—21no—
33D4×C163—21no—
34D4×C163—21no—
35D4×C163D411yescharacteristic
36C2×C4×C163—21no—
37C2×C4×C163C2311yescharacteristic
38C8×C163—21no—
39C22×C163—21no—
40C22×C163—41no—
41C22×C163—81no—
42C22×C163#4111yescharacteristic
43C4×C163—21no—
44C4×C163C2×D411yescharacteristic
45C4×C163C2×D411yescharacteristic
46Dic163—41no—
47C2×C163—21no—
48C2×C163—41no—
49C2×C163—81no—
50C2×C163#12111yescharacteristic
51C163#47111yescharacteristic, complemented, Sylow
52#471—1631nomaximal, Sylow
53#137—1631no—
54AGL(1,ℤ/8)D16311yescharacteristic
55C2×SD16—1631no—
56#131—1631no—
57#108—1631no—
58#101—1631no—
59#100—1631no—
60#41C2×D16311yescharacteristic
61C2×Q8—1631no—
62C2×D4C2×D16311yescharacteristic
63Q16—3261no—
64SD16—21no—
65SD16—3261no—
66SD16—3261no—
67SD16—3261no—
68D8—21no—
69M16—3261no—
70M16—1631no—
71M16—1631no—
72M16C2×D16311yescharacteristic
73C2×C8—3261no—
74C2×C8—1631no—
75C23—21no—
76Q8—3261no—
77Q8—3261no—
78Q8C22⋊D16311yescharacteristic
79D4—21no—
80D4—21no—
81D4—21no—
82D4C22⋊D16311yescharacteristic
83C2×C4—21no—
84C2×C4—3261no—
85C2×C4C22×D16311yescharacteristic
86C8—21no—
87C8—3261no—
88C8—3261no—
89C8—1631no—
90C8—1631no—
91C22—21no—
92C22—41no—
93C22—81no—
94C22#1457969811yescharacteristic
95C4—21no—
96C4—6521no—
97C4D4×D16311yescharacteristic
98C4C2×C22⋊D16311yescharacteristic
99C2—21no—
100C2—41no—
101C2—81no—
102C2#1910470711yescharacteristic
subgroupG/H
centerC2#19104707
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting, prime radicalAGL(1,ℤ/8)×C163C2
socleC2×C163#121
hypercenterAGL(1,ℤ/8)D163
hypocenterC163#471
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #19104765C2semidirect
2. C2×#14579687C2semidirect
3. #19104742C2semidirect
4. #19104670C2semidirect
5. #19104653C2semidirect
6. #19104652C2semidirect
51. C163#471semidirect