Finite Group Databasebeta

← #23781819

Subgroups — #23781819

Order 10432.

148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C2×Q8×D163C211yesmaximal, characteristic
2C2×#14579689C211yesmaximal, characteristic, complemented
3#19104711C211yesmaximal, characteristic
4#19104660C211yesmaximal, characteristic, complemented
5#19104659C211yesmaximal, characteristic, complemented
6(C2×D163)⋊C8C211yesmaximal, characteristic
7C2×Q16×C163C211yesmaximal, characteristic, complemented
8C2×Dic326—21no—
9C2×Dic326C2211yescharacteristic
10Q8×D163—22no—
11Q8×D163—22no—
12C2×C4×D163—21no—
13C2×C4×D163C2211yescharacteristic
14#14579689—22no—
15C2×C163⋊C8C2211yescharacteristic
16C4⋊Dic163C2211yescharacteristic
17Dic163⋊C4—21no—
18(C2×D163)⋊C4—21no—
19C2×Q8×C163C2211yescharacteristic
20C2×Q8×C163C2211yescharacteristic
21Q16×C163—22no—
22C2×C8×C163C2211yescharacteristic
23C22×D163D411yescharacteristic
24Dic326—24no—
25Dic326—21no—
26Dic326D412yes—
27C2×Dic163—21no—
28C2×Dic163—21no—
29C2×Dic163D411yescharacteristic
30C4×D163—24no—
31C4×D163—21no—
32C4×D163—21no—
33C163⋊C8—21no—
34Q8×C163—21no—
35Q8×C163—21no—
36Q8×C163—21no—
37Q8×C163D412yes—
38C2×C4×C163—21no—
39C2×C4×C163—21no—
40C2×C4×C163C2311yescharacteristic
41C8×C163—21no—
42C22×C163C2×D411yescharacteristic
43C2×D163—21no—
44C2×D163—21no—
45C2×D163Q1612yescomplemented
46C4×C163—22no—
47C4×C163—41no—
48C4×C163C2×D411yescharacteristic
49C4×C163C2×D411yescharacteristic
50Dic163—22no—
51Dic163—21no—
52Dic163—41no—
53C2×C163#12011yescharacteristic
54C2×C163C2×Q1611yescharacteristic
55C2×C163#13711yescharacteristic
56D163—22no—
57C163#45111yescharacteristic, complemented, Sylow
58#451—1631nomaximal, Sylow
59C22×Q8—1631no—
60C2×Q16—1631no—
61C2×Q16D16311yescharacteristic, complemented
62C22⋊Q8—1631no—
63#103—1631no—
64#103—1631no—
65C22⋊C8—1631no—
66C2×Q8—3261no—
67C2×Q8—3262no—
68C2×Q8—3262no—
69C2×Q8—1631no—
70C2×Q8C2×D16311yescharacteristic
71C2×Q8C2×D16311yescharacteristic
72C22×C4—3261no—
73C22×C4—1631no—
74Q16—22no—
75Q16—3262no—
76C2×C8—1631no—
77C2×C8C2×D16311yescharacteristic
78C4⋊C4—3261no—
79C4⋊C4—1631no—
80C22⋊C4—3261no—
81C23—1631no—
82Q8—21no—
83Q8—21no—
84Q8—21no—
85Q8—3264no—
86Q8—3261no—
87Q8—1632no—
88Q8C22⋊D16312yes—
89C2×C4—21no—
90C2×C4—21no—
91C2×C4—3264no—
92C2×C4—3261no—
93C2×C4—3261no—
94C2×C4—3261no—
95C2×C4—3261no—
96C2×C4—1631no—
97C2×C4C22×D16311yescharacteristic
98C8—21no—
99C8—3261no—
100C22—3261no—
101C22—3261no—
102C22—1632no—
103C22D4×D16311yescharacteristic
104C4—22no—
105C4—41no—
106C4—3262no—
107C4—3261no—
108C4—6521no—
109C4D4×D16311yescharacteristic
110C4C2×C22⋊D16311yescharacteristic
111C2—3262no—
112C2#1910470311yescharacteristic
113C2Q16×D16311yescharacteristic
114C2#1910476711yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
FittingC2×Q16×C163C2
socleC22×C163C2×D4
prime radicalC22×D163D4
hypercenterC2×Q16D163
hypocenterC163#451
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#14579689C2semidirect
4. #19104660C2semidirect
5. #19104659C2semidirect
7. C2×Q16×C163C2semidirect
45. C2×D163Q16semidirect
57. C163#451semidirect
61. C2×Q16D163semidirect