Finite Group Databasebeta

← #23782478

Subgroups — #23782478

Order 10432.

248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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#19104783C212yesmaximal, complemented
2#19104767C214yesmaximal, complemented
3#19104766C212yesmaximal, complemented
4#19104758C212yesmaximal, complemented
5#19104757C211yesmaximal, characteristic, complemented
6Q16×D163C212yesmaximal, complemented
7#19104741C211yesmaximal, characteristic, complemented
8C2×Q16×C163C211yesmaximal, characteristic, complemented
9#14579700—22no—
10#14579700C2214yes—
11#14579699—24no—
12#14579699C2212yes—
13#14579699C2211yescharacteristic
14Q8×D163—22no—
15Q8×D163C2214yes—
16Dic652C2211yescharacteristic
17#14579689C2214yes—
18#14579688C2212yes—
19#14579686C2214yes—
20D1304C2211yescharacteristic
21#14579683C2211yescharacteristic
22#14579682C2212yes—
23C8×D163C2212yes—
24C2×Q8×C163C2212yes—
25Q16×C163C2212yes—
26Q16×C163C2212yes—
27C2×C8×C163C2211yescharacteristic
28Dic326—24no—
29Dic326D411yescharacteristic
30Dic326C2312yes—
31D652—24no—
32D652D411yescharacteristic
33D652C2312yes—
34C22⋊D163—22no—
35C22⋊D163D412yes—
36C4×D163—24no—
37C4×D163—22no—
38C4×D163—24no—
39C4×D163C2312yes—
40C163⋊C8C2312yes—
41Q8×C163—22no—
42Q8×C163C2314yes—
43C2×C4×C163—22no—
44C2×C4×C163C2311yescharacteristic
45C8×C163C2311yescharacteristic
46C8×C163C2311yescharacteristic
47C22×C163C2×D411yescharacteristic
48C2×D163—22no—
49C2×D163C2×D412yes—
50C4×C163—24no—
51C4×C163C2×D411yescharacteristic
52C4×C163C2411yescharacteristic
53Dic163—22no—
54Dic163C2×D412yes—
55C2×C163—21no—
56C2×C163C22×D411yescharacteristic
57D163—22no—
58D163—42no—
59C163#57811yescharacteristic, complemented, Sylow
60#578—1631nomaximal, Sylow
612−1+4—1632no—
62#137—1632no—
63#137—1634no—
64#135—1632no—
65#135—1631no—
66C2×Q16—1632no—
67C2×Q16D16311yescharacteristic, complemented
68#131—1631no—
69#41—3264no—
70#41—3262no—
71#41—1634no—
72#41—1632no—
73#41—1631no—
74C2×Q8—3262no—
75C2×Q8—1634no—
76C2×Q8C2×D16312yes—
77Q16—1634no—
78Q16—1631no—
79Q16C2×D16312yes—
80Q16C2×D16312yes—
81SD16—1634no—
82SD16—1632no—
83D8—1631no—
84M16—1631no—
85M16—1632no—
86C2×C8—1632no—
87C2×C8C2×D16311yescharacteristic
88Q8—22no—
89Q8—3264no—
90Q8—1632no—
91Q8—1631no—
92Q8C22×D16314yes—
93D4—3264no—
94D4—3262no—
95D4—1632no—
96D4—1631no—
97D4—1632no—
98C2×C4—22no—
99C2×C4—3264no—
100C2×C4—3264no—
101C2×C4—3262no—
102C2×C4—1632no—
103C2×C4C22×D16311yescharacteristic
104C8—1632no—
105C8C22×D16311yescharacteristic
106C8C22×D16311yescharacteristic
107C22—3262no—
108C22—1632no—
109C22D4×D16311yescharacteristic
110C4—24no—
111C4—3262no—
112C4—1632no—
113C4D4×D16311yescharacteristic
114C4C23×D16311yescharacteristic
115C2—21no—
116C2—3262no—
117C2—6522no—
118C2C2×D4×D16311yescharacteristic
subgroupG/H
centerC2C2×D4×D163
commutator, cosocleC4×C163C24
FrattiniC4C23×D163
FittingC2×Q16×C163C2
socleC2×C163C22×D4
hypercenterC2×Q16D163
hypocenterC163#578
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. #19104783C2semidirect
2. #19104767C2semidirect
3. #19104766C2semidirect
4. #19104758C2semidirect
5. #19104757C2semidirect
6. Q16×D163C2semidirect
7. #19104741C2semidirect
8. C2×Q16×C163C2semidirect
59. C163#578semidirect
67. C2×Q16D163semidirect