Finite Group Databasebeta

← #23782479

Subgroups — #23782479

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#19104782C212yesmaximal, complemented
2#19104765C212yesmaximal, complemented
3#19104764C214yesmaximal, complemented
4#19104754C212yesmaximal, complemented
5C2×Dic652C211yesmaximal, characteristic, complemented
6Q16×D163C212yesmaximal, complemented
7#19104741C211yesmaximal, characteristic, complemented
8#135×C163C211yesmaximal, characteristic, complemented
9#14579699—22no—
10#14579699C2211yescharacteristic
11#14579698—24no—
12#14579698C2214yes—
13C2×Dic326—22no—
14C2×Dic326C2212yes—
15Q8×D163C2214yes—
16Dic652C2212yes—
17Dic652C2212yes—
18#14579689C2214yes—
19#14579687C2214yes—
20#14579683C2211yescharacteristic
21#14579682C2212yes—
22C8×D163C2212yes—
23#41×C163C2212yes—
24Q16×C163C2211yescharacteristic
25SD16×C163C2212yes—
26D8×C163C2211yescharacteristic
27C2×C8×C163C2211yescharacteristic
28Dic326—22no—
29Dic326—24no—
30Dic326D411yescharacteristic
31Dic326C2314yes—
32D652D411yescharacteristic
33C22⋊D163—24no—
34C22⋊D163D412yes—
35C2×Dic163—22no—
36C2×Dic163—24no—
37C4×D163—24no—
38C4×D163C2312yes—
39C163⋊C8C2312yes—
40Q8×C163C2312yes—
41D4×C163—22no—
42D4×C163C2312yes—
43C2×C4×C163—22no—
44C2×C4×C163C2311yescharacteristic
45C8×C163C2311yescharacteristic
46C8×C163C2311yescharacteristic
47C22×C163—22no—
48C22×C163C2×D411yescharacteristic
49C2×D163C2×D412yes—
50C4×C163—22no—
51C4×C163C2×D411yescharacteristic
52C4×C163C2411yescharacteristic
53Dic163—24no—
54Dic163C2×D412yes—
55C2×C163—21no—
56C2×C163—42no—
57C2×C163C22×D411yescharacteristic
58D163—22no—
59C163#57811yescharacteristic, complemented, Sylow
60#578—1631nomaximal, Sylow
612−1+4—1632no—
62#137—1632no—
63#137—1634no—
64#135—1632no—
65#135D16311yescharacteristic, complemented
66C2×Q16—1632no—
67C2×Q16—1631no—
68#131—1631no—
69#41—3262no—
70#41—3264no—
71#41—1634no—
72#41—1631no—
73#41C2×D16312yes—
74C2×Q8—3262no—
75C2×Q8—1634no—
76C2×Q8—1632no—
77Q16—1634no—
78Q16—1632no—
79Q16—1632no—
80Q16C2×D16311yescharacteristic
81SD16—1634no—
82SD16C2×D16312yes—
83D8C2×D16311yescharacteristic
84M16—1631no—
85M16—1632no—
86C2×C8—1632no—
87C2×C8C2×D16311yescharacteristic
88Q8—3264no—
89Q8—3262no—
90Q8—1634no—
91Q8—1631no—
92Q8C22×D16312yes—
93D4—22no—
94D4—3264no—
95D4—1632no—
96D4—1631no—
97D4C22×D16312yes—
98C2×C4—22no—
99C2×C4—3264no—
100C2×C4—3262no—
101C2×C4—3264no—
102C2×C4—1632no—
103C2×C4C22×D16311yescharacteristic
104C8—1632no—
105C8C22×D16311yescharacteristic
106C8C22×D16311yescharacteristic
107C22—22no—
108C22—1632no—
109C22D4×D16311yescharacteristic
110C4—22no—
111C4—3264no—
112C4—1632no—
113C4D4×D16311yescharacteristic
114C4C23×D16311yescharacteristic
115C2—21no—
116C2—42no—
117C2—3262no—
118C2C2×D4×D16311yescharacteristic
subgroupG/H
centerC2C2×D4×D163
commutator, cosocleC4×C163C24
FrattiniC4C23×D163
Fitting#135×C163C2
socleC2×C163C22×D4
hypercenter#135D163
hypocenterC163#578
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #19104782C2semidirect
2. #19104765C2semidirect
3. #19104764C2semidirect
4. #19104754C2semidirect
5. C2×Dic652C2semidirect
6. Q16×D163C2semidirect
7. #19104741C2semidirect
8. #135×C163C2semidirect
59. C163#578semidirect
65. #135D163semidirect