Finite Group Databasebeta

← #103×D101 #20265166

Subgroups — #103×D101 #20265166

Order 6464.

162 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 63 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×D101C211yesmaximal, characteristic
2C2×C8×D101C211yesmaximal, characteristic
3C4⋊C4×D101C211yesmaximal, characteristic
4#15692180C211yesmaximal, characteristic, complemented
5#15692179C211yesmaximal, characteristic, complemented
6#15692178C211yesmaximal, characteristic, complemented
7#103×C101C211yesmaximal, characteristic, complemented
8C2×Dic202—21no—
9C2×Dic202C2211yescharacteristic
10Q8×D101—22no—
11Q8×D101C414yescomplemented
12C2×C4×D101—21no—
13C2×C4×D101—21no—
14C2×C4×D101C2211yescharacteristic
15C2×#11717579C2211yescharacteristic
16C8×D101—22no—
17C4⋊Dic101C2211yescharacteristic
18#13108053—21no—
19C2×Q8×C101C2211yescharacteristic
20C2×C8×C101C2211yescharacteristic
21C4⋊C4×C101C2211yescharacteristic
22C22×D101D411yescharacteristic
23Q8×C101—21no—
24Q8×C101C2×C412yescomplemented
25C2×C4×C101—21no—
26C2×C4×C101—21no—
27C2×C4×C101C2311yescharacteristic
28C2×Dic101—21no—
29C2×Dic101—21no—
30C2×Dic101D411yescharacteristic
31C4×D101—24no—
32C4×D101—42no—
33C4×D101C2×C412yes—
34C4×D101D412yes—
35Dic202—21no—
36Dic202—24no—
37Dic202C2×C412yescomplemented
38C8×C101—21no—
39#11717579—21no—
40C22×C101C2×D411yescharacteristic
41C2×D101C22⋊C412yes—
42C2×D101SD1612yes—
43C2×D101Q1612yes—
44C4×C101—22no—
45C4×C101—41no—
46C4×C101C22×C411yescharacteristic
47C4×C101C2×D411yescharacteristic
48Dic101—22no—
49Dic101—41no—
50Dic101C22⋊C412yes—
51C2×C101C2×C22⋊C411yescharacteristic
52C2×C101C2×SD1611yescharacteristic
53C2×C101C2×Q1611yescharacteristic
54D101#10314yesdirect product factor
55C101C2×#10311yescharacteristic, complemented, Sylow
56C2×#103—1011nomaximal, Sylow
57C22×Q8—1011no—
58C22×C8—1011no—
59C2×C4⋊C4—1011no—
60#103—1011no—
61#103—1011no—
62#103—1011no—
63#103D10111yescharacteristic, direct product factor
64C2×Q8—1014no—
65C2×Q8—1011no—
66C2×Q8—2021no—
67C2×Q8—2022no—
68C2×Q8C2×D10111yescharacteristic
69C22×C4—1011no—
70C22×C4—2021no—
71C22×C4—2021no—
72C2×C8—1011no—
73C2×C8—2022no—
74C2×C8C2×D10111yescharacteristic
75C4⋊C4—1011no—
76C4⋊C4—2021no—
77C4⋊C4C2×D10111yescharacteristic
78C23—1011no—
79Q8—21no—
80Q8—1012no—
81Q8—2024no—
82Q8—2021no—
83Q8C4×D10112yescomplemented
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—1011no—
87C2×C4—1012no—
88C2×C4—1012no—
89C2×C4—4042no—
90C2×C4—2024no—
91C2×C4—2021no—
92C2×C4—2021no—
93C2×C4C22×D10111yescharacteristic
94C8—21no—
95C8—2021no—
96C22—1012no—
97C22—1012no—
98C22—1012no—
99C22D4×D10111yescharacteristic
100C4—22no—
101C4—41no—
102C4—1012no—
103C4—4041no—
104C4—2022no—
105C4C2×C4×D10111yescharacteristic
106C4D4×D10111yescharacteristic
107C2—1014no—
108C2C22⋊C4×D10111yescharacteristic
109C2SD16×D10111yescharacteristic
110C2Q16×D10111yescharacteristic
subgroupG/H
centerC22D4×D101
commutatorC4×C101C22×C4
FrattiniC2×C4C22×D101
Fitting#103×C101C2
socleC22×C101C2×D4
hypercenter#103D101
hypocenterC101C2×#103
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
4. #15692180C2semidirect
5. #15692179C2semidirect
6. #15692178C2semidirect
7. #103×C101C2semidirect
11. Q8×D101C4semidirect
24. Q8×C101C2×C4semidirect
37. Dic202C2×C4semidirect
54. D101#103direct (N × H)
55. C101C2×#103semidirect
63. #103D101direct (N × H)
83. Q8C4×D101semidirect