Finite Group Databasebeta

← #20265417

Subgroups — #20265417

Order 6464.

114 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 41 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×#13108064C211yesmaximal, characteristic, complemented
2C2×C8×D101C211yesmaximal, characteristic
3#15692235C211yesmaximal, characteristic
4#15692231C211yesmaximal, characteristic
5#15692188C211yesmaximal, characteristic, complemented
6#15692180C211yesmaximal, characteristic, complemented
7#103×C101C211yesmaximal, characteristic, complemented
8C2×Dic202C2211yescharacteristic
9C2×C4×D101C2211yescharacteristic
10#13108064—22no—
11C2×#11717579C2211yescharacteristic
12C8×D101—22no—
13C4⋊Dic101—21no—
14C4⋊Dic101C2211yescharacteristic
15#13108053—21no—
16#13108051—21no—
17#13108051—21no—
18C2×Q8×C101C2211yescharacteristic
19C2×C8×C101C2211yescharacteristic
20C4⋊C4×C101C2211yescharacteristic
21C22×D101D411yescharacteristic
22Q8×C101—21no—
23Q8×C101—21no—
24C2×C4×C101—21no—
25C2×C4×C101—21no—
26C2×C4×C101C2311yescharacteristic
27C2×Dic101—21no—
28C2×Dic101—21no—
29C2×Dic101D411yescharacteristic
30C4×D101—21no—
31C4×D101—21no—
32Dic202—21no—
33Dic202—21no—
34C8×C101—21no—
35#11717579D412yes—
36C22×C101C2×D411yescharacteristic
37C2×D101—21no—
38C2×D101—21no—
39C2×D101Q1612yescomplemented
40C4×C101—41no—
41C4×C101—41no—
42C4×C101C2×D411yescharacteristic
43C4×C101#4111yescharacteristic
44Dic101—21no—
45Dic101—41no—
46Dic101—41no—
47C2×C101#12111yescharacteristic
48C2×C101C2×Q1611yescharacteristic
49C2×C101#13511yescharacteristic
50D101—22no—
51C101#46711yescharacteristic, complemented, Sylow
52#467—1011nomaximal, Sylow
53C2×Q16—1011no—
54C22×C8—1011no—
55C22⋊Q8—1011no—
56C22⋊Q8—1011no—
57#107—1011no—
58#103—1011no—
59#103D10111yescharacteristic, complemented
60C2×Q8—1011no—
61C2×Q8C2×D10111yescharacteristic
62C22×C4—1011no—
63Q16—2022no—
64C2×C8—1011no—
65C2×C8—2022no—
66C2×C8C2×D10111yescharacteristic
67C4⋊C4—1011no—
68C4⋊C4—2021no—
69C4⋊C4—2021no—
70C4⋊C4C2×D10111yescharacteristic
71C22⋊C4—2021no—
72C22⋊C4—2021no—
73C23—1011no—
74Q8—21no—
75Q8—21no—
76Q8—2021no—
77Q8—2021no—
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—1011no—
81C2×C4—2021no—
82C2×C4—2021no—
83C2×C4—2021no—
84C2×C4—2021no—
85C2×C4C22×D10111yescharacteristic
86C8—21no—
87C8—1012no—
88C22—1012no—
89C22—2021no—
90C22—2021no—
91C22D4×D10111yescharacteristic
92C4—41no—
93C4—41no—
94C4—4041no—
95C4—4041no—
96C4—2021no—
97C4D4×D10111yescharacteristic
98C4#1310807411yescharacteristic
99C2—2022no—
100C2#1569222811yescharacteristic
101C2Q16×D10111yescharacteristic
102C2#1569227611yescharacteristic
subgroupG/H
centerC22D4×D101
commutatorC2×C4×C101C23
FrattiniC2×C4C22×D101
Fitting#103×C101C2
socleC22×C101C2×D4
hypercenter#103D101
hypocenterC101#467
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. C2×#13108064C2semidirect
5. #15692188C2semidirect
6. #15692180C2semidirect
7. #103×C101C2semidirect
39. C2×D101Q16semidirect
51. C101#467semidirect
59. #103D101semidirect