Finite Group Databasebeta

← #20265179

Subgroups — #20265179

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×#13108074C211yesmaximal, characteristic
2C2×C4⋊Dic101C211yesmaximal, characteristic, complemented
3#15692180C212yesmaximal, complemented
4#15692177C212yesmaximal, complemented
5C2×M16×C101C211yesmaximal, characteristic, complemented
6#13108074—22no—
7#13108074C414yescomplemented
8C2×Dic202C2211yescharacteristic
9C2×D404C2211yescharacteristic
10C2×C22⋊D101—21no—
11C22×Dic101—21no—
12C2×C4×D101—21no—
13C4⋊Dic101—21no—
14C4⋊Dic101C2212yes—
15C22×C4×C101C2211yescharacteristic
16M16×C101—22no—
17C2×C8×C101C2212yes—
18C23×C101D411yescharacteristic
19C22×D101—21no—
20C2×C4×C101C2×C412yes—
21C2×C4×C101D411yescharacteristic
22C2×C4×C101D412yes—
23C2×C4×C101C2311yescharacteristic
24C22⋊D101—24no—
25C2×Dic101—21no—
26C2×Dic101—22no—
27C2×Dic101—42no—
28D404—21no—
29D404C2×C412yescomplemented
30C4×D101—24no—
31Dic202—21no—
32Dic202C2×C412yescomplemented
33C8×C101—22no—
34C22×C101—21no—
35C22×C101—21no—
36C22×C101C22⋊C412yes—
37C22×C101C2×D411yescharacteristic
38C2×D101—22no—
39C2×D101—41no—
40C2×D101—41no—
41C4×C101C22⋊C412yes—
42C4×C101C22×C411yescharacteristic
43C4×C101C2×D411yescharacteristic
44Dic101—22no—
45Dic101—42no—
46C2×C101—22no—
47C2×C101C2×C22⋊C411yescharacteristic
48C2×C101AGL(1,ℤ/8)11yescharacteristic
49C2×C101#13711yescharacteristic
50D101—42no—
51C101#41711yescharacteristic, complemented, Sylow
52#417—1011nomaximal, Sylow
53C2×#41—1011no—
54C2×M16D10111yescharacteristic, complemented
55C2×C4⋊C4—1011no—
56#103—1012no—
57#102—1012no—
58#41—1014no—
59#41—2022no—
60C2×Q8—1011no—
61C2×D4—1011no—
62C2×D4—2021no—
63C22×C4—2021no—
64C22×C4—2021no—
65C22×C4C2×D10111yescharacteristic
66M16—22no—
67C2×C8C2×D10112yes—
68C4⋊C4—1012no—
69C4⋊C4—2021no—
70C23—2021no—
71C23D40411yescharacteristic
72Q8—1012no—
73Q8—2021no—
74D4—1012no—
75D4—2024no—
76D4—2021no—
77C2×C4—4042no—
78C2×C4—2022no—
79C2×C4—2021no—
80C2×C4—2024no—
81C2×C4C4×D10112yes—
82C2×C4D40411yescharacteristic
83C2×C4C22⋊D10112yes—
84C2×C4C22×D10111yescharacteristic
85C8—22no—
86C22—21no—
87C22—21no—
88C22—4041no—
89C22—4041no—
90C22—2022no—
91C22#1310805112yes—
92C22C2×D40411yescharacteristic
93C4—4042no—
94C4—2022no—
95C4#1310805112yes—
96C4C2×C4×D10111yescharacteristic
97C4C2×C22⋊D10111yescharacteristic
98C2—22no—
99C2—4042no—
100C2C2×#1310805111yescharacteristic
101C2#1569228311yescharacteristic
102C2#1569228811yescharacteristic
subgroupG/H
centerC22C2×D404
commutatorC4×C101C22×C4
FrattiniC2×C4C22×D101
FittingC2×M16×C101C2
socleC22×C101C2×D4
hypercenterC2×M16D101
hypocenterC101#417
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊Dic101C2semidirect
3. #15692180C2semidirect
4. #15692177C2semidirect
5. C2×M16×C101C2semidirect
7. #13108074C4semidirect
29. D404C2×C4semidirect
32. Dic202C2×C4semidirect
51. C101#417semidirect
54. C2×M16D101semidirect