Finite Group Databasebeta

← #20265150

Subgroups — #20265150

Order 6464.

158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 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
2#15692214C211yesmaximal, characteristic, complemented
3#15692169C214yesmaximal, complemented
4#117×C101C211yesmaximal, characteristic, complemented
5#13108074—21no—
6#13108074—21no—
7#13108074—21no—
8#13108074—21no—
9C2×Dic202C411yescharacteristic, complemented
10C2×D404C411yescharacteristic, complemented
11C2×C22⋊D101C2212yes—
12C2×C4×D101C412yescomplemented
13C4⋊Dic101—21no—
14C22⋊Dic101C2212yes—
15C4×Dic101—21no—
16C22×C4×C101C2211yescharacteristic
17C4⋊C4×C101—21no—
18C22⋊C4×C101C2212yes—
19C42×C101—21no—
20C23×C101C2311yescharacteristic
21C22×D101C2×C412yes—
22C2×C4×C101—22no—
23C2×C4×C101C2×C411yescharacteristic
24C2×C4×C101C2×C411yescharacteristic
25C2×C4×C101D411yescharacteristic
26C2×C4×C101D411yescharacteristic
27C2×C4×C101D411yescharacteristic
28C2×C4×C101D411yescharacteristic
29C22⋊D101—22no—
30C22⋊D101—22no—
31C2×Dic101—22no—
32C2×Dic101C2×C412yes—
33D404—21no—
34D404—21no—
35C4×D101—22no—
36C4×D101—22no—
37Dic202—21no—
38Dic202—21no—
39C22×C101—41no—
40C22×C101C22×C411yescharacteristic
41C22×C101C2×D411yescharacteristic
42C22×C101C2×D411yescharacteristic
43C2×D101—22no—
44C2×D101—42no—
45C4×C101—42no—
46C4×C101C22⋊C411yescharacteristic
47C4×C101C22⋊C411yescharacteristic
48C4×C101C22⋊C411yescharacteristic
49C4×C101C22⋊C411yescharacteristic
50Dic101—22no—
51Dic101—42no—
52C2×C101—21no—
53C2×C101—21no—
54C2×C101—21no—
55C2×C101C2×C22⋊C411yescharacteristic
56D101—42no—
57C101#41011yescharacteristic, complemented, Sylow
58#410—1011nomaximal, Sylow
59C2×#41—1011no—
60#117—1011no—
61#117D10111yescharacteristic, complemented
62#99—1014no—
63#41—2021no—
64#41—2021no—
65#41—2021no—
66#41—2021no—
67C2×Q8—1011no—
68C2×D4—1012no—
69C2×D4—1011no—
70C22×C4—1012no—
71C22×C4C2×D10111yescharacteristic
72C4⋊C4—21no—
73C4⋊C4—2021no—
74C22⋊C4—1012no—
75C22⋊C4C2×D10112yes—
76C42—21no—
77C42—2021no—
78C23—1012no—
79C23C22×D10111yescharacteristic
80Q8—2021no—
81Q8—2021no—
82D4—2022no—
83D4—2022no—
84D4—2021no—
85D4—2021no—
86C2×C4—22no—
87C2×C4—1012no—
88C2×C4—2022no—
89C2×C4—2022no—
90C2×C4—2022no—
91C2×C4C4×D10111yescharacteristic
92C2×C4C4×D10111yescharacteristic
93C2×C4D40411yescharacteristic
94C2×C4D40411yescharacteristic
95C2×C4C22⋊D10111yescharacteristic
96C2×C4C22⋊D10111yescharacteristic
97C22—41no—
98C22—4042no—
99C22—2022no—
100C22C2×C4×D10111yescharacteristic
101C22C2×C22⋊D10111yescharacteristic
102C22C2×D40411yescharacteristic
103C4—42no—
104C4—4042no—
105C4—2022no—
106C4#1310805111yescharacteristic
107C4#1310805111yescharacteristic
108C4#1310805111yescharacteristic
109C4#1310805111yescharacteristic
110C2—21no—
111C2—21no—
112C2—21no—
113C2—4042no—
114C2C2×#1310805111yescharacteristic
subgroupG/H
centerC4#13108051
commutatorC22×C101C22×C4
FrattiniC23C22×D101
Fitting#117×C101C2
socleC2×C101C2×C22⋊C4
hypercenter#117D101
hypocenterC101#410
LCSG ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #15692214C2semidirect
3. #15692169C2semidirect
4. #117×C101C2semidirect
9. C2×Dic202C4semidirect
10. C2×D404C4semidirect
12. C2×C4×D101C4semidirect
57. C101#410semidirect
61. #117D101semidirect