Finite Group Databasebeta

← #20265324

Subgroups — #20265324

Order 6464.

162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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, complemented
2C2×#13108063C211yesmaximal, characteristic, complemented
3C2×D808C211yesmaximal, characteristic, complemented
4#15692229C211yesmaximal, characteristic, complemented
5#15692180C211yesmaximal, characteristic, complemented
6#15692177C211yesmaximal, characteristic, complemented
7C22⋊C8×C101C211yesmaximal, characteristic, complemented
8#13108074—22no—
9#13108074—22no—
10C2×Dic202C2211yescharacteristic
11C2×D404C2211yescharacteristic
12C2×D404C2211yescharacteristic
13C2×C22⋊D101—21no—
14C2×C22⋊D101—21no—
15C2×C4×D101—21no—
16#13108063—22no—
17D808—22no—
18C4⋊Dic101C2211yescharacteristic
19#13108051—21no—
20C22×C4×C101C2211yescharacteristic
21C2×C8×C101C2211yescharacteristic
22C2×C8×C101C2211yescharacteristic
23C23×C101D411yescharacteristic
24C22×D101—21no—
25C22×D101—21no—
26C2×C4×C101—21no—
27C2×C4×C101—21no—
28C2×C4×C101D411yescharacteristic
29C2×C4×C101C2311yescharacteristic
30C22⋊D101—24no—
31C22⋊D101—42no—
32C2×Dic101—21no—
33C2×Dic101—21no—
34D404—21no—
35D404—21no—
36D404—21no—
37D404D412yescomplemented
38C4×D101—24no—
39Dic202—21no—
40Dic202D412yescomplemented
41C8×C101—21no—
42C8×C101—21no—
43C22×C101—21no—
44C22×C101—21no—
45C22×C101—21no—
46C22×C101C2×D411yescharacteristic
47C2×D101—22no—
48C2×D101—41no—
49C2×D101—41no—
50C2×D101—41no—
51C2×D101—41no—
52C2×D101—41no—
53C4×C101—21no—
54C4×C101C2×D411yescharacteristic
55C4×C101C2×D411yescharacteristic
56Dic101—22no—
57Dic101—41no—
58C2×C101—41no—
59C2×C101#12011yescharacteristic
60C2×C101#13511yescharacteristic
61C2×C101AGL(1,ℤ/8)11yescharacteristic
62D101—42no—
63D101—81no—
64C101#44911yescharacteristic, complemented, Sylow
65#449—1011nomaximal, Sylow
66C2×#41—1011no—
67C2×SD16—1011no—
68C2×D8—1011no—
69#121—1011no—
70#103—1011no—
71#102—1011no—
72C22⋊C8D10111yescharacteristic, complemented
73#41—2022no—
74#41—2022no—
75C2×Q8—1011no—
76C2×D4—1011no—
77C2×D4—1011no—
78C2×D4—2021no—
79C2×D4—2021no—
80C22×C4—2021no—
81C22×C4C2×D10111yescharacteristic
82SD16—2022no—
83D8—2022no—
84C2×C8C2×D10111yescharacteristic
85C2×C8C2×D10111yescharacteristic
86C4⋊C4—1011no—
87C22⋊C4—2021no—
88C23—2021no—
89C23—2021no—
90C23D40411yescharacteristic
91Q8—1012no—
92Q8—2021no—
93D4—1012no—
94D4—4042no—
95D4—2024no—
96D4—2021no—
97D4—2021no—
98D4—2021no—
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—2024no—
102C2×C4—2021no—
103C2×C4—2021no—
104C2×C4D40411yescharacteristic
105C2×C4C22×D10111yescharacteristic
106C8—21no—
107C8—21no—
108C22—21no—
109C22—21no—
110C22—21no—
111C22—4041no—
112C22—4041no—
113C22—4041no—
114C22—4041no—
115C22—4041no—
116C22—2022no—
117C22C2×D40411yescharacteristic
118C4—21no—
119C4—4041no—
120C4—2022no—
121C4D4×D10111yescharacteristic
122C4D4×D10111yescharacteristic
123C2—41no—
124C2—8081no—
125C2—4042no—
126C2#1569222511yescharacteristic
127C2#1569227711yescharacteristic
128C2#1569228311yescharacteristic
subgroupG/H
centerC22C2×D404
commutatorC2×C4×C101C23
FrattiniC2×C4C22×D101
FittingC22⋊C8×C101C2
socleC22×C101C2×D4
hypercenterC22⋊C8D101
hypocenterC101#449
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#13108074C2semidirect
2. C2×#13108063C2semidirect
3. C2×D808C2semidirect
4. #15692229C2semidirect
5. #15692180C2semidirect
6. #15692177C2semidirect
7. C22⋊C8×C101C2semidirect
37. D404D4semidirect
40. Dic202D4semidirect
64. C101#449semidirect
72. C22⋊C8D101semidirect