Finite Group Databasebeta

← #20265343

Subgroups — #20265343

Order 6464.

168 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 39 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
1#15692301C211yesmaximal, characteristic, complemented
2#15692281C211yesmaximal, characteristic, complemented
3#15692251C211yesmaximal, characteristic, complemented
4#15692182C211yesmaximal, characteristic, complemented
5#15692181C211yesmaximal, characteristic, complemented
6#15692171C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C101C211yesmaximal, characteristic, complemented
8#13108075—21no—
9#13108074—21no—
10#13108074C2211yescharacteristic
11C2×D404—21no—
12C2×D404C2211yescharacteristic
13C2×C22⋊D101—22no—
14D4×D101—22no—
15D4×D101—21no—
16#13108062—21no—
17#13108059—21no—
18#13108058C2211yescharacteristic, complemented
19C4×Dic101C2211yescharacteristic, complemented
20#41×C101C2211yescharacteristic
21C2×D4×C101C2211yescharacteristic, complemented
22SD16×C101—21no—
23D8×C101—21no—
24M16×C101C2211yescharacteristic, complemented
25C23×C101—21no—
26C22×D101—22no—
27C22×D101D412yes—
28Q8×C101D411yescharacteristic, complemented
29D4×C101—21no—
30D4×C101—21no—
31D4×C101—21no—
32D4×C101D411yescharacteristic, complemented
33C2×C4×C101—21no—
34C2×C4×C101C2311yescharacteristic
35C22⋊D101—22no—
36C22⋊D101—21no—
37C22⋊D101—44no—
38C2×Dic101—21no—
39D404—22no—
40D404—21no—
41D404—21no—
42D404D411yescharacteristic, complemented
43C4×D101—22no—
44C4×D101—21no—
45Dic202D411yescharacteristic, complemented
46C8×C101—21no—
47#11717579—21no—
48C22×C101—21no—
49C22×C101—42no—
50C22×C101—41no—
51C22×C101C2×D411yescharacteristic
52C2×D101—22no—
53C2×D101—21no—
54C2×D101—42no—
55C2×D101—82no—
56C4×C101—21no—
57C4×C101C2×D411yescharacteristic
58C4×C101C2×D411yescharacteristic
59Dic101—22no—
60Dic101—21no—
61C2×C101—21no—
62C2×C101—41no—
63C2×C101—81no—
64C2×C101#12011yescharacteristic
65D101—42no—
66D101—41no—
67C101#45311yescharacteristic, complemented, Sylow
68#453—1011nomaximal, Sylow
69H(5,𝔽2)—1011no—
70AGL(1,ℤ/8)—1011no—
71AGL(1,ℤ/8)D10111yescharacteristic, complemented
72#127—1011no—
73#104—1011no—
74#104—1011no—
75#100—1011no—
76#41—1011no—
77#41—2021no—
78#41—2021no—
79#41C2×D10111yescharacteristic
80C2×D4—1011no—
81C2×D4—2021no—
82C2×D4—2022no—
83C2×D4—2022no—
84C2×D4—2021no—
85C2×D4C2×D10111yescharacteristic, complemented
86SD16—21no—
87SD16—2021no—
88D8—21no—
89D8—2021no—
90M16—1011no—
91M16C2×D10111yescharacteristic, complemented
92C42—1011no—
93C23—21no—
94C23—1012no—
95C23—2022no—
96Q8—1011no—
97Q8C22⋊D10111yescharacteristic, complemented
98D4—21no—
99D4—21no—
100D4—21no—
101D4—1011no—
102D4—4044no—
103D4—2022no—
104D4—2022no—
105D4—2021no—
106D4—2021no—
107D4—2021no—
108D4C22⋊D10111yescharacteristic, complemented
109C2×C4—21no—
110C2×C4—2022no—
111C2×C4—2021no—
112C2×C4—2021no—
113C2×C4C22×D10111yescharacteristic
114C8—21no—
115C8—2021no—
116C22—21no—
117C22—42no—
118C22—41no—
119C22—8082no—
120C22—4042no—
121C22—2021no—
122C22—2022no—
123C22D4×D10111yescharacteristic
124C4—21no—
125C4—2022no—
126C4—2021no—
127C4D4×D10111yescharacteristic
128C4C2×C22⋊D10111yescharacteristic
129C2—21no—
130C2—41no—
131C2—81no—
132C2—4041no—
133C2—4042no—
134C2#1569222311yescharacteristic
subgroupG/H
centerC2#15692223
commutatorC2×C4×C101C23
FrattiniC2×C4C22×D101
FittingAGL(1,ℤ/8)×C101C2
socleC2×C101#120
hypercenterAGL(1,ℤ/8)D101
hypocenterC101#453
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #15692301C2semidirect
2. #15692281C2semidirect
3. #15692251C2semidirect
4. #15692182C2semidirect
5. #15692181C2semidirect
6. #15692171C2semidirect
7. AGL(1,ℤ/8)×C101C2semidirect
18. #13108058C22semidirect
19. C4×Dic101C22semidirect
21. C2×D4×C101C22semidirect
24. M16×C101C22semidirect
28. Q8×C101D4semidirect
32. D4×C101D4semidirect
42. D404D4semidirect
45. Dic202D4semidirect
67. C101#453semidirect
71. AGL(1,ℤ/8)D101semidirect
85. C2×D4C2×D101semidirect
91. M16C2×D101semidirect
97. Q8C22⋊D101semidirect
108. D4C22⋊D101semidirect