Finite Group Databasebeta

← #20265353

Subgroups — #20265353

Order 6464.

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

normal subgroups only

This group has 152 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
2#15692286C211yesmaximal, characteristic, complemented
3#15692244C211yesmaximal, characteristic, complemented
4#15692182C211yesmaximal, characteristic, complemented
5#15692181C211yesmaximal, characteristic, complemented
6#15692171C211yesmaximal, characteristic, complemented
7#137×C101C211yesmaximal, characteristic, complemented
8#13108075—21no—
9#13108074—21no—
10#13108074C2211yescharacteristic
11C2×D404—21no—
12C2×D404C2211yescharacteristic
13D4×D101—22no—
14D4×D101—21no—
15#13108064—21no—
16#13108061—21no—
17#13108058C2211yescharacteristic, complemented
18#13108051—22no—
19C4×Dic101C2211yescharacteristic, complemented
20#41×C101C2211yescharacteristic
21C2×Q8×C101C2211yescharacteristic, complemented
22Q16×C101—21no—
23SD16×C101—21no—
24M16×C101C2211yescharacteristic, complemented
25C22×D101—22no—
26C22×D101D412yes—
27Q8×C101—21no—
28Q8×C101—21no—
29Q8×C101D411yescharacteristic
30D4×C101—21no—
31D4×C101D411yescharacteristic
32C2×C4×C101—21no—
33C2×C4×C101—21no—
34C2×C4×C101C2311yescharacteristic
35C22⋊D101—22no—
36C22⋊D101—21no—
37C2×Dic101—21no—
38D404—22no—
39D404—21no—
40D404—21no—
41D404D411yescharacteristic
42C4×D101—22no—
43C4×D101—21no—
44Dic202D411yescharacteristic
45C8×C101—21no—
46#11717579—21no—
47C22×C101—21no—
48C22×C101C2×D411yescharacteristic
49C2×D101—22no—
50C2×D101—21no—
51C2×D101—42no—
52C2×D101—82no—
53C4×C101—21no—
54C4×C101—41no—
55C4×C101C2×D411yescharacteristic
56C4×C101C2×D411yescharacteristic
57Dic101—21no—
58Dic101—41no—
59C2×C101—21no—
60C2×C101—41no—
61C2×C101#12011yescharacteristic
62D101—42no—
63D101—41no—
64C101#45511yescharacteristic, complemented, Sylow
65#455—1011nomaximal, Sylow
66H(5,𝔽2)—1011no—
67#137—1011no—
68#137D10111yescharacteristic, complemented
69#124—1011no—
70#104—1011no—
71#104—1011no—
72#100—1011no—
73#41—1011no—
74#41—2021no—
75#41—2021no—
76#41C2×D10111yescharacteristic
77C2×Q8C2×D10111yescharacteristic, complemented
78C2×D4—1011no—
79C2×D4—2021no—
80C2×D4—2022no—
81C2×D4—2021no—
82Q16—21no—
83Q16—2021no—
84SD16—21no—
85SD16—2021no—
86M16—1011no—
87M16C2×D10111yescharacteristic, complemented
88C22⋊C4—2022no—
89C42—1011no—
90C23—1012no—
91C23—2022no—
92Q8—21no—
93Q8—21no—
94Q8—1011no—
95Q8C22⋊D10111yescharacteristic
96D4—21no—
97D4—1011no—
98D4—2022no—
99D4—2022no—
100D4—2021no—
101D4—2021no—
102D4—2021no—
103D4C22⋊D10111yescharacteristic
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—2022no—
107C2×C4—2021no—
108C2×C4—2021no—
109C2×C4C22×D10111yescharacteristic
110C8—21no—
111C8—2021no—
112C22—21no—
113C22—8082no—
114C22—4042no—
115C22—2021no—
116C22—2022no—
117C22D4×D10111yescharacteristic
118C4—21no—
119C4—41no—
120C4—4041no—
121C4—2021no—
122C4D4×D10111yescharacteristic
123C4C2×C22⋊D10111yescharacteristic
124C2—21no—
125C2—41no—
126C2—4041no—
127C2—4042no—
128C2#1569222311yescharacteristic
subgroupG/H
centerC2#15692223
commutatorC2×C4×C101C23
FrattiniC2×C4C22×D101
Fitting#137×C101C2
socleC2×C101#120
hypercenter#137D101
hypocenterC101#455
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #15692286C2semidirect
3. #15692244C2semidirect
4. #15692182C2semidirect
5. #15692181C2semidirect
6. #15692171C2semidirect
7. #137×C101C2semidirect
17. #13108058C22semidirect
19. C4×Dic101C22semidirect
21. C2×Q8×C101C22semidirect
24. M16×C101C22semidirect
64. C101#455semidirect
68. #137D101semidirect
77. C2×Q8C2×D101semidirect
87. M16C2×D101semidirect