Finite Group Databasebeta

← #20265358

Subgroups — #20265358

Order 6464.

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

normal subgroups only

This group has 142 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#15692302C211yesmaximal, characteristic
2#15692286C211yesmaximal, characteristic, complemented
3#15692253C211yesmaximal, characteristic, complemented
4#15692182C211yesmaximal, characteristic, complemented
5#15692181C211yesmaximal, characteristic, complemented
6#15692173C211yesmaximal, characteristic, complemented
7#137×C101C211yesmaximal, characteristic, complemented
8#13108074—21no—
9#13108074C2211yescharacteristic
10#13108073—21no—
11#13108073—22no—
12C2×Dic202—21no—
13C2×Dic202C2211yescharacteristic
14Q8×D101—21no—
15#13108064—21no—
16#13108061—21no—
17#13108058C2211yescharacteristic
18#13108053—22no—
19C4×Dic101C2211yescharacteristic
20#41×C101C2211yescharacteristic
21C2×Q8×C101C2211yescharacteristic
22Q16×C101—21no—
23SD16×C101—21no—
24M16×C101C2211yescharacteristic
25Q8×C101—21no—
26Q8×C101—21no—
27Q8×C101D411yescharacteristic
28D4×C101—21no—
29D4×C101D411yescharacteristic
30C2×C4×C101—21no—
31C2×C4×C101—21no—
32C2×C4×C101C2311yescharacteristic
33C22⋊D101—22no—
34C22⋊D101—21no—
35C2×Dic101—22no—
36C2×Dic101—21no—
37C2×Dic101D412yes—
38D404D411yescharacteristic
39C4×D101—22no—
40C4×D101—21no—
41Dic202—22no—
42Dic202—21no—
43Dic202—21no—
44Dic202D411yescharacteristic
45C8×C101—21no—
46#11717579—21no—
47C22×C101—21no—
48C22×C101C2×D411yescharacteristic
49C2×D101—21no—
50C4×C101—21no—
51C4×C101—41no—
52C4×C101C2×D411yescharacteristic
53C4×C101C2×D411yescharacteristic
54Dic101—22no—
55Dic101—22no—
56Dic101—21no—
57C2×C101—21no—
58C2×C101—41no—
59C2×C101#12011yescharacteristic
60D101—41no—
61C101#45611yescharacteristic, complemented, Sylow
62#456—1011nomaximal, Sylow
632−1+4—1011no—
64#137—1011no—
65#137D10111yescharacteristic, complemented
66C4⋊Q8—1011no—
67#104—1011no—
68#104—1011no—
69#101—1011no—
70#41—1011no—
71#41—2021no—
72#41—2022no—
73#41—2021no—
74#41C2×D10111yescharacteristic
75C2×Q8—1011no—
76C2×Q8—2021no—
77C2×Q8—2021no—
78C2×Q8C2×D10111yescharacteristic
79Q16—21no—
80Q16—2021no—
81SD16—21no—
82SD16—2021no—
83M16—1011no—
84M16C2×D10111yescharacteristic
85C4⋊C4—2022no—
86C42—1011no—
87Q8—21no—
88Q8—21no—
89Q8—1011no—
90Q8—2022no—
91Q8—2021no—
92Q8—2021no—
93Q8C22⋊D10111yescharacteristic
94D4—21no—
95D4—1011no—
96D4—2022no—
97D4—2021no—
98D4C22⋊D10111yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—1012no—
102C2×C4—2022no—
103C2×C4—2022no—
104C2×C4—2021no—
105C2×C4—2021no—
106C2×C4C22×D10111yescharacteristic
107C8—21no—
108C8—2021no—
109C22—21no—
110C22—2021no—
111C22D4×D10111yescharacteristic
112C4—21no—
113C4—41no—
114C4—2022no—
115C4—2022no—
116C4—2021no—
117C4D4×D10111yescharacteristic
118C4C2×C22⋊D10111yescharacteristic
119C2—21no—
120C2—41no—
121C2—4041no—
122C2#1569222311yescharacteristic
subgroupG/H
centerC2#15692223
commutatorC2×C4×C101C23
FrattiniC2×C4C22×D101
Fitting#137×C101C2
socleC2×C101#120
hypercenter#137D101
hypocenterC101#456
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. #15692253C2semidirect
4. #15692182C2semidirect
5. #15692181C2semidirect
6. #15692173C2semidirect
7. #137×C101C2semidirect
61. C101#456semidirect
65. #137D101semidirect