Finite Group Databasebeta

← #20265376

Subgroups — #20265376

Order 6464.

128 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 41 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×#13108063C211yesmaximal, characteristic, complemented
2C2×#13108062C211yesmaximal, characteristic, complemented
3#15692251C211yesmaximal, characteristic
4#15692220C211yesmaximal, characteristic, complemented
5#15692184C211yesmaximal, characteristic, complemented
6#15692175C211yesmaximal, characteristic, complemented
7#102×C101C211yesmaximal, characteristic, complemented
8C2×Dic202C2211yescharacteristic
9C2×D404C2211yescharacteristic
10C2×C22⋊D101—21no—
11C2×C22⋊D101—21no—
12#13108063—22no—
13#13108062—22no—
14C2×#11717579C2211yescharacteristic
15#13108053—21no—
16C4×Dic101—21no—
17C4×Dic101C2211yescharacteristic
18C2×D4×C101C2211yescharacteristic
19C2×C8×C101C2211yescharacteristic
20C4⋊C4×C101C2211yescharacteristic
21C23×C101—21no—
22C22×D101—21no—
23D4×C101—21no—
24D4×C101—21no—
25C2×C4×C101—21no—
26C2×C4×C101C2311yescharacteristic
27C22⋊D101—42no—
28C22⋊D101—42no—
29C2×Dic101—21no—
30C2×Dic101D411yescharacteristic
31C2×Dic101D411yescharacteristic
32D404—21no—
33D404—21no—
34Dic202—21no—
35Dic202D412yescomplemented
36C8×C101—21no—
37#11717579—21no—
38C22×C101—41no—
39C22×C101—41no—
40C22×C101—41no—
41C22×C101C2×D411yescharacteristic
42C2×D101—41no—
43C2×D101—41no—
44C2×D101—41no—
45C4×C101—41no—
46C4×C101C2×D411yescharacteristic
47C4×C101#4111yescharacteristic
48Dic101—22no—
49Dic101—21no—
50Dic101SD1612yescomplemented
51C2×C101—81no—
52C2×C101#12111yescharacteristic
53C2×C101C2×SD1611yescharacteristic
54C2×C101AGL(1,ℤ/8)11yescharacteristic
55D101—81no—
56C101#46011yescharacteristic, complemented, Sylow
57#460—1011nomaximal, Sylow
58C2×SD16—1011no—
59C2×SD16—1011no—
60#127—1011no—
61C4×Q8—1011no—
62C4⋊C8—1011no—
63#102—1011no—
64#102D10111yescharacteristic, complemented
65C2×Q8—1011no—
66C2×D4—1011no—
67C2×D4—2021no—
68C2×D4—2021no—
69C2×D4C2×D10111yescharacteristic
70SD16—2022no—
71SD16—2022no—
72C2×C8—1011no—
73C2×C8C2×D10111yescharacteristic
74C4⋊C4—2021no—
75C4⋊C4C2×D10111yescharacteristic
76C42—1011no—
77C42—2021no—
78C23—21no—
79C23—2021no—
80Q8—1012no—
81Q8—2021no—
82D4—21no—
83D4—21no—
84D4—4042no—
85D4—4042no—
86D4—2021no—
87D4—2021no—
88C2×C4—21no—
89C2×C4—1011no—
90C2×C4—1011no—
91C2×C4—2021no—
92C2×C4C22×D10111yescharacteristic
93C8—21no—
94C8—2021no—
95C22—41no—
96C22—41no—
97C22—41no—
98C22—4041no—
99C22—4041no—
100C22—4041no—
101C22D4×D10111yescharacteristic
102C4—41no—
103C4—1012no—
104C4—2022no—
105C4—2021no—
106C4D4×D10111yescharacteristic
107C4#1310807411yescharacteristic
108C2—81no—
109C2—8081no—
110C2#1569222811yescharacteristic
111C2SD16×D10111yescharacteristic
112C2#1569227911yescharacteristic
subgroupG/H
centerC22D4×D101
commutatorC2×C4×C101C23
FrattiniC2×C4C22×D101
Fitting#102×C101C2
socleC22×C101C2×D4
hypercenter#102D101
hypocenterC101#460
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. C2×#13108063C2semidirect
2. C2×#13108062C2semidirect
4. #15692220C2semidirect
5. #15692184C2semidirect
6. #15692175C2semidirect
7. #102×C101C2semidirect
35. Dic202D4semidirect
50. Dic101SD16semidirect
56. C101#460semidirect
64. #102D101semidirect