Finite Group Databasebeta

← #20265317

Subgroups — #20265317

Order 6464.

158 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 45 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×Q8×D101C211yesmaximal, characteristic, complemented
2C2×#13108063C211yesmaximal, characteristic, complemented
3C2×#13108061C211yesmaximal, characteristic, complemented
4#15692230C211yesmaximal, characteristic
5#15692178C211yesmaximal, characteristic, complemented
6#15692167C211yesmaximal, characteristic, complemented
7#103×C101C211yesmaximal, characteristic, complemented
8C2×Dic202—21no—
9C2×Dic202C2211yescharacteristic
10Q8×D101—22no—
11Q8×D101—22no—
12C2×D404—21no—
13C2×D404C2211yescharacteristic
14C2×C4×D101—21no—
15C2×C4×D101C2211yescharacteristic
16#13108063—22no—
17#13108061—22no—
18C2×#11717579C2211yescharacteristic
19#13108051—21no—
20C2×Q8×C101C2211yescharacteristic
21C2×C8×C101C2211yescharacteristic
22C4⋊C4×C101C2211yescharacteristic
23C22×D101—21no—
24C22×D101D411yescharacteristic
25Q8×C101—21no—
26Q8×C101D412yescomplemented
27C2×C4×C101—21no—
28C2×C4×C101—21no—
29C2×C4×C101C2311yescharacteristic
30C2×Dic101—21no—
31C2×Dic101D411yescharacteristic
32D404—21no—
33D404—21no—
34D404—42no—
35C4×D101—24no—
36C4×D101—21no—
37C4×D101—21no—
38Dic202—24no—
39Dic202—21no—
40Dic202D412yescomplemented
41C8×C101—21no—
42#11717579—21no—
43C22×C101C2×D411yescharacteristic
44C2×D101—21no—
45C2×D101—21no—
46C2×D101—41no—
47C2×D101—41no—
48C2×D101—41no—
49C2×D101SD1612yescomplemented
50C4×C101—22no—
51C4×C101—41no—
52C4×C101C2×D411yescharacteristic
53C4×C101C2×D411yescharacteristic
54Dic101—21no—
55Dic101—22no—
56C2×C101#12011yescharacteristic
57C2×C101C2×SD1611yescharacteristic
58C2×C101#13711yescharacteristic
59D101—22no—
60D101—81no—
61C101#44811yescharacteristic, complemented, Sylow
62#448—1011nomaximal, Sylow
63C22×Q8—1011no—
64C2×SD16—1011no—
65C2×SD16—1011no—
66#121—1011no—
67#103—1011no—
68#103D10111yescharacteristic, complemented
69C22⋊C8—1011no—
70C2×Q8—1011no—
71C2×Q8—2021no—
72C2×Q8—2022no—
73C2×Q8—2022no—
74C2×Q8C2×D10111yescharacteristic
75C2×D4—1011no—
76C2×D4—2021no—
77C22×C4—1011no—
78C22×C4—2021no—
79SD16—2022no—
80SD16—2022no—
81C2×C8—1011no—
82C2×C8C2×D10111yescharacteristic
83C4⋊C4C2×D10111yescharacteristic
84C22⋊C4—2021no—
85C23—1011no—
86C23—2021no—
87Q8—21no—
88Q8—1012no—
89Q8—2024no—
90Q8—2021no—
91Q8D40412yescomplemented
92D4—4042no—
93D4—2021no—
94D4—2021no—
95C2×C4—21no—
96C2×C4—21no—
97C2×C4—1011no—
98C2×C4—2024no—
99C2×C4—2021no—
100C2×C4—2021no—
101C2×C4—2021no—
102C2×C4C22×D10111yescharacteristic
103C8—21no—
104C8—2021no—
105C22—1012no—
106C22—4041no—
107C22—4041no—
108C22—4041no—
109C22—2021no—
110C22—2021no—
111C22D4×D10111yescharacteristic
112C4—22no—
113C4—41no—
114C4—2021no—
115C4—2022no—
116C4D4×D10111yescharacteristic
117C4C2×D40411yescharacteristic
118C2—8081no—
119C2—2022no—
120C2#1569222511yescharacteristic
121C2SD16×D10111yescharacteristic
122C2#1569228711yescharacteristic
subgroupG/H
centerC22D4×D101
commutatorC2×C4×C101C23
FrattiniC2×C4C22×D101
Fitting#103×C101C2
socleC22×C101C2×D4
hypercenter#103D101
hypocenterC101#448
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. C2×Q8×D101C2semidirect
2. C2×#13108063C2semidirect
3. C2×#13108061C2semidirect
5. #15692178C2semidirect
6. #15692167C2semidirect
7. #103×C101C2semidirect
26. Q8×C101D4semidirect
40. Dic202D4semidirect
49. C2×D101SD16semidirect
61. C101#448semidirect
68. #103D101semidirect
91. Q8D404semidirect