Finite Group Databasebeta

← #20276959

Subgroups — #20276959

Order 6784.

132 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 47 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#16811024C211yesmaximal, characteristic
2#16811001C211yesmaximal, characteristic
3#16810428C211yesmaximal, characteristic
4#16810427C211yesmaximal, characteristic
5#16810426C211yesmaximal, characteristic
6#16810398C211yesmaximal, characteristic
7C53×#358C211yesmaximal, characteristic
8C2×Dic212C2211yescharacteristic
9C2×#11719925—21no—
10#13133215—21no—
11#13133208—21no—
12C2×#11719908C2211yescharacteristic
13#13133151C2211yescharacteristic
14#13133148—21no—
15C8×Dic53C2211yescharacteristic
16C2×Q16×C53C2211yescharacteristic
17C2×C16×C53C2211yescharacteristic
18#107×C53C2211yescharacteristic
19C2×Q8×C53—21no—
20C2×Dic106—21no—
21Q16×C53—21no—
22Q16×C53—21no—
23C2×C8×C53C2311yescharacteristic
24C4⋊C4×C53—21no—
25#11719925—42no—
26C4⋊Dic53—21no—
27C4⋊Dic53—41no—
28#11719919—41no—
29#11719919—41no—
30#11719919—41no—
31C4×Dic53D411yescharacteristic
32C2×#88322D411yescharacteristic
33Dic212—21no—
34Dic212—21no—
35C16×C53—21no—
36#11719908—21no—
37Q8×C53—41no—
38Q8×C53—41no—
39C2×C4×C53—41no—
40C2×C4×C53—41no—
41C2×C4×C53C2×D411yescharacteristic
42C2×Dic53—41no—
43C2×Dic53—41no—
44C2×Dic53D811yescharacteristic
45C2×Dic53D811yescharacteristic
46Dic106—41no—
47Dic106—41no—
48C8×C53#4111yescharacteristic
49C8×C53#4111yescharacteristic
50#88322SD1612yes—
51C22×C53C2×D811yescharacteristic
52C4×C53—81no—
53C4×C53—81no—
54C4×C53#12411yescharacteristic
55C4×C53C2×SD1611yescharacteristic
56Dic53—21no—
57Dic53—21no—
58Dic53—81no—
59Dic53—81no—
60#2245—531nomaximal, Sylow
61C2×C53#48611yescharacteristic
62C2×C53#51011yescharacteristic
63C2×C53#51011yescharacteristic
64#499—531no—
65#494—531no—
66#358—531no—
67#358—531no—
68#358—531no—
69#358D5311yescharacteristic
70#346—531no—
71C53#224511yescharacteristic, complemented, Sylow
72C2×Q16—531no—
73C2×Q16—1061no—
74C2×Q16C2×D5311yescharacteristic
75C4⋊Q8—1061no—
76#125—1061no—
77C2×C16—531no—
78C2×C16C2×D5311yescharacteristic
79#107—531no—
80#107C2×D5311yescharacteristic
81#106—1061no—
82C4×C8—531no—
83C2×Q8—21no—
84C2×Q8—1061no—
85Q16—21no—
86Q16—21no—
87Q16—1061no—
88Q16—1061no—
89Q16—2122no—
90C2×C8—531no—
91C2×C8C22×D5311yescharacteristic
92C4⋊C4—21no—
93C4⋊C4—1061no—
94C4⋊C4—2121no—
95C4⋊C4—2121no—
96C4⋊C4—2121no—
97C4⋊C4—2121no—
98C42—531no—
99C16—21no—
100C16—1061no—
101Q8—41no—
102Q8—41no—
103Q8—2121no—
104Q8—2121no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—531no—
108C2×C4—531no—
109C2×C4—2121no—
110C2×C4—2121no—
111C2×C4D4×D5311yescharacteristic
112C8—532no—
113C8#1171994511yescharacteristic
114C8#1171994711yescharacteristic
115C22D8×D5311yescharacteristic
116C4—81no—
117C4—81no—
118C4—1061no—
119C4—1061no—
120C4—4241no—
121C4—4241no—
122C4#1313320311yescharacteristic
123C4SD16×D5311yescharacteristic
124C2#1681096811yescharacteristic
125C2#1681106211yescharacteristic
126C2#1681106511yescharacteristic
subgroupG/H
centerC22D8×D53
commutatorC2×C8×C53C23
FrattiniC2×C8C22×D53
FittingC53×#358C2
socleC22×C53C2×D8
hypercenter#358D53
hypocenterC53#2245
LCSG ▷ C2×C8×C53 ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
71. C53#2245semidirect