Finite Group Databasebeta

← #27193308

Subgroups — #27193308

Order 13184.

110 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 23 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#20268163C211yesmaximal, characteristic
2#20267584C211yesmaximal, characteristic
3#353×C103C211yesmaximal, characteristic
4C2×#13110093—21no—
5C2×#13110093—21no—
6#15693021C411yescharacteristic, complemented
7#15692936—21no—
8C4×C103⋊C8C411yescharacteristic, complemented
9#127×C103C2211yescharacteristic
10#99×C103—21no—
11C2×Dic206—21no—
12#13110093—42no—
13#13110093—42no—
14C2×C103⋊C8—21no—
15C4⋊Dic103—41no—
16C22⋊Dic103—41no—
17C2×D4×C103—41no—
18C2×D4×C103D411yescharacteristic
19C2×D4×C103D411yescharacteristic
20C22⋊C4×C103—41no—
21C42×C103C2×C411yescharacteristic
22C23×C103—21no—
23C23×C103—21no—
24D4×C103—41no—
25D4×C103—41no—
26D4×C103—82no—
27C2×C4×C103—21no—
28C2×C4×C103—81no—
29C2×C4×C103C22⋊C411yescharacteristic
30C2×Dic103—41no—
31C2×Dic103—81no—
32Dic206—41no—
33Dic206—41no—
34C103⋊C8—22no—
35C22×C103—41no—
36C22×C103—41no—
37C22×C103—81no—
38C22×C103—81no—
39C22×C103#9911yescharacteristic
40C4×C103—22no—
41C4×C103—21no—
42C4×C103—161no—
43Dic103—81no—
44Dic103—161no—
45C2×C103—21no—
46C2×C103—81no—
47C2×C103—81no—
48C2×C103#35311yescharacteristic
49#1409—1031nomaximal, Sylow
50C103#140911yescharacteristic, complemented, Sylow
51#492—1031no—
52#353—1031no—
53#353D10311yescharacteristic
54C2×SD16—2061no—
55C2×SD16—2061no—
56C4⋊Q8—1031no—
57#127C2×D10311yescharacteristic
58#99—21no—
59#99—2061no—
60C4×C8—1031no—
61C2×Q8—2061no—
62C2×D4—41no—
63C2×D4D41211yescharacteristic
64C2×D4C22⋊D10311yescharacteristic
65SD16—4122no—
66SD16—4122no—
67C2×C8—2061no—
68C4⋊C4—4121no—
69C22⋊C4—41no—
70C22⋊C4—4121no—
71C42C4×D10311yescharacteristic
72C23—21no—
73C23—21no—
74Q8—4121no—
75Q8—4121no—
76D4—41no—
77D4—41no—
78D4—82no—
79C2×C4—21no—
80C2×C4—81no—
81C2×C4—8241no—
82C2×C4—4121no—
83C2×C4(C2×D103)⋊C411yescharacteristic
84C8—2062no—
85C22—41no—
86C22—41no—
87C22—81no—
88C22—81no—
89C22#1569293511yescharacteristic
90C4—22no—
91C4—21no—
92C4—161no—
93C4—8241no—
94C4—16481no—
95C2—21no—
96C2—81no—
97C2—81no—
98C2#2026758311yescharacteristic
subgroupG/H
centerC2#20267583
commutatorC42×C103C2×C4
Frattini#127C2×D103
Fitting#353×C103C2
socleC2×C103#353
prime radical, cosocle#127×C103C22
hypercenter#353D103
hypocenterC103#1409
LCSG ▷ C42×C103 ▷ C2×C4×C103 ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #353

Complements

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

NH ≅ G/Ntype
6. #15693021C4semidirect
8. C4×C103⋊C8C4semidirect
50. C103#1409semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202681632
#202675842
#353×C1032
#1409103