Finite Group Databasebeta

← #27193174

Subgroups — #27193174

Order 13184.

140 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 37 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#20267560C211yesmaximal, characteristic
2#20267517C211yesmaximal, characteristic
3#395×C103C211yesmaximal, characteristic
4C2×#13110089—21no—
5C22⋊(C103⋊C8)—21no—
6C22×Q8×C103C411yescharacteristic
7C2×C4⋊C4×C103—21no—
8C2×C4⋊C4×C103C2211yescharacteristic
9#95×C103—21no—
10#95×C103C411yescharacteristic
11#13110089—22no—
12#13110089—41no—
13C2×C103⋊C8—41no—
14C2×C103⋊C8—41no—
15C2×Q8×C103—42no—
16C2×Q8×C103—41no—
17C22×C4×C103—21no—
18C22×C4×C103—21no—
19C22×C4×C103C2×C411yescharacteristic
20C22×C4×C103D411yescharacteristic
21C22×C4×C103D411yescharacteristic
22C4⋊C4×C103—41no—
23C4⋊C4×C103—42no—
24C23×C103C22⋊C411yescharacteristic
25Q8×C103—42no—
26Q8×C103—42no—
27C2×C4×C103—21no—
28C2×C4×C103—21no—
29C2×C4×C103—22no—
30C2×C4×C103—22no—
31C2×C4×C103—21no—
32C2×C4×C103—21no—
33C2×C4×C103—41no—
34C2×C4×C103—41no—
35C2×C4×C103—41no—
36C2×C4×C103—41no—
37C2×C4×C103—41no—
38C2×C4×C103—41no—
39C2×C4×C103SD1611yescharacteristic
40C2×C4×C103Q1611yescharacteristic
41C103⋊C8—42no—
42C103⋊C8—81no—
43C22×C103—21no—
44C22×C103—21no—
45C22×C103#9911yescharacteristic
46C22×C103#10311yescharacteristic
47C22×C103#10411yescharacteristic
48C4×C103—21no—
49C4×C103—21no—
50C4×C103—42no—
51C4×C103—41no—
52C4×C103—42no—
53C4×C103—41no—
54C2×C103—21no—
55C2×C103—21no—
56C2×C103#32811yescharacteristic
57C2×C103AΣL(1,𝔽16)11yescharacteristic
58C2×C103#35611yescharacteristic
59#1354—1031nomaximal, Sylow
60C103#135411yescharacteristic, complemented, Sylow
61#395D10311yescharacteristic
62#343—1031no—
63#324—1031no—
64C22×Q8Dic10311yescharacteristic
65C2×M16—2061no—
66C2×C4⋊C4—21no—
67C2×C4⋊C4C2×D10311yescharacteristic
68C22⋊C8—2061no—
69#95—21no—
70#95Dic10311yescharacteristic
71C2×Q8—42no—
72C2×Q8—41no—
73C22×C4—21no—
74C22×C4—21no—
75C22×C4C2×Dic10311yescharacteristic
76C22×C4C22⋊D10311yescharacteristic
77C22×C4C22⋊D10311yescharacteristic
78M16—4121no—
79M16—2062no—
80C2×C8—4121no—
81C2×C8—4121no—
82C4⋊C4—41no—
83C4⋊C4—42no—
84C23C22⋊Dic10311yescharacteristic
85Q8—42no—
86Q8—42no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—22no—
90C2×C4—22no—
91C2×C4—21no—
92C2×C4—21no—
93C2×C4—41no—
94C2×C4—41no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—41no—
98C2×C4—41no—
99C2×C4#1311009211yescharacteristic
100C2×C4#1311009511yescharacteristic
101C8—8241no—
102C8—4122no—
103C22—21no—
104C22—21no—
105C22#1569293611yescharacteristic
106C22#1569294511yescharacteristic
107C22#1569294811yescharacteristic
108C4—21no—
109C4—21no—
110C4—42no—
111C4—41no—
112C4—42no—
113C4—41no—
114C2—21no—
115C2—21no—
116C2#2026752811yescharacteristic
117C2#2026757811yescharacteristic
118C2#2026759011yescharacteristic
subgroupG/H
centerC22#15692936
commutatorC22×C4×C103C2×C4
FrattiniC2×C4⋊C4C2×D103
Fitting#395×C103C2
socleC22×C103#99
prime radicalC23×C103C22⋊C4
cosocleC2×C4⋊C4×C103C22
hypercenter#395D103
hypocenterC103#1354
LCSG ▷ C22×C4×C103 ▷ C23×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #395

Complements

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

NH ≅ G/Ntype
60. C103#1354semidirect

Maximal subgroups

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

subgroupindex
#202675602
#202675172
#395×C1032
#1354103