Finite Group Databasebeta

← #27193288

Subgroups — #27193288

Order 13184.

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

normal subgroups only

This group has 122 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#20267958C211yesmaximal, characteristic
2#20267535C211yesmaximal, characteristic, complemented
3#353×C103C211yesmaximal, characteristic, complemented
4#15693066C411yescharacteristic, complemented
5#15693047—21no—
6C4⋊(C103⋊C8)—21no—
7#15692949—21no—
8#15692938C411yescharacteristic, complemented
9#127×C103C2211yescharacteristic
10#99×C103—21no—
11#13110105—21no—
12#13110104—41no—
13C2×C22⋊D103—41no—
14D4×D103—41no—
15#13110093—41no—
16#13110090—41no—
17#13110089—21no—
18C2×C103⋊C8—41no—
19C2×D4×C103—41no—
20C2×D4×C103C2×C411yescharacteristic
21C2×D4×C103D411yescharacteristic
22C22⋊C4×C103—41no—
23C42×C103D411yescharacteristic
24C23×C103—21no—
25C23×C103—21no—
26C22×D103—41no—
27D4×C103—41no—
28D4×C103—41no—
29D4×C103—81no—
30D4×C103—81no—
31C2×C4×C103—21no—
32C2×C4×C103—81no—
33C2×C4×C103C22⋊C411yescharacteristic
34C22⋊D103—42no—
35C22⋊D103—41no—
36C2×Dic103—41no—
37D412—21no—
38C4×D103—41no—
39Dic206—21no—
40C103⋊C8—41no—
41C103⋊C8—81no—
42C22×C103—41no—
43C22×C103—41no—
44C22×C103—81no—
45C22×C103—81no—
46C22×C103#9911yescharacteristic
47C2×D103—41no—
48C2×D103—161no—
49C4×C103—21no—
50C4×C103—21no—
51C4×C103—21no—
52C4×C103—161no—
53Dic103—41no—
54C2×C103—21no—
55C2×C103—81no—
56C2×C103—81no—
57C2×C103AΣL(1,𝔽16)11yescharacteristic
58D103—81no—
59#1402—1031nomaximal, Sylow
60C103#140211yescharacteristic, complemented, Sylow
61#453—1031no—
62#353D10311yescharacteristic, complemented
63#331—1031no—
64H(5,𝔽2)—1031no—
65AGL(1,ℤ/8)—2061no—
66#127C2×D10311yescharacteristic
67C4⋊C8—2061no—
68#104—2061no—
69#100—1031no—
70#99—21no—
71#41—4121no—
72#41—2061no—
73C2×D4—41no—
74C2×D4—4121no—
75C2×D4—4121no—
76C2×D4C4×D10311yescharacteristic
77C2×D4C22⋊D10311yescharacteristic
78SD16—4121no—
79D8—4121no—
80M16—2061no—
81C2×C8—4121no—
82C22⋊C4—41no—
83C42D41211yescharacteristic
84C23—21no—
85C23—21no—
86C23—4121no—
87Q8—2061no—
88D4—41no—
89D4—41no—
90D4—81no—
91D4—81no—
92D4—4122no—
93D4—4121no—
94D4—2061no—
95C2×C4—21no—
96C2×C4—81no—
97C2×C4—4121no—
98C2×C4—4121no—
99C2×C4(C2×D103)⋊C411yescharacteristic
100C8—8241no—
101C8—4121no—
102C22—41no—
103C22—41no—
104C22—81no—
105C22—81no—
106C22—16481no—
107C22—4121no—
108C22#1569293511yescharacteristic
109C4—21no—
110C4—21no—
111C4—21no—
112C4—161no—
113C4—4121no—
114C2—21no—
115C2—81no—
116C2—81no—
117C2—8241no—
118C2#2026757711yescharacteristic
subgroupG/H
centerC2#20267577
commutatorC2×D4×C103C2×C4
Frattini#127C2×D103
Fitting#353×C103C2
socleC2×C103AΣL(1,𝔽16)
prime radical#20267958C2
cosocle#127×C103C22
hypercenter#353D103
hypocenterC103#1402
LCSG ▷ C2×D4×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
2. #20267535C2semidirect
3. #353×C103C2semidirect
4. #15693066C4semidirect
8. #15692938C4semidirect
60. C103#1402semidirect
62. #353D103semidirect

Maximal subgroups

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

subgroupindex
#202679582
#202675352
#353×C1032
#1402103