Finite Group Databasebeta

← #27197305

Subgroups — #27197305

Order 13184.

124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C4×Dic412C211yesmaximal, characteristic
2#20267618C211yesmaximal, characteristic
3#20267616C211yesmaximal, characteristic
4C4⋊(C103⋊C16)C211yesmaximal, characteristic
5#20267594C211yesmaximal, characteristic
6#20267594C211yesmaximal, characteristic
7#499×C103C211yesmaximal, characteristic
8C2×Dic412C2211yescharacteristic
9C4×Dic206—21no—
10C2×C103⋊C16C2211yescharacteristic
11C2×C103⋊C16C2211yescharacteristic
12#15692955C2211yescharacteristic
13#15692946—21no—
14#125×C103—21no—
15#107×C103C2211yescharacteristic
16#107×C103C2211yescharacteristic
17#106×C103—21no—
18C4×C8×C103C2211yescharacteristic
19C2×Dic206—21no—
20Dic412—21no—
21Dic412Q812yes—
22C4⋊Dic103—21no—
23Dic103⋊C4—41no—
24C4×Dic103—41no—
25C103⋊C16—21no—
26C103⋊C16—21no—
27C2×C8×C103D411yescharacteristic
28C2×C8×C103C2311yescharacteristic
29C4⋊C4×C103—21no—
30C4⋊C4×C103—21no—
31C4⋊C4×C103—41no—
32C4⋊C4×C103—41no—
33C42×C103D411yescharacteristic
34C2×C4×C103—41no—
35C2×C4×C103—41no—
36C2×C4×C103D811yescharacteristic
37C2×C4×C103D811yescharacteristic
38C2×C4×C103C2×D411yescharacteristic
39C2×Dic103—41no—
40C2×Dic103—41no—
41Dic206—22no—
42Dic206—41no—
43C8×C103—21no—
44C8×C103C2×Q811yescharacteristic
45C8×C103#4111yescharacteristic
46C22×C103C2×D811yescharacteristic
47C4×C103—21no—
48C4×C103—21no—
49C4×C103—81no—
50C4×C103—81no—
51C4×C103C22⋊Q811yescharacteristic
52C4×C103#13711yescharacteristic
53Dic103—42no—
54Dic103—81no—
55C2×C103#47411yescharacteristic
56C2×C103#50811yescharacteristic
57C2×C103#51011yescharacteristic
58#2229—1031nomaximal, Sylow
59C103#222911yescharacteristic, complemented, Sylow
60#499D10311yescharacteristic
61C4×Q16—1031no—
62#367—1031no—
63#366—1031no—
64C4⋊C16—1031no—
65#358—1031no—
66#358—1031no—
67C2×Q16—1031no—
68#125—21no—
69C4×Q8—2061no—
70C2×C16—1031no—
71C2×C16—1031no—
72#107—1031no—
73#107C2×D10311yescharacteristic
74#107C2×D10311yescharacteristic
75#106—21no—
76#103—2061no—
77C4×C8C2×D10311yescharacteristic
78C2×Q8—2061no—
79Q16—1032no—
80Q16—2061no—
81C2×C8C22⋊D10311yescharacteristic
82C2×C8C22×D10311yescharacteristic
83C4⋊C4—21no—
84C4⋊C4—21no—
85C4⋊C4—41no—
86C4⋊C4—41no—
87C4⋊C4—4121no—
88C4⋊C4—2061no—
89C42—4121no—
90C42C22⋊D10311yescharacteristic
91C16—2061no—
92C16—2061no—
93Q8—4121no—
94Q8—2062no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—4121no—
98C2×C4—4121no—
99C2×C4#1311009011yescharacteristic
100C2×C4#1311009011yescharacteristic
101C2×C4C2×C22⋊D10311yescharacteristic
102C8—21no—
103C8Q8×D10311yescharacteristic
104C8#1311010611yescharacteristic
105C22C2×#1311009011yescharacteristic
106C4—21no—
107C4—21no—
108C4—81no—
109C4—81no—
110C4—8241no—
111C4—4122no—
112C4#1569299711yescharacteristic
113C4#1569305211yescharacteristic
114C2#2026806811yescharacteristic
115C2#2026822111yescharacteristic
116C2#2026823111yescharacteristic
subgroupG/H
centerC22C2×#13110090
commutator, cosocleC2×C8×C103C23
FrattiniC2×C8C22×D103
Fitting#499×C103C2
socle, prime radicalC22×C103C2×D8
hypercenter#499D103
hypocenterC103#2229
LCSG ▷ C2×C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #499

Complements

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

NH ≅ G/Ntype
59. C103#2229semidirect

Maximal subgroups

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

subgroupindex
C4×Dic4122
#202676182
#202676162
C4⋊(C103⋊C16)2
#202675942
#499×C1032
#2229103