Finite Group Databasebeta

← #27197310

Subgroups — #27197310

Order 13184.

124 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 49 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#20268192C211yesmaximal, characteristic
2Q16×Dic103C211yesmaximal, characteristic
3#20267618C211yesmaximal, characteristic
4#20267617C211yesmaximal, characteristic
5Dic103⋊C16C211yesmaximal, characteristic
6#20267595C211yesmaximal, characteristic
7#358×C103C211yesmaximal, characteristic
8#15693012—21no—
9Q8×Dic103—21no—
10C2×C103⋊C16C2211yescharacteristic
11#15692955C2211yescharacteristic
12#15692955C2211yescharacteristic
13#15692952—21no—
14#15692945—21no—
15C8×Dic103C2211yescharacteristic
16C2×Q16×C103C2211yescharacteristic
17C2×C16×C103C2211yescharacteristic
18#107×C103C2211yescharacteristic
19C2×C103⋊C8D411yescharacteristic
20C4⋊Dic103—21no—
21C4⋊Dic103—21no—
22C4⋊Dic103—41no—
23C4⋊Dic103—41no—
24Dic103⋊C4—41no—
25C4×Dic103—41no—
26C4×Dic103D411yescharacteristic
27C103⋊C16—21no—
28C2×Q8×C103—21no—
29Q16×C103—21no—
30Q16×C103Q812yes—
31C2×C8×C103C2311yescharacteristic
32C4⋊C4×C103—21no—
33C16×C103—21no—
34Q8×C103—22no—
35Q8×C103—41no—
36C2×C4×C103—41no—
37C2×C4×C103—41no—
38C2×C4×C103C2×D411yescharacteristic
39C2×Dic103—41no—
40C2×Dic103—41no—
41C2×Dic103D811yescharacteristic
42C2×Dic103D811yescharacteristic
43C8×C103C2×Q811yescharacteristic
44C8×C103#4111yescharacteristic
45C103⋊C8—21no—
46C22×C103C2×D811yescharacteristic
47C4×C103—42no—
48C4×C103—81no—
49C4×C103C22⋊Q811yescharacteristic
50C4×C103#13711yescharacteristic
51Dic103—21no—
52Dic103—21no—
53Dic103—81no—
54Dic103—81no—
55C2×C103#47411yescharacteristic
56C2×C103#50811yescharacteristic
57C2×C103#51011yescharacteristic
58#2229—1031nomaximal, Sylow
59C103#222911yescharacteristic, complemented, Sylow
60#499—1031no—
61C4×Q16—1031no—
62#367—1031no—
63#366—1031no—
64C4⋊C16—1031no—
65#358—1031no—
66#358D10311yescharacteristic
67C2×Q16C2×D10311yescharacteristic
68#125—2061no—
69C4×Q8—2061no—
70C2×C16—1031no—
71C2×C16C2×D10311yescharacteristic
72#107—1031no—
73#107—1031no—
74#107C2×D10311yescharacteristic
75#106—2061no—
76#103—2061no—
77C4×C8—1031no—
78C2×Q8—21no—
79Q16—21no—
80Q16Dic20612yes—
81C2×C8—1031no—
82C2×C8C22×D10311yescharacteristic
83C4⋊C4—21no—
84C4⋊C4—4121no—
85C4⋊C4—4121no—
86C4⋊C4—4121no—
87C4⋊C4—2061no—
88C4⋊C4—2061no—
89C42—1031no—
90C42—4121no—
91C16—21no—
92C16—2061no—
93Q8—22no—
94Q8—41no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—1031no—
98C2×C4—1031no—
99C2×C4—4121no—
100C2×C4—4121no—
101C2×C4D4×D10311yescharacteristic
102C8—2061no—
103C8C2×Dic20611yescharacteristic
104C8#1311010411yescharacteristic
105C22D8×D10311yescharacteristic
106C4—42no—
107C4—81no—
108C4—8241no—
109C4—8241no—
110C4—2061no—
111C4—2061no—
112C4#1569299811yescharacteristic
113C4#1569305011yescharacteristic
114C2#2026806911yescharacteristic
115C2#2026822411yescharacteristic
116C2#2026823011yescharacteristic
subgroupG/H
centerC22D8×D103
commutator, cosocleC2×C8×C103C23
FrattiniC2×C8C22×D103
Fitting#358×C103C2
socle, prime radicalC22×C103C2×D8
hypercenter#358D103
hypocenterC103#2229
LCSG ▷ C2×C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

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
#202681922
Q16×Dic1032
#202676182
#202676172
Dic103⋊C162
#202675952
#358×C1032
#2229103