Finite Group Databasebeta

← #27194445

Subgroups — #27194445

Order 13184.

182 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C103⋊#564C211yesmaximal, characteristic, complemented
2#20268155C212yesmaximal
3#20267533C211yesmaximal, characteristic, complemented
4#20267532C212yesmaximal, complemented
5#490×C103C211yesmaximal, characteristic
6#15693013C2212yes—
7#15693012—22no—
8#15693011—22no—
9#15693011—22no—
10#15692942—22no—
11#15692942—22no—
12#15692932C2212yes—
13#127×C103C2211yescharacteristic
14#125×C103C2211yescharacteristic
15#102×C103—22no—
16#97×C103C2211yescharacteristic
17C2×C103⋊C8—22no—
18C4⋊Dic103—22no—
19C4⋊Dic103D412yes—
20C4⋊Dic103D412yes—
21Dic103⋊C4—22no—
22Dic103⋊C4—22no—
23Dic103⋊C4—22no—
24Dic103⋊C4—22no—
25C4×Dic103—22no—
26C2×D4×C103—21no—
27C2×D4×C103—22no—
28C2×C8×C103—21no—
29C4⋊C4×C103—22no—
30C4⋊C4×C103D412yes—
31C42×C103C2311yescharacteristic
32C23×C103—41no—
33D4×C103—44no—
34D4×C103—42no—
35C2×C4×C103—22no—
36C2×C4×C103C2×D412yes—
37C2×C4×C103C2×D411yescharacteristic
38C2×Dic103—22no—
39C2×Dic103—22no—
40C8×C103—41no—
41C103⋊C8—42no—
42C22×C103—82no—
43C22×C103—81no—
44C22×C103#12011yescharacteristic
45C4×C103—22no—
46C4×C103—21no—
47C4×C103—42no—
48Dic103—42no—
49Dic103—42no—
50C2×C103—161no—
51C2×C103#45412yes—
52C2×C103#45411yescharacteristic
53#1658—1031nomaximal, Sylow
54C103#165811yescharacteristic, complemented, Sylow
55#564—1031no—
56#490—1032no—
57#490D10311yescharacteristic
58#330—1031no—
59#330—1032no—
60#127C2×D10311yescharacteristic
61#125—1032no—
62#125—2062no—
63#125—2062no—
64#125—2062no—
65#125C2×D10311yescharacteristic
66#102—22no—
67#102—2062no—
68#102—2062no—
69#97—1032no—
70#97C2×D10311yescharacteristic
71C2×D4—22no—
72C2×D4—21no—
73C2×C8—21no—
74C2×C8—2062no—
75C4⋊C4—22no—
76C4⋊C4—1032no—
77C4⋊C4—1032no—
78C4⋊C4—2062no—
79C4⋊C4—2062no—
80C4⋊C4—2062no—
81C4⋊C4—2062no—
82C4⋊C4—2062no—
83C4⋊C4C22⋊D10312yes—
84C42—2062no—
85C42C22×D10311yescharacteristic
86C23—41no—
87D4—44no—
88D4—42no—
89C2×C4—22no—
90C2×C4—2062no—
91C2×C4—2062no—
92C2×C4D4×D10312yes—
93C2×C4C2×C22⋊D10311yescharacteristic
94C8—41no—
95C8—4122no—
96C22—82no—
97C22—81no—
98C22#1569298911yescharacteristic
99C4—22no—
100C4—21no—
101C4—42no—
102C4—4122no—
103C4—4122no—
104C2—161no—
105C2#2026796212yes—
106C2#2026796311yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#490×C103C2
socleC22×C103#120
prime radical#127×C103C22
hypercenter#490D103
hypocenterC103#1658
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. C103⋊#564C2semidirect
3. #20267533C2semidirect
4. #20267532C2semidirect
54. C103#1658semidirect

Maximal subgroups

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

subgroupindex
C103⋊#5642
#202681552
#202675332
#202675322
#490×C1032
#1658103