Finite Group Databasebeta

← #27194470

Subgroups — #27194470

Order 13184.

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

normal subgroups only

This group has 172 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
2#20268197C212yesmaximal
3#20267533C211yesmaximal, characteristic
4#20267532C212yesmaximal
5#491×C103C211yesmaximal, characteristic
6#15693013C2212yes—
7#15693012—22no—
8#15693011—22no—
9#15693011—22no—
10#15692954—22no—
11#15692952—22no—
12#15692932C2212yes—
13C4⋊Q8×C103C2211yescharacteristic
14#125×C103C2211yescharacteristic
15#103×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×Q8×C103—21no—
27C2×C8×C103—21no—
28C4⋊C4×C103—22no—
29C4⋊C4×C103—22no—
30C4⋊C4×C103D412yes—
31C42×C103C2311yescharacteristic
32Q8×C103—42no—
33C2×C4×C103—22no—
34C2×C4×C103—41no—
35C2×C4×C103C2×D412yes—
36C2×C4×C103C2×D411yescharacteristic
37C2×Dic103—22no—
38C2×Dic103—22no—
39C8×C103—41no—
40C103⋊C8—24no—
41C22×C103#12011yescharacteristic
42C4×C103—21no—
43C4×C103—22no—
44C4×C103—42no—
45C4×C103—81no—
46Dic103—42no—
47Dic103—42no—
48C2×C103#45411yescharacteristic
49C2×C103#45612yes—
50#1663—1031nomaximal, Sylow
51C103#166311yescharacteristic, complemented, Sylow
52#564—1031no—
53#501—1032no—
54#491D10311yescharacteristic
55#330—1031no—
56#330—1032no—
57C4⋊Q8C2×D10311yescharacteristic
58#125—1032no—
59#125—2062no—
60#125—2062no—
61#125—2062no—
62#125C2×D10311yescharacteristic
63#107—2062no—
64#106—2062no—
65#103—22no—
66#97—1032no—
67#97C2×D10311yescharacteristic
68C2×Q8—21no—
69C2×C8—21no—
70C2×C8—2062no—
71C4⋊C4—22no—
72C4⋊C4—22no—
73C4⋊C4—1032no—
74C4⋊C4—1032no—
75C4⋊C4—2062no—
76C4⋊C4—2062no—
77C4⋊C4—2062no—
78C4⋊C4—2062no—
79C4⋊C4—2062no—
80C4⋊C4C22⋊D10312yes—
81C42—2062no—
82C42C22×D10311yescharacteristic
83Q8—42no—
84C2×C4—22no—
85C2×C4—41no—
86C2×C4—2062no—
87C2×C4—2062no—
88C2×C4D4×D10312yes—
89C2×C4C2×C22⋊D10311yescharacteristic
90C8—41no—
91C8—2064no—
92C22#1569298911yescharacteristic
93C4—21no—
94C4—22no—
95C4—42no—
96C4—81no—
97C4—4122no—
98C4—4122no—
99C2#2026796311yescharacteristic
100C2#2026797212yes—
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#491×C103C2
socle, prime radicalC22×C103#120
hypercenter#491D103
hypocenterC103#1663
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
51. C103#1663semidirect

Maximal subgroups

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

subgroupindex
C103⋊#5642
#202681972
#202675332
#202675322
#491×C1032
#1663103