Finite Group Databasebeta

← #27194472

Subgroups — #27194472

Order 13184.

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

normal subgroups only

This group has 172 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#20268201C212yesmaximal
2#20268161C211yesmaximal, characteristic
3#20267533C211yesmaximal, characteristic
4#20267533C212yesmaximal
5#564×C103C211yesmaximal, characteristic
6#15693021C2211yescharacteristic
7#15692954—22no—
8#15692952—22no—
9#15692944—22no—
10#15692932C2211yescharacteristic
11#15692932C2212yes—
12#125×C103—22no—
13#125×C103—22no—
14#125×C103—22no—
15#125×C103C2211yescharacteristic
16#125×C103C2212yes—
17C2×Dic206—21no—
18C2×C103⋊C8—22no—
19C2×C103⋊C8—21no—
20C4⋊Dic103—22no—
21C4⋊C4×C103—22no—
22C4⋊C4×C103—22no—
23C4⋊C4×C103—22no—
24C4⋊C4×C103—22no—
25C4⋊C4×C103—22no—
26C4⋊C4×C103—22no—
27C4⋊C4×C103D412yes—
28C4⋊C4×C103D412yes—
29C4⋊C4×C103D412yes—
30C42×C103—22no—
31C42×C103C2311yescharacteristic
32C2×C4×C103—22no—
33C2×C4×C103—22no—
34C2×C4×C103—22no—
35C2×C4×C103C2×D412yes—
36C2×C4×C103C2×D411yescharacteristic
37C2×Dic103—41no—
38Dic206—42no—
39C103⋊C8—24no—
40C103⋊C8—41no—
41C22×C103#12011yescharacteristic
42C4×C103—21no—
43C4×C103—22no—
44C4×C103—42no—
45C4×C103—42no—
46C4×C103—42no—
47Dic103—81no—
48C2×C103#45411yescharacteristic
49C2×C103#45612yes—
50#1663—1031nomaximal, Sylow
51C103#166311yescharacteristic, complemented, Sylow
52#564D10311yescharacteristic
53#501—1032no—
54#491—1031no—
55#330—1032no—
56#330—1031no—
57C4⋊Q8—1031no—
58#125—22no—
59#125—22no—
60#125—22no—
61#125C2×D10311yescharacteristic
62#125C2×D10312yes—
63#107—2062no—
64#106—2062no—
65#103—2062no—
66#97—1031no—
67#97—1032no—
68C2×Q8—2061no—
69C2×C8—2061no—
70C2×C8—2062no—
71C4⋊C4—22no—
72C4⋊C4—22no—
73C4⋊C4—22no—
74C4⋊C4—22no—
75C4⋊C4—22no—
76C4⋊C4—22no—
77C4⋊C4—2062no—
78C4⋊C4C22⋊D10312yes—
79C4⋊C4C22⋊D10312yes—
80C4⋊C4C22⋊D10312yes—
81C42—22no—
82C42C22×D10311yescharacteristic
83Q8—4122no—
84C2×C4—22no—
85C2×C4—22no—
86C2×C4—22no—
87C2×C4—4121no—
88C2×C4C2×C22⋊D10312yes—
89C2×C4C2×C22⋊D10311yescharacteristic
90C8—4121no—
91C8—2064no—
92C22#1569299011yescharacteristic
93C4—21no—
94C4—22no—
95C4—42no—
96C4—42no—
97C4—42no—
98C4—8241no—
99C2#2026796411yescharacteristic
100C2#2026797412yes—
subgroupG/H
centerC22#15692990
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#564×C103C2
socle, prime radicalC22×C103#120
hypercenter#564D103
hypocenterC103#1663
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #564

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
#202682012
#202681612
#202675332
#564×C1032
#1663103