Finite Group Databasebeta

← #37533049

Subgroups — #37533049

Order 23168.

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#26041689C212yesmaximal
2#26041649C211yesmaximal, characteristic
3#26041021C211yesmaximal, characteristic
4#26041021C212yesmaximal
5#564×C181C211yesmaximal, characteristic
6#19153816C2211yescharacteristic
7#19153749—22no—
8#19153747—22no—
9#19153739—22no—
10#19153727C2211yescharacteristic
11#19153727C2212yes—
12#125×C181—22no—
13#125×C181—22no—
14#125×C181—22no—
15#125×C181C2211yescharacteristic
16#125×C181C2212yes—
17C2×Dic362—21no—
18C2×#13089678—22no—
19C2×#13089678—21no—
20C4⋊Dic181—22no—
21C4⋊C4×C181—22no—
22C4⋊C4×C181—22no—
23C4⋊C4×C181—22no—
24C4⋊C4×C181—22no—
25C4⋊C4×C181—22no—
26C4⋊C4×C181—22no—
27C4⋊C4×C181D412yes—
28C4⋊C4×C181D412yes—
29C4⋊C4×C181D412yes—
30C42×C181—22no—
31C42×C181C2311yescharacteristic
32Dic362—42no—
33C2×Dic181—41no—
34#13089678—24no—
35#13089678—41no—
36C2×C4×C181—22no—
37C2×C4×C181—22no—
38C2×C4×C181—22no—
39C2×C4×C181C2×D412yes—
40C2×C4×C181C2×D411yescharacteristic
41C22×C181#12011yescharacteristic
42C4×C181—21no—
43C4×C181—22no—
44C4×C181—42no—
45C4×C181—42no—
46C4×C181—42no—
47Dic181—81no—
48C2×C181#45411yescharacteristic
49C2×C181#45612yes—
50C181#166311yescharacteristic, complemented, Sylow
51#1663—1811nomaximal, Sylow
52#564D18111yescharacteristic
53#501—1812no—
54#491—1811no—
55#330—1812no—
56#330—1811no—
57C4⋊Q8—1811no—
58#125—22no—
59#125—22no—
60#125—22no—
61#125C2×D18111yescharacteristic
62#125C2×D18112yes—
63#107—3622no—
64#106—3622no—
65#103—3622no—
66#97—1811no—
67#97—1812no—
68C2×Q8—3621no—
69C2×C8—3622no—
70C2×C8—3621no—
71C4⋊C4—22no—
72C4⋊C4—22no—
73C4⋊C4—22no—
74C4⋊C4—22no—
75C4⋊C4—22no—
76C4⋊C4—22no—
77C4⋊C4—3622no—
78C4⋊C4C22⋊D18112yes—
79C4⋊C4C22⋊D18112yes—
80C4⋊C4C22⋊D18112yes—
81C42—22no—
82C42C22×D18111yescharacteristic
83Q8—7242no—
84C2×C4—22no—
85C2×C4—22no—
86C2×C4—22no—
87C2×C4—7241no—
88C2×C4C2×C22⋊D18112yes—
89C2×C4C2×C22⋊D18111yescharacteristic
90C8—3624no—
91C8—7241no—
92C22#1915378511yescharacteristic
93C4—21no—
94C4—22no—
95C4—42no—
96C4—42no—
97C4—42no—
98C4—14481no—
99C2#2604145211yescharacteristic
100C2#2604146212yes—
subgroupG/H
centerC22#19153785
commutator, cosocleC42×C181C23
FrattiniC42C22×D181
Fitting#564×C181C2
socle, prime radicalC22×C181#120
hypercenter#564D181
hypocenterC181#1663
LCSG ▷ C42×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #564

Complements

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

NH ≅ G/Ntype
50. C181#1663semidirect

Maximal subgroups

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

subgroupindex
#260416892
#260416492
#260410212
#564×C1812
#1663181