Finite Group Databasebeta

← #46782075

Subgroups — #46782075

Order 33664.

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#30682348C212yesmaximal
2#30682308C211yesmaximal, characteristic
3#30681680C212yesmaximal
4#30681680C211yesmaximal, characteristic
5#564×C263C211yesmaximal, characteristic
6#22554470C2211yescharacteristic
7#22554403—22no—
8#22554401—22no—
9#22554393—22no—
10#22554381C2211yescharacteristic
11#22554381C2212yes—
12#125×C263—22no—
13#125×C263—22no—
14#125×C263—22no—
15#125×C263C2211yescharacteristic
16#125×C263C2212yes—
17C2×Dic526—21no—
18C2×C263⋊C8—22no—
19C2×C263⋊C8—21no—
20C4⋊Dic263—22no—
21C4⋊C4×C263—22no—
22C4⋊C4×C263—22no—
23C4⋊C4×C263—22no—
24C4⋊C4×C263—22no—
25C4⋊C4×C263—22no—
26C4⋊C4×C263—22no—
27C4⋊C4×C263D412yes—
28C4⋊C4×C263D412yes—
29C4⋊C4×C263D412yes—
30C42×C263—22no—
31C42×C263C2311yescharacteristic
32Dic526—42no—
33C2×Dic263—41no—
34C263⋊C8—24no—
35C263⋊C8—41no—
36C2×C4×C263—22no—
37C2×C4×C263—22no—
38C2×C4×C263—22no—
39C2×C4×C263C2×D412yes—
40C2×C4×C263C2×D411yescharacteristic
41C22×C263#12011yescharacteristic
42C4×C263—21no—
43C4×C263—22no—
44C4×C263—42no—
45C4×C263—42no—
46C4×C263—42no—
47Dic263—81no—
48C2×C263#45411yescharacteristic
49C2×C263#45612yes—
50C263#166311yescharacteristic, complemented, Sylow
51#1663—2631nomaximal, Sylow
52#564D26311yescharacteristic
53#501—2632no—
54#491—2631no—
55#330—2632no—
56#330—2631no—
57C4⋊Q8—2631no—
58#125—22no—
59#125—22no—
60#125—22no—
61#125C2×D26311yescharacteristic
62#125C2×D26312yes—
63#107—5262no—
64#106—5262no—
65#103—5262no—
66#97—2631no—
67#97—2632no—
68C2×Q8—5261no—
69C2×C8—5262no—
70C2×C8—5261no—
71C4⋊C4—22no—
72C4⋊C4—22no—
73C4⋊C4—22no—
74C4⋊C4—22no—
75C4⋊C4—22no—
76C4⋊C4—22no—
77C4⋊C4—5262no—
78C4⋊C4C22⋊D26312yes—
79C4⋊C4C22⋊D26312yes—
80C4⋊C4C22⋊D26312yes—
81C42—22no—
82C42C22×D26311yescharacteristic
83Q8—10522no—
84C2×C4—22no—
85C2×C4—22no—
86C2×C4—22no—
87C2×C4—10521no—
88C2×C4C2×C22⋊D26312yes—
89C2×C4C2×C22⋊D26311yescharacteristic
90C8—5264no—
91C8—10521no—
92C22#2255443911yescharacteristic
93C4—22no—
94C4—21no—
95C4—42no—
96C4—42no—
97C4—42no—
98C4—21041no—
99C2#3068211111yescharacteristic
100C2#3068212112yes—
subgroupG/H
centerC22#22554439
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#564×C263C2
socle, prime radicalC22×C263#120
hypercenter#564D263
hypocenterC263#1663
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #564

Complements

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

NH ≅ G/Ntype
50. C263#1663semidirect

Maximal subgroups

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

subgroupindex
#306823482
#306823082
#306816802
#564×C2632
#1663263