Finite Group Databasebeta

← #46782073

Subgroups — #46782073

Order 33664.

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
1C263⋊#564C211yesmaximal, characteristic
2#30682344C212yesmaximal
3#30681680C211yesmaximal, characteristic
4#30681679C212yesmaximal
5#491×C263C211yesmaximal, characteristic
6#22554462C2212yes—
7#22554461—22no—
8#22554460—22no—
9#22554460—22no—
10#22554403—22no—
11#22554401—22no—
12#22554381C2212yes—
13C4⋊Q8×C263C2211yescharacteristic
14#125×C263C2211yescharacteristic
15#103×C263—22no—
16#97×C263C2211yescharacteristic
17C2×C263⋊C8—22no—
18C4⋊Dic263—22no—
19C4⋊Dic263D412yes—
20C4⋊Dic263D412yes—
21Dic263⋊C4—22no—
22Dic263⋊C4—22no—
23Dic263⋊C4—22no—
24Dic263⋊C4—22no—
25C4×Dic263—22no—
26C2×Q8×C263—21no—
27C2×C8×C263—21no—
28C4⋊C4×C263—22no—
29C4⋊C4×C263—22no—
30C4⋊C4×C263D412yes—
31C42×C263C2311yescharacteristic
32C2×Dic263—22no—
33C2×Dic263—22no—
34C263⋊C8—24no—
35Q8×C263—42no—
36C2×C4×C263—22no—
37C2×C4×C263—41no—
38C2×C4×C263C2×D412yes—
39C2×C4×C263C2×D411yescharacteristic
40C8×C263—41no—
41C22×C263#12011yescharacteristic
42C4×C263—21no—
43C4×C263—22no—
44C4×C263—42no—
45C4×C263—81no—
46Dic263—42no—
47Dic263—42no—
48C2×C263#45411yescharacteristic
49C2×C263#45612yes—
50C263#166311yescharacteristic, complemented, Sylow
51#1663—2631nomaximal, Sylow
52#564—2631no—
53#501—2632no—
54#491D26311yescharacteristic
55#330—2631no—
56#330—2632no—
57C4⋊Q8C2×D26311yescharacteristic
58#125—2632no—
59#125—5262no—
60#125—5262no—
61#125—5262no—
62#125C2×D26311yescharacteristic
63#107—5262no—
64#106—5262no—
65#103—22no—
66#97—2632no—
67#97C2×D26311yescharacteristic
68C2×Q8—21no—
69C2×C8—21no—
70C2×C8—5262no—
71C4⋊C4—22no—
72C4⋊C4—22no—
73C4⋊C4—2632no—
74C4⋊C4—2632no—
75C4⋊C4—5262no—
76C4⋊C4—5262no—
77C4⋊C4—5262no—
78C4⋊C4—5262no—
79C4⋊C4—5262no—
80C4⋊C4C22⋊D26312yes—
81C42—5262no—
82C42C22×D26311yescharacteristic
83Q8—42no—
84C2×C4—22no—
85C2×C4—41no—
86C2×C4—5262no—
87C2×C4—5262no—
88C2×C4D4×D26312yes—
89C2×C4C2×C22⋊D26311yescharacteristic
90C8—41no—
91C8—5264no—
92C22#2255443811yescharacteristic
93C4—22no—
94C4—21no—
95C4—42no—
96C4—81no—
97C4—10522no—
98C4—10522no—
99C2#3068211011yescharacteristic
100C2#3068211912yes—
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#491×C263C2
socle, prime radicalC22×C263#120
hypercenter#491D263
hypocenterC263#1663
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #491

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
C263⋊#5642
#306823442
#306816802
#306816792
#491×C2632
#1663263