Finite Group Databasebeta

← #46782355

Subgroups — #46782355

Order 33664.

168 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 61 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#30682341C211yesmaximal, characteristic
2#30682341C211yesmaximal, characteristic
3#30682290C211yesmaximal, characteristic
4#30682289C211yesmaximal, characteristic
5#30682288C211yesmaximal, characteristic
6C8×C263⋊C8C211yesmaximal, characteristic
7#487×C263C211yesmaximal, characteristic
8#22554470C2211yescharacteristic
9#22554470C2211yescharacteristic
10#22554403—22no—
11#22554403—22no—
12#22554395—22no—
13#22554394—22no—
14#22554393—22no—
15C4×C263⋊C8C2211yescharacteristic
16C4×C263⋊C8C2211yescharacteristic
17C4⋊Q8×C263C2211yescharacteristic
18C4⋊Q8×C263C2211yescharacteristic
19#103×C263—22no—
20C4×C8×C263C2211yescharacteristic
21C2×Dic526—21no—
22C2×Dic526—21no—
23C2×C263⋊C8D412yes—
24C2×C263⋊C8D412yes—
25C4⋊Dic263—21no—
26C4⋊Dic263—21no—
27C4⋊Dic263—21no—
28C4⋊Dic263—21no—
29C2×Q8×C263—21no—
30C2×Q8×C263—21no—
31C2×C8×C263D412yes—
32C4⋊C4×C263—21no—
33C4⋊C4×C263—21no—
34C4⋊C4×C263—21no—
35C4⋊C4×C263—21no—
36C42×C263C2311yescharacteristic
37Dic526—42no—
38Dic526—42no—
39C2×Dic263—41no—
40C2×Dic263—41no—
41C263⋊C8—22no—
42C263⋊C8Q1614yes—
43Q8×C263—42no—
44Q8×C263—42no—
45C2×C4×C263—41no—
46C2×C4×C263—41no—
47C2×C4×C263C2×D411yescharacteristic
48C2×C4×C263C2×D411yescharacteristic
49C2×C4×C263C2×D411yescharacteristic
50C8×C263—22no—
51C22×C263#12711yescharacteristic
52C4×C263—81no—
53C4×C263—81no—
54C4×C263C2×Q1612yes—
55C4×C263#13512yes—
56C4×C263#13512yes—
57Dic263—81no—
58Dic263—81no—
59C2×C263#49411yescharacteristic
60C2×C263#49511yescharacteristic
61C2×C263#49511yescharacteristic
62C263#171011yescharacteristic, complemented, Sylow
63#1710—2631nomaximal, Sylow
64#500—2631no—
65#500—2631no—
66#487—2631no—
67#487—2631no—
68#487—2631no—
69#487D26311yescharacteristic
70C82—2631no—
71C4⋊Q8—2631no—
72C4⋊Q8—2631no—
73C4⋊Q8C2×D26311yescharacteristic
74C4⋊Q8C2×D26311yescharacteristic
75#107—5262no—
76#107—5262no—
77#103—22no—
78#103—5262no—
79#103—5262no—
80#103—5262no—
81C4×C8—2631no—
82C4×C8—2631no—
83C4×C8C2×D26311yescharacteristic
84C2×Q8—21no—
85C2×Q8—21no—
86C2×Q8—5261no—
87C2×Q8—5261no—
88C2×C8—2632no—
89C2×C8—2632no—
90C2×C8C22⋊D26312yes—
91C4⋊C4—21no—
92C4⋊C4—21no—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—5261no—
96C4⋊C4—5261no—
97C4⋊C4—5261no—
98C4⋊C4—5261no—
99C42C22×D26311yescharacteristic
100Q8—42no—
101Q8—42no—
102Q8—10522no—
103Q8—10522no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—10521no—
107C2×C4—10521no—
108C2×C4D4×D26311yescharacteristic
109C2×C4D4×D26311yescharacteristic
110C2×C4C2×C22⋊D26311yescharacteristic
111C8—22no—
112C8—2634no—
113C8—5262no—
114C22#2255446611yescharacteristic
115C4—81no—
116C4—81no—
117C4—21041no—
118C4—21041no—
119C4Q16×D26312yes—
120C4#2255449012yes—
121C4#2255449112yes—
122C2#3068231611yescharacteristic
123C2#3068231911yescharacteristic
124C2#3068232011yescharacteristic
subgroupG/H
centerC22#22554466
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#487×C263C2
socle, prime radicalC22×C263#127
hypercenter#487D263
hypocenterC263#1710
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
62. C263#1710semidirect

Maximal subgroups

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

subgroupindex
#306823412
#306822902
#306822892
#306822882
C8×C263⋊C82
#487×C2632
#1710263