Finite Group Databasebeta

← #46782342

Subgroups — #46782342

Order 33664.

180 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 69 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#30682336C211yesmaximal, characteristic
3#30682317C211yesmaximal, characteristic
4#30682290C211yesmaximal, characteristic
5#30682288C211yesmaximal, characteristic
6C8×C263⋊C8C211yesmaximal, characteristic
7#498×C263C211yesmaximal, characteristic
8C2×#16862366—22no—
9#22554470C2211yescharacteristic
10#22554470C2211yescharacteristic
11#22554403—22no—
12#22554402—22no—
13#22554394—22no—
14#22554393—22no—
15C4×C263⋊C8C2211yescharacteristic
16C4×C263⋊C8C2211yescharacteristic
17C4⋊Q8×C263C2211yescharacteristic
18C4⋊Q8×C263C2211yescharacteristic
19#106×C263—22no—
20C4×C8×C263C2211yescharacteristic
21C2×Dic526—21no—
22C2×Dic526—21no—
23#16862366—44no—
24C2×C263⋊C8D412yes—
25C2×C263⋊C8D412yes—
26C4⋊Dic263—21no—
27C4⋊Dic263—21no—
28C4⋊Dic263—21no—
29C4⋊Dic263—21no—
30C2×Q8×C263—21no—
31C2×Q8×C263—21no—
32C2×C8×C263D412yes—
33C4⋊C4×C263—21no—
34C4⋊C4×C263—21no—
35C4⋊C4×C263—21no—
36C4⋊C4×C263—21no—
37C42×C263C2311yescharacteristic
38Dic526—42no—
39Dic526—42no—
40C2×Dic263—41no—
41C2×Dic263—41no—
42C263⋊C8—22no—
43C263⋊C8SD1614yes—
44Q8×C263—42no—
45Q8×C263—42no—
46C2×C4×C263—41no—
47C2×C4×C263—41no—
48C2×C4×C263C2×D411yescharacteristic
49C2×C4×C263C2×D411yescharacteristic
50C2×C4×C263C2×D411yescharacteristic
51C8×C263Q1614yescomplemented
52C22×C263#12711yescharacteristic
53C4×C263—81no—
54C4×C263—81no—
55C4×C263C2×SD1612yes—
56C4×C263C2×Q1612yes—
57C4×C263#13512yes—
58Dic263—81no—
59Dic263—81no—
60C2×C263#49211yescharacteristic
61C2×C263#49411yescharacteristic
62C2×C263#49511yescharacteristic
63C263#170711yescharacteristic, complemented, Sylow
64#1707—2631nomaximal, Sylow
65#500—2631no—
66#498—2631no—
67#498D26311yescharacteristic
68#494—2631no—
69#487—2631no—
70#487—2631no—
71C82—2631no—
72C2×Q16—5262no—
73C4⋊Q8—2631no—
74C4⋊Q8—2631no—
75C4⋊Q8C2×D26311yescharacteristic
76C4⋊Q8C2×D26311yescharacteristic
77#107—5262no—
78#106—22no—
79#106—5262no—
80#103—5262no—
81#103—5262no—
82C4×C8—2631no—
83C4×C8—2631no—
84C4×C8C2×D26311yescharacteristic
85C2×Q8—21no—
86C2×Q8—21no—
87C2×Q8—5261no—
88C2×Q8—5261no—
89Q16—10524no—
90C2×C8—2632no—
91C2×C8—2632no—
92C2×C8C22⋊D26312yes—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—21no—
96C4⋊C4—21no—
97C4⋊C4—5261no—
98C4⋊C4—5261no—
99C4⋊C4—5261no—
100C4⋊C4—5261no—
101C42C22×D26311yescharacteristic
102Q8—42no—
103Q8—42no—
104Q8—10522no—
105Q8—10522no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—10521no—
109C2×C4—10521no—
110C2×C4D4×D26311yescharacteristic
111C2×C4D4×D26311yescharacteristic
112C2×C4C2×C22⋊D26311yescharacteristic
113C8—2634no—
114C8—5262no—
115C8#1686236614yescomplemented
116C22#2255446611yescharacteristic
117C4—81no—
118C4—81no—
119C4—21041no—
120C4—21041no—
121C4SD16×D26312yes—
122C4C2×#1686236612yes—
123C4#2255449112yes—
124C2#3068230911yescharacteristic
125C2#3068231711yescharacteristic
126C2#3068231911yescharacteristic
subgroupG/H
centerC22#22554466
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#498×C263C2
socle, prime radicalC22×C263#127
hypercenter#498D263
hypocenterC263#1707
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
51. C8×C263Q16semidirect
63. C263#1707semidirect
115. C8#16862366semidirect

Maximal subgroups

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

subgroupindex
#306823412
#306823362
#306823172
#306822902
#306822882
C8×C263⋊C82
#498×C2632
#1707263