Finite Group Databasebeta

← #46782071

Subgroups — #46782071

Order 33664.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 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
1#30682686C211yesmaximal, characteristic
2#30682308C211yesmaximal, characteristic, complemented
3#30682298C212yesmaximal, complemented
4#30681677C212yesmaximal, complemented
5#330×C263C211yesmaximal, characteristic, complemented
6#22554470C2211yescharacteristic
7#22554458C2212yes—
8#22554455—22no—
9#22554448—22no—
10#22554445—22no—
11#22554395—22no—
12#22554393—22no—
13#22554392—22no—
14#22554381C2211yescharacteristic
15#125×C263C2211yescharacteristic
16#97×C263C2212yes—
17C2×Dic526—21no—
18C2×Dic526D412yes—
19C2×D1052—22no—
20C2×D1052D412yes—
21C2×C4×D263—22no—
22C2×C263⋊C8—21no—
23C4⋊Dic263—22no—
24Dic263⋊C4—22no—
25(C2×D263)⋊C4—22no—
26(C2×D263)⋊C4—22no—
27(C2×D263)⋊C4—22no—
28C2×C8×C263—22no—
29C4⋊C4×C263—22no—
30C4⋊C4×C263D412yes—
31C42×C263C2311yescharacteristic
32C22×D263—22no—
33Dic526—42no—
34Dic526—42no—
35D1052—42no—
36D1052—82no—
37C2×Dic263—22no—
38C2×Dic263—41no—
39C4×D263—82no—
40C263⋊C8—41no—
41C2×C4×C263—22no—
42C2×C4×C263C2×D412yes—
43C2×C4×C263C2×D411yescharacteristic
44C8×C263—42no—
45C22×C263#12011yescharacteristic
46C2×D263—42no—
47C2×D263—42no—
48C2×D263—42no—
49C4×C263—21no—
50C4×C263—22no—
51C4×C263—42no—
52Dic263—42no—
53Dic263—81no—
54C2×C263#45411yescharacteristic
55C2×C263#45512yes—
56D263—82no—
57C263#166211yescharacteristic, complemented, Sylow
58#1662—2631nomaximal, Sylow
59#562—2631no—
60#491—2631no—
61#489—2632no—
62#330D26311yescharacteristic, complemented
63#329—2632no—
64C4⋊Q8—2631no—
65#125C2×D26311yescharacteristic
66#124—2632no—
67#123—5262no—
68C22⋊Q8—5262no—
69#121—5262no—
70#103—5262no—
71#103—5262no—
72#102—5262no—
73#97—2631no—
74#97C2×D26312yes—
75C2×Q8—2632no—
76C2×Q8—5261no—
77C2×D4—2632no—
78C2×D4—5262no—
79C22×C4—5262no—
80C2×C8—22no—
81C2×C8—5261no—
82C4⋊C4—22no—
83C4⋊C4—5262no—
84C4⋊C4—5262no—
85C4⋊C4D105212yes—
86C22⋊C4—5262no—
87C22⋊C4—5262no—
88C22⋊C4—5262no—
89C42C22×D26311yescharacteristic
90C23—5262no—
91Q8—10522no—
92Q8—10522no—
93D4—10522no—
94D4—21042no—
95C2×C4—22no—
96C2×C4—5262no—
97C2×C4—10521no—
98C2×C4—21042no—
99C2×C4D4×D26312yes—
100C2×C4C2×D105211yescharacteristic
101C8—42no—
102C8—10521no—
103C22—10522no—
104C22—10522no—
105C22—10522no—
106C22#2255444011yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—10522no—
111C4—21041no—
112C2—21042no—
113C2#3068211311yescharacteristic
114C2#3068211712yes—
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#330×C263C2
socleC22×C263#120
prime radical#30682686C2
hypercenter#330D263
hypocenterC263#1662
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #30682308C2semidirect
3. #30682298C2semidirect
4. #30681677C2semidirect
5. #330×C263C2semidirect
57. C263#1662semidirect
62. #330D263semidirect

Maximal subgroups

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

subgroupindex
#306826862
#306823082
#306822982
#306816772
#330×C2632
#1662263