Finite Group Databasebeta

← #46782070

Subgroups — #46782070

Order 33664.

196 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 196 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#30682308C211yesmaximal, characteristic, complemented
2#30682297C212yesmaximal, complemented
3#30681680C211yesmaximal, characteristic, complemented
4#30681678C212yesmaximal, complemented
5#562×C263C211yesmaximal, characteristic
6#22554470C2211yescharacteristic
7#22554394—22no—
8#22554393—22no—
9#22554391—22no—
10#22554381C2211yescharacteristic
11#22554381C2212yes—
12#125×C263C2211yescharacteristic
13#124×C263C2212yes—
14#123×C263—22no—
15C22⋊Q8×C263—22no—
16#121×C263—22no—
17C2×Dic526—21no—
18C2×C263⋊C8—22no—
19C2×C263⋊C8—21no—
20C4⋊Dic263—22no—
21C2×Q8×C263D412yes—
22C2×D4×C263—22no—
23C2×D4×C263D412yes—
24C22×C4×C263—22no—
25C4⋊C4×C263—22no—
26C4⋊C4×C263—22no—
27C4⋊C4×C263D412yes—
28C22⋊C4×C263—22no—
29C22⋊C4×C263—22no—
30C22⋊C4×C263—22no—
31C42×C263C2311yescharacteristic
32Dic526—42no—
33C2×Dic263—41no—
34C263⋊C8—41no—
35C263⋊C8—42no—
36C23×C263—22no—
37Q8×C263—42no—
38D4×C263—42no—
39D4×C263—82no—
40C2×C4×C263—22no—
41C2×C4×C263—22no—
42C2×C4×C263—82no—
43C2×C4×C263C2×D411yescharacteristic
44C2×C4×C263C2×D412yes—
45C22×C263—42no—
46C22×C263—42no—
47C22×C263—42no—
48C22×C263#12011yescharacteristic
49C4×C263—21no—
50C4×C263—22no—
51C4×C263—42no—
52C4×C263—42no—
53Dic263—81no—
54C2×C263—82no—
55C2×C263#45411yescharacteristic
56C2×C263#45512yes—
57C263#166211yescharacteristic, complemented, Sylow
58#1662—2631nomaximal, Sylow
59#562D26311yescharacteristic
60#491—2631no—
61#489—2632no—
62#330—2631no—
63#329—2632no—
64C4⋊Q8—2631no—
65#125C2×D26311yescharacteristic
66#124C2×D26312yes—
67#123—22no—
68C22⋊Q8—22no—
69#121—22no—
70#103—5262no—
71#103—5262no—
72#102—5262no—
73#97—2631no—
74#97—2632no—
75C2×Q8—5261no—
76C2×Q8C22⋊D26312yes—
77C2×D4—22no—
78C2×D4C22⋊D26312yes—
79C22×C4—22no—
80C2×C8—5262no—
81C2×C8—5261no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—5262no—
85C4⋊C4C22⋊D26312yes—
86C22⋊C4—22no—
87C22⋊C4—22no—
88C22⋊C4—22no—
89C42C22×D26311yescharacteristic
90C23—22no—
91Q8—42no—
92Q8—10522no—
93D4—42no—
94D4—82no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—82no—
98C2×C4—10521no—
99C2×C4C2×C22⋊D26311yescharacteristic
100C2×C4C2×C22⋊D26312yes—
101C8—10522no—
102C8—10521no—
103C22—42no—
104C22—42no—
105C22—42no—
106C22#2255443911yescharacteristic
107C4—22no—
108C4—21no—
109C4—42no—
110C4—42no—
111C4—21041no—
112C2—82no—
113C2#3068211111yescharacteristic
114C2#3068211612yes—
subgroupG/H
centerC22#22554439
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting, prime radical#562×C263C2
socleC22×C263#120
hypercenter#562D263
hypocenterC263#1662
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #30682308C2semidirect
2. #30682297C2semidirect
3. #30681680C2semidirect
4. #30681678C2semidirect
57. C263#1662semidirect

Maximal subgroups

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

subgroupindex
#306823082
#306822972
#306816802
#306816782
#562×C2632
#1662263