Finite Group Databasebeta

← #46781892

Subgroups — #46781892

Order 33664.

218 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 57 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#30682317C211yesmaximal, characteristic, complemented
2#30682228C212yesmaximal, complemented
3#30681687C211yesmaximal, characteristic, complemented
4D4⋊(C263⋊C8)C212yesmaximal, complemented
5#555×C263C211yesmaximal, characteristic
6C2×#16862366—22no—
7#22554470C2211yescharacteristic
8#22554401—22no—
9C4⋊(C263⋊C8)C2212yes—
10#22554391—22no—
11C4×C263⋊C8C2211yescharacteristic
12C4⋊Q8×C263C2211yescharacteristic
13#124×C263—22no—
14#121×C263—22no—
15C4×D4×C263C2212yes—
16#117×C263—22no—
17C2×Dic526—21no—
18#16862366—44no—
19C2×C263⋊C8—21no—
20C2×C263⋊C8—22no—
21C4⋊Dic263—22no—
22C2×Q8×C263D412yes—
23C2×D4×C263—22no—
24C2×D4×C263D412yes—
25C22×C4×C263—22no—
26C4⋊C4×C263—22no—
27C4⋊C4×C263D412yes—
28C22⋊C4×C263—24no—
29C22⋊C4×C263—22no—
30C42×C263—22no—
31C42×C263C2311yescharacteristic
32Dic526—42no—
33C2×Dic263—41no—
34C263⋊C8—22no—
35C263⋊C8—42no—
36C23×C263—22no—
37Q8×C263—42no—
38D4×C263—22no—
39D4×C263—22no—
40D4×C263—82no—
41C2×C4×C263—22no—
42C2×C4×C263—22no—
43C2×C4×C263—42no—
44C2×C4×C263—42no—
45C2×C4×C263C2×D411yescharacteristic
46C2×C4×C263C2×D412yes—
47C22×C263—42no—
48C22×C263—42no—
49C22×C263—42no—
50C22×C263#12011yescharacteristic
51C4×C263—21no—
52C4×C263—42no—
53C4×C263—42no—
54C4×C263#13512yes—
55C4×C263#13712yes—
56Dic263—81no—
57C2×C263—82no—
58C2×C263#45212yes—
59C2×C263#45311yescharacteristic
60C263#163411yescharacteristic, complemented, Sylow
61#1634—2631nomaximal, Sylow
62#555D26311yescharacteristic
63#494—2631no—
64#476—2632no—
65#333—2631no—
66D4⋊C8—2632no—
67C2×Q16—5262no—
68C4⋊Q8—2631no—
69C4⋊Q8C2×D26311yescharacteristic
70#124—22no—
71#121—22no—
72C4×D4C2×D26312yes—
73#117—22no—
74#106—5262no—
75C4⋊C8—2632no—
76#102—5262no—
77C4×C8—2631no—
78C2×Q8—5261no—
79C2×Q8C22⋊D26312yes—
80C2×D4—22no—
81C2×D4C22⋊D26312yes—
82C22×C4—22no—
83Q16—10524no—
84C2×C8—5261no—
85C2×C8—5262no—
86C4⋊C4—22no—
87C4⋊C4—5262no—
88C4⋊C4C22⋊D26312yes—
89C22⋊C4—24no—
90C22⋊C4—22no—
91C42—22no—
92C42C22×D26311yescharacteristic
93C23—22no—
94Q8—42no—
95Q8—10522no—
96D4—22no—
97D4—22no—
98D4—82no—
99C2×C4—22no—
100C2×C4—22no—
101C2×C4—42no—
102C2×C4—42no—
103C2×C4—10521no—
104C2×C4C2×C22⋊D26311yescharacteristic
105C2×C4C2×C22⋊D26312yes—
106C8—5262no—
107C8—10522no—
108C22—42no—
109C22—42no—
110C22—42no—
111C22#2255443911yescharacteristic
112C4—21no—
113C4—42no—
114C4—42no—
115C4—21041no—
116C4#2255449012yes—
117C4#2255450012yes—
118C2—82no—
119C2#3068210012yes—
120C2#3068210611yescharacteristic
subgroupG/H
centerC22#22554439
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting, prime radical#555×C263C2
socleC22×C263#120
hypercenter#555D263
hypocenterC263#1634
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #30682317C2semidirect
2. #30682228C2semidirect
3. #30681687C2semidirect
4. D4⋊(C263⋊C8)C2semidirect
60. C263#1634semidirect

Maximal subgroups

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

subgroupindex
#306823172
#306822282
#306816872
D4⋊(C263⋊C8)2
#555×C2632
#1634263