Finite Group Databasebeta

← #46781868

Subgroups — #46781868

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#30682310C211yesmaximal, characteristic
2#30682233C212yesmaximal, complemented
3#30681682C211yesmaximal, characteristic
4Q8⋊(C263⋊C8)C212yesmaximal, complemented
5#559×C263C211yesmaximal, characteristic
6C2×#16862364—22no—
7#22554470C2211yescharacteristic
8#22554403—22no—
9C4⋊(C263⋊C8)C2212yes—
10#22554394—22no—
11C4×C263⋊C8C2211yescharacteristic
12#127×C263C2211yescharacteristic
13#124×C263—22no—
14#123×C263—22no—
15C4×Q8×C263C2212yes—
16C4×D4×C263—22no—
17C2×Dic526—21no—
18#16862364—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—22no—
38Q8×C263—22no—
39D4×C263—42no—
40D4×C263—42no—
41D4×C263—42no—
42C2×C4×C263—22no—
43C2×C4×C263—22no—
44C2×C4×C263—82no—
45C2×C4×C263C2×D411yescharacteristic
46C2×C4×C263C2×D412yes—
47C22×C263—44no—
48C22×C263—42no—
49C22×C263#12011yescharacteristic
50C4×C263—21no—
51C4×C263—42no—
52C4×C263—42no—
53C4×C263#13512yes—
54C4×C263#13712yes—
55Dic263—81no—
56C2×C263—82no—
57C2×C263#45212yes—
58C2×C263#45311yescharacteristic
59C263#163011yescharacteristic, complemented, Sylow
60#1630—2631nomaximal, Sylow
61#559D26311yescharacteristic
62#492—2631no—
63#477—2632no—
64#331—2631no—
65Q8⋊C8—2632no—
66C2×SD16—5262no—
67C4⋊Q8—2631no—
68#127C2×D26311yescharacteristic
69#124—22no—
70#123—22no—
71C4×Q8C2×D26312yes—
72C4×D4—22no—
73#107—5262no—
74C4⋊C8—2632no—
75#103—5262no—
76C4×C8—2631no—
77C2×Q8—5261no—
78C2×Q8C22⋊D26312yes—
79C2×D4—22no—
80C2×D4C22⋊D26312yes—
81C22×C4—22no—
82SD16—10524no—
83C2×C8—5261no—
84C2×C8—5262no—
85C4⋊C4—22no—
86C4⋊C4—5262no—
87C4⋊C4C22⋊D26312yes—
88C22⋊C4—24no—
89C22⋊C4—22no—
90C42—22no—
91C42C22×D26311yescharacteristic
92C23—22no—
93Q8—22no—
94Q8—22no—
95Q8—10522no—
96D4—42no—
97D4—42no—
98D4—42no—
99C2×C4—22no—
100C2×C4—22no—
101C2×C4—82no—
102C2×C4—10521no—
103C2×C4C2×C22⋊D26311yescharacteristic
104C2×C4C2×C22⋊D26312yes—
105C8—5262no—
106C8—10522no—
107C22—44no—
108C22—42no—
109C22#2255443911yescharacteristic
110C4—21no—
111C4—42no—
112C4—42no—
113C4—21041no—
114C4#2255449012yes—
115C4#2255450012yes—
116C2—82no—
117C2#3068210012yes—
118C2#3068210611yescharacteristic
subgroupG/H
centerC22#22554439
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#559×C263C2
socleC22×C263#120
prime radical#127×C263C22
hypercenter#559D263
hypocenterC263#1630
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #559

Complements

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

NH ≅ G/Ntype
2. #30682233C2semidirect
4. Q8⋊(C263⋊C8)C2semidirect
59. C263#1630semidirect

Maximal subgroups

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

subgroupindex
#306823102
#306822332
#306816822
Q8⋊(C263⋊C8)2
#559×C2632
#1630263