Finite Group Databasebeta

← #46781861

Subgroups — #46781861

Order 33664.

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

normal subgroups only

This group has 314 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#30682573C211yesmaximal, characteristic
2#30682225C212yesmaximal, complemented
3#30681682C211yesmaximal, characteristic, complemented
4#30681667C212yesmaximal, complemented
5#492×C263C211yesmaximal, characteristic, complemented
6C2×D4×D263—22no—
7#22554441—22no—
8#22554438—22no—
9C4×D1052C2212yes—
10#22554401—22no—
11C4⋊(C263⋊C8)C2212yescomplemented
12#22554390—22no—
13C2×SD16×C263—22no—
14C4⋊Q8×C263C2211yescharacteristic, complemented
15#127×C263C2211yescharacteristic
16C4×C8×C263C2211yescharacteristic, complemented
17C23×D263—22no—
18C2×D1052D412yes—
19C2×C22⋊D263—24no—
20D4×D263—44no—
21D4×D263—44no—
22C2×C4×D263—22no—
23C2×C263⋊C8—22no—
24C4⋊Dic263D412yes—
25C22⋊Dic263—22no—
26(C2×D263)⋊C4—22no—
27C2×Q8×C263—21no—
28C2×D4×C263—22no—
29C2×D4×C263D412yes—
30SD16×C263—44no—
31C2×C8×C263—21no—
32C4⋊C4×C263—22no—
33C42×C263C2311yescharacteristic
34C22×D263—22no—
35C22×D263—48no—
36C22×D263—82no—
37D1052—22no—
38D1052SD1614yescomplemented
39C22⋊D263—48no—
40C2×Dic263—22no—
41C4×D263—42no—
42C4×D263—42no—
43C263⋊C8—42no—
44C23×C263—22no—
45Q8×C263—42no—
46D4×C263—42no—
47D4×C263—42no—
48D4×C263—42no—
49C2×C4×C263—41no—
50C2×C4×C263C2×D412yes—
51C2×C4×C263C2×D411yescharacteristic
52C8×C263—22no—
53C22×C263—44no—
54C22×C263—42no—
55C22×C263#12011yescharacteristic
56C2×D263—24no—
57C2×D263—42no—
58C2×D263—42no—
59C2×D263—88no—
60C4×C263—21no—
61C4×C263—81no—
62C4×C263C2×SD1612yes—
63C4×C263AGL(1,ℤ/8)12yes—
64Dic263—42no—
65C2×C263—82no—
66C2×C263#45012yes—
67C2×C263#45311yescharacteristic
68D263—44no—
69C263#162911yescharacteristic, complemented, Sylow
70#1629—2631nomaximal, Sylow
71D42—2631no—
72#492D26311yescharacteristic, complemented
73#476—2632no—
74#331—2631no—
75D4⋊C8—2632no—
76C22×D4—5262no—
77C2×SD16—22no—
78C4⋊Q8C2×D26311yescharacteristic, complemented
79#127C2×D26311yescharacteristic
80#121—5262no—
81#120—5262no—
82C4×D4—2632no—
83#106—5262no—
84C4⋊C8—2632no—
85#102—5262no—
86C4×C8C2×D26311yescharacteristic, complemented
87C24—5262no—
88C2×Q8—21no—
89C2×D4—22no—
90C2×D4—2632no—
91C2×D4—5264no—
92C2×D4—10524no—
93C2×D4—10524no—
94C2×D4C22⋊D26312yes—
95C22×C4—5262no—
96SD16—44no—
97C2×C8—21no—
98C2×C8—5262no—
99C4⋊C4—22no—
100C4⋊C4—2632no—
101C22⋊C4—5262no—
102C22⋊C4—5262no—
103C42C22×D26311yescharacteristic
104C23—22no—
105C23—5262no—
106C23—10528no—
107C23—21042no—
108Q8—42no—
109D4—42no—
110D4—42no—
111D4—42no—
112D4—2634no—
113D4—5262no—
114D4—10528no—
115C2×C4—41no—
116C2×C4—5262no—
117C2×C4—10522no—
118C2×C4—10522no—
119C2×C4D4×D26312yes—
120C2×C4C2×C22⋊D26311yescharacteristic
121C8—22no—
122C8—10522no—
123C22—44no—
124C22—42no—
125C22—5264no—
126C22—10522no—
127C22—10522no—
128C22—21048no—
129C22#2255443811yescharacteristic
130C4—21no—
131C4—81no—
132C4—10522no—
133C4SD16×D26312yes—
134C4#2255449712yes—
135C2—82no—
136C2—10524no—
137C2#3068208712yes—
138C2#3068210511yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#492×C263C2
socleC22×C263#120
prime radical#30682573C2
hypercenter#492D263
hypocenterC263#1629
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
2. #30682225C2semidirect
3. #30681682C2semidirect
4. #30681667C2semidirect
5. #492×C263C2semidirect
11. C4⋊(C263⋊C8)C22semidirect
14. C4⋊Q8×C263C22semidirect
16. C4×C8×C263C22semidirect
38. D1052SD16semidirect
69. C263#1629semidirect
72. #492D263semidirect
78. C4⋊Q8C2×D263semidirect
86. C4×C8C2×D263semidirect

Maximal subgroups

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

subgroupindex
#306825732
#306822252
#306816822
#306816672
#492×C2632
#1629263