Finite Group Databasebeta

← #46781828

Subgroups — #46781828

Order 33664.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#30682654C211yesmaximal, characteristic, complemented
2#30682130C212yesmaximal, complemented
3#30681687C211yesmaximal, characteristic, complemented
4#30681667C212yesmaximal, complemented
5#492×C263C211yesmaximal, characteristic, complemented
6C2×#16862361—22no—
7#22554459—22no—
8#22554445—22no—
9C4×D1052C2212yes—
10#22554428—22no—
11C4⋊(C263⋊C8)C2212yes—
12#22554391—22no—
13C2×SD16×C263—22no—
14C4⋊Q8×C263C2211yescharacteristic
15#127×C263C2211yescharacteristic
16C4×C8×C263C2211yescharacteristic
17C2×D1052—22no—
18C2×D1052D412yes—
19C2×C4×D263—22no—
20#16862361—44no—
21C2×C263⋊C8—22no—
22C4⋊Dic263D412yes—
23(C2×D263)⋊C4—24no—
24(C2×D263)⋊C4—22no—
25C4×Dic263—22no—
26C2×Q8×C263D412yes—
27C2×D4×C263—22no—
28C2×D4×C263—21no—
29SD16×C263—44no—
30C2×C8×C263—21no—
31C4⋊C4×C263—22no—
32C42×C263C2311yescharacteristic
33C22×D263—22no—
34D1052—22no—
35D1052—22no—
36D1052—82no—
37C2×Dic263—22no—
38C4×D263—42no—
39C4×D263—42no—
40C263⋊C8—42no—
41C23×C263—41no—
42Q8×C263—42no—
43D4×C263—42no—
44D4×C263—42no—
45D4×C263—42no—
46C2×C4×C263—22no—
47C2×C4×C263C2×D412yes—
48C2×C4×C263C2×D411yescharacteristic
49C8×C263—22no—
50C22×C263—82no—
51C22×C263—81no—
52C22×C263#12011yescharacteristic
53C2×D263—42no—
54C2×D263—42no—
55C2×D263—42no—
56C4×C263—21no—
57C4×C263—42no—
58C4×C263#13512yes—
59C4×C263AGL(1,ℤ/8)12yes—
60Dic263—42no—
61C2×C263—161no—
62C2×C263#44912yes—
63C2×C263#45311yescharacteristic
64D263—82no—
65C263#162411yescharacteristic, complemented, Sylow
66#1624—2631nomaximal, Sylow
67#555—2631no—
68#492D26311yescharacteristic, complemented
69#459—2632no—
70#333—2631no—
71D4⋊C8—2632no—
72C2×SD16—22no—
73C2×D8—5262no—
74C4⋊Q8C2×D26311yescharacteristic
75#127C2×D26311yescharacteristic
76#124—5262no—
77#121—5262no—
78C4×D4—2632no—
79#117—5262no—
80C4⋊C8—2632no—
81#102—5262no—
82C4×C8C2×D26311yescharacteristic
83C2×Q8C22⋊D26312yes—
84C2×D4—22no—
85C2×D4—21no—
86C2×D4—2632no—
87C2×D4—5262no—
88C22×C4—5262no—
89SD16—44no—
90D8—10524no—
91C2×C8—21no—
92C2×C8—5262no—
93C4⋊C4—22no—
94C4⋊C4—2632no—
95C22⋊C4—5264no—
96C22⋊C4—5262no—
97C42—5262no—
98C42C22×D26311yescharacteristic
99C23—41no—
100C23—5262no—
101Q8—42no—
102D4—42no—
103D4—42no—
104D4—42no—
105D4—5262no—
106D4—5262no—
107D4—21042no—
108C2×C4—22no—
109C2×C4—5262no—
110C2×C4—10522no—
111C2×C4—10522no—
112C2×C4D4×D26312yes—
113C2×C4C2×C22⋊D26311yescharacteristic
114C8—22no—
115C8—10522no—
116C22—82no—
117C22—81no—
118C22—10522no—
119C22—10522no—
120C22—10522no—
121C22#2255443811yescharacteristic
122C4—21no—
123C4—42no—
124C4—10522no—
125C4#2255449112yes—
126C4#2255449712yes—
127C2—161no—
128C2—21042no—
129C2#3068208212yes—
130C2#3068210511yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#492×C263C2
socleC22×C263#120
hypercenter#492D263
hypocenterC263#1624
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #30682654C2semidirect
2. #30682130C2semidirect
3. #30681687C2semidirect
4. #30681667C2semidirect
5. #492×C263C2semidirect
65. C263#1624semidirect
68. #492D263semidirect

Maximal subgroups

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

subgroupindex
#306826542
#306821302
#306816872
#306816672
#492×C2632
#1624263