Finite Group Databasebeta

← #46780911

Subgroups — #46780911

Order 33664.

110 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 23 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#30681731C211yesmaximal, characteristic
3#353×C263C211yesmaximal, characteristic
4C2×#16862364—21no—
5C2×#16862364—21no—
6#22554470C411yescharacteristic, complemented
7#22554385—21no—
8C4×C263⋊C8C411yescharacteristic, complemented
9#127×C263C2211yescharacteristic
10#99×C263—21no—
11C2×Dic526—21no—
12#16862364—42no—
13#16862364—42no—
14C2×C263⋊C8—21no—
15C4⋊Dic263—41no—
16C22⋊Dic263—41no—
17C2×D4×C263—41no—
18C2×D4×C263D411yescharacteristic
19C2×D4×C263D411yescharacteristic
20C22⋊C4×C263—41no—
21C42×C263C2×C411yescharacteristic
22Dic526—41no—
23Dic526—41no—
24C2×Dic263—41no—
25C2×Dic263—81no—
26C263⋊C8—22no—
27C23×C263—21no—
28C23×C263—21no—
29D4×C263—41no—
30D4×C263—41no—
31D4×C263—82no—
32C2×C4×C263—21no—
33C2×C4×C263—81no—
34C2×C4×C263C22⋊C411yescharacteristic
35C22×C263—41no—
36C22×C263—41no—
37C22×C263—81no—
38C22×C263—81no—
39C22×C263#9911yescharacteristic
40C4×C263—22no—
41C4×C263—21no—
42C4×C263—161no—
43Dic263—81no—
44Dic263—161no—
45C2×C263—21no—
46C2×C263—81no—
47C2×C263—81no—
48C2×C263#35311yescharacteristic
49C263#140911yescharacteristic, complemented, Sylow
50#1409—2631nomaximal, Sylow
51#492—2631no—
52#353—2631no—
53#353D26311yescharacteristic
54C2×SD16—5261no—
55C2×SD16—5261no—
56C4⋊Q8—2631no—
57#127C2×D26311yescharacteristic
58#99—21no—
59#99—5261no—
60C4×C8—2631no—
61C2×Q8—5261no—
62C2×D4—41no—
63C2×D4C22⋊D26311yescharacteristic
64C2×D4D105211yescharacteristic
65SD16—10522no—
66SD16—10522no—
67C2×C8—5261no—
68C4⋊C4—10521no—
69C22⋊C4—41no—
70C22⋊C4—10521no—
71C42C4×D26311yescharacteristic
72C23—21no—
73C23—21no—
74Q8—10521no—
75Q8—10521no—
76D4—41no—
77D4—41no—
78D4—82no—
79C2×C4—21no—
80C2×C4—81no—
81C2×C4—10521no—
82C2×C4—21041no—
83C2×C4(C2×D263)⋊C411yescharacteristic
84C8—5262no—
85C22—41no—
86C22—41no—
87C22—81no—
88C22—81no—
89C22#2255438411yescharacteristic
90C4—22no—
91C4—21no—
92C4—161no—
93C4—21041no—
94C4—42081no—
95C2—21no—
96C2—81no—
97C2—81no—
98C2#3068173011yescharacteristic
subgroupG/H
centerC2#30681730
commutatorC42×C263C2×C4
Frattini#127C2×D263
Fitting#353×C263C2
socleC2×C263#353
prime radical, cosocle#127×C263C22
hypercenter#353D263
hypocenterC263#1409
LCSG ▷ C42×C263 ▷ C2×C4×C263 ▷ C22×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #353

Complements

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

NH ≅ G/Ntype
6. #22554470C4semidirect
8. C4×C263⋊C8C4semidirect
49. C263#1409semidirect

Maximal subgroups

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

subgroupindex
#306823102
#306817312
#353×C2632
#1409263