Finite Group Databasebeta

← #46780909

Subgroups — #46780909

Order 33664.

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

normal subgroups only

This group has 120 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#30682314C211yesmaximal, characteristic
2#30681731C211yesmaximal, characteristic, complemented
3#353×C263C211yesmaximal, characteristic, complemented
4C2×#16862361—21no—
5C2×#16862361—21no—
6#22554467C411yescharacteristic, complemented
7#22554385—21no—
8C4×C263⋊C8C411yescharacteristic, complemented
9#127×C263C2211yescharacteristic
10#99×C263—21no—
11C2×D1052—21no—
12C2×D1052—41no—
13#16862361—42no—
14#16862361—42no—
15C2×C263⋊C8—21no—
16C22⋊Dic263—41no—
17C2×D4×C263—41no—
18C2×D4×C263D411yescharacteristic
19C2×D4×C263D411yescharacteristic
20C22⋊C4×C263—41no—
21C42×C263C2×C411yescharacteristic
22C22×D263—41no—
23D1052—41no—
24D1052—41no—
25D1052—82no—
26C2×Dic263—81no—
27C263⋊C8—22no—
28C23×C263—21no—
29C23×C263—21no—
30D4×C263—41no—
31D4×C263—41no—
32D4×C263—82no—
33C2×C4×C263—21no—
34C2×C4×C263—81no—
35C2×C4×C263C22⋊C411yescharacteristic
36C22×C263—41no—
37C22×C263—41no—
38C22×C263—81no—
39C22×C263—81no—
40C22×C263#9911yescharacteristic
41C2×D263—82no—
42C2×D263—81no—
43C4×C263—22no—
44C4×C263—21no—
45C4×C263—161no—
46Dic263—161no—
47C2×C263—21no—
48C2×C263—81no—
49C2×C263—81no—
50C2×C263#35311yescharacteristic
51D263—161no—
52C263#140811yescharacteristic, complemented, Sylow
53#1408—2631nomaximal, Sylow
54#493—2631no—
55#353—2631no—
56#353D26311yescharacteristic, complemented
57C2×D8—5261no—
58C2×D8—5261no—
59#127—2631no—
60#127C2×D26311yescharacteristic
61#99—21no—
62#99—5261no—
63C4×C8—2631no—
64C2×D4—41no—
65C2×D4—5261no—
66C2×D4—10521no—
67C2×D4C22⋊D26311yescharacteristic
68C2×D4D105211yescharacteristic
69D8—10522no—
70D8—10522no—
71C2×C8—5261no—
72C22⋊C4—41no—
73C22⋊C4—10521no—
74C42C4×D26311yescharacteristic
75C23—21no—
76C23—21no—
77C23—10521no—
78D4—41no—
79D4—41no—
80D4—82no—
81D4—10521no—
82D4—10521no—
83D4—21042no—
84C2×C4—21no—
85C2×C4—81no—
86C2×C4—21041no—
87C2×C4(C2×D263)⋊C411yescharacteristic
88C8—5262no—
89C22—41no—
90C22—41no—
91C22—81no—
92C22—81no—
93C22—21042no—
94C22—21041no—
95C22#2255438411yescharacteristic
96C4—22no—
97C4—21no—
98C4—161no—
99C4—42081no—
100C2—21no—
101C2—81no—
102C2—81no—
103C2—42081no—
104C2#3068173011yescharacteristic
subgroupG/H
centerC2#30681730
commutatorC42×C263C2×C4
Frattini#127C2×D263
Fitting#353×C263C2
socleC2×C263#353
prime radical#30682314C2
cosocle#127×C263C22
hypercenter#353D263
hypocenterC263#1408
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
2. #30681731C2semidirect
3. #353×C263C2semidirect
6. #22554467C4semidirect
8. C4×C263⋊C8C4semidirect
52. C263#1408semidirect
56. #353D263semidirect

Maximal subgroups

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

subgroupindex
#306823142
#306817312
#353×C2632
#1408263