Finite Group Databasebeta

← #93857

Subgroups — #93857

Order 512.

114 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 32 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#13514C211yesmaximal, characteristic
2#7362C211yesmaximal, characteristic
3#7242C211yesmaximal, characteristic
4C2×#366C411yescharacteristic
5C2×C4⋊C16C2211yescharacteristic
6#1942—21no—
7#1568—21no—
8C22⋊C32—21no—
9#1380—21no—
10#1380C411yescharacteristic
11C22×C16C2×C411yescharacteristic
12C22×C16D411yescharacteristic
13#432—41no—
14C2×#107—21no—
15C2×#107—21no—
16C2×C4×C8D411yescharacteristic
17#389—41no—
18C2×C32—41no—
19#366—41no—
20C4⋊C16—41no—
21#340—41no—
22#335—41no—
23#334—22no—
24C22×C8C22⋊C411yescharacteristic
25C22×C8SD1611yescharacteristic
26C2×C4⋊C4—41no—
27C2×C4⋊C4—41no—
28C2×C4⋊C4—81no—
29C2×C42D811yescharacteristic
30C2×C16—21no—
31C2×C16—21no—
32C2×C16—41no—
33C2×C16—41no—
34#107—22no—
35#107—41no—
36#107—41no—
37#107—41no—
38C4⋊C8—42no—
39C22⋊C8—81no—
40#97—81no—
41C4×C8—21no—
42C4×C8—21no—
43#95—81no—
44C32—81no—
45C22×C4—81no—
46C22×C4—81no—
47C22×C4#10211yescharacteristic
48C22×C4D1611yescharacteristic
49C22×C4SD3211yescharacteristic
50C2×C8—21no—
51C2×C8—21no—
52C2×C8—21no—
53C2×C8—41no—
54C2×C8—82no—
55C2×C8#9911yescharacteristic
56C2×C8#10411yescharacteristic
57C4⋊C4—42no—
58C4⋊C4—81no—
59C4⋊C4—81no—
60C4⋊C4—81no—
61C4⋊C4—162no—
62C42—21no—
63C42—21no—
64C16—41no—
65C16—41no—
66C23#35711yescharacteristic
67C2×C4—21no—
68C2×C4—21no—
69C2×C4—21no—
70C2×C4—21no—
71C2×C4—21no—
72C2×C4—21no—
73C2×C4—41no—
74C2×C4—82no—
75C2×C4—161no—
76C2×C4—161no—
77C2×C4—161no—
78C2×C4—161no—
79C2×C4—161no—
80C2×C4#32711yescharacteristic
81C2×C4#36011yescharacteristic
82C8—21no—
83C8—41no—
84C8—162no—
85C8#35211yescharacteristic
86C8#35611yescharacteristic
87C22—21no—
88C22—21no—
89C22#134711yescharacteristic
90C22#141711yescharacteristic
91C22#141911yescharacteristic
92C4—21no—
93C4—41no—
94C4—41no—
95C4—162no—
96C4—321no—
97C4#134211yescharacteristic
98C4#134611yescharacteristic
99C2—21no—
100C2—21no—
101C2#709111yescharacteristic
102C2#742011yescharacteristic
103C2#742311yescharacteristic
subgroupG/H
center, socleC22#1347
commutatorC22×C16C2×C4
Frattini, cosocleC2×C4⋊C16C22
prime radicalC23#357
LCSG ▷ C22×C16 ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×C4⋊C16 ◁ G
LECSG ▷ C2×C4⋊C16 ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#135142
#73622
#72422