Finite Group Databasebeta

← #93248

Subgroups — #93248

Order 512.

123 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 123 conjugacy classes of subgroups — too many to draw. Only its 26 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#10663C211yesmaximal, characteristic
2#7286C211yesmaximal, characteristic
3#7061C211yesmaximal, characteristic
4#1985C2211yescharacteristic
5#1849C411yescharacteristic
6#1570—21no—
7#1487—21no—
8#1461—21no—
9#1322—21no—
10#1275C411yescharacteristic
11C2×C4×Q8D411yescharacteristic
12#431—21no—
13#431—41no—
14C2×#108—41no—
15#423—21no—
16C2×C4⋊C8D411yescharacteristic
17C2×#97C2×C411yescharacteristic
18C22⋊C16—41no—
19#336—41no—
20#334—42no—
21Q8⋊C8—42no—
22#324—22no—
23#324—41no—
24C22×Q8Q1611yescharacteristic
25C2×M16—41no—
26C22×C8—21no—
27C22×C8—21no—
28C4×Q8—41no—
29C4×Q8—41no—
30C2×C4⋊C4—21no—
31C2×C4⋊C4SD1611yescharacteristic
32C2×C42—21no—
33C2×C42C22⋊C411yescharacteristic
34C2×C16—81no—
35#108—82no—
36C4⋊C8—41no—
37C4⋊C8—41no—
38C4⋊C8—41no—
39C4⋊C8—41no—
40C4⋊C8—81no—
41C22⋊C8—41no—
42C22⋊C8—42no—
43#97—41no—
44C4×C8—22no—
45C4×C8—81no—
46C2×Q8—42no—
47C2×Q8—41no—
48C22×C4—21no—
49C22×C4—21no—
50C22×C4#9911yescharacteristic
51C22×C4#10311yescharacteristic
52C22×C4#10411yescharacteristic
53M16—82no—
54C2×C8—22no—
55C2×C8—41no—
56C2×C8—41no—
57C2×C8—42no—
58C2×C8—41no—
59C2×C8—81no—
60C2×C8—82no—
61C2×C8—81no—
62C4⋊C4—41no—
63C4⋊C4—81no—
64C42—21no—
65C42—21no—
66C42—41no—
67C42—41no—
68C16—161no—
69C23#32811yescharacteristic
70Q8—42no—
71Q8—81no—
72C2×C4—21no—
73C2×C4—21no—
74C2×C4—22no—
75C2×C4—21no—
76C2×C4—21no—
77C2×C4—41no—
78C2×C4—41no—
79C2×C4—41no—
80C2×C4—41no—
81C2×C4—41no—
82C2×C4—81no—
83C2×C4#35211yescharacteristic
84C2×C4#35311yescharacteristic
85C8—42no—
86C8—82no—
87C8—81no—
88C8—162no—
89C8—161no—
90C22—21no—
91C22—21no—
92C22—21no—
93C22#135211yescharacteristic
94C4—21no—
95C4—42no—
96C4—41no—
97C4—41no—
98C4—81no—
99C4#140711yescharacteristic
100C4#141011yescharacteristic
101C2—41no—
102C2#743311yescharacteristic
103C2#743711yescharacteristic
104C2#743811yescharacteristic
subgroupG/H
centerC2×C4#353
commutatorC2×#97C2×C4
Frattini, cosocle#1985C22
socleC22#1352
prime radicalC23#328
LCSG ▷ C2×#97 ▷ C2×C42 ▷ C23 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #1985 ◁ G
LECSG ▷ #1985 ▷ C2×C42 ▷ C23 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#106632
#72862
#70612