Finite Group Databasebeta

← #93809

Subgroups — #93809

Order 512.

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

normal subgroups only

This group has 134 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#13492C211yesmaximal, characteristic
2#7334C211yesmaximal, characteristic
3#7231C211yesmaximal, characteristic
4C2×#366C411yescharacteristic
5C2×C22⋊C16C2211yescharacteristic
6#1810—21no—
7#1808—21no—
8C22⋊C32—21no—
9#1380—21no—
10#1380C411yescharacteristic
11C23×C8D411yescharacteristic
12C22×C16C2×C411yescharacteristic
13C22×C16D411yescharacteristic
14C2×#108—41no—
15C2×#107—21no—
16C2×#107—21no—
17#407—41no—
18#380—41no—
19C2×C32—41no—
20#366—41no—
21C22⋊C16—41no—
22#341—22no—
23#340—41no—
24C23×C4D811yescharacteristic
25C2×M16—42no—
26C22×C8—21no—
27C22×C8—21no—
28C22×C8—41no—
29C22×C8—41no—
30C22×C8C22⋊C411yescharacteristic
31C22×C8SD1611yescharacteristic
32C2×C4⋊C4—41no—
33C2×C4⋊C4—41no—
34C2×C22⋊C4—81no—
35C2×C16—21no—
36C2×C16—21no—
37C2×C16—41no—
38C2×C16—41no—
39#108—81no—
40#108—81no—
41#107—41no—
42#107—41no—
43#107—41no—
44#107—41no—
45C22⋊C8—81no—
46C22⋊C8—81no—
47#95—81no—
48C32—81no—
49C24SD3211yescharacteristic
50C22×C4—21no—
51C22×C4—21no—
52C22×C4—41no—
53C22×C4—41no—
54C22×C4—81no—
55C22×C4—81no—
56C22×C4#10211yescharacteristic
57C22×C4D1611yescharacteristic
58M16—82no—
59M16—82no—
60C2×C8—21no—
61C2×C8—21no—
62C2×C8—21no—
63C2×C8—41no—
64C2×C8—41no—
65C2×C8—41no—
66C2×C8—81no—
67C2×C8—82no—
68C2×C8#9911yescharacteristic
69C2×C8#10411yescharacteristic
70C4⋊C4—81no—
71C4⋊C4—81no—
72C4⋊C4—81no—
73C4⋊C4—81no—
74C22⋊C4—162no—
75C16—41no—
76C16—41no—
77C23—21no—
78C23—21no—
79C23—21no—
80C23—41no—
81C23—41no—
82C23#35711yescharacteristic
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—41no—
87C2×C4—41no—
88C2×C4—41no—
89C2×C4—81no—
90C2×C4—161no—
91C2×C4—161no—
92C2×C4—161no—
93C2×C4—161no—
94C2×C4—161no—
95C2×C4—161no—
96C2×C4#32711yescharacteristic
97C2×C4#36011yescharacteristic
98C8—21no—
99C8—41no—
100C8—162no—
101C8#35211yescharacteristic
102C8#35411yescharacteristic
103C22—21no—
104C22—21no—
105C22—42no—
106C22—41no—
107C22—41no—
108C22—41no—
109C22—81no—
110C22#134711yescharacteristic
111C22#141711yescharacteristic
112C22#141911yescharacteristic
113C4—21no—
114C4—41no—
115C4—321no—
116C4—321no—
117C4#134011yescharacteristic
118C4#134411yescharacteristic
119C2—21no—
120C2—21no—
121C2—81no—
122C2#707911yescharacteristic
123C2#742011yescharacteristic
124C2#742511yescharacteristic
subgroupG/H
center, socleC22#1347
commutatorC22×C16C2×C4
Frattini, cosocleC2×C22⋊C16C22
prime radicalC24SD32
LCSG ▷ C22×C16 ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C8 ◁ C2×C22⋊C16 ◁ G
LECSG ▷ C2×C22⋊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
#134922
#73342
#72312