Finite Group Databasebeta

← #93938

Subgroups — #93938

Order 512.

130 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 50 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#13168C211yesmaximal, characteristic
2#7466C211yesmaximal, characteristic
3#7161C211yesmaximal, characteristic
4C2×M64—21no—
5C2×#367C411yescharacteristic
6C2×#366C411yescharacteristic
7C2×#364—21no—
8C2×#346C2211yescharacteristic
9#1942—21no—
10#1380—21no—
11C2×M32—41no—
12C22×C16C2×C411yescharacteristic
13C22×C16D411yescharacteristic
14C2×#107—21no—
15C2×#107—21no—
16C2×C4×C8D411yescharacteristic
17#389—41no—
18M64—41no—
19M64—41no—
20C2×C32—22no—
21#367—41no—
22#366—21no—
23#366C812yes—
24#364—22no—
25#364—41no—
26#346—41no—
27#340—41no—
28C22×C8C22⋊C411yescharacteristic
29C22×C8D811yescharacteristic
30C2×C4⋊C4—41no—
31C2×C4⋊C4—41no—
32C2×C4⋊C4—81no—
33C2×C42SD1611yescharacteristic
34M32—42no—
35M32—81no—
36C2×C16—21no—
37C2×C16—21no—
38C2×C16—21no—
39C2×C16—21no—
40C2×C16—81no—
41C2×C16C2×C811yescharacteristic
42C2×C16M1611yescharacteristic
43C2×C16SD1611yescharacteristic
44C2×C16Q1611yescharacteristic
45#107—22no—
46#107—41no—
47#107—41no—
48#107—41no—
49C4×C8—21no—
50C4×C8—21no—
51#95—81no—
52C32—42no—
53C22×C4—21no—
54C22×C4—81no—
55C22×C4—81no—
56C22×C4#10211yescharacteristic
57C2×C8—21no—
58C2×C8—21no—
59C2×C8C22⋊C811yescharacteristic
60C2×C8#9911yescharacteristic
61C2×C8#10111yescharacteristic
62C2×C8#10311yescharacteristic
63C2×C8#10411yescharacteristic
64C2×C8#10411yescharacteristic
65C2×C8SD3211yescharacteristic
66C2×C8Q3211yescharacteristic
67C4⋊C4—42no—
68C4⋊C4—81no—
69C4⋊C4—81no—
70C4⋊C4—81no—
71C4⋊C4—162no—
72C42—21no—
73C42—21no—
74C16—21no—
75C16—21no—
76C16—21no—
77C16—21no—
78C16—82no—
79C23#36111yescharacteristic
80C2×C4—41no—
81C2×C4—41no—
82C2×C4—41no—
83C2×C4—82no—
84C2×C4—161no—
85C2×C4—161no—
86C2×C4—161no—
87C2×C4—161no—
88C2×C4—161no—
89C2×C4D4⋊C811yescharacteristic
90C2×C4#32711yescharacteristic
91C2×C4#33211yescharacteristic
92C2×C4#35811yescharacteristic
93C2×C4#35911yescharacteristic
94C2×C4#36011yescharacteristic
95C8—21no—
96C8—21no—
97C8#32411yescharacteristic
98C8Q8⋊C811yescharacteristic
99C8#32811yescharacteristic
100C8#33011yescharacteristic
101C22—21no—
102C22—21no—
103C22#133311yescharacteristic
104C22#134911yescharacteristic
105C22#136511yescharacteristic
106C4—81no—
107C4—162no—
108C4—321no—
109C4#127111yescharacteristic
110C4#133211yescharacteristic
111C4#134811yescharacteristic
112C4#136311yescharacteristic
113C2—21no—
114C2—21no—
115C2#712111yescharacteristic
116C2#739011yescharacteristic
117C2#739111yescharacteristic
subgroupG/H
center, socleC22#1333
commutatorC2×C16C2×C8
Frattini, cosocleC2×#346C22
prime radicalC23#361
LCSG ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#346 ◁ G
LECSG ▷ C2×#346 ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#131682
#74662
#71612