Finite Group Databasebeta

← #93731

Subgroups — #93731

Order 512.

138 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 36 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#12913C211yesmaximal, characteristic
2#7334C211yesmaximal, characteristic
3#7334C211yesmaximal, characteristic
4C22×M32C411yescharacteristic
5C2×C4⋊C16—21no—
6C2×C22⋊C16C2211yescharacteristic
7C8×C22⋊C4C411yescharacteristic
8C22⋊C32—21no—
9C22⋊C32—21no—
10#1374—21no—
11C23×C8C2×C411yescharacteristic
12C2×M32—42no—
13C2×M32—41no—
14C22×C16—21no—
15C22×C16D411yescharacteristic
16C22×C16D411yescharacteristic
17C2×C22⋊C8C811yescharacteristic
18C2×C4×C8—21no—
19C4×C22⋊C4C811yescharacteristic
20C2×C32—41no—
21C2×C32—41no—
22C4⋊C16—42no—
23C22⋊C16—41no—
24#336—21no—
25C23×C4C2×C811yescharacteristic
26C22×C8—21no—
27C22×C8—21no—
28C22×C8—21no—
29C22×C8—41no—
30C22×C8—41no—
31C22×C8C22⋊C411yescharacteristic
32C22×C8M1611yescharacteristic
33C2×C22⋊C4—21no—
34C2×C42—21no—
35M32—42no—
36M32—42no—
37C2×C16—22no—
38C2×C16—21no—
39C2×C16—21no—
40C2×C16—41no—
41C2×C16—41no—
42C2×C16—41no—
43C2×C16—41no—
44C22⋊C8—41no—
45C4×C8—41no—
46C4×C8—41no—
47#95C1611yescharacteristic
48#95C1611yescharacteristic
49C32—81no—
50C32—81no—
51C24M3211yescharacteristic
52C22×C4—21no—
53C22×C4—21no—
54C22×C4—21no—
55C22×C4—21no—
56C22×C4—41no—
57C22×C4—41no—
58C22×C4C22⋊C811yescharacteristic
59C22×C4C2×C1611yescharacteristic
60C2×C8—21no—
61C2×C8—21no—
62C2×C8—21no—
63C2×C8—42no—
64C2×C8—41no—
65C2×C8—41no—
66C2×C8—41no—
67C2×C8—41no—
68C2×C8—41no—
69C2×C8—41no—
70C2×C8#9911yescharacteristic
71C2×C8#10111yescharacteristic
72C22⋊C4—42no—
73C42—41no—
74C42—41no—
75C16—41no—
76C16—42no—
77C16—41no—
78C23—21no—
79C23—21no—
80C23—21no—
81C23—41no—
82C23—41no—
83C23C22⋊C1611yescharacteristic
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—22no—
87C2×C4—21no—
88C2×C4—42no—
89C2×C4—41no—
90C2×C4—41no—
91C2×C4—41no—
92C2×C4—41no—
93C2×C4—41no—
94C2×C4—41no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4#32411yescharacteristic
98C2×C4#34911yescharacteristic
99C8—21no—
100C8—41no—
101C8—81no—
102C8AΣL(1,𝔽16)11yescharacteristic
103C8#35211yescharacteristic
104C22—21no—
105C22—21no—
106C22—41no—
107C22—41no—
108C22—41no—
109C22—81no—
110C22—81no—
111C22#132211yescharacteristic
112C22#140111yescharacteristic
113C22#140111yescharacteristic
114C4—21no—
115C4—42no—
116C4—41no—
117C4—81no—
118C4#132611yescharacteristic
119C4#132811yescharacteristic
120C2—21no—
121C2—21no—
122C2—81no—
123C2#706411yescharacteristic
124C2#736311yescharacteristic
125C2#736411yescharacteristic
subgroupG/H
centerC2×C8#99
commutatorC22×C4C2×C16
Frattini, cosocleC2×C22⋊C16C22
socleC22#1322
prime radicalC24M32
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C8 ◁ C22×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
#129132
#73342