Finite Group Databasebeta

← #93243

Subgroups — #93243

Order 512.

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

normal subgroups only

This group has 135 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#10662C211yesmaximal, characteristic
2#7284C211yesmaximal, characteristic
3#7061C211yesmaximal, characteristic
4#1985C2211yescharacteristic
5#1849C411yescharacteristic
6C4×#101—21no—
7#1571—21no—
8#1487—21no—
9#1322—21no—
10#1275C411yescharacteristic
11C2×C4×Q8D411yescharacteristic
12#431—21no—
13C2×#108—41no—
14#423—21no—
15C2×C4⋊C8D411yescharacteristic
16C2×#101—41no—
17C4×M16—41no—
18C2×#97C2×C411yescharacteristic
19C22⋊C16—41no—
20#343—22no—
21#336—41no—
22#335—42no—
23Q8⋊C8—42no—
24C22×Q8SD1611yescharacteristic
25C2×M16—42no—
26C2×M16—41no—
27C22×C8—21no—
28C22×C8—21no—
29C4×Q8—41no—
30C4×Q8—41no—
31C2×C4⋊C4—21no—
32C2×C4⋊C4Q1611yescharacteristic
33C2×C42—21no—
34C2×C42C22⋊C411yescharacteristic
35C2×C16—81no—
36#108—82no—
37C4⋊C8—41no—
38C4⋊C8—41no—
39C4⋊C8—41no—
40C4⋊C8—41no—
41#101—44no—
42C22⋊C8—41no—
43#97—41no—
44#97—81no—
45C4×C8—22no—
46C4×C8—81no—
47C2×Q8—42no—
48C2×Q8—41no—
49C22×C4—21no—
50C22×C4—21no—
51C22×C4#9911yescharacteristic
52C22×C4#10311yescharacteristic
53C22×C4#10411yescharacteristic
54M16—44no—
55M16—82no—
56M16—82no—
57C2×C8—22no—
58C2×C8—41no—
59C2×C8—41no—
60C2×C8—42no—
61C2×C8—41no—
62C2×C8—82no—
63C2×C8—81no—
64C2×C8—81no—
65C4⋊C4—41no—
66C4⋊C4—81no—
67C42—21no—
68C42—21no—
69C42—41no—
70C42—41no—
71C16—161no—
72C23#32811yescharacteristic
73Q8—42no—
74Q8—81no—
75C2×C4—21no—
76C2×C4—21no—
77C2×C4—22no—
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—41no—
81C2×C4—41no—
82C2×C4—41no—
83C2×C4—41no—
84C2×C4—41no—
85C2×C4—81no—
86C2×C4#35211yescharacteristic
87C2×C4#35311yescharacteristic
88C8—42no—
89C8—82no—
90C8—84no—
91C8—81no—
92C8—161no—
93C22—21no—
94C22—21no—
95C22—21no—
96C22#135211yescharacteristic
97C4—21no—
98C4—42no—
99C4—41no—
100C4—41no—
101C4—81no—
102C4#140611yescharacteristic
103C4#141111yescharacteristic
104C2—41no—
105C2#743211yescharacteristic
106C2#743611yescharacteristic
107C2#743911yescharacteristic
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
#106622
#72842
#70612