Finite Group Databasebeta

← #93817

Subgroups — #93817

Order 512.

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

normal subgroups only

This group has 125 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#13441C211yesmaximal, characteristic
2#7365C211yesmaximal, characteristic
3#7239C211yesmaximal, characteristic
4C22×Q32C411yescharacteristic
5#2166—21no—
6#2151C2211yescharacteristic
7C2×#362—21no—
8#1979—21no—
9#1400—21no—
10#1381C411yescharacteristic
11C22×Q16—21no—
12C2×Q32—41no—
13C2×Q32—42no—
14C2×M32D411yescharacteristic
15C22×C16C2×C411yescharacteristic
16C2×#108—21no—
17#419—41no—
18C2×#101—41no—
19#405D411yescharacteristic
20M64—41no—
21#364—41no—
22C4⋊C16—41no—
23#362—42no—
24#349—41no—
25#347—22no—
26C22×Q8—41no—
27C2×Q16—22no—
28C2×Q16—41no—
29C2×Q16—41no—
30C2×Q16—41no—
31C2×Q16—41no—
32C2×Q16—41no—
33C2×M16—41no—
34C2×M16D811yescharacteristic
35C22×C8C22⋊C411yescharacteristic
36#117SD1611yescharacteristic
37Q32—42no—
38Q32—42no—
39M32—41no—
40M32—42no—
41C2×C16—21no—
42C2×C16—21no—
43C2×C16—41no—
44#108—41no—
45#108—41no—
46#103—82no—
47#101—82no—
48#97—21no—
49C4×C8—21no—
50C32—81no—
51C2×Q8—42no—
52C2×Q8—81no—
53C2×Q8—81no—
54C2×Q8—81no—
55C2×Q8—81no—
56C2×Q8—81no—
57C22×C4—81no—
58C22×C4#10211yescharacteristic
59Q16—42no—
60Q16—42no—
61Q16—81no—
62Q16—81no—
63M16—41no—
64M16—81no—
65M16—81no—
66C2×C8—21no—
67C2×C8—21no—
68C2×C8—21no—
69C2×C8—81no—
70C2×C8#9911yescharacteristic
71C2×C8#10411yescharacteristic
72C4⋊C4—21no—
73C22⋊C4—21no—
74C42—21no—
75C16—41no—
76C16—41no—
77C16—82no—
78C23#35911yescharacteristic
79Q8—82no—
80Q8—82no—
81Q8—161no—
82Q8—161no—
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—41no—
86C2×C4—82no—
87C2×C4—161no—
88C2×C4—161no—
89C2×C4#32711yescharacteristic
90C2×C4#36111yescharacteristic
91C8—21no—
92C8—41no—
93C8—161no—
94C8AΣL(1,𝔽16)11yescharacteristic
95C8#35511yescharacteristic
96C22—21no—
97C22—41no—
98C22#134911yescharacteristic
99C4—21no—
100C4—81no—
101C4—162no—
102C4#133911yescharacteristic
103C4#134511yescharacteristic
104C2—21no—
105C2—41no—
106C2#708011yescharacteristic
subgroupG/H
center, socleC2#7080
commutatorC22×C16C2×C4
Frattini, cosocle#2151C22
prime radicalC23#359
LCSG ▷ C22×C16 ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C8 ◁ #2151 ◁ G
LECSG ▷ #2151 ▷ 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
#134412
#73652
#72392