Finite Group Databasebeta

← #94586

Subgroups — #94586

Order 512.

139 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 139 conjugacy classes of subgroups — too many to draw. Only its 28 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#8820C211yesmaximal, characteristic
2#7371C211yesmaximal, characteristic
3#7371C211yesmaximal, characteristic
4#1845—21no—
5#1845C411yescharacteristic
6#1844C2211yescharacteristic
7#1834—21no—
8C2×#322C411yescharacteristic
9#1325—21no—
10#1325—21no—
11C2×#107—42no—
12C2×#107—41no—
13C2×#106—41no—
14C2×C4×C8—21no—
15C2×C4×C8C2×C411yescharacteristic
16#384—21no—
17#384D411yescharacteristic
18#384D411yescharacteristic
19#340—42no—
20#324—41no—
21#324—41no—
22#322—21no—
23#322C812yescomplemented
24C22×C8—21no—
25C22×C8—22no—
26C2×C4⋊C4—21no—
27C2×C4⋊C4—21no—
28C2×C4⋊C4—41no—
29C2×C4⋊C4—41no—
30C2×C4⋊C4—41no—
31C2×C4⋊C4—41no—
32C2×C4⋊C4—41no—
33C2×C42C22⋊C411yescharacteristic
34#107—82no—
35#107—84no—
36#106—82no—
37C22⋊C8—81no—
38C22⋊C8—81no—
39C4×C8—22no—
40C4×C8—22no—
41C4×C8—21no—
42C4×C8C2×C811yescharacteristic
43C4×C8M1611yescharacteristic
44C22×C4—21no—
45C22×C4—41no—
46C22×C4—41no—
47C22×C4—81no—
48C22×C4#9911yescharacteristic
49C2×C8—22no—
50C2×C8—22no—
51C2×C8—21no—
52C2×C8—21no—
53C2×C8—24no—
54C2×C8—42no—
55C2×C8—42no—
56C2×C8—161no—
57C2×C8—161no—
58C4⋊C4—81no—
59C4⋊C4—81no—
60C4⋊C4—82no—
61C4⋊C4—82no—
62C4⋊C4—82no—
63C4⋊C4—82no—
64C4⋊C4—82no—
65C42—21no—
66C42C22⋊C811yescharacteristic
67C42#10111yescharacteristic
68C23#35311yescharacteristic
69C2×C4—22no—
70C2×C4—22no—
71C2×C4—21no—
72C2×C4—21no—
73C2×C4—21no—
74C2×C4—21no—
75C2×C4—81no—
76C2×C4—81no—
77C2×C4—161no—
78C2×C4—161no—
79C2×C4—161no—
80C2×C4—161no—
81C2×C4—161no—
82C2×C4#32411yescharacteristic
83C2×C4#35611yescharacteristic
84C8—22no—
85C8—22no—
86C8—44no—
87C8—321no—
88C8—321no—
89C22—21no—
90C22—21no—
91C22#132511yescharacteristic
92C22#140811yescharacteristic
93C22#141111yescharacteristic
94C4—22no—
95C4—22no—
96C4—21no—
97C4—21no—
98C4—161no—
99C4—161no—
100C4—321no—
101C2—21no—
102C2—21no—
103C2#737011yescharacteristic
104C2#752711yescharacteristic
105C2#752811yescharacteristic
subgroupG/H
center, socleC22#1408
commutatorC4×C8C2×C8
Frattini, cosocle#1844C22
prime radicalC23#353
LCSG ▷ C4×C8 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #1844 ◁ G
LECSG ▷ #1844 ▷ C2×C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
23. #322C8semidirect

Maximal subgroups

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

subgroupindex
#88202
#73712