Finite Group Databasebeta

← #94572

Subgroups — #94572

Order 512.

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

normal subgroups only

This group has 161 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#9819C211yesmaximal, characteristic
2#7371C211yesmaximal, characteristic
3#7371C211yesmaximal, characteristic
4C2×#498C411yescharacteristic
5#1990—21no—
6#1956—21no—
7#1844C2211yescharacteristic
8C2×C82C411yescharacteristic
9#1325—21no—
10#1325—21no—
11C2×C4⋊Q8—21no—
12#498—21no—
13#498—41no—
14#498C812yescomplemented
15C2×#106—41no—
16C2×#106—41no—
17C2×#103—42no—
18C2×C4×C8—21no—
19C2×C4×C8C2×C411yescharacteristic
20#384D411yescharacteristic
21#384D411yescharacteristic
22#340—42no—
23#324—41no—
24#324—41no—
25C82—41no—
26C22×Q8—41no—
27C22×C8—21no—
28C22×C8—22no—
29C4⋊Q8—22no—
30C4⋊Q8—41no—
31C4⋊Q8—41no—
32C4⋊Q8—41no—
33C2×C4⋊C4—21no—
34C2×C4⋊C4—21no—
35C2×C4⋊C4—41no—
36C2×C4⋊C4—41no—
37C2×C4⋊C4—41no—
38C2×C4⋊C4—41no—
39C2×C42C22⋊C411yescharacteristic
40#106—42no—
41#106—42no—
42#106—82no—
43#103—84no—
44C22⋊C8—81no—
45C22⋊C8—81no—
46C4×C8—21no—
47C4×C8—41no—
48C4×C8—41no—
49C4×C8C2×C811yescharacteristic
50C4×C8M1611yescharacteristic
51C2×Q8—42no—
52C2×Q8—81no—
53C2×Q8—82no—
54C2×Q8—82no—
55C22×C4—21no—
56C22×C4—41no—
57C22×C4—41no—
58C22×C4—81no—
59C22×C4#9911yescharacteristic
60C2×C8—22no—
61C2×C8—22no—
62C2×C8—21no—
63C2×C8—21no—
64C2×C8—24no—
65C2×C8—42no—
66C2×C8—42no—
67C2×C8—161no—
68C2×C8—161no—
69C4⋊C4—42no—
70C4⋊C4—42no—
71C4⋊C4—81no—
72C4⋊C4—81no—
73C4⋊C4—81no—
74C4⋊C4—82no—
75C4⋊C4—82no—
76C4⋊C4—81no—
77C42—21no—
78C42C22⋊C811yescharacteristic
79C42#10011yescharacteristic
80C23#35311yescharacteristic
81Q8—84no—
82Q8—162no—
83C2×C4—22no—
84C2×C4—22no—
85C2×C4—21no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—82no—
90C2×C4—81no—
91C2×C4—81no—
92C2×C4—161no—
93C2×C4—161no—
94C2×C4—161no—
95C2×C4—161no—
96C2×C4#32311yescharacteristic
97C2×C4#35511yescharacteristic
98C8—22no—
99C8—22no—
100C8—44no—
101C8—321no—
102C8—321no—
103C22—21no—
104C22—21no—
105C22#131811yescharacteristic
106C22#140911yescharacteristic
107C22#141111yescharacteristic
108C4—22no—
109C4—22no—
110C4—21no—
111C4—21no—
112C4—162no—
113C4—161no—
114C4—161no—
115C2—21no—
116C2—21no—
117C2#735511yescharacteristic
118C2#753511yescharacteristic
119C2#753611yescharacteristic
subgroupG/H
center, socleC22#1409
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
14. #498C8semidirect

Maximal subgroups

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

subgroupindex
#98192
#73712