Finite Group Databasebeta

← #93108

Subgroups — #93108

Order 512.

406 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 42 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#8550C212yesmaximal
2#8308C211yesmaximal, characteristic
3C22×C22⋊Q8C2211yescharacteristic
4#1784—22no—
5#1779C412yes—
6#1463—22no—
7#1462C414yes—
8C2×#324—22no—
9C23×Q8D411yescharacteristic
10C24×C4C2×C411yescharacteristic
11C2×C22⋊Q8—44no—
12C2×C22⋊Q8—42no—
13C22×C4⋊C4D412yes—
14C22×C4⋊C4Q811yescharacteristic
15C22×C22⋊C4C2×C412yes—
16C2×#101—44no—
17#407—24no—
18C2×C22⋊C8—22no—
19C2×C22⋊C8—42no—
20#324—44no—
21#324—44no—
22#323—44no—
23C25C4211yescharacteristic
24C22×Q8—24no—
25C22×Q8—41no—
26C22×Q8—82no—
27C23×C4—22no—
28C23×C4—42no—
29C23×C4—82no—
30C23×C4C22⋊C412yes—
31C23×C4C22⋊C411yescharacteristic
32C23×C4C4⋊C412yes—
33C23×C4C4⋊C411yescharacteristic
34C2×M16—44no—
35C22×C8—42no—
36C22⋊Q8—416no—
37C2×C4⋊C4—24no—
38C2×C4⋊C4—24no—
39C2×C4⋊C4—42no—
40C2×C4⋊C4—41no—
41C2×C4⋊C4—42no—
42C2×C22⋊C4—24no—
43C2×C22⋊C4—42no—
44C2×C22⋊C4—42no—
45#101—88no—
46C22⋊C8—44no—
47C22⋊C8—44no—
48C22⋊C8—44no—
49C22⋊C8—84no—
50C24—21no—
51C24—22no—
52C24—42no—
53C24—42no—
54C24—81no—
55C24#9511yescharacteristic
56C2×Q8—44no—
57C2×Q8—48no—
58C2×Q8—82no—
59C2×Q8—84no—
60C2×Q8—82no—
61C22×C4—22no—
62C22×C4—21no—
63C22×C4—22no—
64C22×C4—22no—
65C22×C4—22no—
66C22×C4—22no—
67C22×C4—22no—
68C22×C4—22no—
69C22×C4—42no—
70C22×C4—44no—
71C22×C4—44no—
72C22×C4—44no—
73C22×C4—84no—
74C22×C4—82no—
75C22×C4—82no—
76C22×C4—81no—
77C22×C4—84no—
78C22×C4#9914yes—
79C22×C4#9912yes—
80M16—88no—
81C2×C8—82no—
82C2×C8—84no—
83C2×C8—84no—
84C4⋊C4—48no—
85C4⋊C4—44no—
86C22⋊C4—48no—
87C23—22no—
88C23—22no—
89C23—24no—
90C23—41no—
91C23—41no—
92C23—42no—
93C23—41no—
94C23—42no—
95C23—41no—
96C23—42no—
97C23—82no—
98C23—82no—
99C23—88no—
100C23#34212yes—
101C23#34211yescharacteristic
102Q8—88no—
103C2×C4—22no—
104C2×C4—24no—
105C2×C4—24no—
106C2×C4—22no—
107C2×C4—44no—
108C2×C4—41no—
109C2×C4—42no—
110C2×C4—41no—
111C2×C4—42no—
112C2×C4—44no—
113C2×C4—44no—
114C2×C4—42no—
115C2×C4—44no—
116C2×C4—82no—
117C2×C4—82no—
118C2×C4—88no—
119C2×C4—82no—
120C8—162no—
121C8—164no—
122C22—21no—
123C22—21no—
124C22—22no—
125C22—22no—
126C22—22no—
127C22—44no—
128C22—44no—
129C22—42no—
130C22—82no—
131C22—84no—
132C22—84no—
133C22—81no—
134C22—81no—
135C22#130411yescharacteristic
136C22#139212yes—
137C4—44no—
138C4—42no—
139C4—42no—
140C4—82no—
141C2—22no—
142C2—42no—
143C2—82no—
144C2#730611yescharacteristic
145C2#731011yescharacteristic
146C2#731711yescharacteristic
subgroupG/H
center, socleC22#1304
commutator, prime radicalC25C42
Frattini, cosocleC22×C22⋊Q8C22
LCSG ▷ C25 ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊Q8 ◁ G
LECSG ▷ C22×C22⋊Q8 ▷ C24 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#85502
#83082