Finite Group Databasebeta

← #93133

Subgroups — #93133

Order 512.

469 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 469 conjugacy classes of subgroups — too many to draw. Only its 46 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#11381C211yesmaximal, characteristic
2#8550C212yesmaximal
3C22×C22⋊Q8C2211yescharacteristic
4#1784—22no—
5C2×#342—22no—
6#1463C414yescomplemented
7#1462—22no—
8C22⋊#95C412yes—
9C23×Q8D411yescharacteristic
10C24×C4C2×C411yescharacteristic
11C2×C22⋊Q8—42no—
12C2×C22⋊Q8—44no—
13C22×C4⋊C4C2×C412yes—
14C22×C4⋊C4Q811yescharacteristic
15C22×C22⋊C4—22no—
16C22×C22⋊C4D412yes—
17C2×#101—44no—
18#407—24no—
19C2×#95—42no—
20#342—44no—
21#324—44no—
22#323—44no—
23C25C22⋊C411yescharacteristic
24C22×Q8—24no—
25C22×Q8—41no—
26C22×Q8—82no—
27C23×C4—22no—
28C23×C4—42no—
29C23×C4—42no—
30C23×C4—82no—
31C23×C4C4211yescharacteristic
32C23×C4C22⋊C412yes—
33C23×C4C4⋊C411yescharacteristic
34C23×C4C4⋊C412yes—
35C2×M16—44no—
36C22⋊Q8—416no—
37C2×C4⋊C4—24no—
38C2×C4⋊C4—42no—
39C2×C4⋊C4—42no—
40C2×C4⋊C4—41no—
41C2×C4⋊C4—42no—
42C2×C22⋊C4—24no—
43C2×C22⋊C4—24no—
44C2×C22⋊C4—24no—
45C2×C22⋊C4—42no—
46C2×C22⋊C4—44no—
47C2×C22⋊C4—44no—
48C2×C22⋊C4—42no—
49#101—88no—
50C22⋊C8—44no—
51C22⋊C8—44no—
52#95—84no—
53C24—22no—
54C24—22no—
55C24—22no—
56C24—81no—
57C24—81no—
58C24#9511yescharacteristic
59C24#9912yes—
60C2×Q8—44no—
61C2×Q8—48no—
62C2×Q8—82no—
63C2×Q8—84no—
64C2×Q8—82no—
65C22×C4—22no—
66C22×C4—21no—
67C22×C4—22no—
68C22×C4—22no—
69C22×C4—22no—
70C22×C4—21no—
71C22×C4—22no—
72C22×C4—22no—
73C22×C4—22no—
74C22×C4—42no—
75C22×C4—44no—
76C22×C4—44no—
77C22×C4—44no—
78C22×C4—84no—
79C22×C4—82no—
80C22×C4—82no—
81C22×C4—81no—
82C22×C4—82no—
83C22×C4—84no—
84C22×C4—82no—
85C22×C4—84no—
86C22×C4—84no—
87C22×C4—82no—
88C22×C4#9914yes—
89M16—88no—
90C2×C8—84no—
91C4⋊C4—48no—
92C4⋊C4—44no—
93C22⋊C4—48no—
94C22⋊C4—48no—
95C22⋊C4—84no—
96C23—24no—
97C23—22no—
98C23—22no—
99C23—22no—
100C23—22no—
101C23—22no—
102C23—41no—
103C23—41no—
104C23—42no—
105C23—42no—
106C23—82no—
107C23—82no—
108C23—84no—
109C23—84no—
110C23#34212yes—
111C23#34211yescharacteristic
112C23#35512yes—
113C23#35612yes—
114Q8—88no—
115C2×C4—22no—
116C2×C4—24no—
117C2×C4—24no—
118C2×C4—44no—
119C2×C4—41no—
120C2×C4—42no—
121C2×C4—41no—
122C2×C4—44no—
123C2×C4—42no—
124C2×C4—44no—
125C2×C4—42no—
126C2×C4—41no—
127C2×C4—82no—
128C2×C4—88no—
129C2×C4—82no—
130C2×C4—82no—
131C2×C4—82no—
132C2×C4—84no—
133C2×C4—88no—
134C2×C4—164no—
135C2×C4—162no—
136C2×C4—162no—
137C8—164no—
138C22—21no—
139C22—21no—
140C22—22no—
141C22—22no—
142C22—22no—
143C22—22no—
144C22—22no—
145C22—42no—
146C22—42no—
147C22—44no—
148C22—44no—
149C22—42no—
150C22—42no—
151C22—82no—
152C22—84no—
153C22—82no—
154C22#130411yescharacteristic
155C22#139412yes—
156C4—44no—
157C4—42no—
158C4—81no—
159C4—82no—
160C4—164no—
161C2—22no—
162C2—42no—
163C2—42no—
164C2—42no—
165C2#730811yescharacteristic
166C2#731011yescharacteristic
167C2#731911yescharacteristic
subgroupG/H
center, socleC22#1304
commutatorC23×C4C42
Frattini, cosocleC22×C22⋊Q8C22
prime radicalC25C22⋊C4
LCSG ▷ C23×C4 ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊Q8 ◁ G
LECSG ▷ C22×C22⋊Q8 ▷ C24 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
6. #1463C4semidirect

Maximal subgroups

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

subgroupindex
#113812
#85502