Finite Group Databasebeta

← #93644

Subgroups — #93644

Order 512.

510 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 56 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#8299C211yesmaximal, characteristic
2#8299C212yesmaximal
3C23×C4⋊C4C2211yescharacteristic
4#1779—22no—
5#1779C412yes—
6C2×#324—22no—
7C2×#324—22no—
8C2×#324C414yes—
9C24×C4C2×C411yescharacteristic
10C24×C4D411yescharacteristic
11C24×C4Q811yescharacteristic
12C22×C4⋊C4—44no—
13C22×C4⋊C4—42no—
14C22×C4⋊C4C2×C412yes—
15C22×C4⋊C4D412yes—
16C2×C22⋊C8—22no—
17C2×C22⋊C8—24no—
18C2×C22⋊C8—44no—
19C2×C22⋊C8—42no—
20#324—44no—
21#324—44no—
22#324—44no—
23C25C4⋊C411yescharacteristic
24C23×C4—22no—
25C23×C4—24no—
26C23×C4—22no—
27C23×C4—24no—
28C23×C4—41no—
29C23×C4—42no—
30C23×C4—41no—
31C23×C4—42no—
32C23×C4—41no—
33C23×C4—82no—
34C23×C4—82no—
35C23×C4C4211yescharacteristic
36C23×C4C22⋊C412yes—
37C23×C4C22⋊C411yescharacteristic
38C23×C4C4⋊C412yes—
39C22×C8—44no—
40C22×C8—42no—
41C2×C4⋊C4—24no—
42C2×C4⋊C4—24no—
43C2×C4⋊C4—24no—
44C2×C4⋊C4—42no—
45C2×C4⋊C4—42no—
46C2×C4⋊C4—42no—
47C2×C4⋊C4—416no—
48C22⋊C8—44no—
49C22⋊C8—44no—
50C22⋊C8—44no—
51C22⋊C8—88no—
52C22⋊C8—84no—
53C24—21no—
54C24—22no—
55C24—21no—
56C24—22no—
57C24—42no—
58C24—42no—
59C24#9511yescharacteristic
60C24#10812yes—
61C22×C4—22no—
62C22×C4—22no—
63C22×C4—22no—
64C22×C4—22no—
65C22×C4—22no—
66C22×C4—22no—
67C22×C4—22no—
68C22×C4—22no—
69C22×C4—22no—
70C22×C4—21no—
71C22×C4—22no—
72C22×C4—44no—
73C22×C4—44no—
74C22×C4—48no—
75C22×C4—48no—
76C22×C4—44no—
77C22×C4—44no—
78C22×C4—44no—
79C22×C4—48no—
80C22×C4—44no—
81C22×C4—82no—
82C22×C4—84no—
83C22×C4—82no—
84C22×C4—81no—
85C22×C4—81no—
86C22×C4—82no—
87C22×C4—84no—
88C22×C4—82no—
89C22×C4—84no—
90C22×C4#9914yes—
91C22×C4#9912yes—
92C22×C4#10814yes—
93C2×C8—82no—
94C2×C8—84no—
95C2×C8—88no—
96C2×C8—84no—
97C4⋊C4—48no—
98C4⋊C4—48no—
99C23—22no—
100C23—24no—
101C23—22no—
102C23—24no—
103C23—22no—
104C23—24no—
105C23—41no—
106C23—41no—
107C23—44no—
108C23—41no—
109C23—42no—
110C23—41no—
111C23—42no—
112C23—44no—
113C23—48no—
114C23—42no—
115C23—41no—
116C23—41no—
117C23#33811yescharacteristic
118C23#34111yescharacteristic
119C23#34112yes—
120C23#34212yes—
121C23#34211yescharacteristic
122C2×C4—24no—
123C2×C4—24no—
124C2×C4—24no—
125C2×C4—24no—
126C2×C4—22no—
127C2×C4—44no—
128C2×C4—416no—
129C2×C4—42no—
130C2×C4—42no—
131C2×C4—42no—
132C2×C4—42no—
133C2×C4—42no—
134C2×C4—44no—
135C2×C4—42no—
136C2×C4—41no—
137C2×C4—82no—
138C2×C4—82no—
139C2×C4—88no—
140C2×C4—88no—
141C2×C4—82no—
142C8—164no—
143C8—162no—
144C22—21no—
145C22—22no—
146C22—21no—
147C22—22no—
148C22—24no—
149C22—28no—
150C22—41no—
151C22—41no—
152C22—42no—
153C22—42no—
154C22—44no—
155C22—44no—
156C22—44no—
157C22—42no—
158C22—42no—
159C22—42no—
160C22—42no—
161C22—42no—
162C22#129312yes—
163C22#129311yescharacteristic
164C22#129811yescharacteristic
165C22#129812yes—
166C22#130411yescharacteristic
167C4—44no—
168C4—44no—
169C4—42no—
170C4—81no—
171C2—21no—
172C2—22no—
173C2—22no—
174C2—21no—
175C2—44no—
176C2#704711yescharacteristic
177C2#731011yescharacteristic
178C2#731511yescharacteristic
subgroupG/H
center, socleC22#1304
commutatorC23×C4C42
Frattini, cosocleC23×C4⋊C4C22
prime radicalC25C4⋊C4
LCSG ▷ C23×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4⋊C4 ◁ G
LECSG ▷ C23×C4⋊C4 ▷ C24 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#82992