Finite Group Databasebeta

← #93240

Subgroups — #93240

Order 512.

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

normal subgroups only

This group has 184 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#10347C211yesmaximal, characteristic
2#7326C211yesmaximal, characteristic
3#7104C211yesmaximal, characteristic
4#2646C411yescharacteristic
5#1824—21no—
6#1463—21no—
7#1445C2211yescharacteristic
8#1294—21no—
9#1280—21no—
10#1280C411yescharacteristic
11C22×C4⋊C4D411yescharacteristic
12#407—41no—
13C2×C22⋊C8—21no—
14C2×C22⋊C8—41no—
15#400—41no—
16#398—41no—
17#385—41no—
18#380—21no—
19C2×#95—41no—
20C2×#95C2×C411yescharacteristic
21C2×#95D411yescharacteristic
22#340—41no—
23#340—41no—
24#324—22no—
25#324—41no—
26C23×C4—21no—
27C23×C4—21no—
28C23×C4—21no—
29C23×C4C22⋊C411yescharacteristic
30C2×M16—81no—
31C22×C8—41no—
32C22×C8—81no—
33C2×C4⋊C4—21no—
34C2×C4⋊C4—21no—
35C2×C4⋊C4—21no—
36C2×C4⋊C4—41no—
37C2×C4⋊C4—41no—
38C2×C4⋊C4—41no—
39C2×C4⋊C4—41no—
40C2×C4⋊C4SD1611yescharacteristic
41C2×C4⋊C4Q1611yescharacteristic
42C2×C22⋊C4—41no—
43C22⋊C8—42no—
44C22⋊C8—41no—
45C22⋊C8—42no—
46C22⋊C8—41no—
47C22⋊C8—81no—
48C22⋊C8—81no—
49#95—41no—
50#95—41no—
51#95—41no—
52#95—41no—
53#95—41no—
54#95—81no—
55#95—81no—
56C24#9911yescharacteristic
57C22×C4—21no—
58C22×C4—21no—
59C22×C4—21no—
60C22×C4—21no—
61C22×C4—21no—
62C22×C4—21no—
63C22×C4—41no—
64C22×C4—41no—
65C22×C4—41no—
66C22×C4—41no—
67C22×C4—41no—
68C22×C4—41no—
69C22×C4—41no—
70C22×C4—41no—
71C22×C4—41no—
72C22×C4—81no—
73C22×C4—81no—
74C22×C4—81no—
75C22×C4—81no—
76C22×C4—81no—
77C22×C4—81no—
78C22×C4—81no—
79C22×C4#10311yescharacteristic
80C22×C4#10411yescharacteristic
81M16—161no—
82M16—161no—
83C2×C8—81no—
84C2×C8—82no—
85C2×C8—82no—
86C2×C8—81no—
87C2×C8—81no—
88C2×C8—161no—
89C2×C8—161no—
90C4⋊C4—41no—
91C4⋊C4—41no—
92C4⋊C4—81no—
93C4⋊C4—81no—
94C4⋊C4—81no—
95C4⋊C4—161no—
96C4⋊C4—161no—
97C22⋊C4—81no—
98C22⋊C4—81no—
99C23—21no—
100C23—21no—
101C23—21no—
102C23—21no—
103C23—41no—
104C23#32811yescharacteristic
105C23AΣL(1,𝔽16)11yescharacteristic
106C23#35411yescharacteristic
107C2×C4—21no—
108C2×C4—21no—
109C2×C4—41no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—41no—
113C2×C4—41no—
114C2×C4—41no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—81no—
118C2×C4—81no—
119C2×C4—81no—
120C2×C4—81no—
121C2×C4—81no—
122C2×C4—81no—
123C2×C4—81no—
124C2×C4—81no—
125C2×C4—81no—
126C2×C4—81no—
127C2×C4—81no—
128C2×C4—81no—
129C2×C4—81no—
130C2×C4—81no—
131C2×C4—81no—
132C2×C4—82no—
133C2×C4—81no—
134C2×C4—81no—
135C2×C4—81no—
136C2×C4—161no—
137C2×C4—161no—
138C2×C4—161no—
139C8—161no—
140C8—162no—
141C8—162no—
142C22—21no—
143C22—21no—
144C22—21no—
145C22—21no—
146C22—21no—
147C22—21no—
148C22—21no—
149C22—41no—
150C22—41no—
151C22—41no—
152C22—41no—
153C22#135111yescharacteristic
154C22#140211yescharacteristic
155C22#140411yescharacteristic
156C22#141311yescharacteristic
157C22#141411yescharacteristic
158C4—41no—
159C4—41no—
160C4—81no—
161C4—81no—
162C4—81no—
163C4—81no—
164C4—161no—
165C4—161no—
166C4—161no—
167C2—21no—
168C2—21no—
169C2—21no—
170C2—21no—
171C2—41no—
172C2#742711yescharacteristic
173C2#742911yescharacteristic
174C2#743011yescharacteristic
subgroupG/H
center, socleC22#1351
commutatorC2×#95C2×C4
Frattini, cosocle#1445C22
prime radicalC24#99
LCSG ▷ C2×#95 ▷ C23×C4 ▷ C23 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ #1445 ◁ G
LECSG ▷ #1445 ▷ C23×C4 ▷ C23 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#103472
#73262
#71042