Finite Group Databasebeta

← #92832

Subgroups — #92832

Order 512.

279 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 279 conjugacy classes of subgroups — too many to draw. Only its 52 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#11373C211yesmaximal, characteristic
2#7184C212yesmaximal
3C2×#384C411yescharacteristic
4#2112—22no—
5C2×#340—22no—
6C2×#336C2211yescharacteristic
7C4⋊#95C411yescharacteristic
8C23×C8D412yes—
9C22×C4⋊C4—21no—
10C22×C4⋊C4—21no—
11C22×C4⋊C4—41no—
12C22×C42C2×C411yescharacteristic
13C2×M32—42no—
14#384—21no—
15#384—41no—
16#384C812yes—
17C2×#95—41no—
18C22⋊C16—24no—
19C22⋊C16—42no—
20#340—42no—
21#340—42no—
22#336—41no—
23C23×C4—21no—
24C23×C4—41no—
25C23×C4—41no—
26C23×C4C22⋊C411yescharacteristic
27C22×C8—22no—
28C22×C8—22no—
29C22×C8—42no—
30C22×C8—42no—
31C22×C8D812yes—
32C22×C8SD1612yes—
33C2×C4⋊C4—22no—
34C2×C4⋊C4—22no—
35C2×C4⋊C4—42no—
36C2×C4⋊C4—42no—
37C2×C4⋊C4—42no—
38C2×C4⋊C4—42no—
39C2×C4⋊C4—42no—
40C2×C4⋊C4—41no—
41C2×C4⋊C4—42no—
42C2×C4⋊C4—41no—
43C2×C4⋊C4—82no—
44C2×C4⋊C4—82no—
45C2×C42—21no—
46C2×C42—42no—
47C2×C42C2×C811yescharacteristic
48C2×C42M1611yescharacteristic
49M32—82no—
50M32—82no—
51C2×C16—44no—
52#95—82no—
53C24#10011yescharacteristic
54C22×C4—22no—
55C22×C4—21no—
56C22×C4—21no—
57C22×C4—22no—
58C22×C4—22no—
59C22×C4—21no—
60C22×C4—21no—
61C22×C4—42no—
62C22×C4—42no—
63C22×C4—42no—
64C22×C4—42no—
65C22×C4—82no—
66C22×C4—81no—
67C22×C4—82no—
68C22×C4—82no—
69C22×C4—82no—
70C22×C4—81no—
71C22×C4—81no—
72C22×C4—81no—
73C22×C4C22⋊C811yescharacteristic
74C22×C4#9911yescharacteristic
75C22×C4#10212yes—
76C22×C4#10412yes—
77C2×C8—22no—
78C2×C8—22no—
79C2×C8—42no—
80C2×C8—42no—
81C2×C8—42no—
82C2×C8—42no—
83C2×C8—82no—
84C4⋊C4—44no—
85C4⋊C4—44no—
86C4⋊C4—82no—
87C4⋊C4—84no—
88C4⋊C4—84no—
89C4⋊C4—82no—
90C42—41no—
91C42—41no—
92C42—42no—
93C16—84no—
94C23—21no—
95C23—21no—
96C23—22no—
97C23—21no—
98C23—21no—
99C23#32311yescharacteristic
100C23#32911yescharacteristic
101C23#33111yescharacteristic
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—22no—
109C2×C4—22no—
110C2×C4—44no—
111C2×C4—44no—
112C2×C4—41no—
113C2×C4—41no—
114C2×C4—41no—
115C2×C4—41no—
116C2×C4—82no—
117C2×C4—84no—
118C2×C4—84no—
119C2×C4—82no—
120C2×C4—162no—
121C2×C4—161no—
122C2×C4—162no—
123C2×C4—161no—
124C2×C4—161no—
125C2×C4—161no—
126C2×C4D4⋊C812yes—
127C2×C4#32712yes—
128C2×C4#35212yes—
129C2×C4#35411yescharacteristic
130C2×C4#35611yescharacteristic
131C8—42no—
132C8—42no—
133C22—22no—
134C22—22no—
135C22—22no—
136C22—22no—
137C22—21no—
138C22—21no—
139C22—21no—
140C22—21no—
141C22—21no—
142C22—21no—
143C22#127011yescharacteristic
144C22#131711yescharacteristic
145C22#131911yescharacteristic
146C22#135612yes—
147C22#135711yescharacteristic
148C22#135911yescharacteristic
149C4—22no—
150C4—42no—
151C4—42no—
152C4—162no—
153C4—162no—
154C4#134412yes—
155C4#134612yes—
156C2—21no—
157C2—21no—
158C2—21no—
159C2—22no—
160C2—21no—
161C2#710411yescharacteristic
162C2#710711yescharacteristic
163C2#711711yescharacteristic
subgroupG/H
center, socleC22#1270
commutatorC2×C42C2×C8
Frattini, cosocleC2×#336C22
prime radicalC24#100
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#336 ◁ G
LECSG ▷ C2×#336 ▷ C23×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#113732
#71842