Finite Group Databasebeta

← #93118

Subgroups — #93118

Order 512.

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

normal subgroups only

This group has 299 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#8554C211yesmaximal, characteristic
2#8554C211yesmaximal, characteristic
3#8306C211yesmaximal, characteristic
4C22×#125C2211yescharacteristic
5#1821—21no—
6#1821—21no—
7#1817C412yes—
8#1463—21no—
9#1463—21no—
10#1463C412yes—
11#1463C412yes—
12C2×#324—21no—
13C2×#324—21no—
14C2×#125—42no—
15C2×#125—42no—
16C2×#125—42no—
17C22×C4⋊C4C2×C411yescharacteristic
18C22×C4⋊C4C2×C411yescharacteristic
19C22×C4⋊C4D411yescharacteristic
20C22×C4⋊C4D411yescharacteristic
21C22×C4⋊C4D411yescharacteristic
22C22×C4⋊C4Q811yescharacteristic
23C22×C42C2×C411yescharacteristic
24#407—22no—
25#407—22no—
26C2×C22⋊C8—22no—
27#343—42no—
28#343—42no—
29#336—42no—
30#324—42no—
31#324—42no—
32#324—42no—
33#324—42no—
34#324—42no—
35#324—42no—
36C23×C4C4211yescharacteristic
37C23×C4C22⋊C411yescharacteristic
38C23×C4C22⋊C411yescharacteristic
39C23×C4C22⋊C411yescharacteristic
40C23×C4C4⋊C411yescharacteristic
41C23×C4C4⋊C411yescharacteristic
42C23×C4C4⋊C411yescharacteristic
43C2×M16—42no—
44C2×M16—42no—
45C22×C8—42no—
46#125—416no—
47C2×C4⋊C4—22no—
48C2×C4⋊C4—22no—
49C2×C4⋊C4—22no—
50C2×C4⋊C4—22no—
51C2×C4⋊C4—22no—
52C2×C4⋊C4—22no—
53C2×C4⋊C4—22no—
54C2×C4⋊C4—22no—
55C2×C4⋊C4—41no—
56C2×C4⋊C4—41no—
57C2×C4⋊C4—41no—
58C2×C4⋊C4—41no—
59C2×C4⋊C4—41no—
60C2×C4⋊C4—41no—
61C2×C4⋊C4—41no—
62C2×C4⋊C4—41no—
63C2×C4⋊C4—41no—
64C2×C4⋊C4—41no—
65C2×C42—22no—
66C2×C42—41no—
67C2×C42—41no—
68C22⋊C8—42no—
69C22⋊C8—42no—
70C22⋊C8—42no—
71C22⋊C8—42no—
72C22⋊C8—42no—
73C22⋊C8—42no—
74C24#9511yescharacteristic
75C22×C4—21no—
76C22×C4—21no—
77C22×C4—21no—
78C22×C4—21no—
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—21no—
82C22×C4—21no—
83C22×C4—21no—
84C22×C4—21no—
85C22×C4—21no—
86C22×C4—21no—
87C22×C4—21no—
88C22×C4—21no—
89C22×C4—21no—
90C22×C4—21no—
91C22×C4—21no—
92C22×C4—21no—
93C22×C4—42no—
94C22×C4—42no—
95C22×C4—42no—
96C22×C4—42no—
97C22×C4—81no—
98C22×C4—81no—
99C22×C4—81no—
100C22×C4#9912yes—
101C22×C4#9912yes—
102C22×C4#9912yes—
103M16—84no—
104M16—84no—
105C2×C8—82no—
106C2×C8—82no—
107C2×C8—82no—
108C2×C8—84no—
109C4⋊C4—44no—
110C4⋊C4—44no—
111C4⋊C4—44no—
112C4⋊C4—44no—
113C4⋊C4—44no—
114C4⋊C4—44no—
115C42—44no—
116C23—22no—
117C23—41no—
118C23—41no—
119C23#34211yescharacteristic
120C23#34211yescharacteristic
121C23#34211yescharacteristic
122C2×C4—22no—
123C2×C4—22no—
124C2×C4—22no—
125C2×C4—22no—
126C2×C4—22no—
127C2×C4—22no—
128C2×C4—42no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—42no—
134C2×C4—42no—
135C2×C4—42no—
136C2×C4—42no—
137C2×C4—42no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—42no—
142C2×C4—42no—
143C2×C4—81no—
144C2×C4—81no—
145C2×C4—81no—
146C2×C4—81no—
147C2×C4—81no—
148C2×C4—81no—
149C2×C4—81no—
150C2×C4—81no—
151C2×C4—81no—
152C2×C4—81no—
153C8—162no—
154C8—162no—
155C8—162no—
156C22—21no—
157C22—21no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22—21no—
164C22—44no—
165C22#130411yescharacteristic
166C22#139512yes—
167C4—42no—
168C4—42no—
169C4—42no—
170C4—42no—
171C4—81no—
172C4—81no—
173C4—81no—
174C2—22no—
175C2—41no—
176C2—41no—
177C2#730911yescharacteristic
178C2#731311yescharacteristic
179C2#731711yescharacteristic
subgroupG/H
center, socleC22#1304
commutatorC23×C4C42
Frattini, cosocleC22×#125C22
prime radicalC24#95
LCSG ▷ C23×C4 ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C24 ◁ C22×#125 ◁ G
LECSG ▷ C22×#125 ▷ C24 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#85542
#83062