Finite Group Databasebeta

← #93136

Subgroups — #93136

Order 512.

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

normal subgroups only

This group has 328 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#11383C211yesmaximal, characteristic
2#8554C211yesmaximal, characteristic
3#8554C211yesmaximal, characteristic
4C22×#125C2211yescharacteristic
5#1821—21no—
6#1821C412yes—
7C2×#343—21no—
8C2×#343—21no—
9#1728C412yes—
10#1463—21no—
11#1463—21no—
12#1463—21no—
13#1463C412yes—
14C22×M16—22no—
15C2×#125—42no—
16C2×#125—42no—
17C2×#125—42no—
18C22×C4⋊C4C2×C411yescharacteristic
19C22×C4⋊C4C2×C411yescharacteristic
20C22×C4⋊C4D411yescharacteristic
21C22×C4⋊C4D411yescharacteristic
22C22×C4⋊C4D411yescharacteristic
23C22×C4⋊C4Q811yescharacteristic
24C22×C42C2×C411yescharacteristic
25#407—22no—
26#407—22no—
27#343—42no—
28#343—42no—
29#343—42no—
30#343—42no—
31#336—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—24no—
44C2×M16—42no—
45C2×M16—42no—
46C2×M16—42no—
47C2×M16—42no—
48C2×M16—42no—
49C2×M16—42no—
50C2×M16—42no—
51C22×C8—42no—
52#125—416no—
53C2×C4⋊C4—22no—
54C2×C4⋊C4—22no—
55C2×C4⋊C4—22no—
56C2×C4⋊C4—22no—
57C2×C4⋊C4—22no—
58C2×C4⋊C4—22no—
59C2×C4⋊C4—22no—
60C2×C4⋊C4—22no—
61C2×C4⋊C4—41no—
62C2×C4⋊C4—41no—
63C2×C4⋊C4—41no—
64C2×C4⋊C4—41no—
65C2×C4⋊C4—41no—
66C2×C4⋊C4—41no—
67C2×C4⋊C4—41no—
68C2×C4⋊C4—41no—
69C2×C4⋊C4—41no—
70C2×C4⋊C4—41no—
71C2×C42—22no—
72C2×C42—41no—
73C2×C42—41no—
74C22⋊C8—42no—
75C22⋊C8—42no—
76C22⋊C8—42no—
77C22⋊C8—42no—
78C24#9511yescharacteristic
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—22no—
82C22×C4—22no—
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—21no—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4—21no—
99C22×C4—81no—
100C22×C4—81no—
101C22×C4—81no—
102C22×C4—81no—
103C22×C4—81no—
104C22×C4—81no—
105C22×C4#9912yes—
106C22×C4#9912yes—
107C22×C4#9912yes—
108M16—44no—
109M16—44no—
110M16—82no—
111M16—82no—
112M16—84no—
113M16—84no—
114C2×C8—44no—
115C2×C8—82no—
116C2×C8—82no—
117C2×C8—82no—
118C2×C8—82no—
119C4⋊C4—44no—
120C4⋊C4—44no—
121C4⋊C4—44no—
122C4⋊C4—44no—
123C4⋊C4—44no—
124C4⋊C4—44no—
125C42—44no—
126C23—22no—
127C23—41no—
128C23—41no—
129C23#34211yescharacteristic
130C23#34211yescharacteristic
131C23#34211yescharacteristic
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—22no—
141C2×C4—22no—
142C2×C4—42no—
143C2×C4—42no—
144C2×C4—42no—
145C2×C4—42no—
146C2×C4—42no—
147C2×C4—42no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—81no—
153C2×C4—81no—
154C2×C4—81no—
155C2×C4—81no—
156C2×C4—81no—
157C2×C4—81no—
158C2×C4—81no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—81no—
162C2×C4—81no—
163C2×C4—81no—
164C2×C4#35512yes—
165C2×C4#35612yes—
166C8—84no—
167C8—162no—
168C8—162no—
169C22—21no—
170C22—21no—
171C22—21no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—44no—
178C22#130411yescharacteristic
179C22#139412yes—
180C4—22no—
181C4—22no—
182C4—42no—
183C4—42no—
184C4—81no—
185C4—81no—
186C4—81no—
187C4—81no—
188C2—22no—
189C2—41no—
190C2—41no—
191C2#730811yescharacteristic
192C2#731211yescharacteristic
193C2#731911yescharacteristic
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
#113832
#85542