Finite Group Databasebeta

← #93046

Subgroups — #93046

Order 512.

248 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 72 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#11459C211yesmaximal, characteristic
2#8599C211yesmaximal, characteristic
3#8001C211yesmaximal, characteristic
4C2×#431C2211yescharacteristic
5C2×#423—21no—
6#2162—21no—
7#1797—21no—
8C2×#335C411yescharacteristic
9C2×#335C411yescharacteristic
10#1322—21no—
11#1314C412yes—
12#1292—21no—
13#1292C412yes—
14#1277—21no—
15C22×M16—41no—
16C22×C42D411yescharacteristic
17#431—41no—
18#431—41no—
19#423—22no—
20#423—22no—
21#423—41no—
22#423—41no—
23C2×C4⋊C8—22no—
24C2×C4⋊C8—21no—
25C2×C4⋊C8—21no—
26C2×C4⋊C8—41no—
27C2×C4⋊C8C2×C411yescharacteristic
28C2×C4⋊C8D411yescharacteristic
29C2×C22⋊C8—41no—
30C2×C22⋊C8C2×C411yescharacteristic
31C2×C22⋊C8Q811yescharacteristic
32C2×C4×C8C2×C411yescharacteristic
33C2×C4×C8D411yescharacteristic
34C4⋊C16—41no—
35C22⋊C16—22no—
36C4×C16—41no—
37#336—41no—
38#335—41no—
39#335—41no—
40C23×C4C4⋊C411yescharacteristic
41C23×C4D811yescharacteristic
42C23×C4Q1611yescharacteristic
43C2×M16—42no—
44C2×M16—42no—
45C2×M16—81no—
46C2×M16—81no—
47C2×M16—81no—
48C2×M16—81no—
49C22×C8—42no—
50C22×C8—41no—
51C22×C8—41no—
52C22×C8C4211yescharacteristic
53C22×C8C22⋊C411yescharacteristic
54C22×C8C4⋊C411yescharacteristic
55C22×C8C4⋊C411yescharacteristic
56C2×C42—21no—
57C2×C42—21no—
58C2×C42—21no—
59C2×C42—21no—
60C2×C42C22⋊C411yescharacteristic
61C2×C42C22⋊C411yescharacteristic
62C2×C42SD1611yescharacteristic
63C2×C42SD1611yescharacteristic
64C2×C16—42no—
65C4⋊C8—24no—
66C4⋊C8—41no—
67C4⋊C8—41no—
68C4⋊C8—42no—
69C4⋊C8—42no—
70C4⋊C8—42no—
71C4⋊C8—41no—
72C4⋊C8—41no—
73C4⋊C8—41no—
74C4⋊C8—41no—
75C22⋊C8—41no—
76C22⋊C8—41no—
77C22⋊C8—81no—
78C22⋊C8—81no—
79C4×C8—21no—
80C4×C8—21no—
81C4×C8—21no—
82C4×C8—21no—
83C24#10711yescharacteristic
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—41no—
93C22×C4—41no—
94C22×C4—81no—
95C22×C4#9511yescharacteristic
96C22×C4#10211yescharacteristic
97C22×C4#10211yescharacteristic
98C22×C4#10311yescharacteristic
99C22×C4#10311yescharacteristic
100C22×C4#10611yescharacteristic
101C22×C4D1611yescharacteristic
102C22×C4SD3211yescharacteristic
103C22×C4SD3211yescharacteristic
104C22×C4Q3211yescharacteristic
105M16—82no—
106M16—82no—
107M16—82no—
108M16—82no—
109C2×C8—21no—
110C2×C8—21no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—41no—
114C2×C8—41no—
115C2×C8—41no—
116C2×C8—41no—
117C2×C8—44no—
118C2×C8—82no—
119C2×C8—82no—
120C2×C8—81no—
121C2×C8—81no—
122C2×C8—81no—
123C2×C8—81no—
124C2×C8—81no—
125C2×C8—81no—
126C42—21no—
127C42—21no—
128C42—21no—
129C42—21no—
130C42—21no—
131C42—21no—
132C42#9911yescharacteristic
133C42#9911yescharacteristic
134C42#10411yescharacteristic
135C42#10411yescharacteristic
136C16—82no—
137C23—21no—
138C23—21no—
139C23—41no—
140C23—41no—
141C23#34011yescharacteristic
142C23#36611yescharacteristic
143C23#36711yescharacteristic
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—81no—
165C2×C4—81no—
166C2×C4#32711yescharacteristic
167C2×C4#32711yescharacteristic
168C2×C4#32811yescharacteristic
169C2×C4#32811yescharacteristic
170C2×C4#33911yescharacteristic
171C2×C4#34211yescharacteristic
172C2×C4#35711yescharacteristic
173C2×C4#35711yescharacteristic
174C2×C4#35811yescharacteristic
175C2×C4#35811yescharacteristic
176C2×C4#36011yescharacteristic
177C2×C4#36011yescharacteristic
178C8—41no—
179C8—41no—
180C8—41no—
181C8—41no—
182C8—84no—
183C8—161no—
184C8—161no—
185C22—21no—
186C22—21no—
187C22—21no—
188C22—21no—
189C22—41no—
190C22—41no—
191C22—41no—
192C22—41no—
193C22—81no—
194C22#129411yescharacteristic
195C22#138011yescharacteristic
196C22#138611yescharacteristic
197C4—21no—
198C4—21no—
199C4—21no—
200C4—21no—
201C4—21no—
202C4—41no—
203C4—41no—
204C4#134711yescharacteristic
205C4#134711yescharacteristic
206C4#134811yescharacteristic
207C4#134811yescharacteristic
208C4#139211yescharacteristic
209C4#139511yescharacteristic
210C2—21no—
211C2—21no—
212C2—41no—
213C2—41no—
214C2#725311yescharacteristic
215C2#725711yescharacteristic
216C2#725811yescharacteristic
subgroupG/H
centerC2×C4#327
commutatorC22×C8C42
Frattini, cosocleC2×#431C22
socleC22#1294
prime radicalC24#107
LCSG ▷ C22×C8 ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#431 ◁ G
LECSG ▷ C2×#431 ▷ C22×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#114592
#85992
#80012