Finite Group Databasebeta

← #135476

Subgroups — #135476

Order 512.

462 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 66 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#14289C211yesmaximal, characteristic
2#8554C211yesmaximal, characteristic
3#8554C211yesmaximal, characteristic
4#7215C214yesmaximal
5C22×#125C2211yescharacteristic
6C2×#383C411yescharacteristic
7C2×C4×C4⋊C4C411yescharacteristic
8#1821—21no—
9#1821C2212yes—
10#1463—21no—
11#1463—21no—
12#1463—21no—
13#1463C2212yes—
14#1445—21no—
15#1445—21no—
16#1441—21no—
17#1441—21no—
18#1436C412yes—
19#1436C2212yes—
20C2×#125—24no—
21C2×#125—42no—
22C2×#125—42no—
23C22×C4⋊C4—21no—
24C22×C4⋊C4C2×C411yescharacteristic
25C22×C4⋊C4D411yescharacteristic
26C22×C4⋊C4D411yescharacteristic
27C22×C4⋊C4D411yescharacteristic
28C22×C4⋊C4D411yescharacteristic
29C22×C4⋊C4C2311yescharacteristic
30C22×C42C2×C411yescharacteristic
31C22×C42C2×C412yes—
32#407—22no—
33#407—22no—
34#383—42no—
35C4×C4⋊C4—42no—
36C2×#95—22no—
37C2×#95—21no—
38C2×#95—21no—
39C2×#95—21no—
40C2×#95—22no—
41C2×#95—22no—
42C2×#95—22no—
43C2×#95C2×C412yes—
44#343—24no—
45#343—42no—
46#324—24no—
47#324—42no—
48#324—42no—
49#324—42no—
50C23×C4—22no—
51C23×C4—22no—
52C23×C4C22⋊C411yescharacteristic
53C23×C4C22⋊C411yescharacteristic
54C23×C4C22⋊C411yescharacteristic
55C23×C4C22⋊C411yescharacteristic
56C23×C4C22×C411yescharacteristic
57C23×C4C2×D411yescharacteristic
58C23×C4C2×D411yescharacteristic
59C2×M16—42no—
60C2×M16—42no—
61#125—416no—
62C2×C4⋊C4—22no—
63C2×C4⋊C4—22no—
64C2×C4⋊C4—22no—
65C2×C4⋊C4—22no—
66C2×C4⋊C4—22no—
67C2×C4⋊C4—22no—
68C2×C4⋊C4—22no—
69C2×C4⋊C4—22no—
70C2×C4⋊C4—22no—
71C2×C4⋊C4—41no—
72C2×C4⋊C4—41no—
73C2×C4⋊C4—41no—
74C2×C4⋊C4—41no—
75C2×C4⋊C4—41no—
76C2×C4⋊C4—41no—
77C2×C4⋊C4—41no—
78C2×C4⋊C4—41no—
79C2×C4⋊C4—44no—
80C2×C4⋊C4—42no—
81C2×C4⋊C4#4114yes—
82C2×C42—22no—
83C2×C42—22no—
84C2×C42—22no—
85C2×C42—42no—
86C2×C42—82no—
87C22⋊C8—42no—
88C22⋊C8—42no—
89C22⋊C8—42no—
90C22⋊C8—42no—
91#95—42no—
92#95—44no—
93#95—44no—
94#95—42no—
95#95—42no—
96#95—42no—
97#95—82no—
98#95—82no—
99C24C2×C22⋊C411yescharacteristic
100C22×C4—21no—
101C22×C4—21no—
102C22×C4—21no—
103C22×C4—21no—
104C22×C4—21no—
105C22×C4—21no—
106C22×C4—21no—
107C22×C4—21no—
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—24no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—21no—
117C22×C4—42no—
118C22×C4—42no—
119C22×C4—41no—
120C22×C4—42no—
121C22×C4—41no—
122C22×C4—41no—
123C22×C4—41no—
124C22×C4—41no—
125C22×C4—41no—
126C22×C4—42no—
127C22×C4—42no—
128C22×C4—42no—
129C22×C4—42no—
130C22×C4—42no—
131C22×C4—42no—
132C22×C4—42no—
133C22×C4—42no—
134C22×C4—42no—
135C22×C4—42no—
136C22×C4—42no—
137C22×C4—42no—
138C22×C4—42no—
139C22×C4—42no—
140C22×C4#9912yes—
141C22×C4#9912yes—
142C22×C4#11712yes—
143C22×C4#12312yes—
144C22×C4#12312yes—
145M16—84no—
146M16—82no—
147M16—82no—
148C2×C8—82no—
149C2×C8—82no—
150C4⋊C4—44no—
151C4⋊C4—44no—
152C4⋊C4—44no—
153C4⋊C4—44no—
154C4⋊C4—44no—
155C4⋊C4—44no—
156C4⋊C4—48no—
157C42—28no—
158C42—84no—
159C23—22no—
160C23—21no—
161C23—21no—
162C23—22no—
163C23#38111yescharacteristic
164C23C2×#9911yescharacteristic
165C23C2×#9911yescharacteristic
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—24no—
172C2×C4—24no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—44no—
186C2×C4—44no—
187C2×C4—44no—
188C2×C4—42no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—42no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—81no—
195C2×C4—81no—
196C2×C4—81no—
197C2×C4—82no—
198C2×C4—82no—
199C2×C4—82no—
200C2×C4—82no—
201C2×C4—81no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4—82no—
205C2×C4—82no—
206C2×C4—82no—
207C2×C4—82no—
208C2×C4—82no—
209C2×C4—82no—
210C2×C4—82no—
211C8—162no—
212C8—162no—
213C22—22no—
214C22—22no—
215C22—22no—
216C22—22no—
217C22—21no—
218C22—21no—
219C22—21no—
220C22—21no—
221C22—21no—
222C22—21no—
223C22#181911yescharacteristic
224C22#182712yes—
225C22#212211yescharacteristic
226C22#212311yescharacteristic
227C22#213312yes—
228C4—42no—
229C4—42no—
230C4—42no—
231C4—42no—
232C4—42no—
233C4—84no—
234C4—81no—
235C4—81no—
236C4—162no—
237C2—21no—
238C2—22no—
239C2—22no—
240C2—21no—
241C2#873811yescharacteristic
242C2#1285511yescharacteristic
243C2#1286211yescharacteristic
subgroupG/H
center, socleC22#1819
commutatorC23×C4C22×C4
Frattini, cosocleC22×C4⋊C4C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C24 ◁ C22×#125 ◁ G
LECSG ▷ C22×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#142892
#85542
#72152