Finite Group Databasebeta

← #101016

Subgroups — #101016

Order 512.

558 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 112 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#21912C211yesmaximal, characteristic
2#15151C211yesmaximal, characteristic
3#8723C212yesmaximal
4#8558C211yesmaximal, characteristic
5#7039C212yesmaximal
6C2×#398—21no—
7C2×#398C412yes—
8C2×#389—21no—
9C2×#384C2211yescharacteristic
10C2×C4×C4⋊C4C2211yescharacteristic
11#1916—24no—
12#1817—21no—
13#1797C2212yes—
14#1797C2212yes—
15C4×C22⋊C8—21no—
16C2×#324—21no—
17#1445—21no—
18#1445C412yes—
19C4⋊#95—21no—
20C4⋊#95C2211yescharacteristic
21#1296—24no—
22#1280—21no—
23C22×C4⋊C4—21no—
24C22×C4⋊C4—22no—
25C22×C4⋊C4—21no—
26C22×C4⋊C4—21no—
27C22×C4⋊C4C2×C411yescharacteristic
28C22×C4⋊C4C2×C412yes—
29C22×C4⋊C4D411yescharacteristic
30C22×C42D411yescharacteristic
31C22×C42D411yescharacteristic
32C22×C42C2311yescharacteristic
33C2×C4⋊C8—22no—
34C2×C4⋊C8D414yes—
35C2×C22⋊C8—22no—
36C2×C22⋊C8—22no—
37C2×C4×C8—22no—
38#398—42no—
39#398—42no—
40#398—44no—
41#389—44no—
42#384—22no—
43#384—22no—
44C4×C4⋊C4—22no—
45C4×C4⋊C4—22no—
46C2×#95—22no—
47C2×#95—22no—
48C2×#95—22no—
49C2×#95—21no—
50C2×#95C2×C411yescharacteristic
51C2×#95C2×C412yes—
52C2×#95D411yescharacteristic
53#336—24no—
54#336—22no—
55#336—22no—
56#336—22no—
57#324—42no—
58C23×C4—22no—
59C23×C4—22no—
60C23×C4C22⋊C411yescharacteristic
61C23×C4C22⋊C411yescharacteristic
62C23×C4C22⋊C411yescharacteristic
63C23×C4C22⋊C411yescharacteristic
64C23×C4C22×C411yescharacteristic
65C23×C4C2×D411yescharacteristic
66C23×C4C2×D411yescharacteristic
67C22×C8—24no—
68C22×C8—42no—
69C2×C4⋊C4—22no—
70C2×C4⋊C4—22no—
71C2×C4⋊C4—24no—
72C2×C4⋊C4—22no—
73C2×C4⋊C4—22no—
74C2×C4⋊C4—24no—
75C2×C4⋊C4—41no—
76C2×C4⋊C4—42no—
77C2×C4⋊C4—42no—
78C2×C4⋊C4—42no—
79C2×C4⋊C4—42no—
80C2×C4⋊C4—44no—
81C2×C4⋊C4—44no—
82C2×C4⋊C4—44no—
83C2×C4⋊C4—41no—
84C2×C4⋊C4—42no—
85C2×C4⋊C4—41no—
86C2×C4⋊C4—41no—
87C2×C4⋊C4—41no—
88C2×C4⋊C4—42no—
89C2×C4⋊C4—42no—
90C2×C4⋊C4—42no—
91C2×C4⋊C4D812yes—
92C2×C4⋊C4SD1612yes—
93C2×C42—21no—
94C2×C42—21no—
95C2×C42—21no—
96C2×C42—22no—
97C2×C42—22no—
98C2×C42—21no—
99C2×C42—42no—
100C2×C42—42no—
101C2×C42C2×D412yes—
102C2×C42#4112yes—
103C4⋊C8—44no—
104C4⋊C8—44no—
105C22⋊C8—42no—
106C22⋊C8—42no—
107C22⋊C8—42no—
108C22⋊C8—42no—
109C4×C8—82no—
110#95—22no—
111#95—22no—
112#95—42no—
113#95—44no—
114#95—44no—
115#95—44no—
116#95—41no—
117#95—41no—
118C24C2×C22⋊C411yescharacteristic
119C22×C4—22no—
120C22×C4—22no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—24no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—41no—
138C22×C4—41no—
139C22×C4—41no—
140C22×C4—41no—
141C22×C4—41no—
142C22×C4—41no—
143C22×C4—41no—
144C22×C4—41no—
145C22×C4—41no—
146C22×C4—41no—
147C22×C4—42no—
148C22×C4—42no—
149C22×C4—42no—
150C22×C4—42no—
151C22×C4—42no—
152C22×C4—42no—
153C22×C4—42no—
154C22×C4—42no—
155C22×C4—42no—
156C22×C4—42no—
157C22×C4—42no—
158C22×C4—42no—
159C22×C4—42no—
160C22×C4#10012yes—
161C22×C4#10212yes—
162C22×C4#10212yes—
163C22×C4C4×D412yes—
164C22×C4#12011yescharacteristic
165C22×C4#12112yes—
166C22×C4#12311yescharacteristic
167C22×C4C2×D811yescharacteristic
168C22×C4C2×SD1611yescharacteristic
169C22×C4#13512yes—
170C22×C4#13512yes—
171C22×C4AGL(1,ℤ/8)12yes—
172C2×C8—44no—
173C2×C8—44no—
174C2×C8—44no—
175C2×C8—82no—
176C2×C8—82no—
177C2×C8—82no—
178C4⋊C4—24no—
179C4⋊C4—24no—
180C4⋊C4—44no—
181C4⋊C4—48no—
182C4⋊C4—84no—
183C4⋊C4—88no—
184C4⋊C4—82no—
185C4⋊C4—82no—
186C4⋊C4—82no—
187C4⋊C4—82no—
188C42—24no—
189C42—42no—
190C42—42no—
191C42—42no—
192C42—42no—
193C42—81no—
194C23—21no—
195C23—21no—
196C23—21no—
197C23—21no—
198C23#38611yescharacteristic
199C23C2×#10011yescharacteristic
200C23#41311yescharacteristic
201C23C2×#10211yescharacteristic
202C23#41611yescharacteristic
203C23#41611yescharacteristic
204C23#41811yescharacteristic
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—24no—
210C2×C4—24no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—44no—
235C2×C4—44no—
236C2×C4—44no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—82no—
244C2×C4—82no—
245C2×C4—82no—
246C2×C4—82no—
247C2×C4—81no—
248C2×C4—82no—
249C2×C4—82no—
250C2×C4—82no—
251C2×C4—82no—
252C2×C4—82no—
253C2×C4—82no—
254C2×C4—82no—
255C2×C4#44912yes—
256C2×C4#45612yes—
257C2×C4#45812yes—
258C2×C4#46512yes—
259C2×C4#46612yes—
260C2×C4#48212yes—
261C8—84no—
262C8—162no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22#154011yescharacteristic
276C22#154311yescharacteristic
277C22#154511yescharacteristic
278C22#155311yescharacteristic
279C22#187511yescharacteristic
280C22#188611yescharacteristic
281C22#189011yescharacteristic
282C22#189311yescharacteristic
283C22#190011yescharacteristic
284C22#190911yescharacteristic
285C22#191511yescharacteristic
286C4—22no—
287C4—22no—
288C4—22no—
289C4—42no—
290C4—42no—
291C4—42no—
292C4—42no—
293C4—84no—
294C4—81no—
295C4—162no—
296C4#160914yes—
297C2—21no—
298C2—21no—
299C2—21no—
300C2—21no—
301C2#902611yescharacteristic
302C2#913411yescharacteristic
303C2#919611yescharacteristic
304C2#939411yescharacteristic
305C2#945211yescharacteristic
306C2#947011yescharacteristic
307C2#950711yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#219122
#151512
#87232
#85582
#70392