Finite Group Databasebeta

← #101013

Subgroups — #101013

Order 512.

566 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 124 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#21951C211yesmaximal, characteristic
2#15196C211yesmaximal, characteristic
3#8724C212yesmaximal
4#8558C211yesmaximal, characteristic
5#7039C212yesmaximal
6C2×#431—21no—
7C2×#389—21no—
8C2×#384C2211yescharacteristic
9C2×C4×C4⋊C4C2211yescharacteristic
10#1939—24no—
11#1797—21no—
12#1797C2212yes—
13#1797C2212yes—
14C2×#324—21no—
15#1444—21no—
16#1444C412yes—
17#1441—21no—
18#1441C412yes—
19C4⋊#95—21no—
20C4⋊#95C2211yescharacteristic
21#1296—24no—
22#1280—21no—
23C22×C4⋊C4—21no—
24C22×C4⋊C4—21no—
25C22×C4⋊C4—22no—
26C22×C4⋊C4—21no—
27C22×C4⋊C4C2×C411yescharacteristic
28C22×C4⋊C4C2×C412yes—
29C22×C4⋊C4D411yescharacteristic
30C22×C42D411yescharacteristic
31C22×C42D411yescharacteristic
32C22×C42C2311yescharacteristic
33#431—42no—
34#431—42no—
35C2×C4⋊C8—22no—
36C2×C4⋊C8—22no—
37C2×C4⋊C8—22no—
38C2×C4⋊C8D414yes—
39C2×C22⋊C8—22no—
40C2×C22⋊C8—22no—
41C2×C4×C8—22no—
42#389—42no—
43#389—42no—
44#384—22no—
45#384—22no—
46C4×C4⋊C4—22no—
47C4×C4⋊C4—22no—
48C2×#95—22no—
49C2×#95—21no—
50C2×#95—22no—
51C2×#95—22no—
52C2×#95C2×C411yescharacteristic
53C2×#95C2×C412yes—
54C2×#95D411yescharacteristic
55#336—22no—
56#336—22no—
57#336—22no—
58#324—42no—
59C23×C4—22no—
60C23×C4—22no—
61C23×C4C22⋊C411yescharacteristic
62C23×C4C22⋊C411yescharacteristic
63C23×C4C22⋊C411yescharacteristic
64C23×C4C22⋊C411yescharacteristic
65C23×C4C22×C411yescharacteristic
66C23×C4C2×D411yescharacteristic
67C23×C4C2×D411yescharacteristic
68C22×C8—24no—
69C22×C8—42no—
70C2×C4⋊C4—22no—
71C2×C4⋊C4—22no—
72C2×C4⋊C4—24no—
73C2×C4⋊C4—22no—
74C2×C4⋊C4—22no—
75C2×C4⋊C4—24no—
76C2×C4⋊C4—41no—
77C2×C4⋊C4—42no—
78C2×C4⋊C4—41no—
79C2×C4⋊C4—41no—
80C2×C4⋊C4—44no—
81C2×C4⋊C4—41no—
82C2×C4⋊C4—42no—
83C2×C4⋊C4—41no—
84C2×C4⋊C4—41no—
85C2×C4⋊C4—41no—
86C2×C4⋊C4—41no—
87C2×C4⋊C4—41no—
88C2×C4⋊C4—82no—
89C2×C4⋊C4—82no—
90C2×C4⋊C4—82no—
91C2×C4⋊C4—82no—
92C2×C4⋊C4SD1612yes—
93C2×C4⋊C4Q1612yes—
94C2×C42—21no—
95C2×C42—21no—
96C2×C42—21no—
97C2×C42—21no—
98C2×C42—21no—
99C2×C42—21no—
100C2×C42—42no—
101C2×C42—42no—
102C2×C42D812yes—
103C2×C42SD1612yes—
104C2×C42C2×D412yes—
105C2×C42#4112yes—
106C4⋊C8—44no—
107C4⋊C8—44no—
108C4⋊C8—44no—
109C4⋊C8—82no—
110C22⋊C8—42no—
111C22⋊C8—42no—
112C22⋊C8—42no—
113C22⋊C8—42no—
114C4×C8—44no—
115#95—22no—
116#95—22no—
117#95—42no—
118#95—44no—
119#95—42no—
120#95—82no—
121#95—82no—
122C24C2×C22⋊C411yescharacteristic
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—21no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—24no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—21no—
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—41no—
148C22×C4—41no—
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—42no—
161C22×C4—42no—
162C22×C4#10112yes—
163C22×C4#10212yes—
164C22×C4#10212yes—
165C22×C4#10312yes—
166C22×C4#10312yes—
167C22×C4C4×D412yes—
168C22×C4#12011yescharacteristic
169C22×C4#12112yes—
170C22×C4#12311yescharacteristic
171C22×C4C2×D811yescharacteristic
172C22×C4C2×SD1611yescharacteristic
173C22×C4C2×SD1611yescharacteristic
174C22×C4C2×Q1611yescharacteristic
175C22×C4#13512yes—
176C22×C4AGL(1,ℤ/8)11yescharacteristic
177C22×C4#13711yescharacteristic
178C2×C8—44no—
179C2×C8—44no—
180C2×C8—44no—
181C2×C8—82no—
182C2×C8—82no—
183C2×C8—82no—
184C4⋊C4—24no—
185C4⋊C4—24no—
186C4⋊C4—44no—
187C4⋊C4—44no—
188C4⋊C4—44no—
189C4⋊C4—84no—
190C4⋊C4—84no—
191C4⋊C4—88no—
192C4⋊C4—81no—
193C4⋊C4—81no—
194C4⋊C4—81no—
195C4⋊C4—81no—
196C42—22no—
197C42—22no—
198C42—24no—
199C42—22no—
200C42—22no—
201C42—42no—
202C42—42no—
203C42—81no—
204C23—21no—
205C23—21no—
206C23—21no—
207C23—21no—
208C23#38611yescharacteristic
209C23C2×#10111yescharacteristic
210C23#41311yescharacteristic
211C23C2×#10211yescharacteristic
212C23C2×#10311yescharacteristic
213C23#41611yescharacteristic
214C23#41711yescharacteristic
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—44no—
246C2×C4—44no—
247C2×C4—44no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—81no—
253C2×C4—81no—
254C2×C4—82no—
255C2×C4—82no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4—81no—
259C2×C4—82no—
260C2×C4—82no—
261C2×C4—82no—
262C2×C4—82no—
263C2×C4—82no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4#33214yes—
267C2×C4#44711yescharacteristic
268C2×C4#44811yescharacteristic
269C2×C4#45612yes—
270C2×C4#45812yes—
271C2×C4#46512yes—
272C2×C4#46712yes—
273C2×C4#48011yescharacteristic
274C2×C4#48111yescharacteristic
275C8—84no—
276C8—162no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22C2×#33211yescharacteristic
290C22#154011yescharacteristic
291C22#155011yescharacteristic
292C22#155211yescharacteristic
293C22#187411yescharacteristic
294C22#188611yescharacteristic
295C22#189011yescharacteristic
296C22#189211yescharacteristic
297C22#190111yescharacteristic
298C22#191011yescharacteristic
299C22#191411yescharacteristic
300C4—21no—
301C4—21no—
302C4—24no—
303C4—22no—
304C4—22no—
305C4—42no—
306C4—42no—
307C4—42no—
308C4—84no—
309C4—81no—
310C4—162no—
311C4#161012yes—
312C4#161112yes—
313C2—21no—
314C2—21no—
315C2—21no—
316C2—21no—
317C2#902711yescharacteristic
318C2#913111yescharacteristic
319C2#919711yescharacteristic
320C2#939211yescharacteristic
321C2#945411yescharacteristic
322C2#946911yescharacteristic
323C2#951011yescharacteristic
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
#219512
#151962
#87242
#85582
#70392