Finite Group Databasebeta

← #121025

Subgroups — #121025

Order 512.

459 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20814C211yesmaximal, characteristic
2#8089C211yesmaximal, characteristic
3C2×#1300C211yesmaximal, characteristic
4#8013C211yesmaximal, characteristic
5#7972C211yesmaximal, characteristic
6#7932C211yesmaximal, characteristic
7#7926C211yesmaximal, characteristic
8C2×#432C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×C4×M16C2211yescharacteristic
13#2283C2211yescharacteristic
14C2×#376C2211yescharacteristic
15#1843—21no—
16#1832—21no—
17#1797—22no—
18#1768—22no—
19#1302—22no—
20#1300—21no—
21#1300—21no—
22#1294C412yes—
23#1294C412yes—
24#1288—22no—
25#1283—22no—
26#1282—22no—
27C22×M16—21no—
28C22×C42—21no—
29C22×C42C2311yescharacteristic
30#432—21no—
31#432—21no—
32#432—21no—
33#432—21no—
34#432—21no—
35#432—21no—
36#432—21no—
37#432—21no—
38#431—21no—
39#431—21no—
40#431—21no—
41#431—21no—
42#431—21no—
43#431—21no—
44#431—21no—
45#431—21no—
46C2×C4⋊C8—24no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8—21no—
50C2×C4⋊C8Q812yes—
51C2×C22⋊C8—21no—
52C2×C22⋊C8—21no—
53C2×C22⋊C8C2×C412yes—
54C2×C22⋊C8D412yes—
55C4×M16—21no—
56C4×M16—21no—
57C4×M16—21no—
58C4×M16D412yes—
59C2×#97—21no—
60C2×#97—21no—
61C2×#97D412yes—
62C2×C4×C8—21no—
63C2×C4×C8—21no—
64C2×C4×C8—21no—
65#383—21no—
66#382—21no—
67#381—21no—
68#380C2×C411yescharacteristic
69#380C2×C411yescharacteristic
70C4×C4⋊C4—21no—
71C4×C22⋊C4—21no—
72#376—21no—
73#376—21no—
74#376—21no—
75#376D411yescharacteristic
76#376D411yescharacteristic
77#376Q812yes—
78C2×#95—21no—
79C2×#95C2×C412yes—
80#336—24no—
81C23×C4—22no—
82C23×C4C22×C411yescharacteristic
83C23×C4C2×D411yescharacteristic
84C23×C4#4111yescharacteristic
85C2×M16—24no—
86C2×M16—22no—
87C2×M16—42no—
88C2×M16—41no—
89C22×C8—22no—
90C22×C8—22no—
91C22×C8—22no—
92C22×C8—22no—
93C22×C8—41no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C22⋊C4—21no—
97C2×C22⋊C4—21no—
98C2×C42—21no—
99C2×C42—21no—
100C2×C42—22no—
101C2×C42—44no—
102C2×C42—41no—
103C2×C42C2×D411yescharacteristic
104C2×C42C2×D411yescharacteristic
105C2×C42C2×D411yescharacteristic
106C2×C42C2×Q811yescharacteristic
107C2×C42C2×Q811yescharacteristic
108C2×C42#4111yescharacteristic
109C2×C42#4111yescharacteristic
110C2×C42#4111yescharacteristic
111C2×C42#4111yescharacteristic
112C2×C42#4111yescharacteristic
113C2×C42#4111yescharacteristic
114C2×C42#4111yescharacteristic
115C4⋊C8—22no—
116C4⋊C8—22no—
117C4⋊C8—48no—
118C4⋊C8—41no—
119C4⋊C8—41no—
120C4⋊C8—41no—
121C4⋊C8—41no—
122C4⋊C8—41no—
123C4⋊C8—41no—
124C22⋊C8—22no—
125C22⋊C8—22no—
126C22⋊C8—22no—
127C22⋊C8—22no—
128C22⋊C8—41no—
129C22⋊C8—41no—
130C22⋊C8—41no—
131C22⋊C8—41no—
132#97—22no—
133#97—22no—
134#97—22no—
135#97—41no—
136#97—41no—
137#97—41no—
138C4×C8—22no—
139C4×C8—41no—
140C4×C8—41no—
141C4×C8—41no—
142C4×C8—41no—
143C4×C8—41no—
144#95—22no—
145#95—22no—
146#95—21no—
147#95—21no—
148#95—21no—
149#95—21no—
150#95—41no—
151#95—41no—
152#95—41no—
153#95C4⋊C412yes—
154#95C4⋊C412yes—
155C24C4×D411yescharacteristic
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—42no—
161C22×C4—44no—
162C22×C4—42no—
163C22×C4—42no—
164C22×C4—41no—
165C22×C4—41no—
166C22×C4—81no—
167C22×C4—82no—
168C22×C4C2×C4⋊C411yescharacteristic
169C22×C4#11711yescharacteristic
170C22×C4#11711yescharacteristic
171C22×C4C4×D411yescharacteristic
172C22×C4C4×D411yescharacteristic
173C22×C4C4×Q811yescharacteristic
174C22×C4#12011yescharacteristic
175C22×C4#12111yescharacteristic
176C22×C4C22⋊Q811yescharacteristic
177C22×C4C22⋊Q811yescharacteristic
178C22×C4C22⋊Q811yescharacteristic
179C22×C4#12311yescharacteristic
180C22×C4#12311yescharacteristic
181C22×C4#12311yescharacteristic
182C22×C4#12411yescharacteristic
183C22×C4#12511yescharacteristic
184C22×C4#12611yescharacteristic
185C22×C4#12611yescharacteristic
186M16—24no—
187M16—44no—
188M16—42no—
189C2×C8—44no—
190C2×C8—42no—
191C2×C8—44no—
192C2×C8—44no—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—42no—
196C2×C8—42no—
197C2×C8—82no—
198C2×C8—82no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C22⋊C4—42no—
202C22⋊C4—42no—
203C42—24no—
204C42—42no—
205C42—44no—
206C42—82no—
207C42#12111yescharacteristic
208C42#12111yescharacteristic
209C42C22⋊Q811yescharacteristic
210C42C22⋊Q811yescharacteristic
211C42#12311yescharacteristic
212C42#12311yescharacteristic
213C42#12411yescharacteristic
214C42#12411yescharacteristic
215C42#12411yescharacteristic
216C42#12511yescharacteristic
217C42#12511yescharacteristic
218C42#12511yescharacteristic
219C42#12511yescharacteristic
220C42#12611yescharacteristic
221C42#12611yescharacteristic
222C42C4⋊Q811yescharacteristic
223C23—41no—
224C23—41no—
225C23#38511yescharacteristic
226C23#38711yescharacteristic
227C23#38811yescharacteristic
228C23#44312yes—
229C23#44412yes—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—24no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—84no—
257C2×C4—84no—
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4#38211yescharacteristic
265C2×C4#38711yescharacteristic
266C2×C4#38811yescharacteristic
267C2×C4#38911yescharacteristic
268C2×C4#39311yescharacteristic
269C2×C4#39411yescharacteristic
270C2×C4#39711yescharacteristic
271C2×C4#39811yescharacteristic
272C2×C4#39811yescharacteristic
273C2×C4#40011yescharacteristic
274C2×C4#40011yescharacteristic
275C2×C4#40011yescharacteristic
276C8—44no—
277C8—82no—
278C8—82no—
279C8—82no—
280C8—82no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—42no—
288C22—42no—
289C22#144211yescharacteristic
290C22#186612yes—
291C22#192212yes—
292C22#193711yescharacteristic
293C22#193811yescharacteristic
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—44no—
306C4—82no—
307C4—161no—
308C4—161no—
309C4#203112yes—
310C2—22no—
311C2—21no—
312C2—21no—
313C2—22no—
314C2#1126211yescharacteristic
315C2#1128011yescharacteristic
316C2#1129111yescharacteristic
subgroupG/H
centerC2×C4#393
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
socleC22#1442
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#208142
#80892
C2×#13002
#80132
#79722
#79322
#79262