Finite Group Databasebeta

← #121036

Subgroups — #121036

Order 512.

414 conjugacy classes of subgroups.

The subgroup lattice has 319 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17796C211yesmaximal, characteristic
2#8060C211yesmaximal, characteristic
3#8033C211yesmaximal, characteristic
4#7990C211yesmaximal, characteristic
5#7959C211yesmaximal, characteristic
6C2×#1286C211yesmaximal, characteristic
7#7933C211yesmaximal, characteristic
8#2920C2211yescharacteristic
9#2920C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C2×C4×M16C2211yescharacteristic
14C2×#382C2211yescharacteristic
15#1569—22no—
16#1567—21no—
17#1566—21no—
18#1565—22no—
19#1299—22no—
20#1295C414yes—
21#1290—22no—
22#1286—22no—
23#1286—21no—
24#1286—21no—
25#1283—22no—
26C22×M16—21no—
27C22×M16—21no—
28C22×C4⋊C4—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#431D412yes—
46#423—21no—
47#423—21no—
48#423—21no—
49#423—21no—
50#423—21no—
51#423D411yescharacteristic
52#423D411yescharacteristic
53C2×C4⋊C8—21no—
54C2×C4⋊C8—21no—
55C2×C4⋊C8—21no—
56C2×C4⋊C8D412yes—
57#407—21no—
58#407—21no—
59C2×C22⋊C8—21no—
60C2×C22⋊C8—21no—
61C4×M16—21no—
62C4×M16—21no—
63C4×M16—21no—
64C4×M16D412yes—
65C4×M16Q812yes—
66C4×M16Q811yescharacteristic
67C4×M16Q811yescharacteristic
68C2×#97C2×C412yes—
69C2×#97C2×C412yes—
70C2×C4×C8—21no—
71C2×C4×C8—21no—
72#382—21no—
73#382—21no—
74#382—21no—
75#382C2×C412yes—
76C2×#95—21no—
77C2×#95—21no—
78#335—24no—
79#334—24no—
80C23×C4—41no—
81C23×C4#4111yescharacteristic
82C23×C4#4111yescharacteristic
83C23×C4#4111yescharacteristic
84C2×M16—21no—
85C2×M16—21no—
86C2×M16—22no—
87C2×M16—21no—
88C2×M16—21no—
89C2×M16—22no—
90C2×M16—44no—
91C2×M16—41no—
92C2×M16—41no—
93C2×M16—81no—
94C2×M16—81no—
95C22×C8—22no—
96C22×C8—22no—
97C22×C8—22no—
98C22×C8—41no—
99C2×C4⋊C4—22no—
100C2×C4⋊C4—41no—
101C2×C4⋊C4—81no—
102C2×C4⋊C4—81no—
103C2×C42C22×C411yescharacteristic
104C2×C42C2×D411yescharacteristic
105C2×C42C2×D411yescharacteristic
106C2×C42C2×D411yescharacteristic
107C2×C42C2×D411yescharacteristic
108C2×C42C2×Q811yescharacteristic
109C2×C42C2×Q811yescharacteristic
110C2×C42#4111yescharacteristic
111C2×C42#4111yescharacteristic
112C2×C42#4111yescharacteristic
113C2×C42#4111yescharacteristic
114C2×C42#4111yescharacteristic
115C4⋊C8—21no—
116C4⋊C8—22no—
117C4⋊C8—21no—
118C4⋊C8—22no—
119C4⋊C8—22no—
120C4⋊C8—21no—
121C4⋊C8—21no—
122C4⋊C8—41no—
123C4⋊C8—41no—
124C4⋊C8—41no—
125C4⋊C8—41no—
126C4⋊C8—41no—
127C4⋊C8—41no—
128C4⋊C8—41no—
129C22⋊C8—22no—
130C22⋊C8—41no—
131C22⋊C8—41no—
132C22⋊C8—41no—
133C22⋊C8—41no—
134C22⋊C8—41no—
135C22⋊C8—41no—
136C22⋊C8—41no—
137#97—22no—
138#97—22no—
139#97—22no—
140#97—22no—
141#97—41no—
142#97C4⋊C412yes—
143#97C4⋊C412yes—
144C4×C8—22no—
145C4×C8—21no—
146C4×C8—21no—
147C4×C8—22no—
148C4×C8—22no—
149C4×C8—41no—
150C4×C8—41no—
151#95—22no—
152#95—22no—
153#95—41no—
154#95—41no—
155C24#12611yescharacteristic
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—42no—
161C22×C4—42no—
162C22×C4—81no—
163C22×C4—82no—
164C22×C4—82no—
165C22×C4—82no—
166C22×C4#11711yescharacteristic
167C22×C4C4×D411yescharacteristic
168C22×C4C4×D411yescharacteristic
169C22×C4#12111yescharacteristic
170C22×C4C22⋊Q811yescharacteristic
171C22×C4C22⋊Q811yescharacteristic
172C22×C4#12311yescharacteristic
173C22×C4#12311yescharacteristic
174C22×C4#12311yescharacteristic
175C22×C4#12411yescharacteristic
176C22×C4#12411yescharacteristic
177C22×C4#12411yescharacteristic
178C22×C4#12511yescharacteristic
179C22×C4#12511yescharacteristic
180C22×C4#12511yescharacteristic
181C22×C4#12511yescharacteristic
182C22×C4#12611yescharacteristic
183C22×C4#12611yescharacteristic
184M16—24no—
185M16—44no—
186M16—42no—
187M16—41no—
188M16—41no—
189M16—41no—
190M16—41no—
191M16—82no—
192M16—81no—
193M16—81no—
194M16—82no—
195C2×C8—22no—
196C2×C8—22no—
197C2×C8—44no—
198C2×C8—42no—
199C2×C8—42no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—42no—
203C2×C8—42no—
204C2×C8—82no—
205C2×C8—82no—
206C2×C8—82no—
207C4⋊C4—82no—
208C4⋊C4—81no—
209C4⋊C4—81no—
210C42C2×C4⋊C411yescharacteristic
211C42#11711yescharacteristic
212C42C4×D411yescharacteristic
213C42C4×Q811yescharacteristic
214C42#12011yescharacteristic
215C42#12111yescharacteristic
216C42#12111yescharacteristic
217C42C22⋊Q811yescharacteristic
218C42C22⋊Q811yescharacteristic
219C42C22⋊Q811yescharacteristic
220C42#12311yescharacteristic
221C42#12311yescharacteristic
222C42#12411yescharacteristic
223C42#12511yescharacteristic
224C42#12611yescharacteristic
225C42C4⋊Q811yescharacteristic
226C23—22no—
227C23—21no—
228C23—21no—
229C23—41no—
230C23#38811yescharacteristic
231C23#40011yescharacteristic
232C23#40011yescharacteristic
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—82no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4—164no—
259C2×C4#38211yescharacteristic
260C2×C4#38511yescharacteristic
261C2×C4#38711yescharacteristic
262C2×C4#38711yescharacteristic
263C2×C4#38811yescharacteristic
264C2×C4#38911yescharacteristic
265C2×C4#39311yescharacteristic
266C2×C4#39411yescharacteristic
267C2×C4#39711yescharacteristic
268C2×C4#39811yescharacteristic
269C2×C4#39811yescharacteristic
270C2×C4#40011yescharacteristic
271C2×C4#47111yescharacteristic
272C2×C4#47111yescharacteristic
273C2×C4#47211yescharacteristic
274C2×C4#47311yescharacteristic
275C8—24no—
276C8—42no—
277C8—82no—
278C8—82no—
279C8—82no—
280C8—82no—
281C8—81no—
282C8—81no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—42no—
291C22—42no—
292C22#144211yescharacteristic
293C22#193011yescharacteristic
294C22#193111yescharacteristic
295C22#210212yes—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—21no—
306C4—162no—
307C4#205111yescharacteristic
308C4#205211yescharacteristic
309C4#208911yescharacteristic
310C4#209011yescharacteristic
311C2—21no—
312C2—22no—
313C2—21no—
314C2—41no—
315C2#1126111yescharacteristic
316C2#1127811yescharacteristic
317C2#1129011yescharacteristic
subgroupG/H
center, socleC22#1442
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#126
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ 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
#177962
#80602
#80332
#79902
#79592
C2×#12862
#79332