Finite Group Databasebeta

← #507585

Subgroups — #507585

Order 512.

476 conjugacy classes of subgroups.

The subgroup lattice has 315 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#499C211yesmaximal, characteristic
2C4×#500C211yesmaximal, characteristic
3#13539C212yesmaximal
4#13453C212yesmaximal
5#13276C211yesmaximal, characteristic
6#13276C211yesmaximal, characteristic
7#13177C211yesmaximal, characteristic
8#13176C211yesmaximal, characteristic
9#13111C212yesmaximal
10#13109C212yesmaximal
11#12879C211yesmaximal, characteristic
12C2×#500C2211yescharacteristic
13C2×#499C2211yescharacteristic
14C4×C4⋊Q8—21no—
15C4×#125—21no—
16C2×#367C2212yes—
17C2×#366C2212yes—
18C2×C4⋊C16C2211yescharacteristic
19C2×C4⋊C16C2211yescharacteristic
20#1991—21no—
21#1990—21no—
22#1942—21no—
23#1942C2211yescharacteristic
24#1942C2211yescharacteristic
25#1942C2212yes—
26#1941—21no—
27#1846C2211yescharacteristic
28#1845C2211yescharacteristic
29C4×#107—21no—
30C4×#107C2212yes—
31C4×#107C2211yescharacteristic
32C4×#107C2211yescharacteristic
33C4×#106—21no—
34C42×C8C2211yescharacteristic
35#1380C2212yes—
36#1380C2212yes—
37#1380C2212yes—
38#1380C2212yes—
39#1380C2212yes—
40#1380C2212yes—
41#1374C2212yes—
42#1374C2212yes—
43C2×C4⋊Q8—21no—
44C2×#125—21no—
45C2×C4×Q8—41no—
46C22×C16C2312yes—
47C22×C16C2312yes—
48#500—22no—
49#500Q814yes—
50#499—22no—
51#499—22no—
52C2×#107—21no—
53C2×#107—21no—
54C2×#107C2312yes—
55C2×#107C2311yescharacteristic
56C2×#107C2311yescharacteristic
57C2×#107C2312yes—
58C2×#107C2311yescharacteristic
59C2×#107C2311yescharacteristic
60C2×#106—21no—
61C2×#106—21no—
62C2×C4×C8D411yescharacteristic
63C2×C4×C8D411yescharacteristic
64C2×C4×C8D411yescharacteristic
65C2×C4×C8C2311yescharacteristic
66C2×C4×C8C2311yescharacteristic
67C2×C4×C8C2311yescharacteristic
68#391—41no—
69#389—21no—
70#389—21no—
71#389—22no—
72#389—41no—
73#387—41no—
74#387—41no—
75#384—21no—
76#382—21no—
77C4×C4⋊C4—21no—
78C4×C4⋊C4—21no—
79C4×C4⋊C4—22no—
80C4×C4⋊C4—41no—
81C4×C4⋊C4—41no—
82C4×C4⋊C4—41no—
83C43D411yescharacteristic
84#367—24no—
85#366—24no—
86C4⋊C16—22no—
87C4⋊C16—22no—
88#340—21no—
89#340—21no—
90#340—22no—
91#340—22no—
92#340—21no—
93#340—21no—
94C22×Q8—41no—
95C22×C8C2×D411yescharacteristic
96C22×C8C2×D411yescharacteristic
97C22×C8C2×D411yescharacteristic
98C22×C8C2411yescharacteristic
99C4⋊Q8—24no—
100C4⋊Q8—42no—
101#125—24no—
102#125—42no—
103C4×Q8—84no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—42no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C42—42no—
119C2×C42—41no—
120C2×C42—41no—
121C2×C42D811yescharacteristic
122C2×C42D811yescharacteristic
123C2×C42D811yescharacteristic
124C2×C42D811yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C16—22no—
129C2×C16—22no—
130C2×C16—22no—
131C2×C16—22no—
132C2×C16—22no—
133C2×C16—22no—
134#107—24no—
135#107—21no—
136#107—21no—
137#107—22no—
138#107—22no—
139#107—22no—
140#107—21no—
141#107—21no—
142#107—21no—
143#107—21no—
144#107—42no—
145#107C2×Q814yes—
146#107#4112yes—
147#107#4112yes—
148#106—24no—
149#106—42no—
150C4×C8—22no—
151C4×C8—21no—
152C4×C8—21no—
153C4×C8—21no—
154C4×C8—21no—
155C4×C8—22no—
156C4×C8—41no—
157C4×C8C2×Q812yes—
158C4×C8#4112yes—
159#95—41no—
160#95—41no—
161#95—42no—
162#95—41no—
163#95—41no—
164#95—41no—
165#95—41no—
166#95—42no—
167C2×Q8—44no—
168C2×Q8—82no—
169C2×Q8—82no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4—42no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—42no—
176C22×C4C2×D811yescharacteristic
177C22×C4C2×D811yescharacteristic
178C22×C4C2×D811yescharacteristic
179C22×C4C2×D811yescharacteristic
180C22×C4C2×D811yescharacteristic
181C22×C4C2×D811yescharacteristic
182C22×C4C22×D411yescharacteristic
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—21no—
186C2×C8—21no—
187C2×C8—21no—
188C2×C8—21no—
189C2×C8—21no—
190C2×C8C22⋊Q812yes—
191C2×C8#13712yes—
192C2×C8C22×Q811yescharacteristic
193C2×C8C2×#4111yescharacteristic
194C2×C8C2×#4111yescharacteristic
195C2×C8C2×#4111yescharacteristic
196C2×C82−1+411yescharacteristic
197C2×C82−1+411yescharacteristic
198C4⋊C4—24no—
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—44no—
202C4⋊C4—44no—
203C4⋊C4—42no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—44no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—42no—
213C4⋊C4—82no—
214C4⋊C4—82no—
215C4⋊C4—84no—
216C4⋊C4—82no—
217C4⋊C4—82no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—22no—
223C42—22no—
224C42—22no—
225C42—41no—
226C42—82no—
227C42—84no—
228C42—82no—
229C42C22⋊Q812yes—
230C42#13712yes—
231C16—42no—
232C16—42no—
233C23C22×D811yescharacteristic
234Q8—88no—
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—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—44no—
251C2×C4—81no—
252C2×C4—82no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4—81no—
259C2×C4—82no—
260C2×C4—82no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4#47412yes—
267C2×C4#47412yes—
268C2×C4#50812yes—
269C2×C4#50912yes—
270C2×C4#51012yes—
271C2×C4C2×C22⋊Q811yescharacteristic
272C2×C4#52511yescharacteristic
273C2×C4#53611yescharacteristic
274C2×C4C2×#13711yescharacteristic
275C2×C4C2×#13711yescharacteristic
276C2×C4#57511yescharacteristic
277C8—22no—
278C8—22no—
279C8—41no—
280C8#55611yescharacteristic
281C8#55611yescharacteristic
282C8#55711yescharacteristic
283C8#55711yescharacteristic
284C22C2×#47411yescharacteristic
285C22#310011yescharacteristic
286C22#322611yescharacteristic
287C22C2×#50811yescharacteristic
288C22C2×#50911yescharacteristic
289C22C2×#51011yescharacteristic
290C22#341411yescharacteristic
291C4—22no—
292C4—22no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—84no—
297C4—82no—
298C4—82no—
299C4—161no—
300C4—161no—
301C4—162no—
302C4#222914yes—
303C4#258111yescharacteristic
304C4#307811yescharacteristic
305C4#311311yescharacteristic
306C4#323711yescharacteristic
307C2#2927211yescharacteristic
308C2C2×#222911yescharacteristic
309C2#3362711yescharacteristic
310C2#3366611yescharacteristic
311C2#3367611yescharacteristic
312C2#3379911yescharacteristic
313C2#3380411yescharacteristic
subgroupG/H
center, socle, prime radicalC23C22×D8
commutator, Frattini, cosocleC22×C8C24
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ C42×C8 ◁ G
LECSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C4×#4992
C4×#5002
#135392
#134532
#132762
#131772
#131762
#131112
#131092
#128792