Finite Group Databasebeta

← #507464

Subgroups — #507464

Order 512.

448 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33258C211yesmaximal, characteristic
2C4×#499C211yesmaximal, characteristic
3#13516C212yesmaximal
4#13515C212yesmaximal
5#13284C211yesmaximal, characteristic
6#13284C211yesmaximal, characteristic
7#13110C212yesmaximal
8#13109C212yesmaximal
9#12908C211yesmaximal, characteristic
10#12890C211yesmaximal, characteristic
11#12653C211yesmaximal, characteristic
12C2×#499C2211yescharacteristic
13#2859—21no—
14C4×#125—21no—
15C2×#367C2212yes—
16C2×#366C2212yes—
17C2×C4⋊C16C2212yes—
18C2×#346C2211yescharacteristic
19C2×#346C2211yescharacteristic
20#1991—21no—
21#1942—21no—
22#1942—21no—
23#1942C2212yes—
24#1942C2211yescharacteristic
25#1942C2212yes—
26#1942C2211yescharacteristic
27#1941—21no—
28#1846C2211yescharacteristic
29#1845C2211yescharacteristic
30#1845C2211yescharacteristic
31#1834—21no—
32C4×#107C2211yescharacteristic
33C4×#107C2211yescharacteristic
34C4×#106—21no—
35C42×C8C2211yescharacteristic
36#1380C2212yes—
37#1380C2212yes—
38#1380C2212yes—
39#1380C2212yes—
40#1380C2212yes—
41#1380C2212yes—
42#1374C2212yes—
43C2×#125—21no—
44C2×#125—41no—
45C22×C16C2312yes—
46C22×C16C2312yes—
47#499—22no—
48#499Q814yes—
49C2×#107—21no—
50C2×#107—21no—
51C2×#107C2312yes—
52C2×#107C2312yes—
53C2×#107C2311yescharacteristic
54C2×#107C2311yescharacteristic
55C2×#107C2311yescharacteristic
56C2×#107C2311yescharacteristic
57C2×#106—21no—
58C2×#106—21no—
59C2×C4×C8D411yescharacteristic
60C2×C4×C8D411yescharacteristic
61C2×C4×C8D411yescharacteristic
62C2×C4×C8C2311yescharacteristic
63C2×C4×C8C2311yescharacteristic
64C2×C4×C8C2311yescharacteristic
65#389—21no—
66#389—21no—
67#389—22no—
68#389—22no—
69#389—41no—
70#389—41no—
71#387—41no—
72#387—41no—
73#384—21no—
74#384—21no—
75#382—21no—
76#382—41no—
77C4×C4⋊C4—21no—
78C4×C4⋊C4—21no—
79C4×C4⋊C4—41no—
80C4×C4⋊C4—41no—
81C43D411yescharacteristic
82#367—24no—
83#366—24no—
84C4⋊C16—24no—
85#346—22no—
86#346—22no—
87#340—22no—
88#340—22no—
89#340—21no—
90#340—21no—
91#340—21no—
92#340—21no—
93C22×C8C2×D411yescharacteristic
94C22×C8C2×D411yescharacteristic
95C22×C8C2×D411yescharacteristic
96C22×C8C2411yescharacteristic
97#125—24no—
98#125—42no—
99#125—84no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—41no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4—42no—
111C2×C4⋊C4—42no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C42—41no—
117C2×C42—41no—
118C2×C42D811yescharacteristic
119C2×C42D811yescharacteristic
120C2×C42D811yescharacteristic
121C2×C42D811yescharacteristic
122C2×C42C2×D411yescharacteristic
123C2×C42C2×D411yescharacteristic
124C2×C42C2×D411yescharacteristic
125C2×C16—22no—
126C2×C16—22no—
127C2×C16—22no—
128C2×C16—22no—
129C2×C16—22no—
130C2×C16#4114yes—
131#107—21no—
132#107—21no—
133#107—22no—
134#107—22no—
135#107—22no—
136#107—22no—
137#107—24no—
138#107—42no—
139#107—42no—
140#107C2×Q812yes—
141#107C2×Q812yes—
142#106—24no—
143#106—42no—
144C4×C8—22no—
145C4×C8—22no—
146C4×C8—22no—
147C4×C8—22no—
148C4×C8—22no—
149C4×C8C2×Q812yes—
150C4×C8#4112yes—
151#95—41no—
152#95—41no—
153#95—41no—
154#95—41no—
155#95—41no—
156#95—41no—
157#95—42no—
158#95—42no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4—42no—
164C22×C4—42no—
165C22×C4C2×D811yescharacteristic
166C22×C4C2×D811yescharacteristic
167C22×C4C2×D811yescharacteristic
168C22×C4C2×D811yescharacteristic
169C22×C4C2×D811yescharacteristic
170C22×C4C2×D811yescharacteristic
171C22×C4C22×D411yescharacteristic
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8C22⋊Q812yes—
179C2×C8#13512yes—
180C2×C8#13712yes—
181C2×C8C22×Q811yescharacteristic
182C2×C8C2×#4111yescharacteristic
183C2×C8C2×#4112yes—
184C2×C82−1+412yes—
185C4⋊C4—22no—
186C4⋊C4—22no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—44no—
190C4⋊C4—44no—
191C4⋊C4—41no—
192C4⋊C4—42no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—82no—
200C4⋊C4—82no—
201C4⋊C4—82no—
202C4⋊C4—82no—
203C4⋊C4—82no—
204C4⋊C4—84no—
205C4⋊C4—84no—
206C4⋊C4—82no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—22no—
212C42—22no—
213C42—41no—
214C42—41no—
215C42—82no—
216C42—82no—
217C42C22⋊Q812yes—
218C42#13712yes—
219C16—24no—
220C16—42no—
221C23C22×D811yescharacteristic
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—82no—
244C2×C4—82no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—82no—
248C2×C4—81no—
249C2×C4—82no—
250C2×C4—81no—
251C2×C4—82no—
252C2×C4—81no—
253C2×C4—82no—
254C2×C4#47412yes—
255C2×C4#47412yes—
256C2×C4#50912yes—
257C2×C4#51012yes—
258C2×C4C2×C22⋊Q811yescharacteristic
259C2×C4#53211yescharacteristic
260C2×C4#53611yescharacteristic
261C2×C4C2×#13511yescharacteristic
262C2×C4C2×#13711yescharacteristic
263C2×C4C2×#13711yescharacteristic
264C8—41no—
265C8—41no—
266C8#47914yes—
267C8#55212yes—
268C8#55712yes—
269C22C2×#47411yescharacteristic
270C22#316911yescharacteristic
271C22#322611yescharacteristic
272C22C2×#50911yescharacteristic
273C22C2×#51011yescharacteristic
274C22#341411yescharacteristic
275C22#341411yescharacteristic
276C4—22no—
277C4—22no—
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—82no—
283C4—82no—
284C4—162no—
285C4—161no—
286C4—162no—
287C4—161no—
288C4#256511yescharacteristic
289C4C2×#47911yescharacteristic
290C4#318511yescharacteristic
291C4#323111yescharacteristic
292C2#2917811yescharacteristic
293C2#3362911yescharacteristic
294C2#3363011yescharacteristic
295C2#3373711yescharacteristic
296C2#3374711yescharacteristic
297C2#3380011yescharacteristic
298C2#3380311yescharacteristic
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
#332582
C4×#4992
#135162
#135152
#132842
#131102
#131092
#129082
#128902
#126532