Finite Group Databasebeta

← #508742

Subgroups — #508742

Order 512.

434 conjugacy classes of subgroups.

The subgroup lattice has 297 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33257C211yesmaximal, characteristic
2C4×#500C211yesmaximal, characteristic
3#13539C212yesmaximal
4#13537C211yesmaximal, characteristic
5#13537C211yesmaximal, characteristic
6#13507C212yesmaximal
7#13452C211yesmaximal, characteristic
8#13451C211yesmaximal, characteristic
9#13112C212yesmaximal
10#13110C212yesmaximal
11#12894C211yesmaximal, characteristic
12C2×#500C2211yescharacteristic
13#2864—21no—
14C4×C4⋊Q8—21no—
15C2×#367C2212yes—
16C2×#366C2212yes—
17#1990—21no—
18#1942—21no—
19#1942C2211yescharacteristic
20#1942C2211yescharacteristic
21#1942C2211yescharacteristic
22#1942C2211yescharacteristic
23#1942C2212yes—
24#1941—21no—
25#1941—21no—
26#1846C2211yescharacteristic
27#1846C2211yescharacteristic
28#1845C2211yescharacteristic
29#1835—21no—
30C4×#107—21no—
31C4×#107C2212yes—
32C42×C8C2211yescharacteristic
33#1380C2212yes—
34#1380C2212yes—
35#1380C2212yes—
36#1380C2212yes—
37#1380C2212yes—
38#1380C2212yes—
39#1374C2212yes—
40#1374C2211yescharacteristic
41#1374C2211yescharacteristic
42#1374C2212yes—
43C2×C4⋊Q8—21no—
44C2×C4×Q8—41no—
45C22×C16C2312yes—
46C22×C16C2312yes—
47#500—24no—
48C2×#107—21no—
49C2×#107—21no—
50C2×#107C2312yes—
51C2×#107C2311yescharacteristic
52C2×#107C2311yescharacteristic
53C2×#107C2311yescharacteristic
54C2×#107C2311yescharacteristic
55C2×#107C2312yes—
56C2×#106—21no—
57C2×#106—21no—
58C2×C4×C8D411yescharacteristic
59C2×C4×C8D411yescharacteristic
60C2×C4×C8D411yescharacteristic
61C2×C4×C8C2311yescharacteristic
62C2×C4×C8C2311yescharacteristic
63C2×C4×C8C2311yescharacteristic
64#391—41no—
65#389—22no—
66#389—21no—
67#389—21no—
68#389—21no—
69#389—21no—
70#389—41no—
71#387—41no—
72#387—41no—
73#387—41no—
74#387—41no—
75#384—21no—
76#382—21no—
77#382—21no—
78C4×C4⋊C4—22no—
79C4×C4⋊C4—41no—
80C43D411yescharacteristic
81#367—24no—
82#366—24no—
83#340—21no—
84#340—21no—
85#340—21no—
86#340—21no—
87#340—22no—
88#340—22no—
89C22×Q8—41no—
90C22×C8C2×D411yescharacteristic
91C22×C8C2×D411yescharacteristic
92C22×C8C2×D411yescharacteristic
93C22×C8C2411yescharacteristic
94C4⋊Q8—24no—
95C4⋊Q8—42no—
96C4×Q8—84no—
97C2×C4⋊C4—22no—
98C2×C4⋊C4—22no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—41no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—42no—
106C2×C4⋊C4—41no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4—41no—
111C2×C42—42no—
112C2×C42D811yescharacteristic
113C2×C42D811yescharacteristic
114C2×C42D811yescharacteristic
115C2×C42D811yescharacteristic
116C2×C42C2×D411yescharacteristic
117C2×C42C2×D411yescharacteristic
118C2×C42C2×D411yescharacteristic
119C2×C16—22no—
120C2×C16—22no—
121C2×C16—22no—
122C2×C16—22no—
123C2×C16—22no—
124C2×C16—22no—
125#107—24no—
126#107—22no—
127#107—22no—
128#107—22no—
129#107—24no—
130#107—21no—
131#107—21no—
132#107—21no—
133#107—21no—
134#107—42no—
135#107#4114yes—
136#106—42no—
137#106—42no—
138C4×C8—22no—
139C4×C8—22no—
140C4×C8—22no—
141C4×C8—22no—
142C4×C8—21no—
143C4×C8—21no—
144C4×C8—41no—
145#95—42no—
146#95—42no—
147#95—41no—
148#95—41no—
149#95—41no—
150#95—41no—
151#95—41no—
152#95—41no—
153#95—41no—
154#95—41no—
155C2×Q8—44no—
156C2×Q8—82no—
157C2×Q8—82no—
158C22×C4—42no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4—42no—
164C22×C4C2×D811yescharacteristic
165C22×C4C2×D811yescharacteristic
166C22×C4C2×D811yescharacteristic
167C22×C4C2×D811yescharacteristic
168C22×C4C2×D811yescharacteristic
169C22×C4C2×D811yescharacteristic
170C22×C4C22×D411yescharacteristic
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8#13712yes—
179C2×C8#13712yes—
180C2×C8C2×#4112yes—
181C2×C82−1+412yes—
182C2×C82−1+411yescharacteristic
183C2×C82−1+411yescharacteristic
184C4⋊C4—24no—
185C4⋊C4—44no—
186C4⋊C4—42no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—42no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—82no—
198C4⋊C4—84no—
199C4⋊C4—82no—
200C4⋊C4—82no—
201C4⋊C4—82no—
202C4⋊C4—82no—
203C4⋊C4—82no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—22no—
211C42—22no—
212C42—22no—
213C42—41no—
214C42—84no—
215C16—42no—
216C16—42no—
217C23C22×D811yescharacteristic
218Q8—88no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
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—44no—
235C2×C4—82no—
236C2×C4—82no—
237C2×C4—81no—
238C2×C4—81no—
239C2×C4—82no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4—82no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—82no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4#50812yes—
253C2×C4#50912yes—
254C2×C4#51012yes—
255C2×C4#52511yescharacteristic
256C2×C4#53611yescharacteristic
257C2×C4#53611yescharacteristic
258C2×C4C2×#13711yescharacteristic
259C2×C4C2×#13711yescharacteristic
260C2×C4#57511yescharacteristic
261C8—22no—
262C8—22no—
263C8—41no—
264C8#54112yes—
265C8#54112yes—
266C22#310011yescharacteristic
267C22#322611yescharacteristic
268C22#322611yescharacteristic
269C22C2×#50811yescharacteristic
270C22C2×#50911yescharacteristic
271C22C2×#51011yescharacteristic
272C22#341411yescharacteristic
273C4—22no—
274C4—22no—
275C4—22no—
276C4—41no—
277C4—41no—
278C4—41no—
279C4—84no—
280C4—162no—
281C4—161no—
282C4—161no—
283C4—161no—
284C4—161no—
285C4#263411yescharacteristic
286C4#311311yescharacteristic
287C4#323611yescharacteristic
288C4#323711yescharacteristic
289C2#3009111yescharacteristic
290C2#3366811yescharacteristic
291C2#3367411yescharacteristic
292C2#3379411yescharacteristic
293C2#3379911yescharacteristic
294C2#3380311yescharacteristic
295C2#3380511yescharacteristic
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
#332572
C4×#5002
#135392
#135372
#135072
#134522
#134512
#131122
#131102
#128942