Finite Group Databasebeta

← #345593

Subgroups — #345593

Order 512.

514 conjugacy classes of subgroups.

The subgroup lattice has 289 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26527C212yesmaximal
2#26513C212yesmaximal
3#10602C212yesmaximal
4#10600C212yesmaximal
5#10576C212yesmaximal
6#9823C211yesmaximal, characteristic
7#9594C211yesmaximal, characteristic
8#9594C211yesmaximal, characteristic
9#9058C212yesmaximal
10C2×#500C2211yescharacteristic
11#2571C2212yes—
12#2365C2212yes—
13#2101—22no—
14#2097—22no—
15#2087—22no—
16#2066—22no—
17#1990C2212yes—
18#1988C2212yes—
19#1981C2212yes—
20#1956C2212yes—
21#1949—22no—
22#1948C2212yes—
23#1948C2212yes—
24#1939C2212yes—
25#1939C2212yes—
26#1919—22no—
27#1863—22no—
28#1845C2211yescharacteristic
29#1805—22no—
30C4×#107C2211yescharacteristic
31C4×#107C2211yescharacteristic
32C2×#335C2211yescharacteristic
33C2×#335C2211yescharacteristic
34C2×#332C2212yes—
35C2×C82C2211yescharacteristic
36#1296C2212yes—
37#1279C2212yes—
38#1279C2212yes—
39C2×C4⋊Q8C2312yes—
40C2×C4×Q8—22no—
41#500—41no—
42#500Q814yes—
43C2×#107—41no—
44C2×#107—41no—
45C2×#107D411yescharacteristic
46C2×#107D411yescharacteristic
47C2×#107D411yescharacteristic
48C2×#107D411yescharacteristic
49C2×#106—22no—
50C2×#106—22no—
51C2×C4⋊C8—22no—
52C2×C4⋊C8—22no—
53C2×C4⋊C8C2312yes—
54C2×C4⋊C8C2312yes—
55C2×#103—22no—
56C2×#103—22no—
57C2×#103—22no—
58C2×#103—22no—
59C2×C4×C8C2311yescharacteristic
60C2×C4×C8C2311yescharacteristic
61C2×C4×C8C2311yescharacteristic
62#400—42no—
63#391—22no—
64#389—22no—
65#389—22no—
66#389—22no—
67#387—42no—
68#384C2312yes—
69#382—22no—
70#382—22no—
71C4×C4⋊C4—22no—
72C4×C4⋊C4C2312yes—
73C4×C4⋊C4C2312yes—
74#340—22no—
75#340—22no—
76#340—22no—
77#340—22no—
78#340—22no—
79#340—22no—
80#340D412yes—
81#340D412yes—
82#336—22no—
83#336—22no—
84#335—41no—
85#335—41no—
86#332—42no—
87C82—41no—
88C22×Q8—22no—
89C22×C8—21no—
90C22×C8—22no—
91C22×C8—22no—
92C22×C8C2×D411yescharacteristic
93C22×C8C2×D411yescharacteristic
94C22×C8C2×D411yescharacteristic
95C22×C8C2×D411yescharacteristic
96C4⋊Q8—22no—
97C4⋊Q8—22no—
98C4⋊Q8—22no—
99C4⋊Q8C2×Q814yes—
100C4×Q8—44no—
101C4×Q8—82no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4—42no—
108C2×C4⋊C4—42no—
109C2×C4⋊C4C2×D412yes—
110C2×C4⋊C4C2×D412yes—
111C2×C4⋊C4C2×D412yes—
112C2×C4⋊C4C2×D412yes—
113C2×C42—22no—
114C2×C42—22no—
115C2×C42—42no—
116C2×C42C2411yescharacteristic
117#107—22no—
118#107—22no—
119#107—44no—
120#107—41no—
121#107—41no—
122#107—82no—
123#106—44no—
124#106—82no—
125C4⋊C8—22no—
126C4⋊C8—22no—
127C4⋊C8—22no—
128C4⋊C8—22no—
129C4⋊C8—44no—
130C4⋊C8—82no—
131#103—44no—
132#103—82no—
133#103—82no—
134#103—82no—
135C4×C8—21no—
136C4×C8—21no—
137C4×C8—21no—
138C4×C8—21no—
139C4×C8—21no—
140C4×C8C2×Q812yes—
141#95—22no—
142#95—22no—
143#95—42no—
144#95—42no—
145#95—42no—
146#95—42no—
147#95—42no—
148C2×Q8—24no—
149C2×Q8—42no—
150C2×Q8—42no—
151C2×Q8—42no—
152C2×Q8—42no—
153C2×Q8—42no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—42no—
159C22×C4—42no—
160C22×C4C22×D411yescharacteristic
161C22×C4C22×D411yescharacteristic
162C22×C4H(5,𝔽2)11yescharacteristic
163C2×C8—22no—
164C2×C8—22no—
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—22no—
168C2×C8—21no—
169C2×C8—21no—
170C2×C8—21no—
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—42no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—42no—
182C2×C8#13512yes—
183C2×C8#13512yes—
184C4⋊C4—24no—
185C4⋊C4—24no—
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—82no—
201C4⋊C4—84no—
202C4⋊C4—162no—
203C42—42no—
204C42—42no—
205C42—42no—
206C42—42no—
207C42—84no—
208C42C22×Q811yescharacteristic
209C42H(5,𝔽2)11yescharacteristic
210C422−1+411yescharacteristic
211C422−1+411yescharacteristic
212C23D4211yescharacteristic
213Q8—44no—
214Q8—44no—
215Q8—82no—
216Q8—82no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—44no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—82no—
233C2×C4—82no—
234C2×C4—82no—
235C2×C4—82no—
236C2×C4—82no—
237C2×C4#53711yescharacteristic
238C2×C4#53711yescharacteristic
239C2×C4#54311yescharacteristic
240C2×C4D4×Q811yescharacteristic
241C2×C4D4×Q811yescharacteristic
242C2×C4#56311yescharacteristic
243C2×C4C2×#13511yescharacteristic
244C2×C4C2×#13511yescharacteristic
245C2×C4#57511yescharacteristic
246C2×C4#57511yescharacteristic
247C2×C4#57611yescharacteristic
248C2×C4#57611yescharacteristic
249C2×C4#57811yescharacteristic
250C2×C4#57811yescharacteristic
251C8—24no—
252C8—22no—
253C8—22no—
254C8—41no—
255C8—41no—
256C8—82no—
257C8—82no—
258C22#268311yescharacteristic
259C22#327311yescharacteristic
260C22#327711yescharacteristic
261C22#328311yescharacteristic
262C22#328711yescharacteristic
263C22#329111yescharacteristic
264C22#329311yescharacteristic
265C4—21no—
266C4—21no—
267C4—84no—
268C4—82no—
269C4—82no—
270C4—82no—
271C4—82no—
272C4—162no—
273C4#325011yescharacteristic
274C4#325011yescharacteristic
275C4#325911yescharacteristic
276C4#326111yescharacteristic
277C4#338011yescharacteristic
278C4#338311yescharacteristic
279C4#338911yescharacteristic
280C4#339011yescharacteristic
281C2#1995411yescharacteristic
282C2#1996511yescharacteristic
283C2#2002011yescharacteristic
284C2#2030611yescharacteristic
285C2#3123611yescharacteristic
286C2#3123811yescharacteristic
287C2#3125611yescharacteristic
subgroupG/H
center, socle, prime radicalC23D42
commutator, Frattini, cosocleC2×C42C24
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#265272
#265132
#106022
#106002
#105762
#98232
#95942
#90582