Finite Group Databasebeta

← #507981

Subgroups — #507981

Order 512.

462 conjugacy classes of subgroups.

The subgroup lattice has 313 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33258C211yesmaximal, characteristic
2#21276C211yesmaximal, characteristic
3#13538C211yesmaximal, characteristic
4#13530C211yesmaximal, characteristic
5#13506C211yesmaximal, characteristic
6#13481C211yesmaximal, characteristic
7#13167C212yesmaximal
8#13150C212yesmaximal
9#13109C212yesmaximal
10#12938C212yesmaximal
11#12591C211yesmaximal, characteristic
12C2×C4×Q16C2211yescharacteristic
13#2859—21no—
14#2295—21no—
15C2×#367C2212yes—
16C2×#366C2212yes—
17C2×#358C2212yes—
18C2×#358C2212yes—
19C2×#346C2212yes—
20#1969C2211yescharacteristic
21#1969C2211yescharacteristic
22#1942—21no—
23#1942—21no—
24#1942C2211yescharacteristic
25#1942C2211yescharacteristic
26#1942C2212yes—
27#1942C2212yes—
28#1933—21no—
29#1933—21no—
30#1845C2211yescharacteristic
31#1845C2211yescharacteristic
32#1834—21no—
33C4×#107C2211yescharacteristic
34C4×#103—21no—
35C42×C8C2211yescharacteristic
36#1380C2212yes—
37#1380C2212yes—
38#1380C2212yes—
39#1380C2212yes—
40#1374C2212yes—
41#1374C2211yescharacteristic
42#1374C2211yescharacteristic
43C22×Q16C2311yescharacteristic
44C2×#125—41no—
45C2×C4×Q8—21no—
46C22×C16C2312yes—
47C22×C16C2312yes—
48C4×Q16—22no—
49C4×Q16—22no—
50C2×#107—21no—
51C2×#107—21no—
52C2×#107C2312yes—
53C2×#107C2312yes—
54C2×#107C2311yescharacteristic
55C2×#107C2311yescharacteristic
56C2×#107C2311yescharacteristic
57C2×#103—21no—
58C2×#103—21no—
59C2×#103—21no—
60C2×C4×C8D411yescharacteristic
61C2×C4×C8D411yescharacteristic
62C2×C4×C8D411yescharacteristic
63C2×C4×C8C2311yescharacteristic
64C2×C4×C8C2311yescharacteristic
65C2×C4×C8C2311yescharacteristic
66#391—21no—
67#391—21no—
68#389—22no—
69#389—22no—
70#389—21no—
71#389—21no—
72#389—41no—
73#389—41no—
74#387—41no—
75#387—41no—
76#384—21no—
77#384—21no—
78#382—41no—
79C4×C4⋊C4—21no—
80C4×C4⋊C4—41no—
81#376—41no—
82C43D411yescharacteristic
83#367—24no—
84#366—24no—
85#358—24no—
86#358—24no—
87#346—24no—
88#340—22no—
89#340—22no—
90#340—21no—
91#340—21no—
92#340—21no—
93C22×Q8—21no—
94C2×Q16—22no—
95C2×Q16—21no—
96C2×Q16—22no—
97C2×Q16#4112yes—
98C22×C8C2×D411yescharacteristic
99C22×C8C2×D411yescharacteristic
100C22×C8C2×D411yescharacteristic
101C22×C8C2411yescharacteristic
102#125—84no—
103C4×Q8—24no—
104C4×Q8—42no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—22no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—42no—
114C2×C4⋊C4—42no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
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#4114yes—
134#107—21no—
135#107—22no—
136#107—22no—
137#107—22no—
138#107—22no—
139#107—22no—
140#107—22no—
141#107—42no—
142#107—42no—
143#107#4112yes—
144#103—24no—
145#103—42no—
146#103—42no—
147C4×C8—22no—
148C4×C8—22no—
149C4×C8—22no—
150C4×C8—21no—
151C4×C8—21no—
152C4×C8—22no—
153C4×C8—41no—
154#95—41no—
155#95—41no—
156#95—41no—
157#95—41no—
158#95—41no—
159#95—41no—
160#95—41no—
161#95—42no—
162#95—42no—
163C2×Q8—22no—
164C2×Q8—41no—
165C2×Q8—41no—
166C2×Q8—41no—
167C2×Q8—41no—
168C2×Q8—41no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4C2×D811yescharacteristic
176C22×C4C2×D811yescharacteristic
177C22×C4C2×D811yescharacteristic
178C22×C4C2×D811yescharacteristic
179C22×C4C2×D811yescharacteristic
180C22×C4C2×D811yescharacteristic
181C22×C4C22×D411yescharacteristic
182Q16—24no—
183Q16—42no—
184C2×C8—21no—
185C2×C8—21no—
186C2×C8—21no—
187C2×C8—21no—
188C2×C8—21no—
189C2×C8—21no—
190C2×C8—21no—
191C2×C8#13512yes—
192C2×C8#13712yes—
193C2×C8C2×#4111yescharacteristic
194C2×C8C2×#4111yescharacteristic
195C2×C8C2×#4112yes—
196C2×C82−1+412yes—
197C4⋊C4—22no—
198C4⋊C4—44no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—42no—
206C4⋊C4—41no—
207C4⋊C4—42no—
208C4⋊C4—82no—
209C4⋊C4—82no—
210C4⋊C4—82no—
211C4⋊C4—82no—
212C4⋊C4—84no—
213C4⋊C4—84no—
214C4⋊C4—82no—
215C4⋊C4—82no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—22no—
223C42—22no—
224C42—22no—
225C42—41no—
226C42—44no—
227C42—82no—
228C16—24no—
229C16—42no—
230C23C22×D811yescharacteristic
231Q8—42no—
232Q8—42no—
233Q8—81no—
234Q8—81no—
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—21no—
249C2×C4—21no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—81no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—82no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4—82no—
260C2×C4—82no—
261C2×C4—81no—
262C2×C4—82no—
263C2×C4—81no—
264C2×C4—82no—
265C2×C4—81no—
266C2×C4—82no—
267C2×C4—81no—
268C2×C4#50912yes—
269C2×C4#51012yes—
270C2×C4#51012yes—
271C2×C4#52511yescharacteristic
272C2×C4#53211yescharacteristic
273C2×C4#53611yescharacteristic
274C2×C4C2×#13511yescharacteristic
275C2×C4C2×#13711yescharacteristic
276C2×C4#57511yescharacteristic
277C8—22no—
278C8—22no—
279C8—41no—
280C8#55212yes—
281C8#55212yes—
282C22#310011yescharacteristic
283C22#316911yescharacteristic
284C22#322611yescharacteristic
285C22C2×#50911yescharacteristic
286C22C2×#51011yescharacteristic
287C22C2×#51011yescharacteristic
288C22#341411yescharacteristic
289C4—22no—
290C4—22no—
291C4—22no—
292C4—41no—
293C4—41no—
294C4—41no—
295C4—82no—
296C4—82no—
297C4—161no—
298C4—162no—
299C4—161no—
300C4—162no—
301C4#261111yescharacteristic
302C4#310711yescharacteristic
303C4#318111yescharacteristic
304C4#323211yescharacteristic
305C2#2957211yescharacteristic
306C2#3367211yescharacteristic
307C2#3367611yescharacteristic
308C2#3373711yescharacteristic
309C2#3374911yescharacteristic
310C2#3380211yescharacteristic
311C2#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
#332582
#212762
#135382
#135302
#135062
#134812
#131672
#131502
#131092
#129382
#125912