Finite Group Databasebeta

← #507651

Subgroups — #507651

Order 512.

456 conjugacy classes of subgroups.

The subgroup lattice has 311 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33258C211yesmaximal, characteristic
2C4×#499C211yesmaximal, characteristic
3#13507C212yesmaximal
4#13453C212yesmaximal
5#13177C211yesmaximal, characteristic
6#13177C211yesmaximal, characteristic
7#13176C211yesmaximal, characteristic
8#13176C211yesmaximal, characteristic
9#13168C212yesmaximal
10#13167C212yesmaximal
11#12653C211yesmaximal, characteristic
12C2×#499C2211yescharacteristic
13#2859—21no—
14C4×#125—21no—
15C2×#367C2212yes—
16C2×#367C2212yes—
17C2×#366C2212yes—
18C2×#366C2212yes—
19C2×C4⋊C16C2211yescharacteristic
20C2×C4⋊C16C2211yescharacteristic
21C2×#346C2212yes—
22#1991—21no—
23#1942—21no—
24#1942—21no—
25#1942C2211yescharacteristic
26#1942C2212yes—
27#1942C2211yescharacteristic
28#1942C2212yes—
29#1941—21no—
30#1846C2211yescharacteristic
31#1845C2211yescharacteristic
32#1845C2211yescharacteristic
33#1834—21no—
34C4×#107C2211yescharacteristic
35C4×#107C2211yescharacteristic
36C4×#106—21no—
37C42×C8C2211yescharacteristic
38#1380C2212yes—
39#1380C2212yes—
40#1380C2212yes—
41#1380C2212yes—
42#1374C2212yes—
43C2×#125—21no—
44C2×#125—41no—
45C22×C16C2312yes—
46C22×C16C2312yes—
47#499—22no—
48#499—22no—
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#367—42no—
84#366—24no—
85#366—42no—
86C4⋊C16Q814yes—
87C4⋊C16Q814yes—
88#346—42no—
89#340—22no—
90#340—22no—
91#340—21no—
92#340—21no—
93#340—21no—
94#340—21no—
95C22×C8C2×D411yescharacteristic
96C22×C8C2×D411yescharacteristic
97C22×C8C2×D411yescharacteristic
98C22×C8C2411yescharacteristic
99#125—24no—
100#125—42no—
101#125—84no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4—22no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—42no—
113C2×C4⋊C4—42no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C42—41no—
119C2×C42—41no—
120C2×C42D811yescharacteristic
121C2×C42D811yescharacteristic
122C2×C42D811yescharacteristic
123C2×C42D811yescharacteristic
124C2×C42C2×D411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C16—22no—
128C2×C16—22no—
129C2×C16—22no—
130C2×C16—22no—
131C2×C16C2×Q814yes—
132C2×C16C2×Q814yes—
133#107—21no—
134#107—21no—
135#107—22no—
136#107—22no—
137#107—21no—
138#107—22no—
139#107—21no—
140#107—22no—
141#107—21no—
142#107—21no—
143#107—42no—
144#107—42no—
145#107#4112yes—
146#107#4112yes—
147#106—24no—
148#106—42no—
149C4×C8—21no—
150C4×C8—21no—
151C4×C8—21no—
152C4×C8—21no—
153C4×C8—41no—
154C4×C8—41no—
155C4×C8Q1614yes—
156C4×C8C2×Q812yes—
157C4×C8C2×Q812yes—
158#95—41no—
159#95—41no—
160#95—41no—
161#95—41no—
162#95—41no—
163#95—41no—
164#95—42no—
165#95—42no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—42no—
171C22×C4—42no—
172C22×C4C2×D811yescharacteristic
173C22×C4C2×D811yescharacteristic
174C22×C4C2×D811yescharacteristic
175C22×C4C2×D811yescharacteristic
176C22×C4C2×D811yescharacteristic
177C22×C4C2×D811yescharacteristic
178C22×C4C22×D411yescharacteristic
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—21no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8C4⋊Q812yes—
186C2×C8C2×Q1612yes—
187C2×C8C2×Q1612yes—
188C2×C8C22×Q811yescharacteristic
189C2×C8C22×Q811yescharacteristic
190C2×C8C2×#4111yescharacteristic
191C2×C8C2×#4111yescharacteristic
192C2×C8H(5,𝔽2)11yescharacteristic
193C2×C82−1+411yescharacteristic
194C4⋊C4—22no—
195C4⋊C4—22no—
196C4⋊C4—44no—
197C4⋊C4—44no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—41no—
202C4⋊C4—42no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—42no—
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—22no—
221C42—22no—
222C42—41no—
223C42—41no—
224C42—82no—
225C42—82no—
226C42C4⋊Q812yes—
227C42C2×Q1612yes—
228C16—24no—
229C16—24no—
230C23C22×D811yescharacteristic
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
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—42no—
246C2×C4—42no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4—82no—
252C2×C4—81no—
253C2×C4—82no—
254C2×C4—82no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—82no—
258C2×C4—81no—
259C2×C4—82no—
260C2×C4—81no—
261C2×C4—82no—
262C2×C4—81no—
263C2×C4#50012yes—
264C2×C4#50012yes—
265C2×C4#50912yes—
266C2×C4#51012yes—
267C2×C4#52511yescharacteristic
268C2×C4C2×C4⋊Q811yescharacteristic
269C2×C4#53711yescharacteristic
270C2×C4C22×Q1611yescharacteristic
271C2×C4#57511yescharacteristic
272C2×C4#57511yescharacteristic
273C8—22no—
274C8—22no—
275C8—22no—
276C8#55411yescharacteristic
277C8#55411yescharacteristic
278C8#55711yescharacteristic
279C8#55711yescharacteristic
280C22#310011yescharacteristic
281C22C2×#50011yescharacteristic
282C22#324511yescharacteristic
283C22C2×#50911yescharacteristic
284C22C2×#51011yescharacteristic
285C22#341411yescharacteristic
286C22#341411yescharacteristic
287C4—22no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—82no—
293C4—82no—
294C4—161no—
295C4—162no—
296C4—161no—
297C4—162no—
298C4#225514yes—
299C4#258411yescharacteristic
300C4#310411yescharacteristic
301C4#316611yescharacteristic
302C4#324911yescharacteristic
303C2#2931211yescharacteristic
304C2#3367511yescharacteristic
305C2#3367611yescharacteristic
306C2C2×#225511yescharacteristic
307C2#3373211yescharacteristic
308C2#3381711yescharacteristic
309C2#3381811yescharacteristic
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
#135072
#134532
#131772
#131762
#131682
#131672
#126532