Finite Group Databasebeta

← #324839

Subgroups — #324839

Order 512.

526 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30228C211yesmaximal, characteristic
2#29210C211yesmaximal, characteristic
3#28755C211yesmaximal, characteristic
4#22299C211yesmaximal, characteristic
5#10598C212yesmaximal
6#10590C212yesmaximal
7#9902C211yesmaximal, characteristic
8#9694C211yesmaximal, characteristic
9#9566C212yesmaximal
10#9565C212yesmaximal
11#8277C211yesmaximal, characteristic
12C2×#491—21no—
13#2868C2211yescharacteristic
14#2859C2211yescharacteristic
15C4×#125C2211yescharacteristic
16#2099—22no—
17#2099—22no—
18#2059—22no—
19#2043—22no—
20#1991—21no—
21#1990C2212yes—
22#1990C2212yes—
23#1981C2212yes—
24#1981C2212yes—
25#1960—21no—
26#1948C2212yes—
27#1947C2212yes—
28#1939—22no—
29#1939C2212yes—
30#1916—22no—
31#1846—21no—
32#1842C2211yescharacteristic
33C8×C4⋊C4C2212yes—
34#1767C2211yescharacteristic
35C4×C4⋊C8C2211yescharacteristic
36#1744C2211yescharacteristic
37C2×#334C2211yescharacteristic
38C2×#334C2211yescharacteristic
39C2×#332C2212yes—
40C2×#332C2212yes—
41#1296C2212yes—
42#1296C2212yes—
43#1277C2211yescharacteristic
44#1277C2211yescharacteristic
45C2×C4⋊Q8—21no—
46C2×C4⋊Q8—21no—
47C2×C4⋊Q8C2312yes—
48C2×#125—21no—
49C2×#125D411yescharacteristic
50#491—44no—
51C2×#107—22no—
52C2×#106—22no—
53C2×C4⋊C8—22no—
54C2×C4⋊C8—22no—
55C2×C4⋊C8C2312yes—
56C2×C4⋊C8C2311yescharacteristic
57C2×C4⋊C8C2311yescharacteristic
58C2×C4⋊C8C2311yescharacteristic
59C2×C4⋊C8C2311yescharacteristic
60C2×#103—22no—
61C2×#103—22no—
62C2×#103—22no—
63C2×#103—22no—
64C2×#97—21no—
65C2×C4×C8—21no—
66C2×C4×C8—22no—
67C2×C4×C8C2311yescharacteristic
68C2×C4×C8C2311yescharacteristic
69#389—22no—
70#389—22no—
71#389D412yes—
72#387—22no—
73#384—22no—
74#384—22no—
75#384C2312yes—
76#382—21no—
77#382D411yescharacteristic
78C4×C4⋊C4—22no—
79C4×C4⋊C4C2312yes—
80C43C2311yescharacteristic
81#340—22no—
82#340—24no—
83#340—22no—
84#340—22no—
85#340—22no—
86#336—22no—
87#336—22no—
88#336—21no—
89#336—21no—
90#336D412yes—
91#336D412yes—
92#334—22no—
93#334—22no—
94#332—24no—
95#332—24no—
96C22×Q8—22no—
97C22×C8—21no—
98C22×C8—21no—
99C22×C8—22no—
100C22×C8—21no—
101C22×C8—21no—
102C22×C8C2×D411yescharacteristic
103C22×C8C2×D412yes—
104C22×C8C2×D411yescharacteristic
105C4⋊Q8—22no—
106C4⋊Q8—22no—
107C4⋊Q8—22no—
108C4⋊Q8—22no—
109C4⋊Q8—42no—
110C4⋊Q8—42no—
111C4⋊Q8—81no—
112C4⋊Q8—81no—
113#125—22no—
114#125—81no—
115#125—81no—
116#125SD1614yes—
117C2×C4⋊C4—22no—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—22no—
120C2×C4⋊C4—22no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—42no—
125C2×C4⋊C4—42no—
126C2×C4⋊C4—42no—
127C2×C4⋊C4C2×D412yes—
128C2×C4⋊C4C2×D412yes—
129C2×C42—22no—
130C2×C42C2×D411yescharacteristic
131C2×C42C2×D412yes—
132C2×C42C2×D411yescharacteristic
133C2×C42#4112yes—
134C2×C42C2411yescharacteristic
135#107—82no—
136#106—82no—
137C4⋊C8—22no—
138C4⋊C8—22no—
139C4⋊C8—21no—
140C4⋊C8—21no—
141C4⋊C8—21no—
142C4⋊C8—21no—
143C4⋊C8—21no—
144C4⋊C8—21no—
145C4⋊C8—82no—
146C4⋊C8—82no—
147C4⋊C8#4112yes—
148C4⋊C8#4112yes—
149#103—44no—
150#103—44no—
151#103—82no—
152#103—82no—
153#97—42no—
154C4×C8—21no—
155C4×C8—21no—
156C4×C8—21no—
157C4×C8—21no—
158C4×C8—42no—
159C4×C8—82no—
160#95—22no—
161#95—22no—
162#95—22no—
163#95—42no—
164C2×Q8—42no—
165C2×Q8—42no—
166C2×Q8—42no—
167C2×Q8—42no—
168C2×Q8—42no—
169C2×Q8—42no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—42no—
173C22×C4—42no—
174C22×C4#12112yes—
175C22×C4#12112yes—
176C22×C4C22×D411yescharacteristic
177C22×C4C22×D411yescharacteristic
178C22×C4C2×#4111yescharacteristic
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—22no—
182C2×C8—22no—
183C2×C8—22no—
184C2×C8—22no—
185C2×C8—22no—
186C2×C8—22no—
187C2×C8—22no—
188C2×C8—41no—
189C2×C8—41no—
190C2×C8—41no—
191C2×C8—41no—
192C2×C8—42no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—42no—
200C2×C8—42no—
201C4⋊C4—22no—
202C4⋊C4—28no—
203C4⋊C4—22no—
204C4⋊C4—22no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—42no—
212C4⋊C4—42no—
213C4⋊C4—82no—
214C4⋊C4—82no—
215C4⋊C4—84no—
216C4⋊C4—84no—
217C4⋊C4—84no—
218C4⋊C4C2×SD1614yes—
219C42—21no—
220C42—21no—
221C42—22no—
222C42—22no—
223C42—42no—
224C42—42no—
225C42—42no—
226C42C2×SD1612yes—
227C42#13512yes—
228C42C2×#4111yescharacteristic
229C42C2×#4111yescharacteristic
230C422−1+411yescharacteristic
231C422−1+411yescharacteristic
232C23C2×#12111yescharacteristic
233Q8—82no—
234Q8—82no—
235Q8—82no—
236Q8—82no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—24no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—82no—
250C2×C4—82no—
251C2×C4—82no—
252C2×C4—82no—
253C2×C4—82no—
254C2×C4—82no—
255C2×C4#46514yes—
256C2×C4#53211yescharacteristic
257C2×C4#53611yescharacteristic
258C2×C4#54811yescharacteristic
259C2×C4#54811yescharacteristic
260C2×C4#55611yescharacteristic
261C2×C4#55611yescharacteristic
262C2×C4C22×SD1611yescharacteristic
263C2×C4C2×#13511yescharacteristic
264C2×C4#57611yescharacteristic
265C2×C4#57611yescharacteristic
266C2×C4#57712yes—
267C2×C4#57812yes—
268C8—42no—
269C8—42no—
270C8—41no—
271C8—41no—
272C8—42no—
273C8—81no—
274C8—81no—
275C8—82no—
276C22#254511yescharacteristic
277C22#304612yes—
278C22C2×#46511yescharacteristic
279C22#305811yescharacteristic
280C22#306912yes—
281C4—21no—
282C4—21no—
283C4—24no—
284C4—42no—
285C4—44no—
286C4—82no—
287C4—162no—
288C4—162no—
289C4#317411yescharacteristic
290C4#317711yescharacteristic
291C4#324212yes—
292C4#336111yescharacteristic
293C4#336111yescharacteristic
294C4#336211yescharacteristic
295C4#336211yescharacteristic
296C2#1941512yes—
297C2#1954612yes—
298C2#2864011yescharacteristic
299C2#2866411yescharacteristic
300C2#2867311yescharacteristic
subgroupG/H
center, socle, prime radicalC23C2×#121
commutator, Frattini, cosocleC2×C42C24
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ 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
#302282
#292102
#287552
#222992
#105982
#105902
#99022
#96942
#95662
#95652
#82772