Finite Group Databasebeta

← #504297

Subgroups — #504297

Order 512.

460 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#28827C211yesmaximal, characteristic
2#23157C211yesmaximal, characteristic
3#13538C212yesmaximal
4#13516C212yesmaximal
5#13282C211yesmaximal, characteristic
6#13275C211yesmaximal, characteristic
7#13177C211yesmaximal, characteristic
8#13177C212yesmaximal
9#13159C211yesmaximal, characteristic
10#13111C212yesmaximal
11C4×#367C211yesmaximal, characteristic
12C2×#500C2211yescharacteristic
13#2552—21no—
14#2365—21no—
15C2×#367C2212yes—
16C2×#367C2211yescharacteristic
17C2×#367C2211yescharacteristic
18C2×C4⋊C16C2212yes—
19C2×C4⋊C16C2211yescharacteristic
20C2×C4×C16C2211yescharacteristic
21#2083—22no—
22#1988—21no—
23#1947—21no—
24#1942C2212yes—
25#1942C2212yes—
26#1918—22no—
27#1845C2211yescharacteristic
28#1845C2212yes—
29C4×#107C2212yes—
30C4×#107C2211yescharacteristic
31C4×#107C2211yescharacteristic
32C8×C4⋊C4C2211yescharacteristic
33#1380C2211yescharacteristic
34#1380C2212yes—
35#1380C2212yes—
36#1380C2212yes—
37#1380C2212yes—
38#1380C2212yes—
39#1380C2211yescharacteristic
40#1374C2212yes—
41C2×C4⋊Q8—21no—
42C2×#125—41no—
43C2×C4×Q8—41no—
44C22×C16C2311yescharacteristic
45C22×C16C2312yes—
46C22×C16C2311yescharacteristic
47#500—22no—
48#500Q814yes—
49C2×#107—21no—
50C2×#107—21no—
51C2×#107—22no—
52C2×#107C2312yes—
53C2×#107C2311yescharacteristic
54C2×#107C2311yescharacteristic
55C2×#107C2311yescharacteristic
56C2×#107C2312yes—
57C2×#107C2311yescharacteristic
58C2×C4⋊C8D411yescharacteristic
59C2×C4×C8C2312yes—
60C2×C4×C8C2311yescharacteristic
61#398—42no—
62#391—41no—
63#389—22no—
64#389—22no—
65#389—41no—
66#387—42no—
67#384—22no—
68#384—21no—
69C4×C4⋊C4—22no—
70C4×C4⋊C4—21no—
71C4×C4⋊C4—21no—
72C4×C4⋊C4D411yescharacteristic
73#367—22no—
74#367—22no—
75#367—24no—
76C4⋊C16—24no—
77C4⋊C16—22no—
78C4×C16—22no—
79#340—21no—
80#340—22no—
81#340—21no—
82#340—22no—
83#340—22no—
84#336D412yes—
85C22×Q8—41no—
86C22×C8C2×D412yes—
87C22×C8C2×D411yescharacteristic
88C22×C8C2411yescharacteristic
89C4⋊Q8—24no—
90C4⋊Q8—42no—
91#125—84no—
92C4×Q8—84no—
93C2×C4⋊C4—22no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—22no—
99C2×C4⋊C4—41no—
100C2×C4⋊C4—42no—
101C2×C4⋊C4—41no—
102C2×C4⋊C4—42no—
103C2×C4⋊C4—42no—
104C2×C4⋊C4—42no—
105C2×C4⋊C4—41no—
106C2×C4⋊C4D811yescharacteristic
107C2×C4⋊C4D811yescharacteristic
108C2×C42—42no—
109C2×C42—41no—
110C2×C42—41no—
111C2×C42C2×D412yes—
112C2×C42C2×D411yescharacteristic
113C2×C16—21no—
114C2×C16—21no—
115C2×C16—21no—
116C2×C16—22no—
117C2×C16—22no—
118C2×C16—22no—
119C2×C16—21no—
120C2×C16—21no—
121C2×C16#4112yes—
122#107—24no—
123#107—22no—
124#107—21no—
125#107—21no—
126#107—21no—
127#107—22no—
128#107—21no—
129#107—21no—
130#107—21no—
131#107—22no—
132#107—21no—
133#107—81no—
134#107—82no—
135#107C2×Q814yes—
136#107#4112yes—
137C4⋊C8—22no—
138C4×C8—22no—
139C4×C8—22no—
140C4×C8C2×Q812yes—
141C4×C8#4112yes—
142#95—41no—
143#95—42no—
144#95—41no—
145#95—42no—
146#95—42no—
147#95D812yes—
148C2×Q8—44no—
149C2×Q8—82no—
150C2×Q8—82no—
151C22×C4—41no—
152C22×C4—42no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—42no—
157C22×C4C2×D812yes—
158C22×C4C2×D811yescharacteristic
159C22×C4C2×D812yes—
160C22×C4C2×D811yescharacteristic
161C22×C4C22×D411yescharacteristic
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—22no—
165C2×C8—22no—
166C2×C8—22no—
167C2×C8C22⋊Q812yes—
168C2×C8C22×Q811yescharacteristic
169C2×C8C2×#4111yescharacteristic
170C2×C8C2×#4111yescharacteristic
171C2×C8C2×#4111yescharacteristic
172C2×C82−1+411yescharacteristic
173C2×C82−1+411yescharacteristic
174C4⋊C4—22no—
175C4⋊C4—24no—
176C4⋊C4—22no—
177C4⋊C4—42no—
178C4⋊C4—41no—
179C4⋊C4—44no—
180C4⋊C4—41no—
181C4⋊C4—41no—
182C4⋊C4—41no—
183C4⋊C4—42no—
184C4⋊C4—41no—
185C4⋊C4—42no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—84no—
189C4⋊C4—84no—
190C4⋊C4—84no—
191C4⋊C4—82no—
192C4⋊C4—162no—
193C4⋊C4—161no—
194C4⋊C4SD3214yes—
195C42—22no—
196C42—22no—
197C42—84no—
198C42—82no—
199C42—82no—
200C42C22⋊Q812yes—
201C42#13712yes—
202C16—22no—
203C16—42no—
204C16—41no—
205C23C22×D811yescharacteristic
206Q8—88no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—42no—
215C2×C4—44no—
216C2×C4—81no—
217C2×C4—82no—
218C2×C4—82no—
219C2×C4—81no—
220C2×C4—81no—
221C2×C4—81no—
222C2×C4—81no—
223C2×C4—82no—
224C2×C4—81no—
225C2×C4—81no—
226C2×C4—81no—
227C2×C4—82no—
228C2×C4—81no—
229C2×C4—82no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4#47412yes—
233C2×C4#47412yes—
234C2×C4C2×SD3214yes—
235C2×C4C2×SD3212yes—
236C2×C4#50912yes—
237C2×C4C2×C22⋊Q811yescharacteristic
238C2×C4#54711yescharacteristic
239C2×C4#54811yescharacteristic
240C2×C4C2×#13711yescharacteristic
241C2×C4#57711yescharacteristic
242C2×C4#57811yescharacteristic
243C8—22no—
244C8—42no—
245C8#52911yescharacteristic
246C8#54111yescharacteristic
247C8#55711yescharacteristic
248C8#55711yescharacteristic
249C22C2×#47411yescharacteristic
250C22#333411yescharacteristic
251C22#335811yescharacteristic
252C22C22×SD3211yescharacteristic
253C22C2×#50911yescharacteristic
254C22#341611yescharacteristic
255C22#341711yescharacteristic
256C4—22no—
257C4—24no—
258C4—42no—
259C4—84no—
260C4—82no—
261C4—161no—
262C4—161no—
263C4—161no—
264C4—162no—
265C4#222614yes—
266C4#245311yescharacteristic
267C4#308211yescharacteristic
268C4#335611yescharacteristic
269C4#337411yescharacteristic
270C2#2650611yescharacteristic
271C2C2×#222611yescharacteristic
272C2#3363211yescharacteristic
273C2#3390211yescharacteristic
274C2#3392011yescharacteristic
275C2#3392611yescharacteristic
276C2#3393511yescharacteristic
subgroupG/H
center, socle, prime radicalC23C22×D8
commutator, Frattini, cosocleC22×C8C24
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ C8×C4⋊C4 ◁ 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
#288272
#231572
#135382
#135162
#132822
#132752
#131772
#131592
#131112
C4×#3672