Finite Group Databasebeta

← #503778

Subgroups — #503778

Order 512.

466 conjugacy classes of subgroups.

The subgroup lattice has 295 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#28827C211yesmaximal, characteristic
2#22808C211yesmaximal, characteristic
3#13531C212yesmaximal
4#13477C212yesmaximal
5#13177C211yesmaximal, characteristic
6#13177C212yesmaximal
7#13159C211yesmaximal, characteristic
8#13110C212yesmaximal
9#12906C211yesmaximal, characteristic
10#12812C211yesmaximal, characteristic
11C4×#358C211yesmaximal, characteristic
12C2×C4×Q16C2211yescharacteristic
13#2552—21no—
14#2355—21no—
15C2×#367C2212yes—
16C2×#367C2212yes—
17C2×#367C2212yes—
18C2×C4⋊C16C2211yescharacteristic
19C2×C4⋊C16C2212yes—
20C2×#358C2211yescharacteristic
21C2×#358C2211yescharacteristic
22C2×#358C2212yes—
23C2×C4×C16C2211yescharacteristic
24#2083—22no—
25#1969C2212yes—
26#1947—21no—
27#1942C2212yes—
28#1928—22no—
29#1845C2211yescharacteristic
30#1845C2211yescharacteristic
31#1845C2212yes—
32#1803—21no—
33C4×#107C2212yes—
34C4×#107C2211yescharacteristic
35C8×C4⋊C4C2211yescharacteristic
36#1380C2212yes—
37#1380C2211yescharacteristic
38#1380C2212yes—
39#1380C2211yescharacteristic
40#1374C2212yes—
41C22×Q16C2311yescharacteristic
42C2×#125—41no—
43C2×C4×Q8—21no—
44C22×C16C2312yes—
45C22×C16C2311yescharacteristic
46C22×C16C2311yescharacteristic
47C4×Q16—22no—
48C4×Q16Q814yes—
49C2×#107—21no—
50C2×#107—22no—
51C2×#107—21no—
52C2×#107C2312yes—
53C2×#107C2311yescharacteristic
54C2×#107C2312yes—
55C2×#107C2311yescharacteristic
56C2×#107C2311yescharacteristic
57C2×C4⋊C8D411yescharacteristic
58C2×#103—21no—
59C2×#103—22no—
60C2×C4×C8C2312yes—
61C2×C4×C8C2311yescharacteristic
62#398—42no—
63#391—22no—
64#389—22no—
65#389—41no—
66#387—42no—
67#384—21no—
68#384—22no—
69#384—21no—
70#382—41no—
71C4×C4⋊C4—22no—
72C4×C4⋊C4—21no—
73C4×C4⋊C4—41no—
74C4×C4⋊C4D411yescharacteristic
75#367—24no—
76#367—42no—
77#367—42no—
78C4⋊C16—24no—
79C4⋊C16—22no—
80#358—22no—
81#358—22no—
82#358—42no—
83C4×C16—22no—
84#340—22no—
85#340—21no—
86#340—22no—
87#336D412yes—
88C22×Q8—21no—
89C2×Q16—21no—
90C2×Q16—21no—
91C2×Q16—21no—
92C2×Q16—21no—
93C2×Q16—21no—
94C2×Q16C2×Q812yes—
95C22×C8C2×D412yes—
96C22×C8C2×D411yescharacteristic
97C22×C8C2411yescharacteristic
98#125—84no—
99C4×Q8—24no—
100C4×Q8—42no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—41no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—42no—
109C2×C4⋊C4—42no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—42no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4D811yescharacteristic
115C2×C4⋊C4D811yescharacteristic
116C2×C42—41no—
117C2×C42—41no—
118C2×C42—42no—
119C2×C42C2×D412yes—
120C2×C42C2×D411yescharacteristic
121C2×C16—21no—
122C2×C16—21no—
123C2×C16—21no—
124C2×C16—21no—
125C2×C16—22no—
126C2×C16—22no—
127C2×C16—22no—
128C2×C16#4112yes—
129C2×C16#4112yes—
130#107—21no—
131#107—21no—
132#107—21no—
133#107—22no—
134#107—22no—
135#107—22no—
136#107—21no—
137#107—22no—
138#107—21no—
139#107—81no—
140#107—81no—
141#107—82no—
142#107C2×Q812yes—
143C4⋊C8—22no—
144#103—24no—
145#103—82no—
146C4×C8—22no—
147C4×C8—22no—
148C4×C8C2×Q812yes—
149C4×C8#4112yes—
150#95—42no—
151#95—41no—
152#95—42no—
153#95—42no—
154#95—42no—
155#95D812yes—
156C2×Q8—22no—
157C2×Q8—41no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8—41no—
161C2×Q8—41no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4—42no—
166C22×C4—41no—
167C22×C4—42no—
168C22×C4C2×D812yes—
169C22×C4C2×D811yescharacteristic
170C22×C4C2×D812yes—
171C22×C4C2×D811yescharacteristic
172C22×C4C22×D411yescharacteristic
173Q16—22no—
174Q16—22no—
175Q16—41no—
176Q16—41no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—22no—
180C2×C8—22no—
181C2×C8—22no—
182C2×C8C22⋊Q812yes—
183C2×C8C22×Q811yescharacteristic
184C2×C8C2×#4111yescharacteristic
185C2×C8C2×#4111yescharacteristic
186C2×C8C2×#4111yescharacteristic
187C2×C8H(5,𝔽2)11yescharacteristic
188C2×C82−1+411yescharacteristic
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—41no—
192C4⋊C4—44no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—42no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—41no—
201C4⋊C4—84no—
202C4⋊C4—84no—
203C4⋊C4—82no—
204C4⋊C4—82no—
205C4⋊C4—161no—
206C4⋊C4—161no—
207C4⋊C4—162no—
208C4⋊C4SD3214yes—
209C42—22no—
210C42—22no—
211C42—44no—
212C42—82no—
213C42—162no—
214C42C22⋊Q812yes—
215C42#13712yes—
216C16—22no—
217C16—22no—
218C16—42no—
219C23C22×D811yescharacteristic
220Q8—42no—
221Q8—42no—
222Q8—81no—
223Q8—81no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—81no—
234C2×C4—81no—
235C2×C4—81no—
236C2×C4—81no—
237C2×C4—81no—
238C2×C4—81no—
239C2×C4—82no—
240C2×C4—82no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—82no—
244C2×C4—82no—
245C2×C4—82no—
246C2×C4—81no—
247C2×C4—82no—
248C2×C4—81no—
249C2×C4#47412yes—
250C2×C4#47412yes—
251C2×C4C2×SD3214yes—
252C2×C4C2×SD3212yes—
253C2×C4#51012yes—
254C2×C4C2×C22⋊Q811yescharacteristic
255C2×C4#54711yescharacteristic
256C2×C4#55011yescharacteristic
257C2×C4C2×#13711yescharacteristic
258C2×C4#57611yescharacteristic
259C2×C4#57811yescharacteristic
260C8—22no—
261C8—42no—
262C8#53311yescharacteristic
263C8#54411yescharacteristic
264C8#55211yescharacteristic
265C8#55311yescharacteristic
266C22C2×#47411yescharacteristic
267C22#333411yescharacteristic
268C22#339111yescharacteristic
269C22C22×SD3211yescharacteristic
270C22C2×#51011yescharacteristic
271C22#341611yescharacteristic
272C22#341611yescharacteristic
273C4—22no—
274C4—24no—
275C4—42no—
276C4—82no—
277C4—82no—
278C4—161no—
279C4—161no—
280C4—162no—
281C4—162no—
282C4#222514yes—
283C4#244111yescharacteristic
284C4#308311yescharacteristic
285C4#335711yescharacteristic
286C4#339811yescharacteristic
287C2#2608611yescharacteristic
288C2C2×#222511yescharacteristic
289C2#3363411yescharacteristic
290C2#3390211yescharacteristic
291C2#3392311yescharacteristic
292C2#3395911yescharacteristic
293C2#3396711yescharacteristic
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
#228082
#135312
#134772
#131772
#131592
#131102
#129062
#128122
C4×#3582