Finite Group Databasebeta

← #330800

Subgroups — #330800

Order 512.

476 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33258C211yesmaximal, characteristic
2#29997C212yesmaximal
3#21341C211yesmaximal, characteristic
4#10658C212yesmaximal
5#10652C211yesmaximal, characteristic
6#10649C211yesmaximal, characteristic
7#10626C212yesmaximal
8#10618C211yesmaximal, characteristic
9#10617C211yesmaximal, characteristic
10#9906C212yesmaximal
11#8784C211yesmaximal, characteristic
12#2859C2212yes—
13#2295C2211yescharacteristic
14#2088—22no—
15#2086—22no—
16#2068—22no—
17#2066—22no—
18#1984C2211yescharacteristic
19#1984C2211yescharacteristic
20#1948C2212yes—
21#1947C2212yes—
22#1942—21no—
23#1942—21no—
24#1942—21no—
25#1942—21no—
26#1939C2211yescharacteristic
27#1939C2211yescharacteristic
28#1916—21no—
29#1916—21no—
30#1845C2211yescharacteristic
31#1845C2211yescharacteristic
32#1842C2212yes—
33#1834C2212yes—
34#1803C2212yes—
35#1803C2212yes—
36#1768—21no—
37#1767C2211yescharacteristic
38#1746—21no—
39C42×C8C2211yescharacteristic
40#1296C2212yes—
41#1296C2212yes—
42#1296C2212yes—
43#1296C2212yes—
44#1277C2211yescharacteristic
45#1277C2211yescharacteristic
46#1277C2212yes—
47C2×#125—22no—
48C2×C4×Q8C2311yescharacteristic
49C2×#107—21no—
50C2×#107—21no—
51C2×#107—21no—
52C2×#107—21no—
53C2×#107—22no—
54C2×#106—22no—
55C2×C4⋊C8—21no—
56C2×C4⋊C8—21no—
57C2×C4⋊C8—22no—
58C2×C4⋊C8—22no—
59C2×C4⋊C8C2312yes—
60C2×C4⋊C8C2312yes—
61C2×C4⋊C8C2311yescharacteristic
62C2×C4⋊C8C2311yescharacteristic
63C2×#103—22no—
64C2×#103—22no—
65C2×#97—21no—
66C2×C4×C8D411yescharacteristic
67C2×C4×C8D411yescharacteristic
68C2×C4×C8D411yescharacteristic
69C2×C4×C8D411yescharacteristic
70C2×C4×C8C2311yescharacteristic
71C2×C4×C8C2311yescharacteristic
72#391D411yescharacteristic
73#391D411yescharacteristic
74#389—22no—
75#389—22no—
76#389—22no—
77#389—22no—
78#389D411yescharacteristic
79#389D411yescharacteristic
80#387—21no—
81#387—21no—
82#384C2312yes—
83#384C2312yes—
84#382—22no—
85C4×C4⋊C4—21no—
86C4×C4⋊C4C2311yescharacteristic
87#376—21no—
88C43C2311yescharacteristic
89#340—22no—
90#340—22no—
91#340—22no—
92#340—22no—
93#340—22no—
94#340—22no—
95#336—21no—
96#336—21no—
97#336—21no—
98#336—21no—
99#336—21no—
100#336—21no—
101#336—21no—
102C22×Q8C2×D411yescharacteristic
103C22×C8—21no—
104C22×C8—21no—
105C22×C8—22no—
106C22×C8—22no—
107C22×C8C2×D411yescharacteristic
108C22×C8C2×D411yescharacteristic
109C22×C8C2×D411yescharacteristic
110C22×C8C2×D411yescharacteristic
111#125—84no—
112C4×Q8—22no—
113C4×Q8—22no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
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—42no—
124C2×C4⋊C4—42no—
125C2×C4⋊C4C2×D411yescharacteristic
126C2×C4⋊C4C2×D411yescharacteristic
127C2×C4⋊C4C2×D411yescharacteristic
128C2×C42—21no—
129C2×C42—21no—
130C2×C42C2×D411yescharacteristic
131C2×C42C2×D411yescharacteristic
132C2×C42C2×D411yescharacteristic
133C2×C42C2×D411yescharacteristic
134C2×C42#4111yescharacteristic
135C2×C42#4111yescharacteristic
136C2×C42C2411yescharacteristic
137#107—42no—
138#107—42no—
139#107—42no—
140#107—42no—
141#107—82no—
142#106—82no—
143C4⋊C8—22no—
144C4⋊C8—22no—
145C4⋊C8—22no—
146C4⋊C8—22no—
147C4⋊C8—22no—
148C4⋊C8—22no—
149C4⋊C8—42no—
150C4⋊C8—42no—
151C4⋊C8—82no—
152C4⋊C8—82no—
153#103—82no—
154#103—82no—
155#97—42no—
156C4×C8—22no—
157C4×C8—22no—
158C4×C8—22no—
159C4×C8—22no—
160C4×C8—41no—
161C4×C8—41no—
162#95—21no—
163#95—21no—
164#95—21no—
165#95—21no—
166#95—21no—
167#95—21no—
168#95—21no—
169#95—42no—
170#95—42no—
171C2×Q8—22no—
172C2×Q8—21no—
173C2×Q8—22no—
174C2×Q8—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—42no—
180C22×C4—42no—
181C22×C4#12111yescharacteristic
182C22×C4#12111yescharacteristic
183C22×C4#12111yescharacteristic
184C22×C4#12111yescharacteristic
185C22×C4C22×D411yescharacteristic
186C22×C4C22×D411yescharacteristic
187C22×C4C2×#4111yescharacteristic
188C2×C8—21no—
189C2×C8—21no—
190C2×C8—21no—
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—21no—
195C2×C8—21no—
196C2×C8—21no—
197C2×C8—21no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—42no—
201C2×C8—42no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—42no—
207C2×C8—42no—
208C2×C8—42no—
209C2×C8—42no—
210C2×C8#13512yes—
211C2×C8#13712yes—
212C4⋊C4—22no—
213C4⋊C4—21no—
214C4⋊C4—22no—
215C4⋊C4—21no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—42no—
227C4⋊C4—82no—
228C4⋊C4—82no—
229C4⋊C4—84no—
230C4⋊C4—84no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—22no—
237C42—21no—
238C42—22no—
239C42—22no—
240C42—41no—
241C42—41no—
242C42—41no—
243C42—41no—
244C422−1+412yes—
245C422−1+412yes—
246C23C2×#12111yescharacteristic
247Q8—42no—
248Q8—42no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—82no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4—82no—
277C2×C4—82no—
278C2×C4—82no—
279C2×C4#47212yes—
280C2×C4#47312yes—
281C2×C4#53611yescharacteristic
282C2×C4#53611yescharacteristic
283C2×C4#53612yes—
284C2×C4#54112yes—
285C2×C4C2×#13511yescharacteristic
286C2×C4C2×#13711yescharacteristic
287C2×C4#57511yescharacteristic
288C2×C4#57511yescharacteristic
289C2×C4#57611yescharacteristic
290C2×C4#57712yes—
291C2×C4#57811yescharacteristic
292C8—22no—
293C8—22no—
294C8—41no—
295C8—41no—
296C8—81no—
297C8—81no—
298C8—82no—
299C8—82no—
300C22#262111yescharacteristic
301C22#303511yescharacteristic
302C22#303711yescharacteristic
303C22#306011yescharacteristic
304C22#306111yescharacteristic
305C22C2×#47211yescharacteristic
306C22C2×#47311yescharacteristic
307C4—22no—
308C4—22no—
309C4—22no—
310C4—41no—
311C4—41no—
312C4—81no—
313C4—81no—
314C4—81no—
315C4—81no—
316C4—162no—
317C4—162no—
318C4#323111yescharacteristic
319C4#323211yescharacteristic
320C4#323611yescharacteristic
321C4#324011yescharacteristic
322C4#324112yes—
323C4#324212yes—
324C2#1922211yescharacteristic
325C2#1922811yescharacteristic
326C2#1934511yescharacteristic
327C2#1934911yescharacteristic
328C2#2987111yescharacteristic
329C2#2988211yescharacteristic
330C2#2988611yescharacteristic
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
#332582
#299972
#213412
#106582
#106522
#106492
#106262
#106182
#106172
#99062
#87842