Finite Group Databasebeta

← #325482

Subgroups — #325482

Order 512.

518 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30304C211yesmaximal, characteristic
2#29150C211yesmaximal, characteristic
3#29141C211yesmaximal, characteristic
4#22242C211yesmaximal, characteristic
5#10623C212yesmaximal
6#10617C212yesmaximal
7#9903C211yesmaximal, characteristic
8#9897C211yesmaximal, characteristic
9#8657C212yesmaximal
10#8653C212yesmaximal
11#8277C211yesmaximal, characteristic
12C2×#446C2212yes—
13#2868C2211yescharacteristic
14#2859C2211yescharacteristic
15C4×C4⋊Q8C2211yescharacteristic
16#2083—22no—
17#2057—22no—
18#2026—22no—
19#2024—22no—
20#1984C2212yes—
21#1960—21no—
22#1956—21no—
23#1917—22no—
24#1917—22no—
25#1845C2211yescharacteristic
26#1845C2211yescharacteristic
27#1836—21no—
28#1834—21no—
29#1834C2211yescharacteristic
30#1834C2211yescharacteristic
31#1831C2211yescharacteristic
32#1803C2212yes—
33#1803C2212yes—
34#1803C2212yes—
35#1803C2212yes—
36#1767C2211yescharacteristic
37C4×C4⋊C8C2211yescharacteristic
38#1744C2211yescharacteristic
39C2×#334C2212yes—
40#1296C2212yes—
41#1296C2212yes—
42#1296C2212yes—
43#1296C2212yes—
44#1277C2212yes—
45C2×C4⋊Q8—21no—
46C2×C4⋊Q8—21no—
47C2×C4⋊Q8—21no—
48C2×C4⋊Q8D411yescharacteristic
49C2×#125—21no—
50C2×C4×Q8C2312yes—
51#446—24no—
52#446—24no—
53C2×#107—22no—
54C2×#107—22no—
55C2×C4⋊C8—22no—
56C2×C4⋊C8C2312yes—
57C2×C4⋊C8C2312yes—
58C2×C4⋊C8C2312yes—
59C2×#103—22no—
60C2×#103—22no—
61C2×#103—22no—
62C2×#103—22no—
63C2×#97—22no—
64C2×#97—21no—
65C2×C4×C8—21no—
66C2×C4×C8C2311yescharacteristic
67C2×C4×C8C2311yescharacteristic
68#391D412yes—
69#389—21no—
70#389—21no—
71#389—21no—
72#389—21no—
73#389—21no—
74#389—21no—
75#384—21no—
76#384—21no—
77#384—21no—
78#384D411yescharacteristic
79#384C2311yescharacteristic
80#384C2311yescharacteristic
81#384C2311yescharacteristic
82#384C2311yescharacteristic
83#382—21no—
84C4×C4⋊C4—21no—
85C4×C4⋊C4—21no—
86C43C2311yescharacteristic
87#340—22no—
88#340—22no—
89#340—22no—
90#340—22no—
91#340—22no—
92#340—22no—
93#336—24no—
94#336—21no—
95#336—21no—
96#336—21no—
97#336—21no—
98#336D412yes—
99#336D412yes—
100#334—24no—
101C22×Q8—41no—
102C22×Q8C2×D412yes—
103C22×C8—22no—
104C22×C8—22no—
105C22×C8—22no—
106C22×C8C2×D412yes—
107C22×C8C2×D412yes—
108C4⋊Q8—22no—
109C4⋊Q8—22no—
110C4⋊Q8—82no—
111C4⋊Q8—82no—
112C4⋊Q8—82no—
113#125—82no—
114C4×Q8—22no—
115C4×Q8—22no—
116C4×Q8—22no—
117C4×Q8—22no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—22no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—21no—
126C2×C4⋊C4—21no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—41no—
136C2×C4⋊C4—41no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—41no—
140C2×C4⋊C4C2×D412yes—
141C2×C42—22no—
142C2×C42C2×D411yescharacteristic
143C2×C42C2×D411yescharacteristic
144C2×C42C2×D411yescharacteristic
145C2×C42C2×D411yescharacteristic
146C2×C42#4111yescharacteristic
147C2×C42#4111yescharacteristic
148C2×C42C2411yescharacteristic
149#107—82no—
150#107—82no—
151C4⋊C8—22no—
152C4⋊C8—22no—
153C4⋊C8—22no—
154C4⋊C8—22no—
155C4⋊C8—22no—
156C4⋊C8—22no—
157C4⋊C8—44no—
158#103—82no—
159#103—82no—
160#103—82no—
161#103—82no—
162#97—44no—
163#97—42no—
164C4×C8—22no—
165C4×C8—42no—
166C4×C8#4114yes—
167#95—22no—
168#95—22no—
169#95—41no—
170#95—41no—
171C2×Q8—22no—
172C2×Q8—22no—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—22no—
177C2×Q8—82no—
178C2×Q8—82no—
179C2×Q8—82no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4#12111yescharacteristic
187C22×C4#12111yescharacteristic
188C22×C4#12111yescharacteristic
189C22×C4#12111yescharacteristic
190C22×C4C22×D411yescharacteristic
191C22×C4C22×D411yescharacteristic
192C22×C4C2×#4111yescharacteristic
193C2×C8—22no—
194C2×C8—22no—
195C2×C8—22no—
196C2×C8—22no—
197C2×C8—22no—
198C2×C8—42no—
199C2×C8—42no—
200C2×C8—42no—
201C2×C8—42no—
202C2×C8—42no—
203C2×C8—42no—
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8#12414yes—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—42no—
211C4⋊C4—42no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—81no—
223C4⋊C4—81no—
224C4⋊C4—81no—
225C4⋊C4—81no—
226C4⋊C4—81no—
227C4⋊C4—81no—
228C4⋊C4—82no—
229C4⋊C4—82no—
230C4⋊C4—82no—
231C4⋊C4—82no—
232C4⋊C4—82no—
233C42—22no—
234C42—22no—
235C42—22no—
236C42—41no—
237C42—41no—
238C42—42no—
239C42—42no—
240C42#13712yes—
241C42#13712yes—
242C42C2×#4112yes—
243C422−1+412yes—
244C23C2×#12111yescharacteristic
245Q8—42no—
246Q8—42no—
247Q8—42no—
248Q8—42no—
249Q8—164no—
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—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4#47012yes—
281C2×C4#47012yes—
282C2×C4C2×#12411yescharacteristic
283C2×C4#53611yescharacteristic
284C2×C4#54712yes—
285C2×C4#55612yes—
286C2×C4C2×#13711yescharacteristic
287C2×C4C2×#13711yescharacteristic
288C2×C4#57612yes—
289C2×C4#57712yes—
290C2×C4#57812yes—
291C8—24no—
292C8—42no—
293C8—82no—
294C8—82no—
295C8—82no—
296C22#254711yescharacteristic
297C22#304311yescharacteristic
298C22#304411yescharacteristic
299C22C2×#47011yescharacteristic
300C22#305811yescharacteristic
301C22#306811yescharacteristic
302C22#306911yescharacteristic
303C4—22no—
304C4—22no—
305C4—22no—
306C4—41no—
307C4—41no—
308C4—82no—
309C4—82no—
310C4—161no—
311C4—161no—
312C4—161no—
313C4—161no—
314C4#313712yes—
315C4#324212yes—
316C4#335712yes—
317C4#335712yes—
318C2#1943511yescharacteristic
319C2#1944111yescharacteristic
320C2#1952211yescharacteristic
321C2#1953011yescharacteristic
322C2#2871111yescharacteristic
323C2#2872911yescharacteristic
324C2#2873511yescharacteristic
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
#303042
#291502
#291412
#222422
#106232
#106172
#99032
#98972
#86572
#86532
#82772