Finite Group Databasebeta

← #325382

Subgroups — #325382

Order 512.

538 conjugacy classes of subgroups.

The subgroup lattice has 287 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33258C211yesmaximal, characteristic
2#29132C212yesmaximal
3C8×C4⋊Q8C211yesmaximal, characteristic
4#10626C214yesmaximal
5#9906C212yesmaximal
6#8645C212yesmaximal
7#8645C212yesmaximal
8#8274C211yesmaximal, characteristic
9C2×C8×Q8C2212yes—
10#2859C2212yes—
11C4×C4⋊Q8C2211yescharacteristic
12#2099—22no—
13#2043—22no—
14#1984C2212yes—
15#1942—21no—
16#1942—21no—
17#1942—21no—
18#1942—21no—
19#1939—21no—
20#1939—21no—
21#1935—24no—
22#1845C2211yescharacteristic
23#1845C2211yescharacteristic
24#1842C2211yescharacteristic
25#1834C2212yes—
26#1803C2214yes—
27#1803C2214yes—
28C8×C4⋊C4—21no—
29C8×C4⋊C4—21no—
30#1767C2212yes—
31C42×C8C2211yescharacteristic
32C2×#335C2212yes—
33#1296C2214yes—
34#1296C2214yes—
35#1277C2212yes—
36C2×C4⋊Q8D411yescharacteristic
37C2×#125—22no—
38C2×C4×Q8C2312yes—
39C8×Q8—24no—
40C8×Q8—24no—
41C2×#107—21no—
42C2×#107—21no—
43C2×#107—21no—
44C2×#107—21no—
45C2×C4⋊C8—22no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8C2314yes—
49C2×C4⋊C8C2312yes—
50C2×#103—24no—
51C2×#103—24no—
52C2×#97—22no—
53C2×C4×C8—22no—
54C2×C4×C8D411yescharacteristic
55C2×C4×C8D411yescharacteristic
56C2×C4×C8D411yescharacteristic
57C2×C4×C8D411yescharacteristic
58C2×C4×C8C2311yescharacteristic
59C2×C4×C8C2311yescharacteristic
60#391D412yes—
61#389—21no—
62#389—21no—
63#389—22no—
64#389—22no—
65#389—22no—
66#389—22no—
67#384D411yescharacteristic
68#384C2312yes—
69#384C2312yes—
70#382—22no—
71C4×C4⋊C4—21no—
72C4×C4⋊C4—21no—
73C43C2311yescharacteristic
74#340—22no—
75#340—22no—
76#340—24no—
77#340—24no—
78#336—22no—
79#336—22no—
80#336—22no—
81#335—24no—
82C22×Q8C2×D412yes—
83C22×C8—22no—
84C22×C8—24no—
85C22×C8C2×D411yescharacteristic
86C22×C8C2×D411yescharacteristic
87C22×C8C2×D411yescharacteristic
88C22×C8C2×D411yescharacteristic
89C4⋊Q8—24no—
90#125—84no—
91C4×Q8—22no—
92C4×Q8—22no—
93C4×Q8—22no—
94C4×Q8—22no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—22no—
100C2×C4⋊C4—22no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—42no—
107C2×C4⋊C4—42no—
108C2×C4⋊C4C2×D412yes—
109C2×C42—22no—
110C2×C42C2×D411yescharacteristic
111C2×C42C2×D411yescharacteristic
112C2×C42C2×D411yescharacteristic
113C2×C42C2×D411yescharacteristic
114C2×C42#4111yescharacteristic
115C2×C42#4111yescharacteristic
116C2×C42C2411yescharacteristic
117#107—42no—
118#107—42no—
119#107—42no—
120#107—42no—
121C4⋊C8—24no—
122C4⋊C8—22no—
123C4⋊C8—22no—
124C4⋊C8—24no—
125C4⋊C8—42no—
126C4⋊C8—42no—
127C4⋊C8—44no—
128#103—48no—
129#103—84no—
130#97—82no—
131C4×C8—22no—
132C4×C8—22no—
133C4×C8—22no—
134C4×C8—41no—
135C4×C8—41no—
136C4×C8—44no—
137C4×C8#4114yes—
138#95—22no—
139#95—22no—
140#95—42no—
141#95—42no—
142C2×Q8—22no—
143C2×Q8—22no—
144C2×Q8—22no—
145C2×Q8—22no—
146C2×Q8—22no—
147C2×Q8#13514yes—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—42no—
151C22×C4—42no—
152C22×C4#12111yescharacteristic
153C22×C4#12111yescharacteristic
154C22×C4#12111yescharacteristic
155C22×C4#12111yescharacteristic
156C22×C4C22×D411yescharacteristic
157C22×C4C22×D411yescharacteristic
158C22×C4C2×#4111yescharacteristic
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—42no—
168C2×C8—44no—
169C2×C8—44no—
170C2×C8—42no—
171C2×C8—42no—
172C2×C8—44no—
173C2×C8#12412yes—
174C2×C8#12412yes—
175C2×C8#13712yes—
176C2×C8#13712yes—
177C4⋊C4—24no—
178C4⋊C4—24no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—42no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—44no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—82no—
193C4⋊C4—82no—
194C4⋊C4—84no—
195C4⋊C4—84no—
196C42—22no—
197C42—21no—
198C42—21no—
199C42—21no—
200C42—21no—
201C42—21no—
202C42—21no—
203C42—22no—
204C42—22no—
205C42—42no—
206C42—42no—
207C42C2×#4112yes—
208C422−1+412yes—
209C23C2×#12111yescharacteristic
210Q8—24no—
211Q8—24no—
212Q8—42no—
213Q8—42no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—24no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—82no—
233C2×C4—82no—
234C2×C4—82no—
235C2×C4—82no—
236C2×C4—82no—
237C2×C4—82no—
238C2×C4#47212yes—
239C2×C4#47312yes—
240C2×C4C2×#12411yescharacteristic
241C2×C4#53611yescharacteristic
242C2×C4#54712yes—
243C2×C4#55612yes—
244C2×C4C2×#13512yes—
245C2×C4C2×#13711yescharacteristic
246C2×C4C2×#13711yescharacteristic
247C2×C4#57511yescharacteristic
248C2×C4#57511yescharacteristic
249C2×C4#57611yescharacteristic
250C2×C4#57811yescharacteristic
251C8—22no—
252C8—41no—
253C8—41no—
254C8—84no—
255C8—82no—
256C8#49114yes—
257C22#254711yescharacteristic
258C22#303711yescharacteristic
259C22#303711yescharacteristic
260C22#305011yescharacteristic
261C22#306111yescharacteristic
262C22C2×#47211yescharacteristic
263C22C2×#47311yescharacteristic
264C4—22no—
265C4—22no—
266C4—22no—
267C4—44no—
268C4—41no—
269C4—41no—
270C4—82no—
271C4—162no—
272C4—162no—
273C4C2×#49111yescharacteristic
274C4#314211yescharacteristic
275C4#323711yescharacteristic
276C4#323711yescharacteristic
277C4#333612yes—
278C4#333912yes—
279C2#1926411yescharacteristic
280C2#1926511yescharacteristic
281C2#1934411yescharacteristic
282C2#1934511yescharacteristic
283C2#2870811yescharacteristic
284C2#2872511yescharacteristic
285C2#2873111yescharacteristic
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
#291322
C8×C4⋊Q82
#106262
#99062
#86452
#82742