Finite Group Databasebeta

← #325192

Subgroups — #325192

Order 512.

498 conjugacy classes of subgroups.

The subgroup lattice has 329 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33258C211yesmaximal, characteristic
2#29314C212yesmaximal
3#21673C211yesmaximal, characteristic
4#10652C211yesmaximal, characteristic
5#10651C211yesmaximal, characteristic
6#10650C211yesmaximal, characteristic
7#10649C211yesmaximal, characteristic
8#9901C212yesmaximal
9#9619C212yesmaximal
10#9619C212yesmaximal
11C4×#335C211yesmaximal, characteristic
12#2859C2212yes—
13C4×#125C2211yescharacteristic
14#2085—22no—
15#2059—22no—
16#1948C2212yes—
17#1948C2212yes—
18#1947C2212yes—
19#1947C2212yes—
20#1942—21no—
21#1942—21no—
22#1942—21no—
23#1942—21no—
24#1942—22no—
25#1941—22no—
26#1939C2211yescharacteristic
27#1939C2211yescharacteristic
28#1916—21no—
29#1916—21no—
30#1845C2211yescharacteristic
31#1845C2211yescharacteristic
32#1834C2212yes—
33#1831C2211yescharacteristic
34#1771—21no—
35#1771—21no—
36#1770C2211yescharacteristic
37#1770C2211yescharacteristic
38C4×C4⋊C8C2212yes—
39C42×C8C2211yescharacteristic
40C2×#335C2212yes—
41#1296C2212yes—
42#1296C2212yes—
43#1296C2212yes—
44#1296C2212yes—
45#1277C2211yescharacteristic
46#1277C2211yescharacteristic
47C2×#125—22no—
48C2×#125D411yescharacteristic
49C2×#107—21no—
50C2×#107—21no—
51C2×#107—21no—
52C2×#107—21no—
53C2×#107—22no—
54C2×#107—22no—
55C2×#106—22no—
56C2×#106—22no—
57C2×C4⋊C8—21no—
58C2×C4⋊C8—21no—
59C2×C4⋊C8C2311yescharacteristic
60C2×C4⋊C8C2311yescharacteristic
61C2×C4⋊C8C2312yes—
62C2×C4⋊C8C2312yes—
63C2×#97—21no—
64C2×#97—21no—
65C2×C4×C8—22no—
66C2×C4×C8D411yescharacteristic
67C2×C4×C8D411yescharacteristic
68C2×C4×C8D411yescharacteristic
69C2×C4×C8D411yescharacteristic
70C2×C4×C8C2311yescharacteristic
71C2×C4×C8C2311yescharacteristic
72#389—22no—
73#389—22no—
74#389—22no—
75#389—22no—
76#389D411yescharacteristic
77#389D411yescharacteristic
78#387—21no—
79#387—21no—
80#384C2312yes—
81#384C2312yes—
82#382—22no—
83#382D411yescharacteristic
84C4×C4⋊C4—21no—
85C4×C4⋊C4—21no—
86C4×C4⋊C4C2311yescharacteristic
87C4×C4⋊C4C2311yescharacteristic
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—22no—
100#336—21no—
101#336—21no—
102#335Q818yes—
103C22×C8—22no—
104C22×C8—22no—
105C22×C8—21no—
106C22×C8—21no—
107C22×C8C2×D411yescharacteristic
108C22×C8C2×D411yescharacteristic
109C22×C8C2×D411yescharacteristic
110C22×C8C2×D411yescharacteristic
111#125—42no—
112#125—84no—
113C2×C4⋊C4—21no—
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×C4⋊C4C2×D411yescharacteristic
129C2×C42—21no—
130C2×C42—21no—
131C2×C42C2×D411yescharacteristic
132C2×C42C2×D411yescharacteristic
133C2×C42C2×D411yescharacteristic
134C2×C42C2×D411yescharacteristic
135C2×C42#4111yescharacteristic
136C2×C42#4111yescharacteristic
137C2×C42C2411yescharacteristic
138#107—44no—
139#107—42no—
140#107—42no—
141#107—42no—
142#107—42no—
143#107—82no—
144#106—44no—
145#106—82no—
146C4⋊C8—22no—
147C4⋊C8—22no—
148C4⋊C8—22no—
149C4⋊C8—22no—
150C4⋊C8—42no—
151C4⋊C8—42no—
152C4⋊C8C2×Q814yes—
153C4⋊C8C2×Q814yes—
154#97—42no—
155#97—42no—
156C4×C8—22no—
157C4×C8—22no—
158C4×C8—22no—
159C4×C8—41no—
160C4×C8—41no—
161C4×C8—82no—
162C4×C8C2×Q814yes—
163#95—21no—
164#95—21no—
165#95—21no—
166#95—21no—
167#95—21no—
168#95—21no—
169#95—42no—
170#95—42no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—42no—
176C22×C4—42no—
177C22×C4#12111yescharacteristic
178C22×C4#12111yescharacteristic
179C22×C4#12111yescharacteristic
180C22×C4#12111yescharacteristic
181C22×C4C22×D411yescharacteristic
182C22×C4C22×D411yescharacteristic
183C22×C4C2×#4111yescharacteristic
184C2×C8—21no—
185C2×C8—21no—
186C2×C8—21no—
187C2×C8—21no—
188C2×C8—21no—
189C2×C8—21no—
190C2×C8—21no—
191C2×C8—21no—
192C2×C8—24no—
193C2×C8—24no—
194C2×C8—42no—
195C2×C8—42no—
196C2×C8—42no—
197C2×C8—42no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8C4⋊Q812yes—
205C2×C8C4⋊Q812yes—
206C2×C8#13512yes—
207C2×C8#13512yes—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—21no—
211C4⋊C4—21no—
212C4⋊C4—21no—
213C4⋊C4—21no—
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—42no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—82no—
227C4⋊C4—82no—
228C4⋊C4—84no—
229C4⋊C4—84no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—22no—
235C42—21no—
236C42—21no—
237C42—22no—
238C42—22no—
239C42—41no—
240C42—41no—
241C42—41no—
242C42—41no—
243C42C22×Q812yes—
244C422−1+412yes—
245C23C2×#12111yescharacteristic
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
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—41no—
259C2×C4—41no—
260C2×C4—41no—
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—82no—
271C2×C4—82no—
272C2×C4—82no—
273C2×C4—82no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4#47212yes—
277C2×C4#47312yes—
278C2×C4C2×C4⋊Q811yescharacteristic
279C2×C4#53611yescharacteristic
280C2×C4D4×Q812yes—
281C2×C4#55712yes—
282C2×C4C2×#13511yescharacteristic
283C2×C4C2×#13511yescharacteristic
284C2×C4#57512yes—
285C2×C4#57511yescharacteristic
286C2×C4#57511yescharacteristic
287C2×C4#57611yescharacteristic
288C2×C4#57811yescharacteristic
289C8—22no—
290C8—22no—
291C8—22no—
292C8—22no—
293C8—44no—
294C8—44no—
295C8—81no—
296C8—81no—
297C22#254611yescharacteristic
298C22#303511yescharacteristic
299C22#303511yescharacteristic
300C22#305411yescharacteristic
301C22#306111yescharacteristic
302C22C2×#47211yescharacteristic
303C22C2×#47311yescharacteristic
304C4—22no—
305C4—22no—
306C4—22no—
307C4—41no—
308C4—41no—
309C4—81no—
310C4—81no—
311C4—81no—
312C4—81no—
313C4—162no—
314C4—162no—
315C4#316011yescharacteristic
316C4#316611yescharacteristic
317C4#323211yescharacteristic
318C4#323211yescharacteristic
319C4#338912yes—
320C4#339012yes—
321C2#1916011yescharacteristic
322C2#1916111yescharacteristic
323C2#1922211yescharacteristic
324C2#1922311yescharacteristic
325C2#2868011yescharacteristic
326C2#2869011yescharacteristic
327C2#2869911yescharacteristic
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
#293142
#216732
#106522
#106512
#106502
#106492
#99012
#96192
C4×#3352