Finite Group Databasebeta

← #352636

Subgroups — #352636

Order 512.

658 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33290C211yesmaximal, characteristic
2#33289C211yesmaximal, characteristic
3#30304C211yesmaximal, characteristic
4#30279C211yesmaximal, characteristic
5#30220C211yesmaximal, characteristic
6#30205C211yesmaximal, characteristic
7#9834C212yesmaximal
8#9833C212yesmaximal
9#9823C212yesmaximal
10#9821C212yesmaximal
11#7841C211yesmaximal, characteristic
12C2×#500C2212yes—
13C2×#487C2212yes—
14#2868C2211yescharacteristic
15#2868C2211yescharacteristic
16#2862C2211yescharacteristic
17#2859C2211yescharacteristic
18#2095—22no—
19#2095—22no—
20#2083—22no—
21#2072—22no—
22#2057—22no—
23#2043—22no—
24#2043—22no—
25#2024—22no—
26#1991—22no—
27#1990—22no—
28#1990C2212yes—
29#1990C2212yes—
30#1990C2211yescharacteristic
31#1990C2211yescharacteristic
32#1990C2211yescharacteristic
33#1990C2211yescharacteristic
34#1990C2212yes—
35#1956C2212yes—
36#1956C2212yes—
37#1956C2212yes—
38#1845C2212yes—
39#1835—22no—
40#1834—22no—
41#1834C2212yes—
42#1744C2211yescharacteristic
43#1744C2211yescharacteristic
44C42×C8C2211yescharacteristic
45C2×#322C2212yes—
46C2×C82C2212yes—
47C2×C4⋊Q8—21no—
48C2×C4⋊Q8—21no—
49C2×C4⋊Q8—21no—
50C2×C4⋊Q8—21no—
51C2×C4⋊Q8—21no—
52C2×C4⋊Q8C2311yescharacteristic
53C2×C4⋊Q8C2311yescharacteristic
54C2×C4⋊Q8C2312yes—
55C2×#125—21no—
56#500—24no—
57#500—24no—
58#487—24no—
59#487—24no—
60C2×#107—24no—
61C2×#107—24no—
62C2×#103—24no—
63C2×#103—24no—
64C2×#103—24no—
65C2×#103—24no—
66C2×C4×C8D412yes—
67C2×C4×C8D412yes—
68C2×C4×C8C2312yes—
69C2×C4×C8C2311yescharacteristic
70C2×C4×C8C2311yescharacteristic
71C2×C4×C8C2312yes—
72#391—21no—
73#391—21no—
74#391—21no—
75#391—21no—
76#389—21no—
77#389—21no—
78#389—21no—
79#389—21no—
80#384—21no—
81#384—21no—
82#384—21no—
83#384—21no—
84#384—21no—
85#384—21no—
86#384—21no—
87#384C2311yescharacteristic
88#384C2312yes—
89#384C2311yescharacteristic
90#382—21no—
91#382—21no—
92#382—21no—
93C43C2311yescharacteristic
94#340—24no—
95#340—24no—
96#340—24no—
97#340—24no—
98#340—22no—
99#340—22no—
100#340—22no—
101#340—22no—
102#336D412yes—
103#336D412yes—
104#336D412yes—
105#336D412yes—
106#322—24no—
107C82—24no—
108C22×Q8—22no—
109C22×Q8—21no—
110C22×Q8—21no—
111C22×Q8—41no—
112C22×C8C2×D414yes—
113C22×C8C2×D414yes—
114C22×C8C2×D412yes—
115C22×C8C2×D412yes—
116C4⋊Q8—22no—
117C4⋊Q8—22no—
118C4⋊Q8—22no—
119C4⋊Q8—22no—
120C4⋊Q8—22no—
121C4⋊Q8—22no—
122C4⋊Q8—22no—
123C4⋊Q8—22no—
124C4⋊Q8—44no—
125C4⋊Q8—82no—
126C4⋊Q8—82no—
127C4⋊Q8—82no—
128C4⋊Q8—82no—
129#125—44no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4—41no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C42C2×D411yescharacteristic
155C2×C42C2×D411yescharacteristic
156C2×C42C2×D411yescharacteristic
157C2×C42C2×D411yescharacteristic
158C2×C42C2×D411yescharacteristic
159C2×C42C2×D411yescharacteristic
160C2×C42C2411yescharacteristic
161#107—48no—
162#107—84no—
163#103—48no—
164#103—84no—
165#103—84no—
166#103—84no—
167C4×C8—24no—
168C4×C8—22no—
169C4×C8—22no—
170C4×C8—22no—
171C4×C8—22no—
172C4×C8Q1618yes—
173C4×C8#4114yes—
174C4×C8#4114yes—
175#95—41no—
176#95—41no—
177#95—41no—
178#95—41no—
179#95—41no—
180#95—41no—
181C2×Q8—42no—
182C2×Q8—42no—
183C2×Q8—42no—
184C2×Q8—42no—
185C2×Q8—42no—
186C2×Q8—44no—
187C2×Q8—44no—
188C2×Q8—42no—
189C2×Q8—42no—
190C2×Q8—42no—
191C2×Q8—82no—
192C2×Q8—82no—
193C2×Q8—82no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4#12711yescharacteristic
201C22×C4#12711yescharacteristic
202C22×C4#12711yescharacteristic
203C22×C4#12711yescharacteristic
204C22×C4C22×D411yescharacteristic
205C22×C4C22×D411yescharacteristic
206C22×C4C22×D411yescharacteristic
207C2×C8—22no—
208C2×C8—22no—
209C2×C8—22no—
210C2×C8—22no—
211C2×C8—24no—
212C2×C8—24no—
213C2×C8—24no—
214C2×C8—24no—
215C2×C8—24no—
216C2×C8#12418yes—
217C2×C8C2×Q1614yes—
218C2×C8C2×Q1614yes—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C4⋊C4—44no—
232C4⋊C4—42no—
233C4⋊C4—44no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—44no—
237C4⋊C4—42no—
238C4⋊C4—82no—
239C4⋊C4—82no—
240C4⋊C4—82no—
241C4⋊C4—82no—
242C4⋊C4—82no—
243C4⋊C4—82no—
244C4⋊C4—82no—
245C4⋊C4—82no—
246C4⋊C4—82no—
247C42—22no—
248C42—22no—
249C42—22no—
250C42—22no—
251C42C2×Q1614yes—
252C42#13514yes—
253C42C2×#4112yes—
254C42C2×#4112yes—
255C23C2×#12711yescharacteristic
256Q8—84no—
257Q8—84no—
258Q8—84no—
259Q8—84no—
260Q8—164no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—81no—
270C2×C4—82no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—82no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—82no—
282C2×C4—81no—
283C2×C4—82no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4#49412yes—
288C2×C4#49412yes—
289C2×C4#49512yes—
290C2×C4#49512yes—
291C2×C4C2×#12412yes—
292C2×C4#53211yescharacteristic
293C2×C4#53211yescharacteristic
294C2×C4#53212yes—
295C2×C4C22×Q1612yes—
296C2×C4C2×#13512yes—
297C2×C4#57612yes—
298C2×C4#57712yes—
299C2×C4#57712yes—
300C2×C4#57812yes—
301C8—28no—
302C8—24no—
303C8—24no—
304C8—44no—
305C22#285811yescharacteristic
306C22C2×#49411yescharacteristic
307C22C2×#49511yescharacteristic
308C22#315411yescharacteristic
309C22#315411yescharacteristic
310C22#315511yescharacteristic
311C22#315611yescharacteristic
312C4—22no—
313C4—22no—
314C4—22no—
315C4—22no—
316C4—161no—
317C4—161no—
318C4—162no—
319C4—161no—
320C4—162no—
321C4—161no—
322C4#313714yes—
323C4#317012yes—
324C4#317012yes—
325C4#317914yes—
326C2#1965711yescharacteristic
327C2#1965811yescharacteristic
328C2#1966311yescharacteristic
329C2#1966411yescharacteristic
330C2#3322911yescharacteristic
331C2#3324211yescharacteristic
332C2#3324311yescharacteristic
subgroupG/H
center, socle, prime radicalC23C2×#127
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
#332902
#332892
#303042
#302792
#302202
#302052
#98342
#98332
#98232
#98212
#78412