Finite Group Databasebeta

← #105131

Subgroups — #105131

Order 512.

387 conjugacy classes of subgroups.

The subgroup lattice has 323 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#28511C211yesmaximal, characteristic
2#9898C211yesmaximal, characteristic
3#9896C211yesmaximal, characteristic
4#9865C211yesmaximal, characteristic
5#9602C211yesmaximal, characteristic
6#8586C211yesmaximal, characteristic
7#7031C211yesmaximal, characteristic
8C2×#477—21no—
9C2×#477—21no—
10#2868C2211yescharacteristic
11C4×C4⋊Q8C2211yescharacteristic
12#2095—22no—
13#1956—21no—
14#1845—21no—
15#1842C2211yescharacteristic
16#1842C2211yescharacteristic
17C4×C4⋊C8C2211yescharacteristic
18C4×C4⋊C8C2211yescharacteristic
19C4×C4⋊C8C2211yescharacteristic
20C2×#334—21no—
21C2×#332—21no—
22#1296—21no—
23#1296—21no—
24#1296—21no—
25#1296—22no—
26#1279—21no—
27#1279—21no—
28#1277—21no—
29C2×C4⋊Q8—21no—
30C2×C4⋊Q8—21no—
31C2×C4⋊Q8—21no—
32C2×C4⋊Q8D411yescharacteristic
33C2×C4×Q8—21no—
34#477—42no—
35#477—42no—
36#477—42no—
37#477—42no—
38C2×#107—22no—
39C2×#107—22no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8D411yescharacteristic
48C2×C4⋊C8D411yescharacteristic
49C2×C4⋊C8D411yescharacteristic
50C2×C4⋊C8D411yescharacteristic
51C2×#103—22no—
52C2×#103—22no—
53C2×C4×C8—21no—
54C2×C4×C8—21no—
55C2×C4×C8—21no—
56#391—21no—
57#389—21no—
58#389—21no—
59#384—21no—
60#384—21no—
61#384—21no—
62#384D411yescharacteristic
63#384D412yes—
64C4×C4⋊C4—21no—
65C4×C4⋊C4—21no—
66C43C2311yescharacteristic
67#336—21no—
68#336—21no—
69#336—21no—
70#334—42no—
71#332—42no—
72C22×Q8—21no—
73C22×Q8—41no—
74C22×C8—21no—
75C22×C8—21no—
76C22×C8—21no—
77C22×C8—21no—
78C22×C8—41no—
79C22×C8—41no—
80C22×C8—41no—
81C4⋊Q8—21no—
82C4⋊Q8—21no—
83C4⋊Q8—21no—
84C4⋊Q8—41no—
85C4⋊Q8—41no—
86C4⋊Q8—41no—
87C4⋊Q8—41no—
88C4⋊Q8—81no—
89C4⋊Q8—81no—
90C4⋊Q8—82no—
91C4⋊Q8SD1612yes—
92C4×Q8—41no—
93C4×Q8—41no—
94C4×Q8—41no—
95C4×Q8—41no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—22no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—41no—
106C2×C4⋊C4—41no—
107C2×C4⋊C4—41no—
108C2×C42—41no—
109C2×C42C2×D411yescharacteristic
110C2×C42C2×D411yescharacteristic
111C2×C42C2×D411yescharacteristic
112C2×C42C2×D411yescharacteristic
113C2×C42#4111yescharacteristic
114C2×C42#4111yescharacteristic
115C2×C42#4111yescharacteristic
116#107—44no—
117#107—44no—
118C4⋊C8—22no—
119C4⋊C8—21no—
120C4⋊C8—21no—
121C4⋊C8—21no—
122C4⋊C8—21no—
123C4⋊C8—21no—
124C4⋊C8—41no—
125C4⋊C8—42no—
126C4⋊C8—41no—
127C4⋊C8—41no—
128C4⋊C8—41no—
129C4⋊C8—41no—
130C4⋊C8—41no—
131C4⋊C8—41no—
132C4⋊C8—41no—
133C4⋊C8—41no—
134C4⋊C8—81no—
135C4⋊C8D812yes—
136C4⋊C8SD1612yes—
137C4⋊C8Q1612yes—
138#103—44no—
139#103—44no—
140C4×C8—41no—
141C4×C8—41no—
142C4×C8—41no—
143C4×C8—41no—
144C4×C8—41no—
145C4×C8—41no—
146#95—41no—
147#95—41no—
148C2×Q8—22no—
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8—41no—
152C2×Q8—41no—
153C2×Q8—41no—
154C2×Q8—82no—
155C2×Q8—82no—
156C2×Q8—81no—
157C2×Q8—81no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—42no—
161C22×C4#12011yescharacteristic
162C22×C4#12111yescharacteristic
163C22×C4#12111yescharacteristic
164C22×C4#12111yescharacteristic
165C22×C4#12311yescharacteristic
166C22×C4#12311yescharacteristic
167C22×C4#12411yescharacteristic
168C2×C8—22no—
169C2×C8—22no—
170C2×C8—22no—
171C2×C8—41no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8—42no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—81no—
182C2×C8—81no—
183C2×C8—81no—
184C2×C8—81no—
185C2×C8—81no—
186C2×C8—81no—
187C2×C8—81no—
188C2×C8—81no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—42no—
194C4⋊C4—41no—
195C4⋊C4—42no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—81no—
200C4⋊C4—82no—
201C4⋊C4—82no—
202C4⋊C4—82no—
203C4⋊C4—81no—
204C4⋊C4—81no—
205C4⋊C4—81no—
206C4⋊C4—81no—
207C4⋊C4—81no—
208C4⋊C4—81no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—41no—
216C42—81no—
217C42—81no—
218C42C2×D811yescharacteristic
219C42C2×SD1611yescharacteristic
220C42C2×SD1611yescharacteristic
221C42C2×Q1611yescharacteristic
222C42#13511yescharacteristic
223C42#13511yescharacteristic
224C42AGL(1,ℤ/8)11yescharacteristic
225C42AGL(1,ℤ/8)11yescharacteristic
226C42#13711yescharacteristic
227C42#13711yescharacteristic
228C42#13711yescharacteristic
229C42#13711yescharacteristic
230C23#39411yescharacteristic
231Q8—42no—
232Q8—42no—
233Q8—81no—
234Q8—81no—
235Q8—162no—
236Q8—162no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—82no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—82no—
253C2×C4—81no—
254C2×C4—82no—
255C2×C4#44711yescharacteristic
256C2×C4#44811yescharacteristic
257C2×C4#45011yescharacteristic
258C2×C4#45211yescharacteristic
259C2×C4#45411yescharacteristic
260C2×C4#45611yescharacteristic
261C2×C4#45911yescharacteristic
262C2×C4#46011yescharacteristic
263C2×C4#46211yescharacteristic
264C2×C4#46211yescharacteristic
265C2×C4#46411yescharacteristic
266C2×C4#46411yescharacteristic
267C2×C4#46511yescharacteristic
268C2×C4#46711yescharacteristic
269C2×C4#47011yescharacteristic
270C2×C4#47011yescharacteristic
271C2×C4#47111yescharacteristic
272C2×C4#47211yescharacteristic
273C2×C4#47311yescharacteristic
274C2×C4#47311yescharacteristic
275C2×C4#48311yescharacteristic
276C2×C4#48511yescharacteristic
277C2×C4#48611yescharacteristic
278C2×C4#49011yescharacteristic
279C8—42no—
280C8—42no—
281C8—42no—
282C8—82no—
283C8—81no—
284C8—161no—
285C8—161no—
286C22#203511yescharacteristic
287C22#203811yescharacteristic
288C22#204111yescharacteristic
289C22#204711yescharacteristic
290C22#204811yescharacteristic
291C22#205111yescharacteristic
292C22#205611yescharacteristic
293C4—21no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—41no—
300C4—82no—
301C4—161no—
302C4—162no—
303C4#162711yescharacteristic
304C4#163511yescharacteristic
305C4#164711yescharacteristic
306C4#165111yescharacteristic
307C4#166911yescharacteristic
308C4#167011yescharacteristic
309C4#167211yescharacteristic
310C4#167811yescharacteristic
311C4#168911yescharacteristic
312C4#169011yescharacteristic
313C4#169611yescharacteristic
314C4#170411yescharacteristic
315C2#1042011yescharacteristic
316C2#1045411yescharacteristic
317C2#1048211yescharacteristic
318C2#1049511yescharacteristic
319C2#1050611yescharacteristic
320C2#1053811yescharacteristic
321C2#1054911yescharacteristic
subgroupG/H
center, socle, prime radicalC23#394
commutator, Frattini, cosocleC43C23
LCSG ▷ C43 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#285112
#98982
#98962
#98652
#96022
#85862
#70312