Finite Group Databasebeta

← #105136

Subgroups — #105136

Order 512.

361 conjugacy classes of subgroups.

The subgroup lattice has 317 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#29218C211yesmaximal, characteristic
2#9898C211yesmaximal, characteristic
3#9896C211yesmaximal, characteristic
4#9673C211yesmaximal, characteristic
5#9602C211yesmaximal, characteristic
6#8586C211yesmaximal, characteristic
7#7031C211yesmaximal, characteristic
8#2868C2211yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10#2100—22no—
11#1990—21no—
12#1987—21no—
13#1987—21no—
14#1842C2211yescharacteristic
15#1842C2211yescharacteristic
16#1834—21no—
17C4×C4⋊C8C2211yescharacteristic
18C4×C4⋊C8C2211yescharacteristic
19C4×C4⋊C8C2211yescharacteristic
20C2×#334—21no—
21C2×#332—21no—
22C2×Q8⋊C8—21no—
23C2×Q8⋊C8—21no—
24#1296—21no—
25#1296—21no—
26#1296—21no—
27#1296—22no—
28#1277—21no—
29C2×C4⋊Q8—21no—
30C2×C4⋊Q8—21no—
31C2×C4⋊Q8—21no—
32C2×C4⋊Q8D411yescharacteristic
33C2×C4×Q8—21no—
34C2×C4⋊C8—21no—
35C2×C4⋊C8—21no—
36C2×C4⋊C8—21no—
37C2×C4⋊C8—21no—
38C2×C4⋊C8—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8D411yescharacteristic
42C2×C4⋊C8D411yescharacteristic
43C2×C4⋊C8D411yescharacteristic
44C2×C4⋊C8D411yescharacteristic
45C2×C4×C8—21no—
46C2×C4×C8—21no—
47C2×C4×C8—21no—
48#391—21no—
49#389—21no—
50#389—21no—
51#384—21no—
52#384—21no—
53#384—21no—
54#384D411yescharacteristic
55#384D412yes—
56C4×C4⋊C4—21no—
57C4×C4⋊C4—21no—
58C43C2311yescharacteristic
59#340—22no—
60#340—22no—
61#340—22no—
62#340—22no—
63#336—21no—
64#336—21no—
65#336—21no—
66#334—42no—
67#332—42no—
68Q8⋊C8—42no—
69Q8⋊C8—42no—
70C22×Q8—21no—
71C22×Q8—41no—
72C22×C8—21no—
73C22×C8—21no—
74C22×C8—21no—
75C22×C8—21no—
76C22×C8—41no—
77C22×C8—41no—
78C22×C8—41no—
79C4⋊Q8—21no—
80C4⋊Q8—21no—
81C4⋊Q8—21no—
82C4⋊Q8—41no—
83C4⋊Q8—41no—
84C4⋊Q8—41no—
85C4⋊Q8—41no—
86C4⋊Q8—81no—
87C4⋊Q8—81no—
88C4⋊Q8—82no—
89C4⋊Q8SD1612yes—
90C4×Q8—41no—
91C4×Q8—41no—
92C4×Q8—41no—
93C4×Q8—41no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—22no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—22no—
100C2×C4⋊C4—22no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—41no—
103C2×C4⋊C4—41no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—41no—
106C2×C42—41no—
107C2×C42C2×D411yescharacteristic
108C2×C42C2×D411yescharacteristic
109C2×C42C2×D411yescharacteristic
110C2×C42C2×D411yescharacteristic
111C2×C42#4111yescharacteristic
112C2×C42#4111yescharacteristic
113C2×C42#4111yescharacteristic
114C4⋊C8—22no—
115C4⋊C8—21no—
116C4⋊C8—21no—
117C4⋊C8—21no—
118C4⋊C8—21no—
119C4⋊C8—21no—
120C4⋊C8—21no—
121C4⋊C8—21no—
122C4⋊C8—41no—
123C4⋊C8—42no—
124C4⋊C8—41no—
125C4⋊C8—41no—
126C4⋊C8—41no—
127C4⋊C8—41no—
128C4⋊C8—41no—
129C4⋊C8—41no—
130C4⋊C8—41no—
131C4⋊C8—41no—
132C4⋊C8—81no—
133C4⋊C8SD1612yes—
134C4×C8—41no—
135C4×C8—41no—
136C4×C8—41no—
137C4×C8—41no—
138C4×C8—41no—
139C4×C8—41no—
140#95—41no—
141#95—41no—
142C2×Q8—22no—
143C2×Q8—41no—
144C2×Q8—41no—
145C2×Q8—41no—
146C2×Q8—41no—
147C2×Q8—41no—
148C2×Q8—82no—
149C2×Q8—82no—
150C2×Q8—81no—
151C2×Q8—81no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—42no—
155C22×C4#12011yescharacteristic
156C22×C4#12111yescharacteristic
157C22×C4#12111yescharacteristic
158C22×C4#12111yescharacteristic
159C22×C4#12311yescharacteristic
160C22×C4#12311yescharacteristic
161C22×C4#12411yescharacteristic
162C2×C8—22no—
163C2×C8—41no—
164C2×C8—41no—
165C2×C8—42no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—41no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—81no—
176C2×C8—81no—
177C2×C8—81no—
178C2×C8—81no—
179C2×C8—81no—
180C2×C8—81no—
181C2×C8—81no—
182C2×C8—81no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—81no—
194C4⋊C4—82no—
195C4⋊C4—82no—
196C4⋊C4—82no—
197C4⋊C4—81no—
198C4⋊C4—81no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C4⋊C4—81no—
202C4⋊C4—81no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—41no—
210C42—81no—
211C42—81no—
212C42C2×SD1611yescharacteristic
213C42C2×SD1611yescharacteristic
214C42#13511yescharacteristic
215C42#13511yescharacteristic
216C42#13511yescharacteristic
217C42#13511yescharacteristic
218C42AGL(1,ℤ/8)11yescharacteristic
219C42AGL(1,ℤ/8)11yescharacteristic
220C42#13711yescharacteristic
221C42#13711yescharacteristic
222C42#13711yescharacteristic
223C42#13711yescharacteristic
224C23#39411yescharacteristic
225Q8—42no—
226Q8—42no—
227Q8—81no—
228Q8—81no—
229Q8—162no—
230Q8—162no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—42no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—82no—
244C2×C4—81no—
245C2×C4—82no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—82no—
249C2×C4#44811yescharacteristic
250C2×C4#44911yescharacteristic
251C2×C4#45211yescharacteristic
252C2×C4#45211yescharacteristic
253C2×C4#45411yescharacteristic
254C2×C4#45611yescharacteristic
255C2×C4#46011yescharacteristic
256C2×C4#46111yescharacteristic
257C2×C4#46311yescharacteristic
258C2×C4#46311yescharacteristic
259C2×C4#46411yescharacteristic
260C2×C4#46411yescharacteristic
261C2×C4#46511yescharacteristic
262C2×C4#46511yescharacteristic
263C2×C4#46811yescharacteristic
264C2×C4#47011yescharacteristic
265C2×C4#47111yescharacteristic
266C2×C4#47211yescharacteristic
267C2×C4#47311yescharacteristic
268C2×C4#47311yescharacteristic
269C2×C4#48311yescharacteristic
270C2×C4#48511yescharacteristic
271C2×C4#48811yescharacteristic
272C2×C4#48911yescharacteristic
273C8—42no—
274C8—82no—
275C8—81no—
276C8—81no—
277C8—81no—
278C8—161no—
279C8—161no—
280C22#203511yescharacteristic
281C22#203811yescharacteristic
282C22#204211yescharacteristic
283C22#204711yescharacteristic
284C22#204811yescharacteristic
285C22#205111yescharacteristic
286C22#205511yescharacteristic
287C4—21no—
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—41no—
294C4—82no—
295C4—161no—
296C4—162no—
297C4#162611yescharacteristic
298C4#163811yescharacteristic
299C4#165011yescharacteristic
300C4#165311yescharacteristic
301C4#167111yescharacteristic
302C4#167711yescharacteristic
303C4#167911yescharacteristic
304C4#168011yescharacteristic
305C4#169511yescharacteristic
306C4#169911yescharacteristic
307C4#170011yescharacteristic
308C4#170311yescharacteristic
309C2#1042311yescharacteristic
310C2#1045411yescharacteristic
311C2#1048011yescharacteristic
312C2#1049511yescharacteristic
313C2#1050211yescharacteristic
314C2#1054211yescharacteristic
315C2#1055311yescharacteristic
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
#292182
#98982
#98962
#96732
#96022
#85862
#70312