Finite Group Databasebeta

← #104993

Subgroups — #104993

Order 512.

384 conjugacy classes of subgroups.

The subgroup lattice has 327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#28284C211yesmaximal, characteristic
2#9870C211yesmaximal, characteristic
3#9870C211yesmaximal, characteristic
4#8805C211yesmaximal, characteristic
5#8587C211yesmaximal, characteristic
6#8586C211yesmaximal, characteristic
7#7050C211yesmaximal, characteristic
8C2×#477—21no—
9C4×C4⋊Q8C2211yescharacteristic
10C4×C4⋊Q8C2211yescharacteristic
11#2068—22no—
12#1981—21no—
13#1947—21no—
14#1842C2211yescharacteristic
15#1842C2211yescharacteristic
16#1842C2211yescharacteristic
17#1842C2211yescharacteristic
18#1803—21no—
19C42×C8C2211yescharacteristic
20C2×#334—22no—
21C2×#333—21no—
22C2×#332—21no—
23#1296—21no—
24#1296—21no—
25#1279—21no—
26#1279—21no—
27#1279—21no—
28#1279—21no—
29C2×C4⋊Q8D411yescharacteristic
30C2×C4⋊Q8D411yescharacteristic
31C2×C4×Q8—21no—
32C2×C4×Q8—21no—
33#477—42no—
34#477—42no—
35C2×#107—22no—
36C2×C4⋊C8—21no—
37C2×C4⋊C8—21no—
38C2×C4⋊C8—21no—
39C2×C4⋊C8—21no—
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⋊C8D412yes—
48C2×#103—22no—
49C2×#103—22no—
50C2×C4×C8—21no—
51C2×C4×C8—21no—
52C2×C4×C8D411yescharacteristic
53C2×C4×C8D411yescharacteristic
54#391—21no—
55#391—21no—
56#389—21no—
57#389—21no—
58#389—21no—
59#389—21no—
60#384D411yescharacteristic
61#384D411yescharacteristic
62C4×C4⋊C4—21no—
63C4×C4⋊C4—21no—
64C4×C4⋊C4—21no—
65C4×C4⋊C4—21no—
66C43C2311yescharacteristic
67#340—22no—
68#334—44no—
69#333—42no—
70#332—42no—
71C22×Q8—21no—
72C22×Q8—21no—
73C22×C8—21no—
74C22×C8—21no—
75C22×C8—22no—
76C22×C8—41no—
77C22×C8—41no—
78C22×C8—41no—
79C4⋊Q8—21no—
80C4⋊Q8—21no—
81C4⋊Q8—21no—
82C4⋊Q8—21no—
83C4⋊Q8—21no—
84C4⋊Q8—21no—
85C4⋊Q8SD1612yes—
86C4⋊Q8SD1612yes—
87C4×Q8—41no—
88C4×Q8—41no—
89C4×Q8—41no—
90C4×Q8—41no—
91C4×Q8—81no—
92C4×Q8—81no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—41no—
104C2×C4⋊C4—41no—
105C2×C42—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
114#107—44no—
115C4⋊C8—42no—
116C4⋊C8—42no—
117C4⋊C8—41no—
118C4⋊C8—41no—
119C4⋊C8—41no—
120C4⋊C8—41no—
121C4⋊C8—41no—
122C4⋊C8—41no—
123C4⋊C8—41no—
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—41no—
133C4⋊C8—81no—
134C4⋊C8—81no—
135#103—44no—
136#103—82no—
137C4×C8—22no—
138C4×C8—22no—
139C4×C8—21no—
140C4×C8—21no—
141C4×C8—21no—
142C4×C8—42no—
143C4×C8Q1612yes—
144#95—41no—
145#95—41no—
146#95—41no—
147#95—41no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—41no—
151C2×Q8—41no—
152C2×Q8—41no—
153C2×Q8—41no—
154C2×Q8—41no—
155C2×Q8—41no—
156C2×Q8—81no—
157C2×Q8—81no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4#12011yescharacteristic
163C22×C4#12111yescharacteristic
164C22×C4#12111yescharacteristic
165C22×C4#12111yescharacteristic
166C22×C4#12311yescharacteristic
167C22×C4#12311yescharacteristic
168C22×C4#12411yescharacteristic
169C2×C8—22no—
170C2×C8—22no—
171C2×C8—22no—
172C2×C8—22no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—81no—
179C2×C8—81no—
180C2×C8—81no—
181C2×C8—81no—
182C2×C8—81no—
183C2×C8—81no—
184C2×C8—81no—
185C2×C8—81no—
186C2×C8—81no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—81no—
204C4⋊C4—81no—
205C4⋊C4—82no—
206C4⋊C4—81no—
207C4⋊C4—81no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—41no—
215C42—81no—
216C42—81no—
217C42—81no—
218C42—81no—
219C42C2×SD1611yescharacteristic
220C42C2×SD1611yescharacteristic
221C42C2×Q1611yescharacteristic
222C42#13511yescharacteristic
223C42#13511yescharacteristic
224C42#13511yescharacteristic
225C42AGL(1,ℤ/8)11yescharacteristic
226C42AGL(1,ℤ/8)11yescharacteristic
227C42#13711yescharacteristic
228C42#13711yescharacteristic
229C42#13711yescharacteristic
230C42#13711yescharacteristic
231C23#39411yescharacteristic
232Q8—42no—
233Q8—42no—
234Q8—82no—
235Q8—82no—
236Q8—81no—
237Q8—81no—
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—21no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4#44811yescharacteristic
260C2×C4#44911yescharacteristic
261C2×C4#45011yescharacteristic
262C2×C4#45211yescharacteristic
263C2×C4#45311yescharacteristic
264C2×C4#45611yescharacteristic
265C2×C4#46211yescharacteristic
266C2×C4#46211yescharacteristic
267C2×C4#46411yescharacteristic
268C2×C4#46411yescharacteristic
269C2×C4#46511yescharacteristic
270C2×C4#46511yescharacteristic
271C2×C4#46711yescharacteristic
272C2×C4#46911yescharacteristic
273C2×C4#47011yescharacteristic
274C2×C4#47011yescharacteristic
275C2×C4#47111yescharacteristic
276C2×C4#47111yescharacteristic
277C2×C4#47211yescharacteristic
278C2×C4#47311yescharacteristic
279C2×C4#48111yescharacteristic
280C2×C4#48211yescharacteristic
281C2×C4#48311yescharacteristic
282C2×C4#48511yescharacteristic
283C8—24no—
284C8—42no—
285C8—82no—
286C8—161no—
287C8—161no—
288C8—161no—
289C22#203411yescharacteristic
290C22#203511yescharacteristic
291C22#203911yescharacteristic
292C22#205011yescharacteristic
293C22#205111yescharacteristic
294C22#205211yescharacteristic
295C22#205611yescharacteristic
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—41no—
303C4—82no—
304C4—82no—
305C4—161no—
306C4—161no—
307C4#162211yescharacteristic
308C4#163111yescharacteristic
309C4#165111yescharacteristic
310C4#165211yescharacteristic
311C4#167211yescharacteristic
312C4#167211yescharacteristic
313C4#167811yescharacteristic
314C4#168011yescharacteristic
315C4#169411yescharacteristic
316C4#169611yescharacteristic
317C4#170211yescharacteristic
318C4#170411yescharacteristic
319C2#1043511yescharacteristic
320C2#1045711yescharacteristic
321C2#1046211yescharacteristic
322C2#1047911yescharacteristic
323C2#1048211yescharacteristic
324C2#1052211yescharacteristic
325C2#1053211yescharacteristic
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
#282842
#98702
#88052
#85872
#85862
#70502