Finite Group Databasebeta

← #317547

Subgroups — #317547

Order 512.

592 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#29287C211yesmaximal, characteristic
2#28284C211yesmaximal, characteristic
3C8×C4⋊Q8C211yesmaximal, characteristic
4C4×#487C211yesmaximal, characteristic
5#10657C212yesmaximal
6#10542C212yesmaximal
7#9565C212yesmaximal
8#9561C212yesmaximal
9#8784C211yesmaximal, characteristic
10#8586C211yesmaximal, characteristic
11#8586C211yesmaximal, characteristic
12C2×#487C2211yescharacteristic
13C2×#477—21no—
14C2×C8×Q8—21no—
15C4×C4⋊Q8C2211yescharacteristic
16C4×C4⋊Q8C2211yescharacteristic
17C4×C4⋊Q8C2211yescharacteristic
18#2088—22no—
19#2068—22no—
20#1990C2211yescharacteristic
21#1988C2212yes—
22#1987—21no—
23#1984—21no—
24#1981C2212yes—
25#1956C2211yescharacteristic
26#1948—21no—
27#1948C2212yes—
28#1947C2212yes—
29#1939—21no—
30#1939C2212yes—
31#1933—21no—
32#1933—21no—
33#1842C2211yescharacteristic
34#1842C2211yescharacteristic
35#1842C2211yescharacteristic
36#1834C2211yescharacteristic
37#1803—21no—
38C8×C4⋊C4—21no—
39C8×C4⋊C4C2212yes—
40C4×#103—21no—
41C4×#103—21no—
42C42×C8C2211yescharacteristic
43C2×#332C2212yes—
44C2×#332C2212yes—
45#1296C2212yes—
46#1296C2212yes—
47#1277C2212yes—
48#1277C2212yes—
49C2×C4⋊Q8D411yescharacteristic
50C2×C4⋊Q8C2311yescharacteristic
51C2×C4⋊Q8C2311yescharacteristic
52C2×C4×Q8—21no—
53C2×C4×Q8—21no—
54C2×C4×Q8—21no—
55#487—22no—
56#487—22no—
57#477—44no—
58C8×Q8—44no—
59C2×#107—22no—
60C2×#106—22no—
61C2×C4⋊C8—22no—
62C2×C4⋊C8—21no—
63C2×C4⋊C8—21no—
64C2×C4⋊C8—21no—
65C2×C4⋊C8—21no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8C2312yes—
69C2×C4⋊C8C2312yes—
70C2×C4⋊C8C2312yes—
71C2×#103—21no—
72C2×#103—21no—
73C2×#103—21no—
74C2×#103—21no—
75C2×#103—22no—
76C2×#103—22no—
77C2×C4×C8—22no—
78C2×C4×C8D411yescharacteristic
79C2×C4×C8D411yescharacteristic
80C2×C4×C8D411yescharacteristic
81C2×C4×C8D411yescharacteristic
82C2×C4×C8C2311yescharacteristic
83C2×C4×C8C2311yescharacteristic
84#391—21no—
85#391—21no—
86#391—21no—
87#389—21no—
88#389—21no—
89#389—21no—
90#389—21no—
91#389—21no—
92#389D412yes—
93#384D411yescharacteristic
94#384C2311yescharacteristic
95#384C2311yescharacteristic
96C4×C4⋊C4—21no—
97C4×C4⋊C4—21no—
98C4×C4⋊C4—21no—
99C4×C4⋊C4—21no—
100C4×C4⋊C4—21no—
101C4×C4⋊C4C2312yes—
102C43C2311yescharacteristic
103#340—21no—
104#340—21no—
105#340—21no—
106#340—21no—
107#340—22no—
108#340—22no—
109#340—22no—
110#340—22no—
111#336—22no—
112#336—22no—
113#332—24no—
114#332—24no—
115C22×Q8—21no—
116C22×Q8—21no—
117C22×Q8—21no—
118C22×C8—22no—
119C22×C8—22no—
120C22×C8—22no—
121C22×C8C2×D411yescharacteristic
122C22×C8C2×D411yescharacteristic
123C22×C8C2×D411yescharacteristic
124C22×C8C2×D411yescharacteristic
125C4⋊Q8—22no—
126C4⋊Q8—21no—
127C4⋊Q8—21no—
128C4⋊Q8—21no—
129C4⋊Q8—21no—
130C4⋊Q8—21no—
131C4⋊Q8—21no—
132C4⋊Q8SD1614yes—
133C4⋊Q8#4112yes—
134C4⋊Q8#4112yes—
135C4×Q8—42no—
136C4×Q8—42no—
137C4×Q8—42no—
138C4×Q8—42no—
139C4×Q8—42no—
140C4×Q8—42no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4C2×D412yes—
158C2×C4⋊C4C2×D412yes—
159C2×C42—22no—
160C2×C42—41no—
161C2×C42—41no—
162C2×C42C2×D411yescharacteristic
163C2×C42C2×D411yescharacteristic
164C2×C42C2×D411yescharacteristic
165C2×C42C2×D411yescharacteristic
166C2×C42#4111yescharacteristic
167C2×C42#4111yescharacteristic
168C2×C42C2411yescharacteristic
169#107—44no—
170#106—82no—
171C4⋊C8—22no—
172C4⋊C8—22no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—42no—
178C4⋊C8—44no—
179C4⋊C8—42no—
180C4⋊C8—42no—
181C4⋊C8—42no—
182C4⋊C8—81no—
183C4⋊C8—81no—
184#103—24no—
185#103—24no—
186#103—42no—
187#103—42no—
188#103—44no—
189#103—82no—
190C4×C8—22no—
191C4×C8—22no—
192C4×C8—22no—
193C4×C8—21no—
194C4×C8—21no—
195C4×C8—21no—
196C4×C8—21no—
197C4×C8—41no—
198C4×C8—44no—
199#95—22no—
200#95—22no—
201#95—41no—
202#95—41no—
203#95—41no—
204#95—41no—
205C2×Q8—24no—
206C2×Q8—22no—
207C2×Q8—22no—
208C2×Q8—42no—
209C2×Q8—42no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×Q8—41no—
213C2×Q8—41no—
214C2×Q8—41no—
215C2×Q8—41no—
216C2×Q8—41no—
217C2×Q8—41no—
218C2×Q8—41no—
219C2×Q8—41no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4#12111yescharacteristic
227C22×C4#12111yescharacteristic
228C22×C4#12111yescharacteristic
229C22×C4#12111yescharacteristic
230C22×C4C22×D411yescharacteristic
231C22×C4C22×D411yescharacteristic
232C22×C4C2×#4111yescharacteristic
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8AGL(1,ℤ/8)12yes—
254C4⋊C4—22no—
255C4⋊C4—24no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—42no—
263C4⋊C4—44no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—81no—
278C4⋊C4—81no—
279C4⋊C4—82no—
280C4⋊C4—82no—
281C4⋊C4C2×SD1614yes—
282C42—21no—
283C42—21no—
284C42—21no—
285C42—21no—
286C42—22no—
287C42—41no—
288C42—42no—
289C42—42no—
290C42—82no—
291C42—82no—
292C42C2×SD1612yes—
293C42#13512yes—
294C42#13512yes—
295C42#13712yes—
296C42C2×#4111yescharacteristic
297C42C2×#4111yescharacteristic
298C422−1+411yescharacteristic
299C422−1+411yescharacteristic
300C23C2×#12111yescharacteristic
301Q8—48no—
302Q8—42no—
303Q8—42no—
304Q8—42no—
305Q8—42no—
306Q8—81no—
307Q8—81no—
308Q8—81no—
309Q8—81no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—24no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4#46412yes—
338C2×C4#46412yes—
339C2×C4#46512yes—
340C2×C4#46512yes—
341C2×C4#47312yes—
342C2×C4#52511yescharacteristic
343C2×C4#53611yescharacteristic
344C2×C4#54811yescharacteristic
345C2×C4#54811yescharacteristic
346C2×C4#55211yescharacteristic
347C2×C4#55211yescharacteristic
348C2×C4C22×SD1611yescharacteristic
349C2×C4C2×#13511yescharacteristic
350C2×C4C2×#13511yescharacteristic
351C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
352C2×C4C2×#13711yescharacteristic
353C2×C4#57511yescharacteristic
354C2×C4#57611yescharacteristic
355C2×C4#57811yescharacteristic
356C8—22no—
357C8—41no—
358C8—41no—
359C8—41no—
360C8—82no—
361C8—82no—
362C8—82no—
363C22#253611yescharacteristic
364C22C2×#46411yescharacteristic
365C22#303611yescharacteristic
366C22C2×#46511yescharacteristic
367C22#306111yescharacteristic
368C22C2×#47311yescharacteristic
369C22#306711yescharacteristic
370C4—22no—
371C4—22no—
372C4—21no—
373C4—21no—
374C4—44no—
375C4—41no—
376C4—82no—
377C4—82no—
378C4—82no—
379C4—161no—
380C4—161no—
381C4#168014yes—
382C4#310611yescharacteristic
383C4#311611yescharacteristic
384C4#323311yescharacteristic
385C4#323811yescharacteristic
386C4#335911yescharacteristic
387C4#336111yescharacteristic
388C4#336211yescharacteristic
389C4#336411yescharacteristic
390C2C2×#168011yescharacteristic
391C2#1921711yescharacteristic
392C2#1925411yescharacteristic
393C2#1933311yescharacteristic
394C2#2818611yescharacteristic
395C2#2820411yescharacteristic
396C2#2821911yescharacteristic
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
#292872
#282842
C8×C4⋊Q82
C4×#4872
#106572
#105422
#95652
#95612
#87842
#85862