Finite Group Databasebeta

← #317686

Subgroups — #317686

Order 512.

576 conjugacy classes of subgroups.

The subgroup lattice has 393 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#29287C211yesmaximal, characteristic
2#28283C211yesmaximal, characteristic
3C4×#498C211yesmaximal, characteristic
4#21712C211yesmaximal, characteristic
5#10654C212yesmaximal
6#10544C212yesmaximal
7#9575C212yesmaximal
8#9573C212yesmaximal
9#8784C211yesmaximal, characteristic
10#8587C211yesmaximal, characteristic
11#8586C211yesmaximal, characteristic
12C2×#498C2211yescharacteristic
13C2×#475—21no—
14C2×#446—21no—
15C4×C4⋊Q8C2211yescharacteristic
16C4×C4⋊Q8C2211yescharacteristic
17C4×C4⋊Q8C2211yescharacteristic
18#2088—22no—
19#2066—22no—
20#1990C2211yescharacteristic
21#1990C2211yescharacteristic
22#1988—21no—
23#1987C2212yes—
24#1984—21no—
25#1981C2212yes—
26#1948—21no—
27#1948C2212yes—
28#1948C2212yes—
29#1941—21no—
30#1941—21no—
31#1939—21no—
32#1939C2212yes—
33#1844C2211yescharacteristic
34#1842C2211yescharacteristic
35#1842C2211yescharacteristic
36#1842C2211yescharacteristic
37#1803—21no—
38C4×#106—21no—
39C4×#106—21no—
40#1770—21no—
41#1770C2212yes—
42C42×C8C2211yescharacteristic
43C2×#333C2212yes—
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#498—22no—
56#498—22no—
57#475—44no—
58#446—44no—
59C2×#106—21no—
60C2×#106—21no—
61C2×#106—21no—
62C2×#106—21no—
63C2×#106—22no—
64C2×#106—22no—
65C2×C4⋊C8—22no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8C2312yes—
73C2×C4⋊C8C2312yes—
74C2×C4⋊C8C2312yes—
75C2×#103—22no—
76C2×#103—22no—
77C2×#97—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#333—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—22no—
127C4⋊Q8—21no—
128C4⋊Q8—21no—
129C4⋊Q8—21no—
130C4⋊Q8—21no—
131C4⋊Q8—21no—
132C4⋊Q8—21no—
133C4⋊Q8#4112yes—
134C4⋊Q8#4112yes—
135C4×Q8—42no—
136C4×Q8—42no—
137C4×Q8—42no—
138C4×Q8—42no—
139C4×Q8—82no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
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—41no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4C2×D412yes—
157C2×C4⋊C4C2×D412yes—
158C2×C42—22no—
159C2×C42—41no—
160C2×C42—41no—
161C2×C42C2×D411yescharacteristic
162C2×C42C2×D411yescharacteristic
163C2×C42C2×D411yescharacteristic
164C2×C42C2×D411yescharacteristic
165C2×C42#4111yescharacteristic
166C2×C42#4111yescharacteristic
167C2×C42C2411yescharacteristic
168#106—24no—
169#106—24no—
170#106—44no—
171#106—42no—
172#106—42no—
173#106—82no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—22no—
180C4⋊C8—42no—
181C4⋊C8—44no—
182C4⋊C8—42no—
183C4⋊C8—42no—
184C4⋊C8—42no—
185C4⋊C8—81no—
186C4⋊C8—81no—
187#103—44no—
188#103—82no—
189#97—44no—
190C4×C8—22no—
191C4×C8—22no—
192C4×C8—21no—
193C4×C8—21no—
194C4×C8—21no—
195C4×C8—21no—
196C4×C8—41no—
197C4×C8SD1614yes—
198#95—22no—
199#95—22no—
200#95—41no—
201#95—41no—
202#95—41no—
203#95—41no—
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8—41no—
207C2×Q8—41no—
208C2×Q8—42no—
209C2×Q8—42no—
210C2×Q8—42no—
211C2×Q8—41no—
212C2×Q8—41no—
213C2×Q8—41no—
214C2×Q8—41no—
215C2×Q8—81no—
216C2×Q8—81no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4#12111yescharacteristic
224C22×C4#12111yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4#12111yescharacteristic
227C22×C4C22×D411yescharacteristic
228C22×C4C22×D411yescharacteristic
229C22×C4C2×#4111yescharacteristic
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8C2×SD1612yes—
249C2×C8C2×SD1612yes—
250C2×C8#13712yes—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—42no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—42no—
265C4⋊C4—44no—
266C4⋊C4—42no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—81no—
276C4⋊C4—81no—
277C4⋊C4—82no—
278C4⋊C4—82no—
279C42—21no—
280C42—21no—
281C42—21no—
282C42—21no—
283C42—22no—
284C42—41no—
285C42—42no—
286C42—42no—
287C42—82no—
288C42—82no—
289C42C2×SD1612yes—
290C42AGL(1,ℤ/8)12yes—
291C42#13712yes—
292C42#13712yes—
293C42C2×#4111yescharacteristic
294C42C2×#4111yescharacteristic
295C422−1+411yescharacteristic
296C422−1+411yescharacteristic
297C23C2×#12111yescharacteristic
298Q8—42no—
299Q8—42no—
300Q8—82no—
301Q8—82no—
302Q8—81no—
303Q8—81no—
304Q8—84no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4#46112yes—
333C2×C4#46112yes—
334C2×C4#46812yes—
335C2×C4#46812yes—
336C2×C4#47112yes—
337C2×C4#52511yescharacteristic
338C2×C4#53611yescharacteristic
339C2×C4#54811yescharacteristic
340C2×C4#54811yescharacteristic
341C2×C4#55211yescharacteristic
342C2×C4#55211yescharacteristic
343C2×C4C22×SD1611yescharacteristic
344C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
345C2×C4C2×#13711yescharacteristic
346C2×C4C2×#13711yescharacteristic
347C2×C4C2×#13711yescharacteristic
348C2×C4#57511yescharacteristic
349C2×C4#57711yescharacteristic
350C2×C4#57711yescharacteristic
351C8—22no—
352C8—22no—
353C8—22no—
354C8—41no—
355C8—82no—
356C8—82no—
357C8—82no—
358C22#253611yescharacteristic
359C22C2×#46111yescharacteristic
360C22#303711yescharacteristic
361C22C2×#46811yescharacteristic
362C22#306011yescharacteristic
363C22C2×#47111yescharacteristic
364C22#306711yescharacteristic
365C4—21no—
366C4—21no—
367C4—22no—
368C4—22no—
369C4—41no—
370C4—82no—
371C4—82no—
372C4—82no—
373C4—82no—
374C4—161no—
375C4—161no—
376C4#169114yes—
377C4#310311yescharacteristic
378C4#311311yescharacteristic
379C4#322911yescharacteristic
380C4#323711yescharacteristic
381C4#336811yescharacteristic
382C4#336911yescharacteristic
383C4#337211yescharacteristic
384C4#337311yescharacteristic
385C2C2×#169111yescharacteristic
386C2#1919411yescharacteristic
387C2#1928511yescharacteristic
388C2#1934311yescharacteristic
389C2#2819511yescharacteristic
390C2#2820511yescharacteristic
391C2#2821811yescharacteristic
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
#282832
C4×#4982
#217122
#106542
#105442
#95752
#95732
#87842
#85872
#85862