Finite Group Databasebeta

← #468886

Subgroups — #468886

Order 512.

1204 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2859C211yesmaximal, characteristic
2C2×#2099C212yesmaximal
3#14712C211yesmaximal, characteristic
4#11292C214yesmaximal
5#11207C212yesmaximal
6#11207C212yesmaximal
7#11207C212yesmaximal
8#10795C211yesmaximal, characteristic
9C22×#125—21no—
10#2859—28no—
11C2×#389—21no—
12C2×#389—21no—
13C2×#389—21no—
14C2×#389—21no—
15C2×#389C2212yes—
16C2×#389C2212yes—
17C2×#389C2212yes—
18C2×#384C2211yescharacteristic
19C2×#384C2211yescharacteristic
20C2×#384C2211yescharacteristic
21C2×#384C2211yescharacteristic
22C2×#382—21no—
23C2×C43C2211yescharacteristic
24#2099—28no—
25C2×#340C2214yes—
26C2×#340C2214yes—
27C2×#340C2214yes—
28C2×#340C2214yes—
29C2×#336C2212yes—
30C2×#336C2212yes—
31C2×#336C2212yes—
32C4⋊#95—21no—
33C4⋊#95—21no—
34C4⋊#95C2212yes—
35C23×C8C2314yes—
36C2×#125—28no—
37C2×#125—44no—
38C2×#125—44no—
39C22×C4⋊C4—21no—
40C22×C4⋊C4—21no—
41C22×C4⋊C4—22no—
42C22×C4⋊C4—22no—
43C22×C4⋊C4—21no—
44C22×C4⋊C4—21no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—21no—
47C22×C4⋊C4—21no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—22no—
50C22×C4⋊C4C2312yes—
51C22×C4⋊C4C2312yes—
52C22×C4⋊C4C2312yes—
53C22×C4⋊C4C2312yes—
54C22×C42D411yescharacteristic
55C22×C42D411yescharacteristic
56C22×C42D411yescharacteristic
57C22×C42D411yescharacteristic
58C22×C42C2311yescharacteristic
59C22×C42C2311yescharacteristic
60C22×C42C2311yescharacteristic
61#389—28no—
62#389—28no—
63#389—24no—
64#389—24no—
65#389—24no—
66#389—24no—
67#389—24no—
68#389—44no—
69#389—44no—
70#389D418yes—
71#384—24no—
72#384—24no—
73#384—24no—
74#384—24no—
75#382—28no—
76C2×#95—22no—
77C2×#95—22no—
78C2×#95—22no—
79C2×#95—22no—
80C2×#95—22no—
81C43—24no—
82#340—28no—
83#340—28no—
84#340—28no—
85#340—44no—
86#336—24no—
87#336—24no—
88#336—42no—
89C23×C4—22no—
90C23×C4—22no—
91C23×C4—22no—
92C23×C4—22no—
93C23×C4C2×D411yescharacteristic
94C23×C4C2×D411yescharacteristic
95C23×C4C2×D411yescharacteristic
96C23×C4C2×D411yescharacteristic
97C23×C4C2×D411yescharacteristic
98C23×C4C2×D411yescharacteristic
99C23×C4C2411yescharacteristic
100C22×C8—24no—
101C22×C8—24no—
102C22×C8—24no—
103C22×C8—24no—
104C22×C8—24no—
105C22×C8—24no—
106C22×C8—24no—
107#125—432no—
108C2×C4⋊C4—24no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—22no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—24no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4—24no—
119C2×C4⋊C4—24no—
120C2×C4⋊C4—28no—
121C2×C4⋊C4—24no—
122C2×C4⋊C4—24no—
123C2×C4⋊C4—24no—
124C2×C4⋊C4—24no—
125C2×C4⋊C4—28no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—24no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—24no—
133C2×C4⋊C4—42no—
134C2×C4⋊C4—42no—
135C2×C4⋊C4—42no—
136C2×C4⋊C4—42no—
137C2×C4⋊C4—42no—
138C2×C4⋊C4—42no—
139C2×C4⋊C4—44no—
140C2×C4⋊C4—44no—
141C2×C4⋊C4—42no—
142C2×C4⋊C4—42no—
143C2×C4⋊C4—44no—
144C2×C4⋊C4—42no—
145C2×C4⋊C4—42no—
146C2×C4⋊C4—44no—
147C2×C4⋊C4—42no—
148C2×C4⋊C4—42no—
149C2×C4⋊C4—42no—
150C2×C4⋊C4—42no—
151C2×C4⋊C4—44no—
152C2×C4⋊C4—42no—
153C2×C4⋊C4—44no—
154C2×C4⋊C4—42no—
155C2×C4⋊C4—44no—
156C2×C4⋊C4—42no—
157C2×C4⋊C4—42no—
158C2×C4⋊C4C2×D414yes—
159C2×C4⋊C4C2×D414yes—
160C2×C4⋊C4#4114yes—
161C2×C42—22no—
162C2×C42—22no—
163C2×C42—22no—
164C2×C42—22no—
165C2×C42—22no—
166C2×C42—22no—
167C2×C42—22no—
168C2×C42—22no—
169C2×C42—22no—
170C2×C42—22no—
171C2×C42—22no—
172C2×C42—22no—
173C2×C42—22no—
174C2×C42—21no—
175C2×C42—21no—
176C2×C42—22no—
177C2×C42—41no—
178C2×C42—41no—
179C2×C42D814yes—
180C2×C42SD1614yes—
181C2×C42C2×D414yes—
182C2×C42#4114yes—
183#95—28no—
184#95—28no—
185#95—44no—
186#95—44no—
187#95—44no—
188C24C22×D411yescharacteristic
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—24no—
218C22×C4—24no—
219C22×C4—24no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4#12012yes—
246C22×C4#12012yes—
247C22×C4#12412yes—
248C22×C4#12412yes—
249C22×C4C2×D812yes—
250C22×C4C2×D812yes—
251C22×C4C2×D812yes—
252C22×C4C2×SD1612yes—
253C22×C4C2×SD1612yes—
254C22×C4C2×SD1612yes—
255C22×C4AGL(1,ℤ/8)12yes—
256C22×C4#13712yes—
257C22×C4#13712yes—
258C22×C4#13712yes—
259C22×C4C22×D412yes—
260C22×C4C2×#4112yes—
261C22×C4C2×#4112yes—
262C22×C4H(5,𝔽2)11yescharacteristic
263C22×C42−1+411yescharacteristic
264C22×C42−1+412yes—
265C22×C42−1+412yes—
266C22×C42−1+412yes—
267C2×C8—44no—
268C2×C8—44no—
269C2×C8—44no—
270C2×C8—44no—
271C2×C8—44no—
272C2×C8—44no—
273C2×C8—44no—
274C4⋊C4—24no—
275C4⋊C4—24no—
276C4⋊C4—28no—
277C4⋊C4—24no—
278C4⋊C4—24no—
279C4⋊C4—48no—
280C4⋊C4—48no—
281C4⋊C4—48no—
282C4⋊C4—48no—
283C4⋊C4—48no—
284C4⋊C4—48no—
285C4⋊C4—416no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C4⋊C4—44no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—416no—
292C4⋊C4—44no—
293C4⋊C4—44no—
294C4⋊C4—84no—
295C4⋊C4—84no—
296C4⋊C4—88no—
297C42—28no—
298C42—28no—
299C42—28no—
300C42—28no—
301C42—44no—
302C42—44no—
303C42—42no—
304C42—42no—
305C23C2×#12011yescharacteristic
306C23#52511yescharacteristic
307C23C2×#12411yescharacteristic
308C23#53611yescharacteristic
309C23#53611yescharacteristic
310C23#53611yescharacteristic
311C23#53711yescharacteristic
312C23C22×D811yescharacteristic
313C23C22×SD1611yescharacteristic
314C23C2×AGL(1,ℤ/8)11yescharacteristic
315C23C2×#13711yescharacteristic
316C23C2×#13711yescharacteristic
317C23C2×#13711yescharacteristic
318C23#57511yescharacteristic
319C23#57511yescharacteristic
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—44no—
364C2×C4—44no—
365C2×C4—44no—
366C2×C4—44no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—82no—
372C2×C4—82no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4—82no—
380C2×C4—82no—
381C2×C4—82no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4#44714yes—
387C2×C4#44814yes—
388C2×C4#48614yes—
389C2×C4#49114yes—
390C2×C4#53612yes—
391C2×C4#53712yes—
392C2×C4#54114yes—
393C2×C4#54114yes—
394C2×C4#54714yes—
395C2×C4#54814yes—
396C2×C4#55212yes—
397C2×C4#55312yes—
398C2×C4#56312yes—
399C2×C4#56412yes—
400C8—84no—
401C22#240611yescharacteristic
402C22#243611yescharacteristic
403C22#256211yescharacteristic
404C22#261611yescharacteristic
405C22#263411yescharacteristic
406C22#264211yescharacteristic
407C22#282211yescharacteristic
408C22C2×#44711yescharacteristic
409C22C2×#44811yescharacteristic
410C22#300711yescharacteristic
411C22#300711yescharacteristic
412C22#310011yescharacteristic
413C22#310111yescharacteristic
414C22#311211yescharacteristic
415C22#311311yescharacteristic
416C22C2×#48611yescharacteristic
417C22C2×#49111yescharacteristic
418C22#314111yescharacteristic
419C22#314211yescharacteristic
420C22#322611yescharacteristic
421C22#322611yescharacteristic
422C22#322611yescharacteristic
423C22#322711yescharacteristic
424C22#322911yescharacteristic
425C22#322911yescharacteristic
426C22#323411yescharacteristic
427C22#323511yescharacteristic
428C22#323611yescharacteristic
429C22#323611yescharacteristic
430C22#323611yescharacteristic
431C22#323711yescharacteristic
432C22#324511yescharacteristic
433C22#324611yescharacteristic
434C22#325411yescharacteristic
435C22#325511yescharacteristic
436C4—24no—
437C4—24no—
438C4—24no—
439C4—24no—
440C4—42no—
441C4—42no—
442C4—84no—
443C4—84no—
444C4—84no—
445C4—162no—
446C4#271914yes—
447C4#272514yes—
448C2#1663411yescharacteristic
449C2#2406011yescharacteristic
450C2#2406311yescharacteristic
451C2#2590311yescharacteristic
452C2#2591211yescharacteristic
453C2#2912111yescharacteristic
454C2#2913211yescharacteristic
455C2#2968711yescharacteristic
456C2#2968811yescharacteristic
457C2#3009111yescharacteristic
458C2#3009211yescharacteristic
459C2#3022811yescharacteristic
460C2#3023511yescharacteristic
461C2#3284811yescharacteristic
462C2#3284911yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#28592
C2×#20992
#147122
#112922
#112072
#107952