Finite Group Databasebeta

← #470421

Subgroups — #470421

Order 512.

1110 conjugacy classes of subgroups.

The subgroup lattice has 485 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2552C211yesmaximal, characteristic
2C2×#2084C211yesmaximal, characteristic
3C2×#1919C211yesmaximal, characteristic
4#15156C211yesmaximal, characteristic
5#11371C211yesmaximal, characteristic
6#11346C211yesmaximal, characteristic
7#11323C212yesmaximal
8#11292C212yesmaximal
9#11267C212yesmaximal
10#11220C212yesmaximal
11#10807C211yesmaximal, characteristic
12C22×#125—21no—
13C22×#106C2211yescharacteristic
14C22×#106C2212yes—
15#2552—24no—
16#2552—24no—
17C2×#400—21no—
18C2×#398—22no—
19C2×#389—21no—
20C2×#389C2212yes—
21C2×#389C2211yescharacteristic
22C2×#384C2212yes—
23C2×#384C2211yescharacteristic
24C2×C4×C4⋊C4C2211yescharacteristic
25C2×C4×C4⋊C4C2211yescharacteristic
26#2084—24no—
27#1919—24no—
28C2×#340C2211yescharacteristic
29C2×#340C2212yes—
30C2×#340C2211yescharacteristic
31C2×#340C2212yes—
32C2×#340C2212yes—
33C2×#340C2211yescharacteristic
34C2×#340C2212yes—
35C2×#340C2212yes—
36C2×#336C2212yes—
37C2×#336C2212yes—
38C2×#336C2211yescharacteristic
39C2×#336C2211yescharacteristic
40#1443—22no—
41#1441—21no—
42C4⋊#95C2212yes—
43C4⋊#95C2211yescharacteristic
44C4⋊#95C2212yes—
45C23×C8C2311yescharacteristic
46C23×C8C2311yescharacteristic
47C23×C8C2312yes—
48C2×#125—28no—
49C2×#125—48no—
50C22×C4⋊C4—22no—
51C22×C4⋊C4—22no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4D411yescharacteristic
57C22×C4⋊C4D411yescharacteristic
58C22×C4⋊C4C2312yes—
59C22×C4⋊C4C2311yescharacteristic
60C22×C4⋊C4C2311yescharacteristic
61C22×C4⋊C4C2312yes—
62C22×C4⋊C4C2311yescharacteristic
63C22×C4⋊C4C2311yescharacteristic
64C22×C42—21no—
65C22×C42C2312yes—
66C22×C42C2311yescharacteristic
67C2×#106—22no—
68C2×#106—22no—
69C2×#106—22no—
70C2×#106—24no—
71C2×#106—24no—
72C2×#106—42no—
73#400—44no—
74#398—216no—
75#389—28no—
76#389—24no—
77#389—24no—
78#389—22no—
79#389—22no—
80#384—24no—
81#384—24no—
82#384—22no—
83#384D414yes—
84C4×C4⋊C4—22no—
85C4×C4⋊C4—22no—
86C4×C4⋊C4—22no—
87C4×C4⋊C4D414yes—
88C2×#95—21no—
89C2×#95—22no—
90C2×#95—21no—
91C2×#95—22no—
92C2×#95—22no—
93C2×#95—22no—
94C2×#95—21no—
95C2×#95—22no—
96C2×#95—21no—
97C2×#95D412yes—
98#340—24no—
99#340—24no—
100#340—24no—
101#340—22no—
102#340—22no—
103#340—22no—
104#340—42no—
105#340—42no—
106#336—24no—
107#336—24no—
108#336—22no—
109#336—22no—
110C23×C4—22no—
111C23×C4—21no—
112C23×C4—21no—
113C23×C4—21no—
114C23×C4—21no—
115C23×C4—22no—
116C23×C4C2×D411yescharacteristic
117C23×C4C2×D412yes—
118C23×C4C2×D412yes—
119C23×C4C2×D411yescharacteristic
120C23×C4C2411yescharacteristic
121C22×C8—21no—
122C22×C8—22no—
123C22×C8—22no—
124C22×C8—21no—
125C22×C8—22no—
126C22×C8—22no—
127C22×C8—22no—
128C22×C8—22no—
129C22×C8—22no—
130C22×C8—22no—
131C22×C8—21no—
132C22×C8—22no—
133C22×C8—21no—
134C22×C8—22no—
135C22×C8—21no—
136C22×C8#4114yes—
137C22×C8#4112yes—
138#125—432no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—24no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—28no—
158C2×C4⋊C4—28no—
159C2×C4⋊C4—24no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—28no—
175C2×C4⋊C4—24no—
176C2×C4⋊C4—44no—
177C2×C4⋊C4—44no—
178C2×C4⋊C4—44no—
179C2×C4⋊C4—44no—
180C2×C4⋊C4—44no—
181C2×C4⋊C4—42no—
182C2×C4⋊C4—42no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—82no—
185C2×C4⋊C4—82no—
186C2×C4⋊C4—82no—
187C2×C4⋊C4SD1614yes—
188C2×C4⋊C4C2×D412yes—
189C2×C4⋊C4C2×D412yes—
190C2×C4⋊C4C2×D414yes—
191C2×C4⋊C4#4112yes—
192C2×C42—22no—
193C2×C42—22no—
194C2×C42—24no—
195C2×C42—22no—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42—22no—
199C2×C42—22no—
200C2×C42—22no—
201C2×C42—44no—
202C2×C42C2×D412yes—
203C2×C42C2×D412yes—
204#106—28no—
205#106—48no—
206#95—28no—
207#95—24no—
208#95—24no—
209#95—42no—
210#95—44no—
211#95—42no—
212#95—44no—
213#95—44no—
214#95—82no—
215#95—81no—
216C24C22×D411yescharacteristic
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—24no—
238C22×C4—22no—
239C22×C4—41no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—42no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—41no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—41no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4#12012yes—
272C22×C4#12012yes—
273C22×C4C2×SD1614yes—
274C22×C4C2×SD1612yes—
275C22×C4AGL(1,ℤ/8)14yes—
276C22×C4#13712yes—
277C22×C4C22×D411yescharacteristic
278C22×C4C22×D411yescharacteristic
279C22×C4C2×#4111yescharacteristic
280C22×C4C2×#4111yescharacteristic
281C22×C4C2×#4112yes—
282C22×C4H(5,𝔽2)11yescharacteristic
283C22×C42−1+412yes—
284C22×C42−1+412yes—
285C22×C42−1+412yes—
286C22×C42−1+411yescharacteristic
287C2×C8—22no—
288C2×C8—24no—
289C2×C8—24no—
290C2×C8—24no—
291C2×C8—24no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—42no—
295C2×C8—42no—
296C2×C8—42no—
297C2×C8—42no—
298C2×C8—42no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—42no—
303C2×C8—42no—
304C4⋊C4—28no—
305C4⋊C4—28no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—24no—
313C4⋊C4—24no—
314C4⋊C4—48no—
315C4⋊C4—416no—
316C4⋊C4—416no—
317C4⋊C4—42no—
318C4⋊C4—41no—
319C4⋊C4—42no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—42no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4—42no—
330C4⋊C4—42no—
331C4⋊C4—84no—
332C4⋊C4—88no—
333C4⋊C4—84no—
334C42—22no—
335C42—22no—
336C42—24no—
337C42—48no—
338C42—42no—
339C42—42no—
340C42—42no—
341C42—42no—
342C23C2×#12011yescharacteristic
343C23#53612yes—
344C23#54712yes—
345C23#54811yescharacteristic
346C23#55011yescharacteristic
347C23C22×SD1611yescharacteristic
348C23C2×AGL(1,ℤ/8)12yes—
349C23C2×#13711yescharacteristic
350C23#57712yes—
351C23#57711yescharacteristic
352C23#57811yescharacteristic
353C2×C4—22no—
354C2×C4—24no—
355C2×C4—24no—
356C2×C4—22no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—22no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—44no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—44no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—81no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4—82no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—81no—
403C2×C4—82no—
404C2×C4—82no—
405C2×C4—82no—
406C2×C4—82no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4#44814yes—
413C2×C4#52511yescharacteristic
414C2×C4#53211yescharacteristic
415C2×C4#53611yescharacteristic
416C2×C4#53611yescharacteristic
417C2×C4#53611yescharacteristic
418C2×C4#53612yes—
419C2×C4#53711yescharacteristic
420C2×C4#53912yes—
421C2×C4#54112yes—
422C2×C4#54112yes—
423C2×C4#54112yes—
424C2×C4#54611yescharacteristic
425C2×C4#54711yescharacteristic
426C2×C4#54812yes—
427C2×C4#55212yes—
428C2×C4#55212yes—
429C2×C4#56312yes—
430C2×C4#56412yes—
431C8—42no—
432C8—44no—
433C8—81no—
434C22#240711yescharacteristic
435C22#243211yescharacteristic
436C22#261411yescharacteristic
437C22#271912yes—
438C22#272112yes—
439C22C2×#44811yescharacteristic
440C22#300311yescharacteristic
441C22#300911yescharacteristic
442C22#301311yescharacteristic
443C22#322712yes—
444C22#323912yes—
445C22#324212yes—
446C22#324412yes—
447C22#333512yes—
448C22#334312yes—
449C22#334512yes—
450C22#335612yes—
451C22#335911yescharacteristic
452C22#336812yes—
453C22#337211yescharacteristic
454C22#339211yescharacteristic
455C22#339712yes—
456C22#339811yescharacteristic
457C4—24no—
458C4—44no—
459C4—44no—
460C4—42no—
461C4—82no—
462C4—82no—
463C4—82no—
464C4—84no—
465C4—162no—
466C4—161no—
467C4#261111yescharacteristic
468C4#263411yescharacteristic
469C4#266411yescharacteristic
470C4#269012yes—
471C4#271912yes—
472C4#282211yescharacteristic
473C2#1668311yescharacteristic
474C2#2418711yescharacteristic
475C2#2420011yescharacteristic
476C2#2570211yescharacteristic
477C2#2570911yescharacteristic
478C2#2963911yescharacteristic
479C2#2964811yescharacteristic
480C2#3231412yes—
481C2#3233012yes—
482C2#3237812yes—
483C2#3239612yes—
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ 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×#25522
C2×#20842
C2×#19192
#151562
#113712
#113462
#113232
#112922
#112672
#112202
#108072