Finite Group Databasebeta

← #470384

Subgroups — #470384

Order 512.

1124 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2552C211yesmaximal, characteristic
2C2×#2099C211yesmaximal, characteristic
3C2×#1918C211yesmaximal, characteristic
4#15149C211yesmaximal, characteristic
5#11357C211yesmaximal, characteristic
6#11346C211yesmaximal, characteristic
7#11328C212yesmaximal
8#11292C212yesmaximal
9#11267C212yesmaximal
10#11207C212yesmaximal
11#10806C211yesmaximal, characteristic
12C22×#125—21no—
13C22×#107C2211yescharacteristic
14#2552—24no—
15#2552—24no—
16C2×#398—22no—
17C2×#398—21no—
18C2×#389—21no—
19C2×#389C2212yes—
20C2×#389C2211yescharacteristic
21C2×#389C2212yes—
22C2×#384C2212yes—
23C2×#384C2211yescharacteristic
24C2×C4×C4⋊C4C2211yescharacteristic
25C2×C4×C4⋊C4C2211yescharacteristic
26#2099—24no—
27#1918—24no—
28C2×#340C2211yescharacteristic
29C2×#340C2212yes—
30C2×#340C2212yes—
31C2×#340C2212yes—
32C2×#340C2211yescharacteristic
33C2×#340C2212yes—
34C2×#340C2211yescharacteristic
35C2×#340C2212yes—
36C2×#340C2212yes—
37C2×#336C2212yes—
38C2×#336C2211yescharacteristic
39C2×#336C2211yescharacteristic
40C2×#336C2212yes—
41#1442—22no—
42#1441—21no—
43C4⋊#95C2212yes—
44C4⋊#95C2211yescharacteristic
45C23×C8C2312yes—
46C23×C8C2311yescharacteristic
47C23×C8C2311yescharacteristic
48C2×#125—28no—
49C2×#125—44no—
50C2×#125—44no—
51C22×C4⋊C4—22no—
52C22×C4⋊C4—22no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—21no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4D411yescharacteristic
59C22×C4⋊C4D411yescharacteristic
60C22×C4⋊C4C2311yescharacteristic
61C22×C4⋊C4C2311yescharacteristic
62C22×C4⋊C4C2311yescharacteristic
63C22×C4⋊C4C2312yes—
64C22×C4⋊C4C2311yescharacteristic
65C22×C4⋊C4C2312yes—
66C22×C42—21no—
67C22×C42C2312yes—
68C22×C42C2311yescharacteristic
69C2×#107—22no—
70C2×#107—22no—
71C2×#107—22no—
72#398—216no—
73#398—44no—
74#389—28no—
75#389—24no—
76#389—24no—
77#389—24no—
78#389—22no—
79#389—22no—
80#389—42no—
81#384—24no—
82#384—24no—
83#384—22no—
84#384D414yes—
85C4×C4⋊C4—22no—
86C4×C4⋊C4—22no—
87C4×C4⋊C4—22no—
88C4×C4⋊C4D414yes—
89C2×#95—21no—
90C2×#95—22no—
91C2×#95—21no—
92C2×#95—22no—
93C2×#95—22no—
94C2×#95—22no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95D412yes—
98#340—24no—
99#340—24no—
100#340—22no—
101#340—22no—
102#340—22no—
103#340—24no—
104#340—24no—
105#340—24no—
106#340—42no—
107#336—24no—
108#336—22no—
109#336—22no—
110#336—42no—
111C23×C4—22no—
112C23×C4—21no—
113C23×C4—21no—
114C23×C4—21no—
115C23×C4—22no—
116C23×C4—21no—
117C23×C4C2×D411yescharacteristic
118C23×C4C2×D412yes—
119C23×C4C2×D412yes—
120C23×C4C2×D411yescharacteristic
121C23×C4C2411yescharacteristic
122C22×C8—21no—
123C22×C8—22no—
124C22×C8—21no—
125C22×C8—22no—
126C22×C8—21no—
127C22×C8—22no—
128C22×C8—22no—
129C22×C8—22no—
130C22×C8—22no—
131C22×C8—21no—
132C22×C8—22no—
133C22×C8—22no—
134C22×C8—22no—
135C22×C8—22no—
136C22×C8—21no—
137C22×C8—22no—
138C22×C8#4112yes—
139#125—432no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—24no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—28no—
163C2×C4⋊C4—28no—
164C2×C4⋊C4—24no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
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—42no—
181C2×C4⋊C4—42no—
182C2×C4⋊C4—44no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—44no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—42no—
187C2×C4⋊C4—82no—
188C2×C4⋊C4—82no—
189C2×C4⋊C4—82no—
190C2×C4⋊C4—82no—
191C2×C4⋊C4D814yes—
192C2×C4⋊C4C2×D412yes—
193C2×C4⋊C4C2×D414yes—
194C2×C4⋊C4C2×D412yes—
195C2×C4⋊C4#4114yes—
196C2×C4⋊C4#4112yes—
197C2×C42—22no—
198C2×C42—22no—
199C2×C42—24no—
200C2×C42—22no—
201C2×C42—22no—
202C2×C42—22no—
203C2×C42—22no—
204C2×C42—22no—
205C2×C42—22no—
206C2×C42—42no—
207C2×C42—42no—
208C2×C42C2×D412yes—
209C2×C42C2×D412yes—
210#107—28no—
211#95—28no—
212#95—24no—
213#95—24no—
214#95—44no—
215#95—42no—
216#95—42no—
217#95—44no—
218#95—44no—
219#95—81no—
220C24C22×D411yescharacteristic
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—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—24no—
242C22×C4—22no—
243C22×C4—24no—
244C22×C4—41no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—42no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—42no—
261C22×C4—41no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—41no—
268C22×C4—42no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—42no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—42no—
277C22×C4#12012yes—
278C22×C4#12012yes—
279C22×C4C2×D814yes—
280C22×C4C2×D812yes—
281C22×C4AGL(1,ℤ/8)12yes—
282C22×C4#13714yes—
283C22×C4C22×D411yescharacteristic
284C22×C4C22×D411yescharacteristic
285C22×C4C2×#4111yescharacteristic
286C22×C4C2×#4111yescharacteristic
287C22×C4C2×#4112yes—
288C22×C4H(5,𝔽2)11yescharacteristic
289C22×C42−1+412yes—
290C22×C42−1+412yes—
291C22×C42−1+412yes—
292C22×C42−1+411yescharacteristic
293C2×C8—22no—
294C2×C8—24no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—42no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—42no—
301C2×C8—41no—
302C2×C8—42no—
303C2×C8—42no—
304C2×C8—42no—
305C2×C8—42no—
306C2×C8—42no—
307C2×C8—42no—
308C2×C8—42no—
309C2×C8—42no—
310C4⋊C4—28no—
311C4⋊C4—28no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—24no—
318C4⋊C4—24no—
319C4⋊C4—24no—
320C4⋊C4—22no—
321C4⋊C4—24no—
322C4⋊C4—416no—
323C4⋊C4—416no—
324C4⋊C4—42no—
325C4⋊C4—42no—
326C4⋊C4—41no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—42no—
333C4⋊C4—48no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—42no—
337C4⋊C4—84no—
338C4⋊C4—88no—
339C4⋊C4—88no—
340C4⋊C4—84no—
341C42—22no—
342C42—22no—
343C42—24no—
344C42—42no—
345C42—42no—
346C42—42no—
347C42—42no—
348C42—48no—
349C23C2×#12011yescharacteristic
350C23#53612yes—
351C23#54611yescharacteristic
352C23#54711yescharacteristic
353C23#54812yes—
354C23C22×D811yescharacteristic
355C23C2×AGL(1,ℤ/8)11yescharacteristic
356C23C2×#13712yes—
357C23#57712yes—
358C23#57711yescharacteristic
359C23#57811yescharacteristic
360C2×C4—22no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—22no—
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—22no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—44no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—81no—
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—82no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—82no—
414C2×C4—81no—
415C2×C4—82no—
416C2×C4—81no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4#44714yes—
422C2×C4#52511yescharacteristic
423C2×C4#53211yescharacteristic
424C2×C4#53611yescharacteristic
425C2×C4#53611yescharacteristic
426C2×C4#53611yescharacteristic
427C2×C4#53612yes—
428C2×C4#53711yescharacteristic
429C2×C4#53912yes—
430C2×C4#54112yes—
431C2×C4#54112yes—
432C2×C4#54112yes—
433C2×C4#54712yes—
434C2×C4#54811yescharacteristic
435C2×C4#55011yescharacteristic
436C2×C4#55212yes—
437C2×C4#55212yes—
438C2×C4#56312yes—
439C2×C4#56412yes—
440C8—42no—
441C8—81no—
442C8—82no—
443C22#240711yescharacteristic
444C22#243211yescharacteristic
445C22#261411yescharacteristic
446C22#269012yes—
447C22#271912yes—
448C22C2×#44711yescharacteristic
449C22#300411yescharacteristic
450C22#300911yescharacteristic
451C22#301311yescharacteristic
452C22#322612yes—
453C22#323812yes—
454C22#324212yes—
455C22#324412yes—
456C22#329411yescharacteristic
457C22#331612yes—
458C22#333011yescharacteristic
459C22#333411yescharacteristic
460C22#334412yes—
461C22#335411yescharacteristic
462C22#335812yes—
463C22#336812yes—
464C22#337212yes—
465C22#337412yes—
466C4—24no—
467C4—44no—
468C4—44no—
469C4—42no—
470C4—82no—
471C4—84no—
472C4—82no—
473C4—82no—
474C4—84no—
475C4—161no—
476C4#261111yescharacteristic
477C4#263411yescharacteristic
478C4#266411yescharacteristic
479C4#271912yes—
480C4#272112yes—
481C4#282211yescharacteristic
482C2#1668311yescharacteristic
483C2#2411611yescharacteristic
484C2#2413411yescharacteristic
485C2#2564511yescharacteristic
486C2#2565711yescharacteristic
487C2#2963811yescharacteristic
488C2#2964811yescharacteristic
489C2#3145412yes—
490C2#3147212yes—
491C2#3231012yes—
492C2#3232812yes—
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×#20992
C2×#19182
#151492
#113572
#113462
#113282
#112922
#112672
#112072
#108062