Finite Group Databasebeta

← #475843

Subgroups — #475843

Order 512.

1048 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2084C211yesmaximal, characteristic
2C2×#2085C212yesmaximal
3C2×#2083C211yesmaximal, characteristic
4#14712C211yesmaximal, characteristic
5#14707C211yesmaximal, characteristic
6#11232C212yesmaximal
7#11231C212yesmaximal
8#11208C212yesmaximal
9#11207C211yesmaximal, characteristic
10#11207C211yesmaximal, characteristic
11#10832C211yesmaximal, characteristic
12C22×#107C2212yes—
13C22×#106C2212yes—
14C22×C4⋊C8C2212yes—
15C2×#389—21no—
16C2×#389—21no—
17C2×#389C2211yescharacteristic
18C2×#389C2212yes—
19C2×#389C2211yescharacteristic
20C2×#384C2211yescharacteristic
21C2×#384C2211yescharacteristic
22C2×#382C2211yescharacteristic
23C2×#382C2211yescharacteristic
24C2×C43C2211yescharacteristic
25#2085—28no—
26#2084—24no—
27#2083—24no—
28C2×#340C2212yes—
29C2×#340C2212yes—
30C2×#340C2212yes—
31C2×#340C2212yes—
32C2×#340C2212yes—
33C2×#340C2212yes—
34C2×#336C2211yescharacteristic
35C2×#336C2212yes—
36C2×#336C2211yescharacteristic
37#1436—21no—
38#1436—21no—
39#1436—21no—
40#1436—21no—
41C4⋊#95—21no—
42C4⋊#95—21no—
43C4⋊#95C2211yescharacteristic
44C4⋊#95C2211yescharacteristic
45C4⋊#95C2212yes—
46C23×C8C2312yes—
47C23×C8C2312yes—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4C2311yescharacteristic
56C22×C4⋊C4C2311yescharacteristic
57C22×C4⋊C4C2312yes—
58C22×C4⋊C4C2311yescharacteristic
59C22×C4⋊C4C2312yes—
60C22×C4⋊C4C2311yescharacteristic
61C22×C42D411yescharacteristic
62C22×C42D411yescharacteristic
63C22×C42D411yescharacteristic
64C22×C42D411yescharacteristic
65C22×C42C2311yescharacteristic
66C22×C42C2311yescharacteristic
67C22×C42C2311yescharacteristic
68C2×#107—24no—
69C2×#107—24no—
70C2×#107—42no—
71C2×#106—24no—
72C2×#106—24no—
73C2×#106—42no—
74C2×C4⋊C8—42no—
75C2×C4⋊C8—42no—
76C2×C4⋊C8Q818yes—
77#389—22no—
78#389—22no—
79#389—24no—
80#389—24no—
81#389—22no—
82#389—22no—
83#389—44no—
84#389—44no—
85#384—22no—
86#384—42no—
87#384D414yes—
88#382—22no—
89#382—42no—
90#382D414yes—
91C2×#95—21no—
92C2×#95—21no—
93C2×#95—22no—
94C2×#95—22no—
95C2×#95—22no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95—21no—
102C2×#95—21no—
103C2×#95—21no—
104C43—42no—
105#340—24no—
106#340—24no—
107#340—24no—
108#340—24no—
109#340—42no—
110#340—42no—
111#336—22no—
112#336—22no—
113#336—24no—
114C23×C4—22no—
115C23×C4—21no—
116C23×C4—21no—
117C23×C4—22no—
118C23×C4—21no—
119C23×C4—21no—
120C23×C4C2×D411yescharacteristic
121C23×C4C2×D411yescharacteristic
122C23×C4C2×D411yescharacteristic
123C23×C4C2×D411yescharacteristic
124C23×C4C2×D411yescharacteristic
125C23×C4C2×D411yescharacteristic
126C23×C4C2411yescharacteristic
127C22×C8—22no—
128C22×C8—22no—
129C22×C8—22no—
130C22×C8—22no—
131C22×C8—22no—
132C22×C8—22no—
133C22×C8—22no—
134C22×C8—22no—
135C22×C8—22no—
136C22×C8—22no—
137C22×C8—22no—
138C22×C8—22no—
139C22×C8C2×Q814yes—
140C22×C8C2×Q814yes—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—24no—
154C2×C4⋊C4—24no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
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—42no—
173C2×C4⋊C4—42no—
174C2×C4⋊C4—42no—
175C2×C4⋊C4—42no—
176C2×C4⋊C4—42no—
177C2×C4⋊C4—42no—
178C2×C4⋊C4—42no—
179C2×C4⋊C4—42no—
180C2×C4⋊C4—44no—
181C2×C4⋊C4—44no—
182C2×C4⋊C4—44no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—42no—
187C2×C4⋊C4—42no—
188C2×C4⋊C4—42no—
189C2×C4⋊C4—42no—
190C2×C4⋊C4—42no—
191C2×C4⋊C4C2×D412yes—
192C2×C4⋊C4C2×D412yes—
193C2×C4⋊C4C2×D414yes—
194C2×C42—22no—
195C2×C42—22no—
196C2×C42—22no—
197C2×C42—21no—
198C2×C42—22no—
199C2×C42—22no—
200C2×C42—21no—
201C2×C42—22no—
202C2×C42—22no—
203C2×C42—22no—
204C2×C42—22no—
205C2×C42—22no—
206C2×C42—22no—
207C2×C42—41no—
208C2×C42—41no—
209C2×C42—41no—
210C2×C42—41no—
211C2×C42—41no—
212C2×C42—41no—
213C2×C42C2×D412yes—
214C2×C42C2×D412yes—
215C2×C42C2×Q814yes—
216C2×C42#4112yes—
217C2×C42#4112yes—
218#107—48no—
219#106—48no—
220C4⋊C8—48no—
221#95—24no—
222#95—24no—
223#95—42no—
224#95—42no—
225#95—42no—
226#95—42no—
227#95—44no—
228#95—44no—
229#95—42no—
230#95—42no—
231#95—42no—
232#95—44no—
233#95—42no—
234C24C22×D411yescharacteristic
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—24no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—42no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—42no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—42no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—42no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—42no—
307C22×C4#12112yes—
308C22×C4#12112yes—
309C22×C4#12112yes—
310C22×C4#12112yes—
311C22×C4C4⋊Q812yes—
312C22×C4C4⋊Q812yes—
313C22×C4#13512yes—
314C22×C4#13512yes—
315C22×C4AGL(1,ℤ/8)12yes—
316C22×C4AGL(1,ℤ/8)12yes—
317C22×C4#13712yes—
318C22×C4#13712yes—
319C22×C4C22×D411yescharacteristic
320C22×C4C22×D411yescharacteristic
321C22×C4C22×Q812yes—
322C22×C4C2×#4111yescharacteristic
323C22×C4C2×#4111yescharacteristic
324C22×C4H(5,𝔽2)12yes—
325C22×C4H(5,𝔽2)11yescharacteristic
326C22×C42−1+412yes—
327C22×C42−1+412yes—
328C22×C42−1+411yescharacteristic
329C2×C8—24no—
330C2×C8—24no—
331C2×C8—24no—
332C2×C8—24no—
333C2×C8—24no—
334C2×C8—24no—
335C2×C8—42no—
336C2×C8—42no—
337C2×C8—42no—
338C2×C8—42no—
339C2×C8—42no—
340C2×C8—42no—
341C2×C8—42no—
342C2×C8—42no—
343C4⋊C4—22no—
344C4⋊C4—24no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—24no—
349C4⋊C4—48no—
350C4⋊C4—41no—
351C4⋊C4—42no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—42no—
355C4⋊C4—41no—
356C4⋊C4—48no—
357C4⋊C4—42no—
358C4⋊C4—42no—
359C4⋊C4—42no—
360C4⋊C4—42no—
361C4⋊C4—42no—
362C4⋊C4—42no—
363C4⋊C4—42no—
364C4⋊C4—42no—
365C4⋊C4—84no—
366C4⋊C4—84no—
367C4⋊C4—88no—
368C4⋊C4—84no—
369C4⋊C4—84no—
370C42—24no—
371C42—24no—
372C42—24no—
373C42—24no—
374C42—24no—
375C42—24no—
376C42—44no—
377C42—44no—
378C42—44no—
379C42—44no—
380C23C2×#12111yescharacteristic
381C23C2×#12111yescharacteristic
382C23C2×C4⋊Q811yescharacteristic
383C23#53411yescharacteristic
384C23#53611yescharacteristic
385C23#53611yescharacteristic
386C23#53711yescharacteristic
387C23C2×#13511yescharacteristic
388C23C2×#13511yescharacteristic
389C23C2×AGL(1,ℤ/8)11yescharacteristic
390C23C2×AGL(1,ℤ/8)11yescharacteristic
391C23C2×#13711yescharacteristic
392C23C2×#13711yescharacteristic
393C23#57511yescharacteristic
394C23#57511yescharacteristic
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—44no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—44no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—44no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—82no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—82no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4—81no—
451C2×C4—82no—
452C2×C4—81no—
453C2×C4—81no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4—81no—
457C2×C4—81no—
458C2×C4—82no—
459C2×C4—81no—
460C2×C4—81no—
461C2×C4—82no—
462C2×C4—81no—
463C2×C4—81no—
464C2×C4—82no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4—82no—
468C2×C4—81no—
469C2×C4—81no—
470C2×C4—81no—
471C2×C4—81no—
472C2×C4—82no—
473C2×C4—81no—
474C2×C4—81no—
475C2×C4—82no—
476C2×C4#46314yes—
477C2×C4#46414yes—
478C2×C4#50114yes—
479C2×C4#53712yes—
480C2×C4#53712yes—
481C2×C4#53912yes—
482C2×C4#53912yes—
483C2×C4#54312yes—
484C2×C4#54412yes—
485C2×C4D4211yescharacteristic
486C2×C4#54711yescharacteristic
487C2×C4#54711yescharacteristic
488C2×C4D4×Q812yes—
489C2×C4D4×Q812yes—
490C2×C4#55511yescharacteristic
491C2×C4#55712yes—
492C2×C4#55712yes—
493C2×C4#56312yes—
494C2×C4#56412yes—
495C8—44no—
496C8—44no—
497C22#253711yescharacteristic
498C22#254611yescharacteristic
499C22#254611yescharacteristic
500C22#261811yescharacteristic
501C22#261811yescharacteristic
502C22#265911yescharacteristic
503C22#282211yescharacteristic
504C22C2×#46311yescharacteristic
505C22C2×#46411yescharacteristic
506C22#303511yescharacteristic
507C22#303511yescharacteristic
508C22#303611yescharacteristic
509C22#303711yescharacteristic
510C22#303811yescharacteristic
511C22#303911yescharacteristic
512C22#316011yescharacteristic
513C22C2×#50111yescharacteristic
514C22#316511yescharacteristic
515C22#316611yescharacteristic
516C22#318811yescharacteristic
517C22#319011yescharacteristic
518C22#319411yescharacteristic
519C22#319611yescharacteristic
520C22#322811yescharacteristic
521C22#323111yescharacteristic
522C22#323211yescharacteristic
523C22#323211yescharacteristic
524C22#323511yescharacteristic
525C22#323711yescharacteristic
526C22#323811yescharacteristic
527C22#323911yescharacteristic
528C22#324711yescharacteristic
529C22#324811yescharacteristic
530C22#325111yescharacteristic
531C22#325211yescharacteristic
532C4—24no—
533C4—24no—
534C4—24no—
535C4—42no—
536C4—42no—
537C4—42no—
538C4—84no—
539C4—82no—
540C4—82no—
541C4—162no—
542C4—161no—
543C4—161no—
544C4#268312yes—
545C4#272612yes—
546C4#272612yes—
547C4#280912yes—
548C2#1707011yescharacteristic
549C2#2825311yescharacteristic
550C2#2825411yescharacteristic
551C2#2868811yescharacteristic
552C2#2869011yescharacteristic
553C2#2869311yescharacteristic
554C2#2869411yescharacteristic
555C2#2975811yescharacteristic
556C2#2975911yescharacteristic
557C2#2976011yescharacteristic
558C2#2976111yescharacteristic
559C2#3029411yescharacteristic
560C2#3029511yescharacteristic
561C2#3285211yescharacteristic
562C2#3285311yescharacteristic
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×#20842
C2×#20852
C2×#20832
#147122
#147072
#112322
#112312
#112082
#112072
#108322