Finite Group Databasebeta

← #432742

Subgroups — #432742

Order 512.

1240 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2582C211yesmaximal, characteristic
2C2×#2099C211yesmaximal, characteristic
3C2×#2072C211yesmaximal, characteristic
4#13926C211yesmaximal, characteristic
5#11380C211yesmaximal, characteristic
6#11292C212yesmaximal
7#11267C212yesmaximal
8#11190C212yesmaximal
9#10932C211yesmaximal, characteristic
10#10885C211yesmaximal, characteristic
11#10789C212yesmaximal
12C22×C4×Q8C2211yescharacteristic
13C22×C4×Q8C2211yescharacteristic
14C22×#103C2212yes—
15C22×#103C2212yes—
16#2582—24no—
17#2582—24no—
18C2×#398—21no—
19C2×#398—21no—
20C2×#391—21no—
21C2×#391—21no—
22C2×#391C2211yescharacteristic
23C2×#391C2211yescharacteristic
24C2×#389—21no—
25C2×#389C2211yescharacteristic
26C2×#389C2211yescharacteristic
27C2×#384C2211yescharacteristic
28C2×#384C2211yescharacteristic
29C2×C4×C4⋊C4C2211yescharacteristic
30#2099—24no—
31#2072—24no—
32C2×#340C2212yes—
33C2×#340C2212yes—
34C2×#340C2212yes—
35C2×#340C2212yes—
36C2×#340C2212yes—
37C2×#340C2212yes—
38C2×#336C2212yes—
39C2×#336C2211yescharacteristic
40C2×#336C2211yescharacteristic
41C2×#336C2212yes—
42#1441—21no—
43#1441—21no—
44C4⋊#95—21no—
45C4⋊#95C2212yes—
46C4⋊#95C2212yes—
47C23×Q8D411yescharacteristic
48C23×Q8C2311yescharacteristic
49C23×C8C2312yes—
50C23×C8C2312yes—
51C2×C4×Q8—22no—
52C2×C4×Q8—22no—
53C2×C4×Q8—22no—
54C2×C4×Q8—22no—
55C2×C4×Q8—24no—
56C2×C4×Q8—24no—
57C2×C4×Q8—42no—
58C2×C4×Q8—42no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4—21no—
61C22×C4⋊C4—21no—
62C22×C4⋊C4—21no—
63C22×C4⋊C4—21no—
64C22×C4⋊C4—21no—
65C22×C4⋊C4—21no—
66C22×C4⋊C4D411yescharacteristic
67C22×C4⋊C4D411yescharacteristic
68C22×C4⋊C4D411yescharacteristic
69C22×C4⋊C4C2312yes—
70C22×C4⋊C4C2311yescharacteristic
71C22×C4⋊C4C2311yescharacteristic
72C22×C4⋊C4C2311yescharacteristic
73C22×C4⋊C4C2312yes—
74C22×C42—21no—
75C22×C42—21no—
76C22×C42C2311yescharacteristic
77C22×C42C2311yescharacteristic
78C22×C42C2311yescharacteristic
79C2×#103—24no—
80C2×#103—24no—
81C2×#103—24no—
82C2×#103—24no—
83C2×#103—24no—
84C2×#103—42no—
85#398—28no—
86#398—28no—
87#391—28no—
88#391—22no—
89#391—22no—
90#391—22no—
91#391—44no—
92#391D414yes—
93#389—28no—
94#389—22no—
95#389—22no—
96#389—22no—
97#389D414yes—
98#384—22no—
99#384—22no—
100#384—22no—
101#384—22no—
102C4×C4⋊C4—42no—
103C2×#95—21no—
104C2×#95—21no—
105C2×#95—21no—
106C2×#95—21no—
107C2×#95—21no—
108C2×#95—21no—
109C2×#95—22no—
110C2×#95—22no—
111C2×#95—21no—
112C2×#95—22no—
113C2×#95—22no—
114#340—24no—
115#340—24no—
116#340—24no—
117#340—24no—
118#340—24no—
119#340—42no—
120#336—22no—
121#336—22no—
122#336—24no—
123#336—42no—
124C22×Q8—22no—
125C22×Q8—22no—
126C22×Q8—22no—
127C22×Q8—22no—
128C22×Q8—21no—
129C22×Q8—22no—
130C22×Q8—22no—
131C22×Q8—22no—
132C22×Q8—22no—
133C22×Q8—22no—
134C22×Q8—41no—
135C22×Q8—41no—
136C22×Q8SD1614yes—
137C22×Q8C2×D412yes—
138C22×Q8#4114yes—
139C23×C4—21no—
140C23×C4—21no—
141C23×C4—21no—
142C23×C4—21no—
143C23×C4—22no—
144C23×C4—22no—
145C23×C4C2×D411yescharacteristic
146C23×C4C2×D411yescharacteristic
147C23×C4C2×D411yescharacteristic
148C23×C4C2×D411yescharacteristic
149C23×C4C2×D411yescharacteristic
150C23×C4C2×D411yescharacteristic
151C23×C4C2411yescharacteristic
152C22×C8—22no—
153C22×C8—22no—
154C22×C8—22no—
155C22×C8—22no—
156C22×C8—22no—
157C22×C8—22no—
158C22×C8—22no—
159C22×C8—22no—
160C22×C8—22no—
161C22×C8—22no—
162C22×C8—22no—
163C22×C8—22no—
164C22×C8—22no—
165C22×C8—22no—
166C4×Q8—48no—
167C4×Q8—48no—
168C4×Q8—48no—
169C4×Q8—48no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—24no—
181C2×C4⋊C4—24no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—24no—
200C2×C4⋊C4—24no—
201C2×C4⋊C4—41no—
202C2×C4⋊C4—41no—
203C2×C4⋊C4—41no—
204C2×C4⋊C4—42no—
205C2×C4⋊C4—42no—
206C2×C4⋊C4—42no—
207C2×C4⋊C4—42no—
208C2×C4⋊C4—42no—
209C2×C4⋊C4—42no—
210C2×C4⋊C4—42no—
211C2×C4⋊C4—42no—
212C2×C4⋊C4—82no—
213C2×C4⋊C4—82no—
214C2×C4⋊C4—82no—
215C2×C4⋊C4—82no—
216C2×C4⋊C4C2×D412yes—
217C2×C4⋊C4C2×D412yes—
218C2×C4⋊C4C2×D412yes—
219C2×C4⋊C4#4114yes—
220C2×C42—21no—
221C2×C42—21no—
222C2×C42—22no—
223C2×C42—22no—
224C2×C42—22no—
225C2×C42—24no—
226C2×C42—21no—
227C2×C42—21no—
228C2×C42—22no—
229C2×C42—22no—
230C2×C42—42no—
231C2×C42—42no—
232C2×C42—42no—
233C2×C42—42no—
234C2×C42—42no—
235C2×C42C2×D412yes—
236C2×C42C2×D412yes—
237C2×C42#4114yes—
238#103—48no—
239#103—48no—
240#95—24no—
241#95—24no—
242#95—24no—
243#95—24no—
244#95—24no—
245#95—24no—
246#95—42no—
247#95—44no—
248#95—44no—
249#95—82no—
250#95—82no—
251C24C22×D411yescharacteristic
252C2×Q8—22no—
253C2×Q8—24no—
254C2×Q8—28no—
255C2×Q8—28no—
256C2×Q8—24no—
257C2×Q8—24no—
258C2×Q8—24no—
259C2×Q8—24no—
260C2×Q8—24no—
261C2×Q8—24no—
262C2×Q8—44no—
263C2×Q8—44no—
264C2×Q8—44no—
265C2×Q8—44no—
266C2×Q8—44no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—42no—
270C2×Q8—42no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—42no—
274C2×Q8#12414yes—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—24no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—24no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—42no—
311C22×C4—41no—
312C22×C4—42no—
313C22×C4—41no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—42no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4#12012yes—
337C22×C4#12012yes—
338C22×C4#12312yes—
339C22×C4#12312yes—
340C22×C4C2×SD1612yes—
341C22×C4C2×SD1612yes—
342C22×C4C2×SD1612yes—
343C22×C4#13712yes—
344C22×C4#13712yes—
345C22×C4C22×D411yescharacteristic
346C22×C4C22×D411yescharacteristic
347C22×C4C2×#4112yes—
348C22×C4C2×#4112yes—
349C22×C4C2×#4112yes—
350C22×C4H(5,𝔽2)12yes—
351C22×C42−1+412yes—
352C22×C42−1+412yes—
353C2×C8—42no—
354C2×C8—42no—
355C2×C8—42no—
356C2×C8—42no—
357C2×C8—42no—
358C2×C8—42no—
359C2×C8—42no—
360C2×C8—42no—
361C2×C8—42no—
362C2×C8—42no—
363C2×C8—42no—
364C2×C8—42no—
365C2×C8—42no—
366C2×C8—42no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—24no—
370C4⋊C4—24no—
371C4⋊C4—24no—
372C4⋊C4—24no—
373C4⋊C4—44no—
374C4⋊C4—44no—
375C4⋊C4—44no—
376C4⋊C4—48no—
377C4⋊C4—48no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—42no—
381C4⋊C4—42no—
382C4⋊C4—42no—
383C4⋊C4—42no—
384C4⋊C4—42no—
385C4⋊C4—42no—
386C4⋊C4—42no—
387C4⋊C4—42no—
388C4⋊C4—84no—
389C4⋊C4—84no—
390C4⋊C4—84no—
391C4⋊C4—84no—
392C4⋊C4—84no—
393C42—24no—
394C42—24no—
395C42—24no—
396C42—24no—
397C42—48no—
398C42—42no—
399C42—42no—
400C42—84no—
401C23C2×#12011yescharacteristic
402C23C2×#12311yescharacteristic
403C23#53411yescharacteristic
404C23#54812yes—
405C23#54812yes—
406C23C22×SD1611yescharacteristic
407C23C2×#13711yescharacteristic
408C23C2×#13711yescharacteristic
409C23#57511yescharacteristic
410C23#57612yes—
411C23#57812yes—
412Q8—28no—
413Q8—416no—
414Q8—44no—
415Q8—44no—
416Q8—44no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—24no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—44no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—44no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—44no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—41no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—82no—
469C2×C4—82no—
470C2×C4—82no—
471C2×C4—82no—
472C2×C4—82no—
473C2×C4—82no—
474C2×C4—82no—
475C2×C4—82no—
476C2×C4—82no—
477C2×C4—82no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4—82no—
483C2×C4—82no—
484C2×C4—82no—
485C2×C4#44814yes—
486C2×C4#48314yes—
487C2×C4C2×#12411yescharacteristic
488C2×C4#52912yes—
489C2×C4#53211yescharacteristic
490C2×C4#53611yescharacteristic
491C2×C4#53611yescharacteristic
492C2×C4#53912yes—
493C2×C4#53912yes—
494C2×C4#54112yes—
495C2×C4#54612yes—
496C2×C4#54612yes—
497C2×C4#54712yes—
498C2×C4#54812yes—
499C2×C4#55112yes—
500C2×C4#55212yes—
501C2×C4#55612yes—
502C2×C4#56312yes—
503C8—82no—
504C8—82no—
505C22#240511yescharacteristic
506C22#242112yes—
507C22#243211yescharacteristic
508C22#243611yescharacteristic
509C22#272812yes—
510C22C2×#44811yescharacteristic
511C22#300711yescharacteristic
512C22#300811yescharacteristic
513C22#301111yescharacteristic
514C22C2×#48311yescharacteristic
515C22#309511yescharacteristic
516C22#309812yes—
517C22#318711yescharacteristic
518C22#319511yescharacteristic
519C22#320312yes—
520C22#335912yes—
521C22#336212yes—
522C22#337012yes—
523C22#337412yes—
524C22#337412yes—
525C22#337512yes—
526C22#337512yes—
527C22#337712yes—
528C4—24no—
529C4—24no—
530C4—44no—
531C4—42no—
532C4—42no—
533C4—42no—
534C4—84no—
535C4—82no—
536C4—82no—
537C4—81no—
538C4—82no—
539C4—162no—
540C4#248812yes—
541C4#256012yes—
542C4#268912yes—
543C4#269012yes—
544C2#1546511yescharacteristic
545C2#2400311yescharacteristic
546C2#2401111yescharacteristic
547C2#2499412yes—
548C2#2500812yes—
549C2#2564711yescharacteristic
550C2#2566011yescharacteristic
551C2#2593211yescharacteristic
552C2#2594311yescharacteristic
553C2#3254612yes—
554C2#3256312yes—
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×Q8 ◁ 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×#25822
C2×#20992
C2×#20722
#139262
#113802
#112922
#112672
#111902
#109322
#108852
#107892