Finite Group Databasebeta

← #404948

Subgroups — #404948

Order 512.

1354 conjugacy classes of subgroups.

The subgroup lattice has 617 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2295C211yesmaximal, characteristic
2C2×#2084C211yesmaximal, characteristic
3C2×#2072C211yesmaximal, characteristic
4C2×#1865C212yesmaximal
5#14712C211yesmaximal, characteristic
6#11220C212yesmaximal
7#11207C211yesmaximal, characteristic
8#11190C212yesmaximal
9#11050C211yesmaximal, characteristic
10#10884C212yesmaximal
11#10795C211yesmaximal, characteristic
12C22×C4×Q8C2211yescharacteristic
13C22×#106C2212yes—
14C22×#103C2212yes—
15C22×#103C2212yes—
16#2295—24no—
17#2295—24no—
18C2×#391C2211yescharacteristic
19C2×#391C2211yescharacteristic
20C2×#389—21no—
21C2×#389—21no—
22C2×#389C2212yes—
23C2×#389C2211yescharacteristic
24C2×#389C2211yescharacteristic
25C2×#387—21no—
26C2×#387—21no—
27C2×#384C2211yescharacteristic
28C2×#384C2211yescharacteristic
29C2×C4×C4⋊C4—21no—
30C2×C4×C4⋊C4C2211yescharacteristic
31C2×#376—21no—
32C2×C43C2211yescharacteristic
33#2084—24no—
34#2072—24no—
35#1865—28no—
36C2×#340C2212yes—
37C2×#340C2212yes—
38C2×#340C2212yes—
39C2×#340C2212yes—
40C2×#340C2212yes—
41C2×#336C2211yescharacteristic
42C2×#336C2211yescharacteristic
43C2×#336C2212yes—
44C2×#336C2212yes—
45C4⋊#95—21no—
46C4⋊#95—21no—
47C4⋊#95C2212yes—
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—22no—
56C2×C4×Q8D414yes—
57C22×C4⋊C4—21no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4—21no—
61C22×C4⋊C4—21no—
62C22×C4⋊C4—21no—
63C22×C4⋊C4—21no—
64C22×C4⋊C4—22no—
65C22×C4⋊C4C2312yes—
66C22×C4⋊C4C2311yescharacteristic
67C22×C4⋊C4C2311yescharacteristic
68C22×C4⋊C4C2312yes—
69C22×C4⋊C4C2311yescharacteristic
70C22×C42—21no—
71C22×C42—21no—
72C22×C42D411yescharacteristic
73C22×C42D411yescharacteristic
74C22×C42D411yescharacteristic
75C22×C42D411yescharacteristic
76C22×C42C2311yescharacteristic
77C22×C42C2311yescharacteristic
78C22×C42C2311yescharacteristic
79C2×#106—24no—
80C2×#106—24no—
81C2×#106—24no—
82C2×#103—24no—
83C2×#103—24no—
84C2×#103—24no—
85C2×#103—24no—
86C2×#103—24no—
87C2×#103—24no—
88#391—22no—
89#391—22no—
90#391—22no—
91#391D414yes—
92#389—22no—
93#389—22no—
94#389—22no—
95#389—24no—
96#389—24no—
97#389—44no—
98#389—44no—
99#389D414yes—
100#387—28no—
101#387—28no—
102#384—24no—
103#384—22no—
104#384—22no—
105C4×C4⋊C4—28no—
106C4×C4⋊C4—22no—
107C4×C4⋊C4—22no—
108#376—28no—
109C2×#95—21no—
110C2×#95—21no—
111C2×#95—21no—
112C2×#95—21no—
113C2×#95—21no—
114C2×#95—21no—
115C2×#95—21no—
116C2×#95—22no—
117C2×#95—22no—
118C2×#95—22no—
119C43—22no—
120C43—22no—
121#340—24no—
122#340—24no—
123#340—24no—
124#340—24no—
125#340—24no—
126#336—24no—
127#336—22no—
128#336—22no—
129#336—24no—
130C22×Q8—21no—
131C22×Q8—21no—
132C22×Q8—21no—
133C22×Q8—22no—
134C22×Q8—22no—
135C22×Q8—22no—
136C22×Q8—22no—
137C22×Q8C2×D412yes—
138C22×Q8C2×D412yes—
139C22×Q8#4112yes—
140C23×C4—21no—
141C23×C4—21no—
142C23×C4—22no—
143C23×C4—21no—
144C23×C4—21no—
145C23×C4—22no—
146C23×C4C2×D411yescharacteristic
147C23×C4C2×D411yescharacteristic
148C23×C4C2×D411yescharacteristic
149C23×C4C2×D411yescharacteristic
150C23×C4C2×D411yescharacteristic
151C23×C4C2×D411yescharacteristic
152C23×C4C2411yescharacteristic
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—
166C22×C8#4114yes—
167C4×Q8—28no—
168C4×Q8—28no—
169C4×Q8—28no—
170C4×Q8—28no—
171C2×C4⋊C4—24no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4—24no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—24no—
186C2×C4⋊C4—24no—
187C2×C4⋊C4—24no—
188C2×C4⋊C4—24no—
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—42no—
199C2×C4⋊C4—42no—
200C2×C4⋊C4—42no—
201C2×C4⋊C4—42no—
202C2×C4⋊C4—42no—
203C2×C4⋊C4—42no—
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—44no—
211C2×C4⋊C4—42no—
212C2×C4⋊C4—44no—
213C2×C4⋊C4—44no—
214C2×C4⋊C4—42no—
215C2×C4⋊C4C2×D412yes—
216C2×C4⋊C4C2×D412yes—
217C2×C4⋊C4C2×D412yes—
218C2×C4⋊C4C2×D412yes—
219C2×C4⋊C4#4114yes—
220C2×C4⋊C4#4112yes—
221C2×C42—24no—
222C2×C42—24no—
223C2×C42—22no—
224C2×C42—24no—
225C2×C42—22no—
226C2×C42—21no—
227C2×C42—21no—
228C2×C42—21no—
229C2×C42—21no—
230C2×C42—22no—
231C2×C42—22no—
232C2×C42—24no—
233C2×C42—22no—
234C2×C42—22no—
235C2×C42—22no—
236C2×C42—22no—
237C2×C42—22no—
238C2×C42—22no—
239C2×C42—22no—
240C2×C42—21no—
241C2×C42—21no—
242C2×C42—22no—
243C2×C42—22no—
244C2×C42—41no—
245C2×C42—41no—
246C2×C42—42no—
247C2×C42—42no—
248C2×C42SD1614yes—
249C2×C42C2×D412yes—
250C2×C42C2×D412yes—
251C2×C42C2×D412yes—
252C2×C42#4112yes—
253#106—48no—
254#103—216no—
255#103—48no—
256#95—24no—
257#95—24no—
258#95—24no—
259#95—24no—
260#95—24no—
261#95—24no—
262#95—24no—
263#95—44no—
264#95—44no—
265#95—44no—
266C24C22×D411yescharacteristic
267C2×Q8—22no—
268C2×Q8—22no—
269C2×Q8—22no—
270C2×Q8—24no—
271C2×Q8—24no—
272C2×Q8—24no—
273C2×Q8—24no—
274C2×Q8—24no—
275C2×Q8—24no—
276C2×Q8—42no—
277C2×Q8—42no—
278C2×Q8—42no—
279C2×Q8—42no—
280C2×Q8—42no—
281C2×Q8—42no—
282C2×Q8#12114yes—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—24no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—42no—
331C22×C4—41no—
332C22×C4—42no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—41no—
339C22×C4—42no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—42no—
347C22×C4—41no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4#12012yes—
356C22×C4#12012yes—
357C22×C4#12112yes—
358C22×C4#12112yes—
359C22×C4C2×SD1612yes—
360C22×C4C2×SD1612yes—
361C22×C4C2×SD1612yes—
362C22×C4#13512yes—
363C22×C4AGL(1,ℤ/8)12yes—
364C22×C4#13712yes—
365C22×C4#13712yes—
366C22×C4#13712yes—
367C22×C4C22×D411yescharacteristic
368C22×C4C22×D411yescharacteristic
369C22×C4C22×D411yescharacteristic
370C22×C4C2×#4111yescharacteristic
371C22×C4C2×#4111yescharacteristic
372C22×C4C2×#4111yescharacteristic
373C22×C4C2×#4112yes—
374C22×C4C2×#4112yes—
375C22×C42−1+412yes—
376C22×C42−1+412yes—
377C2×C8—24no—
378C2×C8—24no—
379C2×C8—24no—
380C2×C8—42no—
381C2×C8—42no—
382C2×C8—42no—
383C2×C8—42no—
384C2×C8—42no—
385C2×C8—42no—
386C2×C8—42no—
387C2×C8—42no—
388C2×C8—42no—
389C2×C8—42no—
390C2×C8—42no—
391C4⋊C4—216no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—24no—
396C4⋊C4—24no—
397C4⋊C4—24no—
398C4⋊C4—24no—
399C4⋊C4—48no—
400C4⋊C4—48no—
401C4⋊C4—48no—
402C4⋊C4—42no—
403C4⋊C4—42no—
404C4⋊C4—42no—
405C4⋊C4—42no—
406C4⋊C4—48no—
407C4⋊C4—42no—
408C4⋊C4—42no—
409C4⋊C4—42no—
410C4⋊C4—42no—
411C4⋊C4—84no—
412C4⋊C4—84no—
413C4⋊C4—88no—
414C4⋊C4#12114yes—
415C42—216no—
416C42—22no—
417C42—22no—
418C42—22no—
419C42—22no—
420C42—24no—
421C42—24no—
422C42—28no—
423C42—44no—
424C42—44no—
425C42—48no—
426C42—42no—
427C42—42no—
428C42—44no—
429C23C2×#12011yescharacteristic
430C23C2×#12111yescharacteristic
431C23#52511yescharacteristic
432C23#52511yescharacteristic
433C23#53211yescharacteristic
434C23#53611yescharacteristic
435C23#53611yescharacteristic
436C23C22×SD1611yescharacteristic
437C23C2×#13511yescharacteristic
438C23C2×AGL(1,ℤ/8)11yescharacteristic
439C23C2×#13711yescharacteristic
440C23C2×#13711yescharacteristic
441C23C2×#13711yescharacteristic
442C23#57511yescharacteristic
443C23#57511yescharacteristic
444Q8—28no—
445Q8—44no—
446Q8—44no—
447Q8—44no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—44no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—81no—
511C2×C4—81no—
512C2×C4—82no—
513C2×C4—81no—
514C2×C4—82no—
515C2×C4—81no—
516C2×C4—81no—
517C2×C4—81no—
518C2×C4—81no—
519C2×C4—81no—
520C2×C4—82no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4—82no—
524C2×C4—82no—
525C2×C4—82no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4#44814yes—
530C2×C4#45214yes—
531C2×C4#46014yes—
532C2×C4C2×#12111yescharacteristic
533C2×C4C2×#12111yescharacteristic
534C2×C4#52512yes—
535C2×C4#52511yescharacteristic
536C2×C4#52511yescharacteristic
537C2×C4#52912yes—
538C2×C4#53612yes—
539C2×C4#54112yes—
540C2×C4#54712yes—
541C2×C4#54712yes—
542C2×C4#54712yes—
543C2×C4#54812yes—
544C2×C4#55212yes—
545C2×C4#55212yes—
546C2×C4#55212yes—
547C2×C4#55612yes—
548C8—44no—
549C8—82no—
550C22#239211yescharacteristic
551C22#240611yescharacteristic
552C22#243211yescharacteristic
553C22#259911yescharacteristic
554C22#261111yescharacteristic
555C22#262111yescharacteristic
556C22#284711yescharacteristic
557C22C2×#44811yescharacteristic
558C22C2×#45211yescharacteristic
559C22#300611yescharacteristic
560C22#300711yescharacteristic
561C22C2×#46011yescharacteristic
562C22#303511yescharacteristic
563C22#303711yescharacteristic
564C22#303911yescharacteristic
565C22#310111yescharacteristic
566C22#310311yescharacteristic
567C22#310511yescharacteristic
568C22#310711yescharacteristic
569C22#311211yescharacteristic
570C22#311311yescharacteristic
571C22#311611yescharacteristic
572C22#311711yescharacteristic
573C22#316711yescharacteristic
574C22#317111yescharacteristic
575C22#318111yescharacteristic
576C22#318511yescharacteristic
577C22#322911yescharacteristic
578C22#322911yescharacteristic
579C22#323111yescharacteristic
580C22#323211yescharacteristic
581C22#323611yescharacteristic
582C22#323911yescharacteristic
583C22#323911yescharacteristic
584C22#324011yescharacteristic
585C4—24no—
586C4—24no—
587C4—24no—
588C4—44no—
589C4—42no—
590C4—42no—
591C4—42no—
592C4—44no—
593C4—82no—
594C4—82no—
595C4—84no—
596C4—162no—
597C4#241312yes—
598C4#241512yes—
599C4#247512yes—
600C4#247812yes—
601C2#1490711yescharacteristic
602C2#2367811yescharacteristic
603C2#2368511yescharacteristic
604C2#2406311yescharacteristic
605C2#2406711yescharacteristic
606C2#2567211yescharacteristic
607C2#2567811yescharacteristic
608C2#2939011yescharacteristic
609C2#2939111yescharacteristic
610C2#2957511yescharacteristic
611C2#2957911yescharacteristic
612C2#2986611yescharacteristic
613C2#2987111yescharacteristic
614C2#3290311yescharacteristic
615C2#3290711yescharacteristic
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×#22952
C2×#20842
C2×#20722
C2×#18652
#147122
#112202
#112072
#111902
#110502
#108842
#107952