Finite Group Databasebeta

← C43×#19911 #24939928

Subgroups — C43×#19911 #24939928

Order 11008.

666 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3366C211yesmaximal, characteristic, complemented
2C43×#3325C211yesmaximal, characteristic, complemented
3C43×#3305C211yesmaximal, characteristic, complemented
4C43×#3295C211yesmaximal, characteristic, complemented
5C43×#1709C211yesmaximal, characteristic, complemented
6C43×#1698C211yesmaximal, characteristic, complemented
7C43×#1697C211yesmaximal, characteristic, complemented
8C43×#1677C211yesmaximal, characteristic, complemented
9C43×#1677C211yesmaximal, characteristic, complemented
10C43×#1634C211yesmaximal, characteristic, complemented
11C43×#1632C211yesmaximal, characteristic, complemented
12C43×#1621C211yesmaximal, characteristic, complemented
13C43×#1619C211yesmaximal, characteristic, complemented
14C43×#1590C211yesmaximal, characteristic, complemented
15C8×D8×C43C211yesmaximal, characteristic, complemented
16C43×#555C2211yescharacteristic
17C43×#554C2211yescharacteristic
18C43×#550C2211yescharacteristic, complemented
19D42×C43C2211yescharacteristic
20C43×#494C2211yescharacteristic, complemented
21C43×#493C2211yescharacteristic
22C43×#490—21no—
23C43×#486C2211yescharacteristic
24C43×#486C2211yescharacteristic
25C43×#486C2211yescharacteristic, complemented
26C43×#486C2211yescharacteristic, complemented
27C43×#482—21no—
28C43×#482—21no—
29C43×#481—21no—
30C43×#478—21no—
31C43×#477C2211yescharacteristic, complemented
32C43×#476C2211yescharacteristic
33C43×#476C2211yescharacteristic
34C43×#476C2211yescharacteristic, complemented
35C43×#469—21no—
36C43×#466—21no—
37C43×#465—21no—
38C43×#460C2211yescharacteristic
39C43×#459—21no—
40C43×#459C2211yescharacteristic
41C43×#459C2211yescharacteristic
42C43×#459C2211yescharacteristic
43C43×#450—21no—
44C43×#449—21no—
45C43×#447—21no—
46C43×#446C2211yescharacteristic, complemented
47C43×#442—21no—
48C4×SD16×C43C2211yescharacteristic
49C4×D8×C43C2211yescharacteristic
50C43×#436C2211yescharacteristic
51C8×D4×C43C2211yescharacteristic
52C8×D4×C43C2211yescharacteristic, complemented
53C43×#418—21no—
54C43×#416—21no—
55C2×#102×C43—21no—
56C43×#335C2211yescharacteristic, complemented
57C43×#334C2211yescharacteristic, complemented
58C43×#333C2211yescharacteristic, complemented
59C43×#333C2211yescharacteristic, complemented
60C43×#331C2211yescharacteristic
61C43×#331C2211yescharacteristic, complemented
62C43×Q8⋊C8C2211yescharacteristic, complemented
63C43×D4⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic, complemented
66C82×C43C2211yescharacteristic, complemented
67C2×#41×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70C2×Q16×C43—41no—
71C2×SD16×C43—21no—
72C2×SD16×C43D411yescharacteristic
73C2×D8×C43—21no—
74C2×D8×C43—21no—
75C2×D8×C43—21no—
76C2×D8×C43—41no—
77C2×D8×C43D411yescharacteristic
78C2×M16×C43—21no—
79C22×C8×C43—21no—
80C22×C8×C43—21no—
81C4⋊Q8×C43C2311yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83#127×C43—21no—
84#127×C43C2311yescharacteristic
85#127×C43C2311yescharacteristic
86#125×C43—21no—
87#124×C43—41no—
88C22⋊Q8×C43—21no—
89C22⋊Q8×C43—41no—
90#121×C43—21no—
91#121×C43—21no—
92#121×C43—21no—
93#121×C43—21no—
94#121×C43—21no—
95#121×C43—41no—
96#120×C43—41no—
97C4×Q8×C43C2311yescharacteristic
98C4×D4×C43—21no—
99C4×D4×C43—21no—
100C4×D4×C43C2311yescharacteristic
101C4×D4×C43C2311yescharacteristic
102C4×D4×C43C2311yescharacteristic
103#117×C43—21no—
104#117×C43—21no—
105C2×C4⋊C4×C43—21no—
106#107×C43—21no—
107#107×C43D411yescharacteristic
108#106×C43—21no—
109#106×C43—21no—
110#106×C43—21no—
111#106×C43D411yescharacteristic
112C4⋊C8×C43—21no—
113C4⋊C8×C43C2311yescharacteristic
114C4⋊C8×C43C2311yescharacteristic
115C4⋊C8×C43C2311yescharacteristic
116C4⋊C8×C43C2311yescharacteristic
117#103×C43—21no—
118#103×C43D411yescharacteristic
119#102×C43—21no—
120#102×C43—21no—
121#102×C43—21no—
122#102×C43—21no—
123#102×C43—21no—
124#102×C43—21no—
125#102×C43—21no—
126#102×C43—21no—
127#102×C43—21no—
128#102×C43—21no—
129#102×C43—21no—
130#102×C43—21no—
131#102×C43—21no—
132#102×C43—21no—
133#102×C43—21no—
134#102×C43D411yescharacteristic
135#102×C43D411yescharacteristic
136#102×C43D411yescharacteristic
137C22⋊C8×C43—21no—
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140#97×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C24×C43—41no—
145#41×C43—42no—
146#41×C43—81no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43—41no—
159C2×D4×C43—41no—
160C2×D4×C43—41no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—81no—
164C2×D4×C43—81no—
165C2×D4×C43C2×D411yescharacteristic
166C2×D4×C43C2×D411yescharacteristic
167C2×D4×C43C2×D411yescharacteristic
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—41no—
172C22×C4×C43—41no—
173Q16×C43—82no—
174SD16×C43—41no—
175SD16×C43—81no—
176D8×C43—22no—
177D8×C43—42no—
178D8×C43—82no—
179D8×C43—81no—
180D8×C43—81no—
181M16×C43—81no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—81no—
188C2×C8×C43—81no—
189C2×C8×C43C2×D411yescharacteristic
190C2×C8×C43C2×D411yescharacteristic
191C2×C8×C43C2×D411yescharacteristic
192C2×C8×C43C2×D411yescharacteristic
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—41no—
199C4⋊C4×C43—41no—
200C4⋊C4×C43C2×D411yescharacteristic
201C4⋊C4×C43C2×D411yescharacteristic
202C4⋊C4×C43C2×D411yescharacteristic
203C4⋊C4×C43C2×D411yescharacteristic
204C22⋊C4×C43—21no—
205C22⋊C4×C43—21no—
206C22⋊C4×C43—21no—
207C22⋊C4×C43—41no—
208C22⋊C4×C43—41no—
209C22⋊C4×C43—41no—
210C22⋊C4×C43—41no—
211C22⋊C4×C43—41no—
212C42×C43—21no—
213C42×C43—41no—
214C42×C43C2411yescharacteristic
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—82no—
221C23×C43—82no—
222C23×C43—161no—
223Q8×C43—21no—
224Q8×C43—21no—
225Q8×C43—81no—
226Q8×C43—81no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—21no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—81no—
241D4×C43—81no—
242D4×C43—82no—
243D4×C43—82no—
244D4×C43—82no—
245D4×C43—161no—
246D4×C43—161no—
247D4×C43#13512yes—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—82no—
262C2×C4×C43—161no—
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C8×C43—22no—
267C8×C43—21no—
268C8×C43—21no—
269C8×C43—21no—
270C8×C43—21no—
271C8×C43—41no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43—41no—
275#19911C4311yesmaximal, characteristic, direct product factor, Sylow
276C22×C43—22no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—164no—
292C22×C43D4211yescharacteristic
293C4×C43—21no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—41no—
299C4×C43—81no—
300C4×C43—81no—
301C4×C43C2×#13511yescharacteristic
302C4×C43#57511yescharacteristic
303C4×C43#57611yescharacteristic
304C4×C43#57711yescharacteristic
305#3366C2×C4311yescharacteristic, complemented
306#3325C2×C4311yescharacteristic, complemented
307#3305C2×C4311yescharacteristic, complemented
308#3295C2×C4311yescharacteristic, complemented
309#1709C2×C4311yescharacteristic, complemented
310#1698C2×C4311yescharacteristic, complemented
311#1697C2×C4311yescharacteristic, complemented
312#1677C2×C4311yescharacteristic, complemented
313#1677C2×C4311yescharacteristic, complemented
314#1634C2×C4311yescharacteristic, complemented
315#1632C2×C4311yescharacteristic, complemented
316#1621C2×C4311yescharacteristic, complemented
317#1619C2×C4311yescharacteristic, complemented
318#1590C2×C4311yescharacteristic, complemented
319C8×D8C2×C4311yescharacteristic, complemented
320C2×C43—42no—
321C2×C43—81no—
322C2×C43—81no—
323C2×C43—161no—
324C2×C43—161no—
325C2×C43#327311yescharacteristic
326C2×C43#328211yescharacteristic
327C2×C43#329211yescharacteristic
328#555C22×C4311yescharacteristic
329#554C22×C4311yescharacteristic
330#550C22×C4311yescharacteristic, complemented
331D42C22×C4311yescharacteristic
332#494C22×C4311yescharacteristic, complemented
333#493C22×C4311yescharacteristic
334#490—21no—
335#486C22×C4311yescharacteristic
336#486C22×C4311yescharacteristic
337#486C22×C4311yescharacteristic, complemented
338#486C22×C4311yescharacteristic, complemented
339#482—21no—
340#482—21no—
341#481—21no—
342#478—21no—
343#477C22×C4311yescharacteristic, complemented
344#476C22×C4311yescharacteristic
345#476C22×C4311yescharacteristic
346#476C22×C4311yescharacteristic, complemented
347#469—21no—
348#466—21no—
349#465—21no—
350#460C22×C4311yescharacteristic
351#459—21no—
352#459C22×C4311yescharacteristic
353#459C22×C4311yescharacteristic
354#459C22×C4311yescharacteristic
355#450—21no—
356#449—21no—
357#447—21no—
358#446C22×C4311yescharacteristic, complemented
359#442—21no—
360C4×SD16C22×C4311yescharacteristic
361C4×D8C22×C4311yescharacteristic
362#436C22×C4311yescharacteristic
363C8×D4C22×C4311yescharacteristic
364C8×D4C22×C4311yescharacteristic, complemented
365#418—21no—
366#416—21no—
367C2×#102—21no—
368#335C22×C4311yescharacteristic, complemented
369#334C22×C4311yescharacteristic, complemented
370#333C22×C4311yescharacteristic, complemented
371#333C22×C4311yescharacteristic, complemented
372#331C22×C4311yescharacteristic
373#331C22×C4311yescharacteristic, complemented
374Q8⋊C8C22×C4311yescharacteristic, complemented
375D4⋊C8C22×C4311yescharacteristic
376D4⋊C8C22×C4311yescharacteristic
377D4⋊C8C22×C4311yescharacteristic, complemented
378C82C22×C4311yescharacteristic, complemented
379C43#1991111yescharacteristic, direct product factor, Sylow
380C2×#41—21no—
381C22×D4—21no—
382C22×D4—21no—
383C2×Q16—41no—
384C2×SD16—21no—
385C2×SD16D4×C4311yescharacteristic
386C2×D8—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8—41no—
390C2×D8D4×C4311yescharacteristic
391C2×M16—21no—
392C22×C8—21no—
393C22×C8—21no—
394C4⋊Q8C23×C4311yescharacteristic
395C4⋊Q8C23×C4311yescharacteristic
396#127—21no—
397#127C23×C4311yescharacteristic
398#127C23×C4311yescharacteristic
399#125—21no—
400#124—41no—
401C22⋊Q8—21no—
402C22⋊Q8—41no—
403#121—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121—41no—
409#120—41no—
410C4×Q8C23×C4311yescharacteristic
411C4×D4—21no—
412C4×D4—21no—
413C4×D4C23×C4311yescharacteristic
414C4×D4C23×C4311yescharacteristic
415C4×D4C23×C4311yescharacteristic
416#117—21no—
417#117—21no—
418C2×C4⋊C4—21no—
419#107—21no—
420#107D4×C4311yescharacteristic
421#106—21no—
422#106—21no—
423#106—21no—
424#106D4×C4311yescharacteristic
425C4⋊C8—21no—
426C4⋊C8C23×C4311yescharacteristic
427C4⋊C8C23×C4311yescharacteristic
428C4⋊C8C23×C4311yescharacteristic
429C4⋊C8C23×C4311yescharacteristic
430#103—21no—
431#103D4×C4311yescharacteristic
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—21no—
447#102D4×C4311yescharacteristic
448#102D4×C4311yescharacteristic
449#102D4×C4311yescharacteristic
450C22⋊C8—21no—
451C22⋊C8—21no—
452C22⋊C8—21no—
453#97—21no—
454C4×C8C23×C4311yescharacteristic
455C4×C8C23×C4311yescharacteristic
456C4×C8C23×C4311yescharacteristic
457C24—41no—
458#41—42no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8C2×D4×C4311yescharacteristic
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—41no—
476C2×D4—81no—
477C2×D4—81no—
478C2×D4C2×D4×C4311yescharacteristic
479C2×D4C2×D4×C4311yescharacteristic
480C2×D4C2×D4×C4311yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—41no—
485C22×C4—41no—
486Q16—82no—
487SD16—41no—
488SD16—81no—
489D8—22no—
490D8—42no—
491D8—82no—
492D8—81no—
493D8—81no—
494M16—81no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—81no—
501C2×C8—81no—
502C2×C8C2×D4×C4311yescharacteristic
503C2×C8C2×D4×C4311yescharacteristic
504C2×C8C2×D4×C4311yescharacteristic
505C2×C8C2×D4×C4311yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4C2×D4×C4311yescharacteristic
514C4⋊C4C2×D4×C4311yescharacteristic
515C4⋊C4C2×D4×C4311yescharacteristic
516C4⋊C4C2×D4×C4311yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C42—21no—
526C42—41no—
527C42C24×C4311yescharacteristic
528C23—21no—
529C23—21no—
530C23—21no—
531C23—41no—
532C23—41no—
533C23—82no—
534C23—82no—
535C23—161no—
536Q8—21no—
537Q8—21no—
538Q8—81no—
539Q8—81no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—81no—
554D4—81no—
555D4—82no—
556D4—82no—
557D4—82no—
558D4—161no—
559D4—161no—
560D4#135×C4312yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—82no—
575C2×C4—161no—
576C2×C4C22×D4×C4311yescharacteristic
577C2×C4C22×D4×C4311yescharacteristic
578C2×C4H(5,𝔽2)×C4311yescharacteristic
579C8—22no—
580C8—21no—
581C8—21no—
582C8—21no—
583C8—21no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—164no—
604C22D42×C4311yescharacteristic
605C4—21no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—81no—
612C4—81no—
613C4C2×#135×C4311yescharacteristic
614C4C43×#57511yescharacteristic
615C4C43×#57611yescharacteristic
616C4C43×#57711yescharacteristic
617C2—42no—
618C2—81no—
619C2—81no—
620C2—161no—
621C2—161no—
622C2C43×#327311yescharacteristic
623C2C43×#328211yescharacteristic
624C2C43×#329211yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C42×C43 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C43×#3366C2semidirect
2. C43×#3325C2semidirect
3. C43×#3305C2semidirect
4. C43×#3295C2semidirect
5. C43×#1709C2semidirect
6. C43×#1698C2semidirect
7. C43×#1697C2semidirect
8. C43×#1677C2semidirect
9. C43×#1677C2semidirect
10. C43×#1634C2semidirect
11. C43×#1632C2semidirect
12. C43×#1621C2semidirect
13. C43×#1619C2semidirect
14. C43×#1590C2semidirect
15. C8×D8×C43C2semidirect
18. C43×#550C22semidirect
20. C43×#494C22semidirect
25. C43×#486C22semidirect
26. C43×#486C22semidirect
31. C43×#477C22semidirect
34. C43×#476C22semidirect
46. C43×#446C22semidirect
52. C8×D4×C43C22semidirect
56. C43×#335C22semidirect
57. C43×#334C22semidirect
58. C43×#333C22semidirect
59. C43×#333C22semidirect
61. C43×#331C22semidirect
62. C43×Q8⋊C8C22semidirect
65. C43×D4⋊C8C22semidirect
66. C82×C43C22semidirect
275. #19911C43direct (N × H)
305. #3366C2×C43semidirect
306. #3325C2×C43semidirect
307. #3305C2×C43semidirect
308. #3295C2×C43semidirect
309. #1709C2×C43semidirect
310. #1698C2×C43semidirect
311. #1697C2×C43semidirect
312. #1677C2×C43semidirect
313. #1677C2×C43semidirect
314. #1634C2×C43semidirect
315. #1632C2×C43semidirect
316. #1621C2×C43semidirect
317. #1619C2×C43semidirect
318. #1590C2×C43semidirect
319. C8×D8C2×C43semidirect
330. #550C22×C43semidirect
332. #494C22×C43semidirect
337. #486C22×C43semidirect
338. #486C22×C43semidirect
343. #477C22×C43semidirect
346. #476C22×C43semidirect
358. #446C22×C43semidirect
364. C8×D4C22×C43semidirect
368. #335C22×C43semidirect
369. #334C22×C43semidirect
370. #333C22×C43semidirect
371. #333C22×C43semidirect
373. #331C22×C43semidirect
374. Q8⋊C8C22×C43semidirect
377. D4⋊C8C22×C43semidirect
378. C82C22×C43semidirect
379. C43#19911direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C43×#33662
C43×#33252
C43×#33052
C43×#32952
C43×#17092
C43×#16982
C43×#16972
C43×#16772
C43×#16342
C43×#16322
C43×#16212
C43×#16192
C43×#15902
C8×D8×C432
#1991143