Finite Group Databasebeta

← C43×#20243 #24940260

Subgroups — C43×#20243 #24940260

Order 11008.

674 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×#3354C211yesmaximal, characteristic, complemented
2C43×#3341C211yesmaximal, characteristic, complemented
3C43×#3325C211yesmaximal, characteristic, complemented
4C43×#3272C211yesmaximal, characteristic, complemented
5C43×#1714C211yesmaximal, characteristic, complemented
6C43×#1697C211yesmaximal, characteristic, complemented
7C43×#1695C211yesmaximal, characteristic, complemented
8C43×#1691C211yesmaximal, characteristic, complemented
9C43×#1665C211yesmaximal, characteristic, complemented
10C43×#1646C211yesmaximal, characteristic, complemented
11C43×#1635C211yesmaximal, characteristic, complemented
12C43×#1629C211yesmaximal, characteristic, complemented
13C43×#1624C211yesmaximal, characteristic, complemented
14C43×#1594C211yesmaximal, characteristic, complemented
15C43×#1581C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C43—21no—
17C43×#555C2211yescharacteristic
18C43×#555C2211yescharacteristic, complemented
19C43×#547C2211yescharacteristic
20D42×C43C2211yescharacteristic
21C43×#500C2211yescharacteristic, complemented
22C43×#498C2211yescharacteristic, complemented
23C43×#492C2211yescharacteristic
24C43×#492C2211yescharacteristic
25C43×#487C2211yescharacteristic, complemented
26C43×#486C2211yescharacteristic
27C43×#482—21no—
28C43×#482—21no—
29C43×#482—21no—
30C43×#482—21no—
31C43×#481—21no—
32C43×#476C2211yescharacteristic
33C43×#476C2211yescharacteristic
34C43×#476C2211yescharacteristic
35C43×#476C2211yescharacteristic, complemented
36C43×#474C2211yescharacteristic, complemented
37C43×#469—21no—
38C43×#469—21no—
39C43×#468—21no—
40C43×#466—21no—
41C43×#461C2211yescharacteristic
42C43×#459C2211yescharacteristic
43C43×#459C2211yescharacteristic
44C43×#450—21no—
45C43×#449—21no—
46C43×#447—21no—
47C4×D8×C43C2211yescharacteristic
48C4×D8×C43C2211yescharacteristic
49C43×#436C2211yescharacteristic
50C43×#436C2211yescharacteristic
51C43×#436C2211yescharacteristic, complemented
52C8×D4×C43C2211yescharacteristic, complemented
53C43×#428—21no—
54C43×#427—21no—
55C43×#418—21no—
56C43×#335C2211yescharacteristic, complemented
57C43×#334C2211yescharacteristic, complemented
58C43×#333C2211yescharacteristic, complemented
59C43×#333C2211yescharacteristic, complemented
60C43×#332C2211yescharacteristic, complemented
61C43×#331C2211yescharacteristic
62C43×D4⋊C8C2211yescharacteristic
63C43×D4⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic, complemented
65C43×D4⋊C8C2211yescharacteristic, complemented
66C43×#322C2211yescharacteristic, complemented
67C2×#41×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70AGL(1,ℤ/8)×C43—44no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—41no—
75C2×D8×C43—21no—
76C2×D8×C43—21no—
77C2×D8×C43D411yescharacteristic
78C2×D8×C43D411yescharacteristic
79C2×M16×C43—21no—
80C2×M16×C43—21no—
81C2×M16×C43—21no—
82C22×C8×C43—21no—
83C4⋊Q8×C43C2311yescharacteristic
84C4⋊Q8×C43C2311yescharacteristic
85C4⋊Q8×C43C2311yescharacteristic
86#127×C43C2311yescharacteristic
87#124×C43—41no—
88#124×C43—41no—
89#123×C43—41no—
90C22⋊Q8×C43—21no—
91#121×C43—21no—
92#121×C43—21no—
93#121×C43—21no—
94#121×C43—21no—
95#121×C43—21no—
96#121×C43—21no—
97#121×C43—21no—
98#120×C43—41no—
99C4×D4×C43C2311yescharacteristic
100C4×D4×C43C2311yescharacteristic
101C4×D4×C43C2311yescharacteristic
102C4×D4×C43C2311yescharacteristic
103#117×C43—21no—
104#117×C43—21no—
105#117×C43—21no—
106#117×C43—21no—
107C2×C4⋊C4×C43—21no—
108#107×C43—21no—
109#107×C43—21no—
110#107×C43—21no—
111#107×C43D411yescharacteristic
112#107×C43D411yescharacteristic
113#106×C43—21no—
114#106×C43—21no—
115#106×C43—21no—
116#106×C43—21no—
117#106×C43—21no—
118#106×C43—21no—
119C4⋊C8×C43C2311yescharacteristic
120C4⋊C8×C43C2311yescharacteristic
121C4⋊C8×C43C2311yescharacteristic
122C4⋊C8×C43C2311yescharacteristic
123#103×C43—21no—
124#103×C43—41no—
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
137#102×C43D411yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
141C22⋊C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C24×C43—41no—
146#41×C43—42no—
147#41×C43—81no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—41no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43—41no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C2×D4×C43—81no—
162C2×D4×C43—81no—
163C2×D4×C43C2×D411yescharacteristic
164C2×D4×C43C2×D411yescharacteristic
165C2×D4×C43C2×D411yescharacteristic
166C2×D4×C43C2×D411yescharacteristic
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—41no—
172SD16×C43—42no—
173SD16×C43—42no—
174SD16×C43—81no—
175SD16×C43—82no—
176D8×C43—22no—
177D8×C43—41no—
178D8×C43—42no—
179D8×C43—81no—
180M16×C43—42no—
181M16×C43—42no—
182M16×C43—81no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—42no—
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—21no—
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—21no—
208C22⋊C4×C43—41no—
209C22⋊C4×C43—41no—
210C22⋊C4×C43—41no—
211C22⋊C4×C43—41no—
212C22⋊C4×C43—41no—
213C22⋊C4×C43—41no—
214C42×C43—41no—
215C42×C43—41no—
216C42×C43C2411yescharacteristic
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—41no—
222C23×C43—82no—
223C23×C43—82no—
224C23×C43—161no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—81no—
228Q8×C43—81no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—21no—
232D4×C43—21no—
233D4×C43—21no—
234D4×C43—21no—
235D4×C43—21no—
236D4×C43—21no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—81no—
242D4×C43—82no—
243D4×C43—82no—
244D4×C43—82no—
245D4×C43—161no—
246D4×C43—161no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
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—41no—
262C2×C4×C43—82no—
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C8×C43—21no—
267C8×C43—21no—
268C8×C43—21no—
269C8×C43—41no—
270C8×C43—41no—
271C8×C43—41no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43AGL(1,ℤ/8)12yes—
275#20243C4311yesmaximal, characteristic, direct product factor, Sylow
276C22×C43—41no—
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—41no—
286C22×C43—41no—
287C22×C43—41no—
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—81no—
299C4×C43—81no—
300C4×C43—81no—
301C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
302C4×C43#57511yescharacteristic
303C4×C43#57711yescharacteristic
304C4×C43#57711yescharacteristic
305#3354C2×C4311yescharacteristic, complemented
306#3341C2×C4311yescharacteristic, complemented
307#3325C2×C4311yescharacteristic, complemented
308#3272C2×C4311yescharacteristic, complemented
309#1714C2×C4311yescharacteristic, complemented
310#1697C2×C4311yescharacteristic, complemented
311#1695C2×C4311yescharacteristic, complemented
312#1691C2×C4311yescharacteristic, complemented
313#1665C2×C4311yescharacteristic, complemented
314#1646C2×C4311yescharacteristic, complemented
315#1635C2×C4311yescharacteristic, complemented
316#1629C2×C4311yescharacteristic, complemented
317#1624C2×C4311yescharacteristic, complemented
318#1594C2×C4311yescharacteristic, complemented
319#1581C2×C4311yescharacteristic, complemented
320C2×C43—81no—
321C2×C43—81no—
322C2×C43—81no—
323C2×C43—81no—
324C2×C43—161no—
325C2×C43#326711yescharacteristic
326C2×C43#327211yescharacteristic
327C2×C43#328811yescharacteristic
328C2×AGL(1,ℤ/8)—21no—
329#555C22×C4311yescharacteristic
330#555C22×C4311yescharacteristic, complemented
331#547C22×C4311yescharacteristic
332D42C22×C4311yescharacteristic
333#500C22×C4311yescharacteristic, complemented
334#498C22×C4311yescharacteristic, complemented
335#492C22×C4311yescharacteristic
336#492C22×C4311yescharacteristic
337#487C22×C4311yescharacteristic, complemented
338#486C22×C4311yescharacteristic
339#482—21no—
340#482—21no—
341#482—21no—
342#482—21no—
343#481—21no—
344#476C22×C4311yescharacteristic
345#476C22×C4311yescharacteristic
346#476C22×C4311yescharacteristic
347#476C22×C4311yescharacteristic, complemented
348#474C22×C4311yescharacteristic, complemented
349#469—21no—
350#469—21no—
351#468—21no—
352#466—21no—
353#461C22×C4311yescharacteristic
354#459C22×C4311yescharacteristic
355#459C22×C4311yescharacteristic
356#450—21no—
357#449—21no—
358#447—21no—
359C4×D8C22×C4311yescharacteristic
360C4×D8C22×C4311yescharacteristic
361#436C22×C4311yescharacteristic
362#436C22×C4311yescharacteristic
363#436C22×C4311yescharacteristic, complemented
364C8×D4C22×C4311yescharacteristic, complemented
365#428—21no—
366#427—21no—
367#418—21no—
368#335C22×C4311yescharacteristic, complemented
369#334C22×C4311yescharacteristic, complemented
370#333C22×C4311yescharacteristic, complemented
371#333C22×C4311yescharacteristic, complemented
372#332C22×C4311yescharacteristic, complemented
373#331C22×C4311yescharacteristic
374D4⋊C8C22×C4311yescharacteristic
375D4⋊C8C22×C4311yescharacteristic
376D4⋊C8C22×C4311yescharacteristic, complemented
377D4⋊C8C22×C4311yescharacteristic, complemented
378#322C22×C4311yescharacteristic, complemented
379C43#2024311yescharacteristic, direct product factor, Sylow
380C2×#41—21no—
381C22×D4—21no—
382C22×D4—21no—
383AGL(1,ℤ/8)—44no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16—41no—
388C2×D8—21no—
389C2×D8—21no—
390C2×D8D4×C4311yescharacteristic
391C2×D8D4×C4311yescharacteristic
392C2×M16—21no—
393C2×M16—21no—
394C2×M16—21no—
395C22×C8—21no—
396C4⋊Q8C23×C4311yescharacteristic
397C4⋊Q8C23×C4311yescharacteristic
398C4⋊Q8C23×C4311yescharacteristic
399#127C23×C4311yescharacteristic
400#124—41no—
401#124—41no—
402#123—41no—
403C22⋊Q8—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121—21no—
409#121—21no—
410#121—21no—
411#120—41no—
412C4×D4C23×C4311yescharacteristic
413C4×D4C23×C4311yescharacteristic
414C4×D4C23×C4311yescharacteristic
415C4×D4C23×C4311yescharacteristic
416#117—21no—
417#117—21no—
418#117—21no—
419#117—21no—
420C2×C4⋊C4—21no—
421#107—21no—
422#107—21no—
423#107—21no—
424#107D4×C4311yescharacteristic
425#107D4×C4311yescharacteristic
426#106—21no—
427#106—21no—
428#106—21no—
429#106—21no—
430#106—21no—
431#106—21no—
432C4⋊C8C23×C4311yescharacteristic
433C4⋊C8C23×C4311yescharacteristic
434C4⋊C8C23×C4311yescharacteristic
435C4⋊C8C23×C4311yescharacteristic
436#103—21no—
437#103—41no—
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
450#102D4×C4311yescharacteristic
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—21no—
454C22⋊C8—21no—
455C4×C8C23×C4311yescharacteristic
456C4×C8C23×C4311yescharacteristic
457C4×C8C23×C4311yescharacteristic
458C24—41no—
459#41—42no—
460#41—81no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—81no—
475C2×D4—81no—
476C2×D4C2×D4×C4311yescharacteristic
477C2×D4C2×D4×C4311yescharacteristic
478C2×D4C2×D4×C4311yescharacteristic
479C2×D4C2×D4×C4311yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—41no—
485SD16—42no—
486SD16—42no—
487SD16—81no—
488SD16—82no—
489D8—22no—
490D8—41no—
491D8—42no—
492D8—81no—
493M16—42no—
494M16—42no—
495M16—81no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—42no—
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—21no—
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—21no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C42—41no—
528C42—41no—
529C42C24×C4311yescharacteristic
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—41no—
535C23—82no—
536C23—82no—
537C23—161no—
538Q8—41no—
539Q8—41no—
540Q8—81no—
541Q8—81no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—81no—
555D4—82no—
556D4—82no—
557D4—82no—
558D4—161no—
559D4—161no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
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—41no—
575C2×C4—82no—
576C2×C4C22×D4×C4311yescharacteristic
577C2×C4C22×D4×C4311yescharacteristic
578C2×C4H(5,𝔽2)×C4311yescharacteristic
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8AGL(1,ℤ/8)×C4312yes—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—164no—
604C22D42×C4311yescharacteristic
605C4—21no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
614C4C43×#57511yescharacteristic
615C4C43×#57711yescharacteristic
616C4C43×#57711yescharacteristic
617C2—81no—
618C2—81no—
619C2—81no—
620C2—81no—
621C2—161no—
622C2C43×#326711yescharacteristic
623C2C43×#327211yescharacteristic
624C2C43×#328811yescharacteristic
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×#3354C2semidirect
2. C43×#3341C2semidirect
3. C43×#3325C2semidirect
4. C43×#3272C2semidirect
5. C43×#1714C2semidirect
6. C43×#1697C2semidirect
7. C43×#1695C2semidirect
8. C43×#1691C2semidirect
9. C43×#1665C2semidirect
10. C43×#1646C2semidirect
11. C43×#1635C2semidirect
12. C43×#1629C2semidirect
13. C43×#1624C2semidirect
14. C43×#1594C2semidirect
15. C43×#1581C2semidirect
18. C43×#555C22semidirect
21. C43×#500C22semidirect
22. C43×#498C22semidirect
25. C43×#487C22semidirect
35. C43×#476C22semidirect
36. C43×#474C22semidirect
51. C43×#436C22semidirect
52. C8×D4×C43C22semidirect
56. C43×#335C22semidirect
57. C43×#334C22semidirect
58. C43×#333C22semidirect
59. C43×#333C22semidirect
60. C43×#332C22semidirect
64. C43×D4⋊C8C22semidirect
65. C43×D4⋊C8C22semidirect
66. C43×#322C22semidirect
275. #20243C43direct (N × H)
305. #3354C2×C43semidirect
306. #3341C2×C43semidirect
307. #3325C2×C43semidirect
308. #3272C2×C43semidirect
309. #1714C2×C43semidirect
310. #1697C2×C43semidirect
311. #1695C2×C43semidirect
312. #1691C2×C43semidirect
313. #1665C2×C43semidirect
314. #1646C2×C43semidirect
315. #1635C2×C43semidirect
316. #1629C2×C43semidirect
317. #1624C2×C43semidirect
318. #1594C2×C43semidirect
319. #1581C2×C43semidirect
330. #555C22×C43semidirect
333. #500C22×C43semidirect
334. #498C22×C43semidirect
337. #487C22×C43semidirect
347. #476C22×C43semidirect
348. #474C22×C43semidirect
363. #436C22×C43semidirect
364. C8×D4C22×C43semidirect
368. #335C22×C43semidirect
369. #334C22×C43semidirect
370. #333C22×C43semidirect
371. #333C22×C43semidirect
372. #332C22×C43semidirect
376. D4⋊C8C22×C43semidirect
377. D4⋊C8C22×C43semidirect
378. #322C22×C43semidirect
379. C43#20243direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33542
C43×#33412
C43×#33252
C43×#32722
C43×#17142
C43×#16972
C43×#16952
C43×#16912
C43×#16652
C43×#16462
C43×#16352
C43×#16292
C43×#16242
C43×#15942
C43×#15812
#2024343