Finite Group Databasebeta

← C43×#20298 #24940315

Subgroups — C43×#20298 #24940315

Order 11008.

662 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3399C211yesmaximal, characteristic, complemented
2C43×#3373C211yesmaximal, characteristic, complemented
3C43×#3332C211yesmaximal, characteristic, complemented
4C43×#3276C211yesmaximal, characteristic, complemented
5C43×#1709C211yesmaximal, characteristic, complemented
6C43×#1702C211yesmaximal, characteristic, complemented
7C43×#1701C211yesmaximal, characteristic, complemented
8C43×#1690C211yesmaximal, characteristic, complemented
9C43×#1687C211yesmaximal, characteristic, complemented
10C43×#1642C211yesmaximal, characteristic, complemented
11C43×#1640C211yesmaximal, characteristic, complemented
12C43×#1627C211yesmaximal, characteristic, complemented
13C43×#1625C211yesmaximal, characteristic, complemented
14C43×#1590C211yesmaximal, characteristic, complemented
15C43×#1590C211yesmaximal, characteristic, complemented
16C2×#137×C43—21no—
17C43×#559C2211yescharacteristic
18C43×#550C2211yescharacteristic
19D4×Q8×C43C2211yescharacteristic
20C43×#547C2211yescharacteristic
21C43×#496—21no—
22C43×#494C2211yescharacteristic
23C43×#493C2211yescharacteristic
24C43×#489—21no—
25C43×#486C2211yescharacteristic
26C43×#486C2211yescharacteristic
27C43×#486C2211yescharacteristic
28C43×#486C2211yescharacteristic
29C43×#481—21no—
30C43×#476—21no—
31C43×#475C2211yescharacteristic
32C43×#475C2211yescharacteristic
33C43×#470—21no—
34C43×#469—21no—
35C43×#463—21no—
36C43×#463—21no—
37C43×#462C2211yescharacteristic
38C43×#461C2211yescharacteristic
39C43×#460C2211yescharacteristic
40C43×#459—21no—
41C43×#459C2211yescharacteristic
42C43×#459C2211yescharacteristic
43C43×#459C2211yescharacteristic
44C43×#452—21no—
45C43×#451—21no—
46C43×#449—21no—
47C43×#446C2211yescharacteristic
48C43×#446C2211yescharacteristic
49C43×#442—21no—
50C43×#442—21no—
51C4×SD16×C43C2211yescharacteristic
52C4×SD16×C43C2211yescharacteristic
53C43×#436C2211yescharacteristic
54C43×#436C2211yescharacteristic
55C43×#417—21no—
56C43×#334C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#332C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#331C2211yescharacteristic
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C82×C43C2211yescharacteristic
67C2×#41×C43—21no—
68C2×#41×C43—21no—
69C22×Q8×C43—21no—
70#137×C43—44no—
71C2×Q16×C43—21no—
72C2×Q16×C43—21no—
73C2×Q16×C43—21no—
74C2×SD16×C43—21no—
75C2×SD16×C43—21no—
76C2×SD16×C43D411yescharacteristic
77C2×SD16×C43D411yescharacteristic
78C2×D8×C43—21no—
79C2×D8×C43—21no—
80C2×D8×C43—21no—
81C2×D8×C43—21no—
82C2×D8×C43—21no—
83C2×M16×C43—21no—
84C2×M16×C43—21no—
85C4⋊Q8×C43—21no—
86C4⋊Q8×C43C2311yescharacteristic
87C4⋊Q8×C43C2311yescharacteristic
88#127×C43—21no—
89#127×C43C2311yescharacteristic
90#127×C43C2311yescharacteristic
91#124×C43—21no—
92#124×C43—21no—
93#123×C43—41no—
94#123×C43—41no—
95C22⋊Q8×C43—21no—
96C22⋊Q8×C43—21no—
97C22⋊Q8×C43—41no—
98#121×C43—21no—
99#121×C43—21no—
100#121×C43—41no—
101C4×Q8×C43C2311yescharacteristic
102C4×Q8×C43C2311yescharacteristic
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43—21no—
106C4×D4×C43—21no—
107C4×D4×C43C2311yescharacteristic
108C4×D4×C43C2311yescharacteristic
109C2×C4⋊C4×C43—21no—
110#106×C43—21no—
111#106×C43—21no—
112#106×C43D411yescharacteristic
113#106×C43D411yescharacteristic
114C4⋊C8×C43—21no—
115C4⋊C8×C43—21no—
116C4⋊C8×C43C2311yescharacteristic
117C4⋊C8×C43C2311yescharacteristic
118C4⋊C8×C43C2311yescharacteristic
119C4⋊C8×C43C2311yescharacteristic
120#103×C43—21no—
121#103×C43—21no—
122#103×C43—21no—
123#103×C43—21no—
124#103×C43D411yescharacteristic
125#103×C43D411yescharacteristic
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×C43—41no—
135#102×C43—41no—
136#102×C43D411yescharacteristic
137#102×C43D411yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140#97×C43—21no—
141#97×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145#41×C43—42no—
146#41×C43—42no—
147#41×C43—81no—
148#41×C43—81no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—41no—
152C2×Q8×C43—42no—
153C2×Q8×C43—81no—
154C2×Q8×C43C2×D411yescharacteristic
155C2×Q8×C43C2×D411yescharacteristic
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—41no—
163C2×D4×C43—41no—
164C2×D4×C43—41no—
165C2×D4×C43C2×D411yescharacteristic
166C2×D4×C43C2×D411yescharacteristic
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—41no—
170C22×C4×C43—41no—
171C22×C4×C43—41no—
172C22×C4×C43—41no—
173Q16×C43—42no—
174Q16×C43—42no—
175Q16×C43—81no—
176SD16×C43—22no—
177SD16×C43—41no—
178SD16×C43—42no—
179SD16×C43—81no—
180D8×C43—42no—
181D8×C43—42no—
182D8×C43—81no—
183D8×C43—81no—
184D8×C43—81no—
185M16×C43—42no—
186M16×C43—81no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43C2×D411yescharacteristic
193C2×C8×C43C2×D411yescharacteristic
194C2×C8×C43C2×D411yescharacteristic
195C2×C8×C43C2×D411yescharacteristic
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—41no—
203C4⋊C4×C43—41no—
204C4⋊C4×C43C2×D411yescharacteristic
205C4⋊C4×C43C2×D411yescharacteristic
206C4⋊C4×C43C2×D411yescharacteristic
207C4⋊C4×C43C2×D411yescharacteristic
208C22⋊C4×C43—21no—
209C22⋊C4×C43—21no—
210C22⋊C4×C43—41no—
211C22⋊C4×C43—41no—
212C22⋊C4×C43—41no—
213C22⋊C4×C43—41no—
214C22⋊C4×C43—41no—
215C22⋊C4×C43—41no—
216C42×C43—21no—
217C42×C43—21no—
218C42×C43C2411yescharacteristic
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—41no—
222C23×C43—41no—
223Q8×C43—21no—
224Q8×C43—21no—
225Q8×C43—21no—
226Q8×C43—21no—
227Q8×C43—41no—
228Q8×C43—41no—
229Q8×C43—41no—
230Q8×C43—41no—
231Q8×C43—82no—
232D4×C43—21no—
233D4×C43—21no—
234D4×C43—21no—
235D4×C43—21no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—81no—
245D4×C43—81no—
246D4×C43—82no—
247D4×C43—82no—
248D4×C43—161no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
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—82no—
263C2×C4×C43—82no—
264C2×C4×C43—161no—
265C2×C4×C43C22×D411yescharacteristic
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43H(5,𝔽2)11yescharacteristic
268C8×C43—21no—
269C8×C43—21no—
270C8×C43—21no—
271C8×C43—41no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43—41no—
275C8×C43—41no—
276C8×C43AGL(1,ℤ/8)12yes—
277#20298C4311yesmaximal, characteristic, direct product factor, Sylow
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43D4211yescharacteristic
291C4×C43—21no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—81no—
299C4×C43—81no—
300C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
301C4×C43#57511yescharacteristic
302C4×C43#57611yescharacteristic
303C4×C43#57711yescharacteristic
304#3399C2×C4311yescharacteristic, complemented
305#3373C2×C4311yescharacteristic, complemented
306#3332C2×C4311yescharacteristic, complemented
307#3276C2×C4311yescharacteristic, complemented
308#1709C2×C4311yescharacteristic, complemented
309#1702C2×C4311yescharacteristic, complemented
310#1701C2×C4311yescharacteristic, complemented
311#1690C2×C4311yescharacteristic, complemented
312#1687C2×C4311yescharacteristic, complemented
313#1642C2×C4311yescharacteristic, complemented
314#1640C2×C4311yescharacteristic, complemented
315#1627C2×C4311yescharacteristic, complemented
316#1625C2×C4311yescharacteristic, complemented
317#1590C2×C4311yescharacteristic, complemented
318#1590C2×C4311yescharacteristic, complemented
319C2×C43—81no—
320C2×C43—81no—
321C2×C43—161no—
322C2×C43—161no—
323C2×C43#327411yescharacteristic
324C2×C43#327511yescharacteristic
325C2×C43#329011yescharacteristic
326C2×#137—21no—
327#559C22×C4311yescharacteristic
328#550C22×C4311yescharacteristic
329D4×Q8C22×C4311yescharacteristic
330#547C22×C4311yescharacteristic
331#496—21no—
332#494C22×C4311yescharacteristic
333#493C22×C4311yescharacteristic
334#489—21no—
335#486C22×C4311yescharacteristic
336#486C22×C4311yescharacteristic
337#486C22×C4311yescharacteristic
338#486C22×C4311yescharacteristic
339#481—21no—
340#476—21no—
341#475C22×C4311yescharacteristic
342#475C22×C4311yescharacteristic
343#470—21no—
344#469—21no—
345#463—21no—
346#463—21no—
347#462C22×C4311yescharacteristic
348#461C22×C4311yescharacteristic
349#460C22×C4311yescharacteristic
350#459—21no—
351#459C22×C4311yescharacteristic
352#459C22×C4311yescharacteristic
353#459C22×C4311yescharacteristic
354#452—21no—
355#451—21no—
356#449—21no—
357#446C22×C4311yescharacteristic
358#446C22×C4311yescharacteristic
359#442—21no—
360#442—21no—
361C4×SD16C22×C4311yescharacteristic
362C4×SD16C22×C4311yescharacteristic
363#436C22×C4311yescharacteristic
364#436C22×C4311yescharacteristic
365#417—21no—
366#334C22×C4311yescharacteristic
367#334C22×C4311yescharacteristic
368#332C22×C4311yescharacteristic
369#332C22×C4311yescharacteristic
370#331C22×C4311yescharacteristic
371#331C22×C4311yescharacteristic
372Q8⋊C8C22×C4311yescharacteristic
373Q8⋊C8C22×C4311yescharacteristic
374D4⋊C8C22×C4311yescharacteristic
375D4⋊C8C22×C4311yescharacteristic
376C82C22×C4311yescharacteristic
377C43#2029811yescharacteristic, direct product factor, Sylow
378C2×#41—21no—
379C2×#41—21no—
380C22×Q8—21no—
381#137—44no—
382C2×Q16—21no—
383C2×Q16—21no—
384C2×Q16—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16D4×C4311yescharacteristic
388C2×SD16D4×C4311yescharacteristic
389C2×D8—21no—
390C2×D8—21no—
391C2×D8—21no—
392C2×D8—21no—
393C2×D8—21no—
394C2×M16—21no—
395C2×M16—21no—
396C4⋊Q8—21no—
397C4⋊Q8C23×C4311yescharacteristic
398C4⋊Q8C23×C4311yescharacteristic
399#127—21no—
400#127C23×C4311yescharacteristic
401#127C23×C4311yescharacteristic
402#124—21no—
403#124—21no—
404#123—41no—
405#123—41no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C22⋊Q8—41no—
409#121—21no—
410#121—21no—
411#121—41no—
412C4×Q8C23×C4311yescharacteristic
413C4×Q8C23×C4311yescharacteristic
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4—21no—
418C4×D4C23×C4311yescharacteristic
419C4×D4C23×C4311yescharacteristic
420C2×C4⋊C4—21no—
421#106—21no—
422#106—21no—
423#106D4×C4311yescharacteristic
424#106D4×C4311yescharacteristic
425C4⋊C8—21no—
426C4⋊C8—21no—
427C4⋊C8C23×C4311yescharacteristic
428C4⋊C8C23×C4311yescharacteristic
429C4⋊C8C23×C4311yescharacteristic
430C4⋊C8C23×C4311yescharacteristic
431#103—21no—
432#103—21no—
433#103—21no—
434#103—21no—
435#103D4×C4311yescharacteristic
436#103D4×C4311yescharacteristic
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—41no—
446#102—41no—
447#102D4×C4311yescharacteristic
448#102D4×C4311yescharacteristic
449C22⋊C8—21no—
450C22⋊C8—21no—
451#97—21no—
452#97—21no—
453C4×C8C23×C4311yescharacteristic
454C4×C8C23×C4311yescharacteristic
455C4×C8C23×C4311yescharacteristic
456#41—42no—
457#41—42no—
458#41—81no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—41no—
463C2×Q8—42no—
464C2×Q8—81no—
465C2×Q8C2×D4×C4311yescharacteristic
466C2×Q8C2×D4×C4311yescharacteristic
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4C2×D4×C4311yescharacteristic
477C2×D4C2×D4×C4311yescharacteristic
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484Q16—42no—
485Q16—42no—
486Q16—81no—
487SD16—22no—
488SD16—41no—
489SD16—42no—
490SD16—81no—
491D8—42no—
492D8—42no—
493D8—81no—
494D8—81no—
495D8—81no—
496M16—42no—
497M16—81no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8C2×D4×C4311yescharacteristic
504C2×C8C2×D4×C4311yescharacteristic
505C2×C8C2×D4×C4311yescharacteristic
506C2×C8C2×D4×C4311yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4C2×D4×C4311yescharacteristic
516C4⋊C4C2×D4×C4311yescharacteristic
517C4⋊C4C2×D4×C4311yescharacteristic
518C4⋊C4C2×D4×C4311yescharacteristic
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—21no—
528C42—21no—
529C42C24×C4311yescharacteristic
530C23—21no—
531C23—21no—
532C23—41no—
533C23—41no—
534Q8—21no—
535Q8—21no—
536Q8—21no—
537Q8—21no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—82no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—81no—
556D4—81no—
557D4—82no—
558D4—82no—
559D4—161no—
560C2×C4—21no—
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—82no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4—161no—
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—81no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22D42×C4311yescharacteristic
601C4—21no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—81no—
609C4—81no—
610C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
611C4C43×#57511yescharacteristic
612C4C43×#57611yescharacteristic
613C4C43×#57711yescharacteristic
614C2—81no—
615C2—81no—
616C2—161no—
617C2—161no—
618C2C43×#327411yescharacteristic
619C2C43×#327511yescharacteristic
620C2C43×#329011yescharacteristic
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×#3399C2semidirect
2. C43×#3373C2semidirect
3. C43×#3332C2semidirect
4. C43×#3276C2semidirect
5. C43×#1709C2semidirect
6. C43×#1702C2semidirect
7. C43×#1701C2semidirect
8. C43×#1690C2semidirect
9. C43×#1687C2semidirect
10. C43×#1642C2semidirect
11. C43×#1640C2semidirect
12. C43×#1627C2semidirect
13. C43×#1625C2semidirect
14. C43×#1590C2semidirect
15. C43×#1590C2semidirect
277. #20298C43direct (N × H)
304. #3399C2×C43semidirect
305. #3373C2×C43semidirect
306. #3332C2×C43semidirect
307. #3276C2×C43semidirect
308. #1709C2×C43semidirect
309. #1702C2×C43semidirect
310. #1701C2×C43semidirect
311. #1690C2×C43semidirect
312. #1687C2×C43semidirect
313. #1642C2×C43semidirect
314. #1640C2×C43semidirect
315. #1627C2×C43semidirect
316. #1625C2×C43semidirect
317. #1590C2×C43semidirect
318. #1590C2×C43semidirect
377. C43#20298direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33992
C43×#33732
C43×#33322
C43×#32762
C43×#17092
C43×#17022
C43×#17012
C43×#16902
C43×#16872
C43×#16422
C43×#16402
C43×#16272
C43×#16252
C43×#15902
#2029843