Finite Group Databasebeta

← C43×#19557 #24939574

Subgroups — C43×#19557 #24939574

Order 11008.

642 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3245C211yesmaximal, characteristic, complemented
2C43×#3214C211yesmaximal, characteristic, complemented
3C43×#3207C211yesmaximal, characteristic, complemented
4C43×#2979C211yesmaximal, characteristic, complemented
5C43×#1701C211yesmaximal, characteristic, complemented
6C43×#1699C211yesmaximal, characteristic, complemented
7C43×#1687C211yesmaximal, characteristic, complemented
8C43×#1685C211yesmaximal, characteristic, complemented
9C43×#1681C211yesmaximal, characteristic, complemented
10C43×#1679C211yesmaximal, characteristic, complemented
11C43×#1667C211yesmaximal, characteristic, complemented
12C43×#1665C211yesmaximal, characteristic, complemented
13C43×#1573C211yesmaximal, characteristic, complemented
14C43×#1553C211yesmaximal, characteristic, complemented
15C43×#1540C211yesmaximal, characteristic, complemented
16C43×#532C2211yescharacteristic
17C43×#532C2211yescharacteristic
18C43×#532C2211yescharacteristic
19C43×#496—21no—
20C43×#493C2211yescharacteristic
21C43×#492C2211yescharacteristic
22C43×#489—21no—
23C43×#487C2211yescharacteristic
24C43×#486C2211yescharacteristic
25C43×#474—21no—
26C43×#474C2211yescharacteristic
27C43×#474C2211yescharacteristic
28C43×#466—21no—
29C43×#466—21no—
30C43×#463—21no—
31C43×#463—21no—
32C43×#461C2211yescharacteristic
33C43×#461C2211yescharacteristic
34C43×#459—21no—
35C43×#459C2211yescharacteristic
36C43×#459C2211yescharacteristic
37C43×#459C2211yescharacteristic
38C43×#459C2211yescharacteristic
39C43×#449—21no—
40C43×#449—21no—
41C43×#449—21no—
42C43×#449—21no—
43C43×#436—21no—
44C43×#436C2211yescharacteristic
45C43×#436C2211yescharacteristic
46C8×D4×C43—21no—
47C8×D4×C43C2211yescharacteristic
48C8×D4×C43C2211yescharacteristic
49C43×#432C2211yescharacteristic
50C43×#431C2211yescharacteristic
51C43×#431C2211yescharacteristic
52C2×C4⋊C8×C43C2211yescharacteristic
53C43×#408—21no—
54C43×#408—21no—
55C43×#335C2211yescharacteristic
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#334C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#332C2211yescharacteristic
62C43×#332C2211yescharacteristic
63C43×#331C2211yescharacteristic
64C43×#331C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#41×C43—21no—
68C2×#41×C43—21no—
69C2×#41×C43—21no—
70C2×SD16×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×D8×C43—21no—
75C2×D8×C43—21no—
76C2×D8×C43—21no—
77C2×D8×C43—21no—
78C2×D8×C43—21no—
79C2×D8×C43—21no—
80C2×M16×C43—21no—
81C2×M16×C43—21no—
82C22×C8×C43—21no—
83C22×C8×C43—21no—
84C22×C8×C43—21no—
85C4⋊Q8×C43D411yescharacteristic
86C4⋊Q8×C43C2311yescharacteristic
87C4⋊Q8×C43C2311yescharacteristic
88#127×C43D411yescharacteristic
89#127×C43C2311yescharacteristic
90#127×C43C2311yescharacteristic
91#124×C43—21no—
92#124×C43—21no—
93#124×C43—21no—
94#121×C43—21no—
95#121×C43—21no—
96#121×C43—21no—
97#121×C43—21no—
98#121×C43—21no—
99#121×C43D411yescharacteristic
100#121×C43D411yescharacteristic
101C4×D4×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43—21no—
106C4×D4×C43C2311yescharacteristic
107C4×D4×C43C2311yescharacteristic
108C2×C42×C43C2311yescharacteristic
109#107×C43—21no—
110#107×C43—21no—
111C4⋊C8×C43—21no—
112C4⋊C8×C43D411yescharacteristic
113C4⋊C8×C43D411yescharacteristic
114C4⋊C8×C43C2311yescharacteristic
115C4⋊C8×C43C2311yescharacteristic
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#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—
132C22⋊C8×C43—21no—
133C22⋊C8×C43—21no—
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43D411yescharacteristic
139C22⋊C8×C43D411yescharacteristic
140#97×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—81no—
145#41×C43—81no—
146#41×C43—81no—
147#41×C43—81no—
148#41×C43—81no—
149#41×C43—81no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
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—21no—
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×C43C2×D411yescharacteristic
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43#4111yescharacteristic
174SD16×C43—81no—
175SD16×C43—81no—
176SD16×C43—81no—
177SD16×C43—81no—
178D8×C43—81no—
179D8×C43—81no—
180D8×C43—81no—
181D8×C43—81no—
182D8×C43—81no—
183D8×C43—81no—
184M16×C43—81no—
185M16×C43—81no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—81no—
193C2×C8×C43—81no—
194C2×C8×C43—81no—
195C2×C8×C43C2×D411yescharacteristic
196C2×C8×C43C2×D411yescharacteristic
197C2×C8×C43C2×D411yescharacteristic
198C2×C8×C43C2×D411yescharacteristic
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43C2×D411yescharacteristic
205C4⋊C4×C43C2×D411yescharacteristic
206C22⋊C4×C43—21no—
207C22⋊C4×C43—21no—
208C22⋊C4×C43—21no—
209C22⋊C4×C43—21no—
210C22⋊C4×C43—41no—
211C22⋊C4×C43—41no—
212C22⋊C4×C43—41no—
213C22⋊C4×C43—41no—
214C42×C43C2×D411yescharacteristic
215C42×C43C2×D411yescharacteristic
216C42×C43#4111yescharacteristic
217C42×C43C2411yescharacteristic
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43#12111yescharacteristic
223Q8×C43—41no—
224Q8×C43—41no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—81no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—21no—
232D4×C43—42no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—81no—
242D4×C43—81no—
243D4×C43—81no—
244D4×C43—81no—
245D4×C43—81no—
246D4×C43—82no—
247D4×C43—82no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
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—82no—
263C2×C4×C43#12111yescharacteristic
264C2×C4×C43#12111yescharacteristic
265C2×C4×C43#12111yescharacteristic
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43C22×D411yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C8×C43—21no—
270C8×C43—21no—
271C8×C43—21no—
272C8×C43—21no—
273C8×C43—41no—
274C8×C43—41no—
275C8×C43—41no—
276C8×C43—41no—
277C8×C43—41no—
278C8×C43—41no—
279#19557C4311yesmaximal, characteristic, direct product factor, Sylow
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—21no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43C2×#12111yescharacteristic
296C4×C43—21no—
297C4×C43—21no—
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—41no—
301C4×C43—41no—
302C4×C43—81no—
303C4×C43—81no—
304C4×C43#57611yescharacteristic
305C4×C43#57611yescharacteristic
306C4×C43#57611yescharacteristic
307C4×C43#57711yescharacteristic
308#3245C2×C4311yescharacteristic, complemented
309#3214C2×C4311yescharacteristic, complemented
310#3207C2×C4311yescharacteristic, complemented
311#2979C2×C4311yescharacteristic, complemented
312#1701C2×C4311yescharacteristic, complemented
313#1699C2×C4311yescharacteristic, complemented
314#1687C2×C4311yescharacteristic, complemented
315#1685C2×C4311yescharacteristic, complemented
316#1681C2×C4311yescharacteristic, complemented
317#1679C2×C4311yescharacteristic, complemented
318#1667C2×C4311yescharacteristic, complemented
319#1665C2×C4311yescharacteristic, complemented
320#1573C2×C4311yescharacteristic, complemented
321#1553C2×C4311yescharacteristic, complemented
322#1540C2×C4311yescharacteristic, complemented
323C2×C43—41no—
324C2×C43—81no—
325C2×C43—81no—
326C2×C43—161no—
327C2×C43—161no—
328C2×C43#304111yescharacteristic
329C2×C43#306211yescharacteristic
330C2×C43#306711yescharacteristic
331#532C22×C4311yescharacteristic
332#532C22×C4311yescharacteristic
333#532C22×C4311yescharacteristic
334#496—21no—
335#493C22×C4311yescharacteristic
336#492C22×C4311yescharacteristic
337#489—21no—
338#487C22×C4311yescharacteristic
339#486C22×C4311yescharacteristic
340#474—21no—
341#474C22×C4311yescharacteristic
342#474C22×C4311yescharacteristic
343#466—21no—
344#466—21no—
345#463—21no—
346#463—21no—
347#461C22×C4311yescharacteristic
348#461C22×C4311yescharacteristic
349#459—21no—
350#459C22×C4311yescharacteristic
351#459C22×C4311yescharacteristic
352#459C22×C4311yescharacteristic
353#459C22×C4311yescharacteristic
354#449—21no—
355#449—21no—
356#449—21no—
357#449—21no—
358#436—21no—
359#436C22×C4311yescharacteristic
360#436C22×C4311yescharacteristic
361C8×D4—21no—
362C8×D4C22×C4311yescharacteristic
363C8×D4C22×C4311yescharacteristic
364#432C22×C4311yescharacteristic
365#431C22×C4311yescharacteristic
366#431C22×C4311yescharacteristic
367C2×C4⋊C8C22×C4311yescharacteristic
368#408—21no—
369#408—21no—
370#335C22×C4311yescharacteristic
371#335C22×C4311yescharacteristic
372#334C22×C4311yescharacteristic
373#334C22×C4311yescharacteristic
374#332C22×C4311yescharacteristic
375#332C22×C4311yescharacteristic
376#332C22×C4311yescharacteristic
377#332C22×C4311yescharacteristic
378#331C22×C4311yescharacteristic
379#331C22×C4311yescharacteristic
380#331C22×C4311yescharacteristic
381#331C22×C4311yescharacteristic
382C43#1955711yescharacteristic, direct product factor, Sylow
383C2×#41—21no—
384C2×#41—21no—
385C2×#41—21no—
386C2×SD16—21no—
387C2×SD16—21no—
388C2×SD16—21no—
389C2×SD16—21no—
390C2×D8—21no—
391C2×D8—21no—
392C2×D8—21no—
393C2×D8—21no—
394C2×D8—21no—
395C2×D8—21no—
396C2×M16—21no—
397C2×M16—21no—
398C22×C8—21no—
399C22×C8—21no—
400C22×C8—21no—
401C4⋊Q8D4×C4311yescharacteristic
402C4⋊Q8C23×C4311yescharacteristic
403C4⋊Q8C23×C4311yescharacteristic
404#127D4×C4311yescharacteristic
405#127C23×C4311yescharacteristic
406#127C23×C4311yescharacteristic
407#124—21no—
408#124—21no—
409#124—21no—
410#121—21no—
411#121—21no—
412#121—21no—
413#121—21no—
414#121—21no—
415#121D4×C4311yescharacteristic
416#121D4×C4311yescharacteristic
417C4×D4—21no—
418C4×D4—21no—
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4C23×C4311yescharacteristic
423C4×D4C23×C4311yescharacteristic
424C2×C42C23×C4311yescharacteristic
425#107—21no—
426#107—21no—
427C4⋊C8—21no—
428C4⋊C8D4×C4311yescharacteristic
429C4⋊C8D4×C4311yescharacteristic
430C4⋊C8C23×C4311yescharacteristic
431C4⋊C8C23×C4311yescharacteristic
432C4⋊C8C23×C4311yescharacteristic
433C4⋊C8C23×C4311yescharacteristic
434C4⋊C8C23×C4311yescharacteristic
435C4⋊C8C23×C4311yescharacteristic
436#103—21no—
437#103—21no—
438#103—21no—
439#103—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—21no—
447#102—21no—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—21no—
454C22⋊C8D4×C4311yescharacteristic
455C22⋊C8D4×C4311yescharacteristic
456#97—21no—
457C4×C8—21no—
458C4×C8C23×C4311yescharacteristic
459C4×C8C23×C4311yescharacteristic
460#41—81no—
461#41—81no—
462#41—81no—
463#41—81no—
464#41—81no—
465#41—81no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4C2×D4×C4311yescharacteristic
482C2×D4C2×D4×C4311yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4C2×D4×C4311yescharacteristic
488C22×C4C2×D4×C4311yescharacteristic
489C22×C4#41×C4311yescharacteristic
490SD16—81no—
491SD16—81no—
492SD16—81no—
493SD16—81no—
494D8—81no—
495D8—81no—
496D8—81no—
497D8—81no—
498D8—81no—
499D8—81no—
500M16—81no—
501M16—81no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—81no—
509C2×C8—81no—
510C2×C8—81no—
511C2×C8C2×D4×C4311yescharacteristic
512C2×C8C2×D4×C4311yescharacteristic
513C2×C8C2×D4×C4311yescharacteristic
514C2×C8C2×D4×C4311yescharacteristic
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4C2×D4×C4311yescharacteristic
521C4⋊C4C2×D4×C4311yescharacteristic
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C22⋊C4—41no—
529C22⋊C4—41no—
530C42C2×D4×C4311yescharacteristic
531C42C2×D4×C4311yescharacteristic
532C42#41×C4311yescharacteristic
533C42C24×C4311yescharacteristic
534C23—21no—
535C23—21no—
536C23—41no—
537C23—41no—
538C23#121×C4311yescharacteristic
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—41no—
543Q8—81no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—42no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—81no—
558D4—81no—
559D4—81no—
560D4—81no—
561D4—81no—
562D4—82no—
563D4—82no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—82no—
578C2×C4—82no—
579C2×C4#121×C4311yescharacteristic
580C2×C4#121×C4311yescharacteristic
581C2×C4#121×C4311yescharacteristic
582C2×C4C22×D4×C4311yescharacteristic
583C2×C4C22×D4×C4311yescharacteristic
584C2×C4C2×#41×C4311yescharacteristic
585C8—21no—
586C8—21no—
587C8—21no—
588C8—21no—
589C8—41no—
590C8—41no—
591C8—41no—
592C8—41no—
593C8—41no—
594C8—41no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22C2×#121×C4311yescharacteristic
611C4—21no—
612C4—21no—
613C4—21no—
614C4—21no—
615C4—41no—
616C4—41no—
617C4—81no—
618C4—81no—
619C4C43×#57611yescharacteristic
620C4C43×#57611yescharacteristic
621C4C43×#57611yescharacteristic
622C4C43×#57711yescharacteristic
623C2—41no—
624C2—81no—
625C2—81no—
626C2—161no—
627C2—161no—
628C2C43×#304111yescharacteristic
629C2C43×#306211yescharacteristic
630C2C43×#306711yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3245C2semidirect
2. C43×#3214C2semidirect
3. C43×#3207C2semidirect
4. C43×#2979C2semidirect
5. C43×#1701C2semidirect
6. C43×#1699C2semidirect
7. C43×#1687C2semidirect
8. C43×#1685C2semidirect
9. C43×#1681C2semidirect
10. C43×#1679C2semidirect
11. C43×#1667C2semidirect
12. C43×#1665C2semidirect
13. C43×#1573C2semidirect
14. C43×#1553C2semidirect
15. C43×#1540C2semidirect
279. #19557C43direct (N × H)
308. #3245C2×C43semidirect
309. #3214C2×C43semidirect
310. #3207C2×C43semidirect
311. #2979C2×C43semidirect
312. #1701C2×C43semidirect
313. #1699C2×C43semidirect
314. #1687C2×C43semidirect
315. #1685C2×C43semidirect
316. #1681C2×C43semidirect
317. #1679C2×C43semidirect
318. #1667C2×C43semidirect
319. #1665C2×C43semidirect
320. #1573C2×C43semidirect
321. #1553C2×C43semidirect
322. #1540C2×C43semidirect
382. C43#19557direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32452
C43×#32142
C43×#32072
C43×#29792
C43×#17012
C43×#16992
C43×#16872
C43×#16852
C43×#16812
C43×#16792
C43×#16672
C43×#16652
C43×#15732
C43×#15532
C43×#15402
#1955743