Finite Group Databasebeta

← C43×#19899 #24939916

Subgroups — C43×#19899 #24939916

Order 11008.

666 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3330C211yesmaximal, characteristic, complemented
2C43×#3325C211yesmaximal, characteristic, complemented
3C43×#3303C211yesmaximal, characteristic, complemented
4C43×#3294C211yesmaximal, characteristic, complemented
5C43×#1711C211yesmaximal, characteristic, complemented
6C43×#1699C211yesmaximal, characteristic, complemented
7C43×#1697C211yesmaximal, characteristic, complemented
8C43×#1683C211yesmaximal, characteristic, complemented
9C43×#1681C211yesmaximal, characteristic, complemented
10C43×#1646C211yesmaximal, characteristic, complemented
11C43×#1639C211yesmaximal, characteristic, complemented
12C43×#1635C211yesmaximal, characteristic, complemented
13C43×#1625C211yesmaximal, characteristic, complemented
14C43×#1589C211yesmaximal, characteristic, complemented
15C8×D8×C43C211yesmaximal, characteristic, complemented
16C43×#555C2211yescharacteristic
17C43×#547C2211yescharacteristic
18C43×#547C2211yescharacteristic, complemented
19D42×C43C2211yescharacteristic
20C43×#487C2211yescharacteristic, complemented
21C43×#487C2211yescharacteristic, complemented
22C43×#487C2211yescharacteristic, complemented
23C43×#486C2211yescharacteristic
24C43×#486C2211yescharacteristic
25C43×#486C2211yescharacteristic
26C43×#485—21no—
27C43×#484—21no—
28C43×#482—21no—
29C43×#480—21no—
30C43×#476C2211yescharacteristic
31C43×#476C2211yescharacteristic, complemented
32C43×#474C2211yescharacteristic
33C43×#474C2211yescharacteristic
34C43×#469—21no—
35C43×#468—21no—
36C43×#466—21no—
37C43×#465—21no—
38C43×#461C2211yescharacteristic
39C43×#461C2211yescharacteristic, complemented
40C43×#459C2211yescharacteristic
41C43×#459C2211yescharacteristic
42C43×#449—21no—
43C43×#449—21no—
44C43×#447—21no—
45C43×#447—21no—
46C4×D8×C43C2211yescharacteristic
47C4×D8×C43C2211yescharacteristic
48C43×#436C2211yescharacteristic
49C43×#436C2211yescharacteristic, complemented
50C8×D4×C43C2211yescharacteristic
51C8×D4×C43C2211yescharacteristic, complemented
52C43×#418—21no—
53C43×#417—21no—
54C43×#416—21no—
55C2×#102×C43—21no—
56C43×#335C2211yescharacteristic, complemented
57C43×#335C2211yescharacteristic, complemented
58C43×#333C2211yescharacteristic, complemented
59C43×#332C2211yescharacteristic, complemented
60C43×#332C2211yescharacteristic, complemented
61C43×#331C2211yescharacteristic
62C43×D4⋊C8C2211yescharacteristic
63C43×D4⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic, complemented
65C43×D4⋊C8C2211yescharacteristic, complemented
66C82×C43C2211yescharacteristic, complemented
67C2×#41×C43—21no—
68C2×#41×C43—21no—
69C22×D4×C43—21no—
70C22×D4×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×D8×C43—21no—
74C2×D8×C43—21no—
75C2×D8×C43D411yescharacteristic
76C2×D8×C43D411yescharacteristic
77C2×M16×C43—21no—
78C2×M16×C43—21no—
79C22×C8×C43—21no—
80C22×C8×C43—21no—
81C4⋊Q8×C43C2311yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83C4⋊Q8×C43C2311yescharacteristic
84#127×C43C2311yescharacteristic
85#124×C43—41no—
86#123×C43—41no—
87#123×C43—41no—
88C22⋊Q8×C43—21no—
89C22⋊Q8×C43—21no—
90#121×C43—21no—
91#121×C43—21no—
92#121×C43—21no—
93#121×C43—21no—
94#121×C43—21no—
95#121×C43—21no—
96#120×C43—41no—
97C4×D4×C43C2311yescharacteristic
98C4×D4×C43C2311yescharacteristic
99C4×D4×C43C2311yescharacteristic
100C4×D4×C43C2311yescharacteristic
101#117×C43—21no—
102#117×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105#107×C43—21no—
106#107×C43—21no—
107#107×C43D411yescharacteristic
108#107×C43D411yescharacteristic
109#106×C43—21no—
110#106×C43—21no—
111C4⋊C8×C43C2311yescharacteristic
112C4⋊C8×C43C2311yescharacteristic
113C4⋊C8×C43C2311yescharacteristic
114C4⋊C8×C43C2311yescharacteristic
115#103×C43—21no—
116#103×C43—21no—
117#103×C43—21no—
118#103×C43—21no—
119#103×C43—21no—
120#103×C43—21no—
121#103×C43—41no—
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—41no—
133#102×C43D411yescharacteristic
134#102×C43D411yescharacteristic
135#102×C43D411yescharacteristic
136#102×C43D411yescharacteristic
137C22⋊C8×C43—21no—
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C24×C43—41no—
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—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43—41no—
159C2×D4×C43—41no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43—81no—
163C2×D4×C43—81no—
164C2×D4×C43C2×D411yescharacteristic
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—21no—
172C22×C4×C43—41no—
173C22×C4×C43—41no—
174SD16×C43—81no—
175SD16×C43—81no—
176D8×C43—22no—
177D8×C43—41no—
178D8×C43—81no—
179D8×C43—81no—
180M16×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—21no—
199C4⋊C4×C43—41no—
200C4⋊C4×C43—41no—
201C4⋊C4×C43C2×D411yescharacteristic
202C4⋊C4×C43C2×D411yescharacteristic
203C4⋊C4×C43C2×D411yescharacteristic
204C4⋊C4×C43C2×D411yescharacteristic
205C22⋊C4×C43—21no—
206C22⋊C4×C43—21no—
207C22⋊C4×C43—21no—
208C22⋊C4×C43—21no—
209C22⋊C4×C43—41no—
210C22⋊C4×C43—41no—
211C22⋊C4×C43—41no—
212C22⋊C4×C43—41no—
213C22⋊C4×C43—41no—
214C42×C43—41no—
215C42×C43C2411yescharacteristic
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—41no—
221C23×C43—82no—
222C23×C43—82no—
223C23×C43—161no—
224Q8×C43—41no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—41no—
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—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—81no—
241D4×C43—82no—
242D4×C43—82no—
243D4×C43—82no—
244D4×C43—82no—
245D4×C43—161no—
246D4×C43#13512yes—
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×C43—82no—
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43C22×D411yescharacteristic
266C2×C4×C43H(5,𝔽2)11yescharacteristic
267C8×C43—21no—
268C8×C43—21no—
269C8×C43—21no—
270C8×C43—21no—
271C8×C43—41no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43—41no—
275C8×C43—41no—
276#19899C4311yesmaximal, characteristic, direct product factor, Sylow
277C22×C43—22no—
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—41no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43—164no—
293C22×C43D4211yescharacteristic
294C4×C43—21no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—41no—
299C4×C43—81no—
300C4×C43—81no—
301C4×C43—81no—
302C4×C43C2×#13511yescharacteristic
303C4×C43#57511yescharacteristic
304C4×C43#57611yescharacteristic
305C4×C43#57611yescharacteristic
306#3330C2×C4311yescharacteristic, complemented
307#3325C2×C4311yescharacteristic, complemented
308#3303C2×C4311yescharacteristic, complemented
309#3294C2×C4311yescharacteristic, complemented
310#1711C2×C4311yescharacteristic, complemented
311#1699C2×C4311yescharacteristic, complemented
312#1697C2×C4311yescharacteristic, complemented
313#1683C2×C4311yescharacteristic, complemented
314#1681C2×C4311yescharacteristic, complemented
315#1646C2×C4311yescharacteristic, complemented
316#1639C2×C4311yescharacteristic, complemented
317#1635C2×C4311yescharacteristic, complemented
318#1625C2×C4311yescharacteristic, complemented
319#1589C2×C4311yescharacteristic, complemented
320C8×D8C2×C4311yescharacteristic, complemented
321C2×C43—42no—
322C2×C43—81no—
323C2×C43—81no—
324C2×C43—81no—
325C2×C43—161no—
326C2×C43#327311yescharacteristic
327C2×C43#328011yescharacteristic
328C2×C43#329011yescharacteristic
329#555C22×C4311yescharacteristic
330#547C22×C4311yescharacteristic
331#547C22×C4311yescharacteristic, complemented
332D42C22×C4311yescharacteristic
333#487C22×C4311yescharacteristic, complemented
334#487C22×C4311yescharacteristic, complemented
335#487C22×C4311yescharacteristic, complemented
336#486C22×C4311yescharacteristic
337#486C22×C4311yescharacteristic
338#486C22×C4311yescharacteristic
339#485—21no—
340#484—21no—
341#482—21no—
342#480—21no—
343#476C22×C4311yescharacteristic
344#476C22×C4311yescharacteristic, complemented
345#474C22×C4311yescharacteristic
346#474C22×C4311yescharacteristic
347#469—21no—
348#468—21no—
349#466—21no—
350#465—21no—
351#461C22×C4311yescharacteristic
352#461C22×C4311yescharacteristic, complemented
353#459C22×C4311yescharacteristic
354#459C22×C4311yescharacteristic
355#449—21no—
356#449—21no—
357#447—21no—
358#447—21no—
359C4×D8C22×C4311yescharacteristic
360C4×D8C22×C4311yescharacteristic
361#436C22×C4311yescharacteristic
362#436C22×C4311yescharacteristic, complemented
363C8×D4C22×C4311yescharacteristic
364C8×D4C22×C4311yescharacteristic, complemented
365#418—21no—
366#417—21no—
367#416—21no—
368C2×#102—21no—
369#335C22×C4311yescharacteristic, complemented
370#335C22×C4311yescharacteristic, complemented
371#333C22×C4311yescharacteristic, complemented
372#332C22×C4311yescharacteristic, complemented
373#332C22×C4311yescharacteristic, complemented
374#331C22×C4311yescharacteristic
375D4⋊C8C22×C4311yescharacteristic
376D4⋊C8C22×C4311yescharacteristic
377D4⋊C8C22×C4311yescharacteristic, complemented
378D4⋊C8C22×C4311yescharacteristic, complemented
379C82C22×C4311yescharacteristic, complemented
380C43#1989911yescharacteristic, direct product factor, Sylow
381C2×#41—21no—
382C2×#41—21no—
383C22×D4—21no—
384C22×D4—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8D4×C4311yescharacteristic
390C2×D8D4×C4311yescharacteristic
391C2×M16—21no—
392C2×M16—21no—
393C22×C8—21no—
394C22×C8—21no—
395C4⋊Q8C23×C4311yescharacteristic
396C4⋊Q8C23×C4311yescharacteristic
397C4⋊Q8C23×C4311yescharacteristic
398#127C23×C4311yescharacteristic
399#124—41no—
400#123—41no—
401#123—41no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121—21no—
409#121—21no—
410#120—41no—
411C4×D4C23×C4311yescharacteristic
412C4×D4C23×C4311yescharacteristic
413C4×D4C23×C4311yescharacteristic
414C4×D4C23×C4311yescharacteristic
415#117—21no—
416#117—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419#107—21no—
420#107—21no—
421#107D4×C4311yescharacteristic
422#107D4×C4311yescharacteristic
423#106—21no—
424#106—21no—
425C4⋊C8C23×C4311yescharacteristic
426C4⋊C8C23×C4311yescharacteristic
427C4⋊C8C23×C4311yescharacteristic
428C4⋊C8C23×C4311yescharacteristic
429#103—21no—
430#103—21no—
431#103—21no—
432#103—21no—
433#103—21no—
434#103—21no—
435#103—41no—
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—41no—
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—42no—
461#41—81no—
462#41—81no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—81no—
477C2×D4—81no—
478C2×D4C2×D4×C4311yescharacteristic
479C2×D4C2×D4×C4311yescharacteristic
480C2×D4C2×D4×C4311yescharacteristic
481C2×D4C2×D4×C4311yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—41no—
487C22×C4—41no—
488SD16—81no—
489SD16—81no—
490D8—22no—
491D8—41no—
492D8—81no—
493D8—81no—
494M16—81no—
495M16—81no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—81no—
502C2×C8—81no—
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—21no—
522C22⋊C4—21no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—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—41no—
541Q8—41no—
542Q8—81no—
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—82no—
559D4—161no—
560D4#135×C4312yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
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—41no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4C22×D4×C4311yescharacteristic
579C2×C4C22×D4×C4311yescharacteristic
580C2×C4H(5,𝔽2)×C4311yescharacteristic
581C8—21no—
582C8—21no—
583C8—21no—
584C8—21no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8—41no—
589C8—41no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—164no—
606C22D42×C4311yescharacteristic
607C4—21no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—81no—
613C4—81no—
614C4—81no—
615C4C2×#135×C4311yescharacteristic
616C4C43×#57511yescharacteristic
617C4C43×#57611yescharacteristic
618C4C43×#57611yescharacteristic
619C2—42no—
620C2—81no—
621C2—81no—
622C2—81no—
623C2—161no—
624C2C43×#327311yescharacteristic
625C2C43×#328011yescharacteristic
626C2C43×#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×#3330C2semidirect
2. C43×#3325C2semidirect
3. C43×#3303C2semidirect
4. C43×#3294C2semidirect
5. C43×#1711C2semidirect
6. C43×#1699C2semidirect
7. C43×#1697C2semidirect
8. C43×#1683C2semidirect
9. C43×#1681C2semidirect
10. C43×#1646C2semidirect
11. C43×#1639C2semidirect
12. C43×#1635C2semidirect
13. C43×#1625C2semidirect
14. C43×#1589C2semidirect
15. C8×D8×C43C2semidirect
18. C43×#547C22semidirect
20. C43×#487C22semidirect
21. C43×#487C22semidirect
22. C43×#487C22semidirect
31. C43×#476C22semidirect
39. C43×#461C22semidirect
49. C43×#436C22semidirect
51. C8×D4×C43C22semidirect
56. C43×#335C22semidirect
57. C43×#335C22semidirect
58. C43×#333C22semidirect
59. C43×#332C22semidirect
60. C43×#332C22semidirect
64. C43×D4⋊C8C22semidirect
65. C43×D4⋊C8C22semidirect
66. C82×C43C22semidirect
276. #19899C43direct (N × H)
306. #3330C2×C43semidirect
307. #3325C2×C43semidirect
308. #3303C2×C43semidirect
309. #3294C2×C43semidirect
310. #1711C2×C43semidirect
311. #1699C2×C43semidirect
312. #1697C2×C43semidirect
313. #1683C2×C43semidirect
314. #1681C2×C43semidirect
315. #1646C2×C43semidirect
316. #1639C2×C43semidirect
317. #1635C2×C43semidirect
318. #1625C2×C43semidirect
319. #1589C2×C43semidirect
320. C8×D8C2×C43semidirect
331. #547C22×C43semidirect
333. #487C22×C43semidirect
334. #487C22×C43semidirect
335. #487C22×C43semidirect
344. #476C22×C43semidirect
352. #461C22×C43semidirect
362. #436C22×C43semidirect
364. C8×D4C22×C43semidirect
369. #335C22×C43semidirect
370. #335C22×C43semidirect
371. #333C22×C43semidirect
372. #332C22×C43semidirect
373. #332C22×C43semidirect
377. D4⋊C8C22×C43semidirect
378. D4⋊C8C22×C43semidirect
379. C82C22×C43semidirect
380. C43#19899direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33302
C43×#33252
C43×#33032
C43×#32942
C43×#17112
C43×#16992
C43×#16972
C43×#16832
C43×#16812
C43×#16462
C43×#16392
C43×#16352
C43×#16252
C43×#15892
C8×D8×C432
#1989943