Finite Group Databasebeta

← C43×#19825 #24939842

Subgroups — C43×#19825 #24939842

Order 11008.

642 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3394C211yesmaximal, characteristic, complemented
2C43×#3361C211yesmaximal, characteristic, complemented
3C43×#3324C211yesmaximal, characteristic, complemented
4C43×#3295C211yesmaximal, characteristic, complemented
5C43×#1717C211yesmaximal, characteristic, complemented
6C43×#1697C211yesmaximal, characteristic, complemented
7C43×#1682C211yesmaximal, characteristic, complemented
8C43×#1678C211yesmaximal, characteristic, complemented
9C43×#1665C211yesmaximal, characteristic, complemented
10C43×#1644C211yesmaximal, characteristic, complemented
11C43×#1638C211yesmaximal, characteristic, complemented
12C43×#1620C211yesmaximal, characteristic, complemented
13C43×#1619C211yesmaximal, characteristic
14C43×#1583C211yesmaximal, characteristic, complemented
15C43×SD16⋊C8C211yesmaximal, characteristic, complemented
16C43×#559C2211yescharacteristic, complemented
17C43×#556C2211yescharacteristic
18C43×#554C2211yescharacteristic
19D42×C43C2211yescharacteristic
20C43×#495—21no—
21C43×#493C2211yescharacteristic
22C43×#492C2211yescharacteristic, complemented
23C43×#488—21no—
24C43×#487C2211yescharacteristic, complemented
25C43×#486C2211yescharacteristic
26C43×#486C2211yescharacteristic
27C43×#486C2211yescharacteristic, complemented
28C43×#482—21no—
29C43×#481—21no—
30C43×#478—21no—
31C43×#477C2211yescharacteristic, complemented
32C43×#476C2211yescharacteristic
33C43×#474C2211yescharacteristic
34C43×#468—21no—
35C43×#465—21no—
36C43×#464—21no—
37C43×#463—21no—
38C43×#463—21no—
39C43×#462C2211yescharacteristic, complemented
40C43×#460C2211yescharacteristic
41C43×#460C2211yescharacteristic
42C43×#459C2211yescharacteristic
43C43×#459C2211yescharacteristic
44C43×#450—21no—
45C43×#450—21no—
46C8×Q8×C43C2211yescharacteristic, complemented
47C8×Q8×C43C2211yescharacteristic, complemented
48C4×SD16×C43—21no—
49C4×SD16×C43C2211yescharacteristic
50C4×SD16×C43C2211yescharacteristic
51C4×D8×C43—21no—
52C43×#436C2211yescharacteristic
53C8×D4×C43C2211yescharacteristic
54C43×#418—21no—
55C2×#102×C43—21no—
56C43×#335C2211yescharacteristic, complemented
57C43×#334C2211yescharacteristic, complemented
58C43×#333C2211yescharacteristic, complemented
59C43×#332C2211yescharacteristic, complemented
60C43×#331C2211yescharacteristic
61C43×#331C2211yescharacteristic, complemented
62C43×Q8⋊C8C2211yescharacteristic, complemented
63C43×Q8⋊C8C2211yescharacteristic, complemented
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic, complemented
67C22×D4×C43—21no—
68C22×D4×C43—21no—
69C2×Q16×C43—21no—
70C2×SD16×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43D411yescharacteristic
75C2×SD16×C43D411yescharacteristic
76C2×D8×C43—21no—
77C2×D8×C43—21no—
78C2×D8×C43—41no—
79C2×M16×C43—21no—
80C22×C8×C43—21no—
81C4⋊Q8×C43C2311yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83#127×C43C2311yescharacteristic
84#127×C43C2311yescharacteristic
85#126×C43—41no—
86#125×C43—21no—
87#124×C43—21no—
88#124×C43—21no—
89#124×C43—21no—
90#123×C43—41no—
91C22⋊Q8×C43—21no—
92C22⋊Q8×C43—21no—
93C22⋊Q8×C43—41no—
94#121×C43—21no—
95#121×C43—21no—
96#120×C43—41no—
97C4×Q8×C43—21no—
98C4×Q8×C43C2311yescharacteristic
99C4×Q8×C43C2311yescharacteristic
100C4×D4×C43—21no—
101C4×D4×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43C2311yescharacteristic
104C4×D4×C43C2311yescharacteristic
105#117×C43—21no—
106C2×C4⋊C4×C43—21no—
107#107×C43—21no—
108#107×C43—21no—
109#106×C43—21no—
110#106×C43D411yescharacteristic
111#106×C43D411yescharacteristic
112C4⋊C8×C43—21no—
113C4⋊C8×C43—21no—
114C4⋊C8×C43C2311yescharacteristic
115C4⋊C8×C43C2311yescharacteristic
116C4⋊C8×C43C2311yescharacteristic
117C4⋊C8×C43C2311yescharacteristic
118#103×C43—21no—
119#103×C43—21no—
120#103×C43—41no—
121#103×C43D411yescharacteristic
122#103×C43D411yescharacteristic
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×C43—21no—
135#102×C43D411yescharacteristic
136#102×C43D411yescharacteristic
137C22⋊C8×C43—21no—
138C22⋊C8×C43—21no—
139C4×C8×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C24×C43—41no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×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—42no—
158C2×D4×C43—42no—
159C2×D4×C43—81no—
160C2×D4×C43—81no—
161C2×D4×C43C2×D411yescharacteristic
162C2×D4×C43C2×D411yescharacteristic
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—41no—
166C22×C4×C43—41no—
167Q16×C43—81no—
168SD16×C43—22no—
169SD16×C43—41no—
170SD16×C43—42no—
171SD16×C43—81no—
172SD16×C43—81no—
173SD16×C43—81no—
174D8×C43—42no—
175D8×C43—81no—
176D8×C43—82no—
177M16×C43—81no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—81no—
184C2×C8×C43C2×D411yescharacteristic
185C2×C8×C43C2×D411yescharacteristic
186C2×C8×C43C2×D411yescharacteristic
187C2×C8×C43C2×D411yescharacteristic
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—41no—
195C4⋊C4×C43—41no—
196C4⋊C4×C43—41no—
197C4⋊C4×C43C2×D411yescharacteristic
198C4⋊C4×C43C2×D411yescharacteristic
199C4⋊C4×C43C2×D411yescharacteristic
200C4⋊C4×C43C2×D411yescharacteristic
201C22⋊C4×C43—21no—
202C22⋊C4×C43—21no—
203C22⋊C4×C43—41no—
204C22⋊C4×C43—41no—
205C22⋊C4×C43—41no—
206C22⋊C4×C43—41no—
207C22⋊C4×C43—41no—
208C22⋊C4×C43—41no—
209C22⋊C4×C43—41no—
210C42×C43—21no—
211C42×C43—21no—
212C42×C43—41no—
213C42×C43C2411yescharacteristic
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—82no—
219C23×C43—82no—
220C23×C43—161no—
221Q8×C43—21no—
222Q8×C43—21no—
223Q8×C43—21no—
224Q8×C43—21no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—81no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—81no—
240D4×C43—81no—
241D4×C43—82no—
242D4×C43—82no—
243D4×C43#13512yes—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—161no—
257C2×C4×C43—161no—
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
261C8×C43—21no—
262C8×C43—21no—
263C8×C43—21no—
264C8×C43—21no—
265C8×C43—41no—
266C8×C43—41no—
267C8×C43—41no—
268C8×C43—41no—
269C8×C43—41no—
270#19825C4311yesmaximal, characteristic, direct product factor, Sylow
271C22×C43—22no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43—164no—
284C22×C43D4211yescharacteristic
285C4×C43—21no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43C2×#13511yescharacteristic
295C4×C43#57511yescharacteristic
296C4×C43#57611yescharacteristic
297C4×C43#57711yescharacteristic
298#3394C2×C4311yescharacteristic, complemented
299#3361C2×C4311yescharacteristic, complemented
300#3324C2×C4311yescharacteristic, complemented
301#3295C2×C4311yescharacteristic, complemented
302#1717C2×C4311yescharacteristic, complemented
303#1697C2×C4311yescharacteristic, complemented
304#1682C2×C4311yescharacteristic, complemented
305#1678C2×C4311yescharacteristic, complemented
306#1665C2×C4311yescharacteristic, complemented
307#1644C2×C4311yescharacteristic, complemented
308#1638C2×C4311yescharacteristic, complemented
309#1620C2×C4311yescharacteristic, complemented
310#1619C2×C4311yescharacteristic
311#1583C2×C4311yescharacteristic, complemented
312SD16⋊C8C2×C4311yescharacteristic, complemented
313C2×C43—42no—
314C2×C43—81no—
315C2×C43—161no—
316C2×C43—161no—
317C2×C43#326811yescharacteristic
318C2×C43#328211yescharacteristic
319C2×C43#328811yescharacteristic
320#559C22×C4311yescharacteristic, complemented
321#556C22×C4311yescharacteristic
322#554C22×C4311yescharacteristic
323D42C22×C4311yescharacteristic
324#495—21no—
325#493C22×C4311yescharacteristic
326#492C22×C4311yescharacteristic, complemented
327#488—21no—
328#487C22×C4311yescharacteristic, complemented
329#486C22×C4311yescharacteristic
330#486C22×C4311yescharacteristic
331#486C22×C4311yescharacteristic, complemented
332#482—21no—
333#481—21no—
334#478—21no—
335#477C22×C4311yescharacteristic, complemented
336#476C22×C4311yescharacteristic
337#474C22×C4311yescharacteristic
338#468—21no—
339#465—21no—
340#464—21no—
341#463—21no—
342#463—21no—
343#462C22×C4311yescharacteristic, complemented
344#460C22×C4311yescharacteristic
345#460C22×C4311yescharacteristic
346#459C22×C4311yescharacteristic
347#459C22×C4311yescharacteristic
348#450—21no—
349#450—21no—
350C8×Q8C22×C4311yescharacteristic, complemented
351C8×Q8C22×C4311yescharacteristic, complemented
352C4×SD16—21no—
353C4×SD16C22×C4311yescharacteristic
354C4×SD16C22×C4311yescharacteristic
355C4×D8—21no—
356#436C22×C4311yescharacteristic
357C8×D4C22×C4311yescharacteristic
358#418—21no—
359C2×#102—21no—
360#335C22×C4311yescharacteristic, complemented
361#334C22×C4311yescharacteristic, complemented
362#333C22×C4311yescharacteristic, complemented
363#332C22×C4311yescharacteristic, complemented
364#331C22×C4311yescharacteristic
365#331C22×C4311yescharacteristic, complemented
366Q8⋊C8C22×C4311yescharacteristic, complemented
367Q8⋊C8C22×C4311yescharacteristic, complemented
368D4⋊C8C22×C4311yescharacteristic
369D4⋊C8C22×C4311yescharacteristic
370#322C22×C4311yescharacteristic, complemented
371C43#1982511yescharacteristic, direct product factor, Sylow
372C22×D4—21no—
373C22×D4—21no—
374C2×Q16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16D4×C4311yescharacteristic
380C2×SD16D4×C4311yescharacteristic
381C2×D8—21no—
382C2×D8—21no—
383C2×D8—41no—
384C2×M16—21no—
385C22×C8—21no—
386C4⋊Q8C23×C4311yescharacteristic
387C4⋊Q8C23×C4311yescharacteristic
388#127C23×C4311yescharacteristic
389#127C23×C4311yescharacteristic
390#126—41no—
391#125—21no—
392#124—21no—
393#124—21no—
394#124—21no—
395#123—41no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—41no—
399#121—21no—
400#121—21no—
401#120—41no—
402C4×Q8—21no—
403C4×Q8C23×C4311yescharacteristic
404C4×Q8C23×C4311yescharacteristic
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4C23×C4311yescharacteristic
409C4×D4C23×C4311yescharacteristic
410#117—21no—
411C2×C4⋊C4—21no—
412#107—21no—
413#107—21no—
414#106—21no—
415#106D4×C4311yescharacteristic
416#106D4×C4311yescharacteristic
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8C23×C4311yescharacteristic
420C4⋊C8C23×C4311yescharacteristic
421C4⋊C8C23×C4311yescharacteristic
422C4⋊C8C23×C4311yescharacteristic
423#103—21no—
424#103—21no—
425#103—41no—
426#103D4×C4311yescharacteristic
427#103D4×C4311yescharacteristic
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
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#102D4×C4311yescharacteristic
441#102D4×C4311yescharacteristic
442C22⋊C8—21no—
443C22⋊C8—21no—
444C4×C8—21no—
445C4×C8—21no—
446C4×C8C23×C4311yescharacteristic
447C4×C8C23×C4311yescharacteristic
448C4×C8C23×C4311yescharacteristic
449C24—41no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8C2×D4×C4311yescharacteristic
453C2×Q8C2×D4×C4311yescharacteristic
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—81no—
465C2×D4—81no—
466C2×D4C2×D4×C4311yescharacteristic
467C2×D4C2×D4×C4311yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472Q16—81no—
473SD16—22no—
474SD16—41no—
475SD16—42no—
476SD16—81no—
477SD16—81no—
478SD16—81no—
479D8—42no—
480D8—81no—
481D8—82no—
482M16—81no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—81no—
489C2×C8C2×D4×C4311yescharacteristic
490C2×C8C2×D4×C4311yescharacteristic
491C2×C8C2×D4×C4311yescharacteristic
492C2×C8C2×D4×C4311yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4C2×D4×C4311yescharacteristic
503C4⋊C4C2×D4×C4311yescharacteristic
504C4⋊C4C2×D4×C4311yescharacteristic
505C4⋊C4C2×D4×C4311yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C42—21no—
516C42—21no—
517C42—41no—
518C42C24×C4311yescharacteristic
519C23—21no—
520C23—21no—
521C23—41no—
522C23—41no—
523C23—82no—
524C23—82no—
525C23—161no—
526Q8—21no—
527Q8—21no—
528Q8—21no—
529Q8—21no—
530Q8—41no—
531Q8—41no—
532Q8—81no—
533D4—21no—
534D4—21no—
535D4—21no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—81no—
545D4—81no—
546D4—82no—
547D4—82no—
548D4#135×C4312yes—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—161no—
562C2×C4—161no—
563C2×C4C22×D4×C4311yescharacteristic
564C2×C4C22×D4×C4311yescharacteristic
565C2×C4H(5,𝔽2)×C4311yescharacteristic
566C8—21no—
567C8—21no—
568C8—21no—
569C8—21no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8—41no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—164no—
588C22D42×C4311yescharacteristic
589C4—21no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—81no—
597C4—81no—
598C4C2×#135×C4311yescharacteristic
599C4C43×#57511yescharacteristic
600C4C43×#57611yescharacteristic
601C4C43×#57711yescharacteristic
602C2—42no—
603C2—81no—
604C2—161no—
605C2—161no—
606C2C43×#326811yescharacteristic
607C2C43×#328211yescharacteristic
608C2C43×#328811yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#1619C2
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×#3394C2semidirect
2. C43×#3361C2semidirect
3. C43×#3324C2semidirect
4. C43×#3295C2semidirect
5. C43×#1717C2semidirect
6. C43×#1697C2semidirect
7. C43×#1682C2semidirect
8. C43×#1678C2semidirect
9. C43×#1665C2semidirect
10. C43×#1644C2semidirect
11. C43×#1638C2semidirect
12. C43×#1620C2semidirect
14. C43×#1583C2semidirect
15. C43×SD16⋊C8C2semidirect
16. C43×#559C22semidirect
22. C43×#492C22semidirect
24. C43×#487C22semidirect
27. C43×#486C22semidirect
31. C43×#477C22semidirect
39. C43×#462C22semidirect
46. C8×Q8×C43C22semidirect
47. C8×Q8×C43C22semidirect
56. C43×#335C22semidirect
57. C43×#334C22semidirect
58. C43×#333C22semidirect
59. C43×#332C22semidirect
61. C43×#331C22semidirect
62. C43×Q8⋊C8C22semidirect
63. C43×Q8⋊C8C22semidirect
66. C43×#322C22semidirect
270. #19825C43direct (N × H)
298. #3394C2×C43semidirect
299. #3361C2×C43semidirect
300. #3324C2×C43semidirect
301. #3295C2×C43semidirect
302. #1717C2×C43semidirect
303. #1697C2×C43semidirect
304. #1682C2×C43semidirect
305. #1678C2×C43semidirect
306. #1665C2×C43semidirect
307. #1644C2×C43semidirect
308. #1638C2×C43semidirect
309. #1620C2×C43semidirect
311. #1583C2×C43semidirect
312. SD16⋊C8C2×C43semidirect
320. #559C22×C43semidirect
326. #492C22×C43semidirect
328. #487C22×C43semidirect
331. #486C22×C43semidirect
335. #477C22×C43semidirect
343. #462C22×C43semidirect
350. C8×Q8C22×C43semidirect
351. C8×Q8C22×C43semidirect
360. #335C22×C43semidirect
361. #334C22×C43semidirect
362. #333C22×C43semidirect
363. #332C22×C43semidirect
365. #331C22×C43semidirect
366. Q8⋊C8C22×C43semidirect
367. Q8⋊C8C22×C43semidirect
370. #322C22×C43semidirect
371. C43#19825direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33942
C43×#33612
C43×#33242
C43×#32952
C43×#17172
C43×#16972
C43×#16822
C43×#16782
C43×#16652
C43×#16442
C43×#16382
C43×#16202
C43×#16192
C43×#15832
C43×SD16⋊C82
#1982543