Finite Group Databasebeta

← C43×#19563 #24939580

Subgroups — C43×#19563 #24939580

Order 11008.

608 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3246C211yesmaximal, characteristic, complemented
2C43×#3228C211yesmaximal, characteristic, complemented
3C43×#3214C211yesmaximal, characteristic
4C43×#2979C211yesmaximal, characteristic, complemented
5C43×#1701C211yesmaximal, characteristic, complemented
6C43×#1697C211yesmaximal, characteristic, complemented
7C43×#1693C211yesmaximal, characteristic, complemented
8C43×#1691C211yesmaximal, characteristic, complemented
9C43×#1681C211yesmaximal, characteristic, complemented
10C43×#1677C211yesmaximal, characteristic, complemented
11C43×#1673C211yesmaximal, characteristic, complemented
12C43×#1671C211yesmaximal, characteristic, complemented
13C43×#1573C211yesmaximal, characteristic, complemented
14C43×#1554C211yesmaximal, characteristic, complemented
15C43×#1540C211yesmaximal, characteristic, complemented
16C43×#533C2211yescharacteristic
17C43×#532C2211yescharacteristic
18C43×#532C2211yescharacteristic
19C43×#500C2211yescharacteristic
20C43×#498C2211yescharacteristic
21C43×#496—21no—
22C43×#489—21no—
23C43×#486C2211yescharacteristic
24C43×#486C2211yescharacteristic
25C43×#482—21no—
26C43×#482—21no—
27C43×#478—21no—
28C43×#478—21no—
29C43×#476C2211yescharacteristic
30C43×#476C2211yescharacteristic
31C43×#475—21no—
32C43×#465—21no—
33C43×#465—21no—
34C43×#461C2211yescharacteristic
35C43×#461C2211yescharacteristic
36C43×#461C2211yescharacteristic
37C43×#461C2211yescharacteristic
38C43×#460—21no—
39C43×#459C2211yescharacteristic
40C43×#459C2211yescharacteristic
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×#333C2211yescharacteristic
60C43×#333C2211yescharacteristic
61C43×#332C2211yescharacteristic
62C43×#332C2211yescharacteristic
63C43×#332C2211yescharacteristic
64C43×#332C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#41×C43—21no—
68C2×#41×C43—21no—
69C2×SD16×C43—21no—
70C2×SD16×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×D8×C43—21no—
74C2×D8×C43—21no—
75C2×M16×C43—21no—
76C2×M16×C43—21no—
77C22×C8×C43—21no—
78C22×C8×C43—21no—
79C22×C8×C43—21no—
80C4⋊Q8×C43D411yescharacteristic
81C4⋊Q8×C43C2311yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83C4⋊Q8×C43C2311yescharacteristic
84#127×C43D411yescharacteristic
85#127×C43C2311yescharacteristic
86#125×C43—21no—
87#124×C43—21no—
88#124×C43—21no—
89C22⋊Q8×C43—21no—
90C22⋊Q8×C43—21no—
91#121×C43—21no—
92#121×C43—21no—
93#121×C43—21no—
94#121×C43D411yescharacteristic
95#121×C43D411yescharacteristic
96C4×Q8×C43—21no—
97C4×Q8×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43—21no—
100C4×D4×C43—21no—
101C4×D4×C43C2311yescharacteristic
102C4×D4×C43C2311yescharacteristic
103#117×C43—21no—
104C2×C42×C43C2311yescharacteristic
105#107×C43—21no—
106#107×C43—21no—
107#106×C43—21no—
108#106×C43—21no—
109#106×C43—21no—
110#106×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—
148C2×Q8×C43—21no—
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—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—41no—
160C2×D4×C43C2×D411yescharacteristic
161C2×D4×C43C2×D411yescharacteristic
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—41no—
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43#4111yescharacteristic
168SD16×C43—81no—
169SD16×C43—81no—
170SD16×C43—81no—
171SD16×C43—81no—
172D8×C43—81no—
173D8×C43—81no—
174M16×C43—81no—
175M16×C43—81no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—81no—
183C2×C8×C43—81no—
184C2×C8×C43—81no—
185C2×C8×C43C2×D411yescharacteristic
186C2×C8×C43C2×D411yescharacteristic
187C2×C8×C43C2×D411yescharacteristic
188C2×C8×C43C2×D411yescharacteristic
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—41no—
197C4⋊C4×C43—41no—
198C4⋊C4×C43C2×D411yescharacteristic
199C4⋊C4×C43C2×D411yescharacteristic
200C22⋊C4×C43—21no—
201C22⋊C4×C43—21no—
202C22⋊C4×C43—21no—
203C22⋊C4×C43—21no—
204C22⋊C4×C43—41no—
205C22⋊C4×C43—41no—
206C22⋊C4×C43—41no—
207C42×C43—41no—
208C42×C43C2×D411yescharacteristic
209C42×C43C2×D411yescharacteristic
210C42×C43#4111yescharacteristic
211C42×C43C2411yescharacteristic
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—41no—
215C23×C43#12111yescharacteristic
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—81no—
221Q8×C43—81no—
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—42no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—81no—
232D4×C43—81no—
233D4×C43—81no—
234D4×C43—81no—
235D4×C43—82no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—82no—
251C2×C4×C43#12111yescharacteristic
252C2×C4×C43#12111yescharacteristic
253C2×C4×C43#12111yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—21no—
261C8×C43—41no—
262C8×C43—41no—
263C8×C43—41no—
264C8×C43—41no—
265C8×C43—41no—
266C8×C43—41no—
267#19563C4311yesmaximal, characteristic, direct product factor, Sylow
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—41no—
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×C43C2×#12111yescharacteristic
281C4×C43—21no—
282C4×C43—21no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43—81no—
290C4×C43#57611yescharacteristic
291C4×C43#57711yescharacteristic
292C4×C43#57711yescharacteristic
293C4×C43#57711yescharacteristic
294#3246C2×C4311yescharacteristic, complemented
295#3228C2×C4311yescharacteristic, complemented
296#3214C2×C4311yescharacteristic
297#2979C2×C4311yescharacteristic, complemented
298#1701C2×C4311yescharacteristic, complemented
299#1697C2×C4311yescharacteristic, complemented
300#1693C2×C4311yescharacteristic, complemented
301#1691C2×C4311yescharacteristic, complemented
302#1681C2×C4311yescharacteristic, complemented
303#1677C2×C4311yescharacteristic, complemented
304#1673C2×C4311yescharacteristic, complemented
305#1671C2×C4311yescharacteristic, complemented
306#1573C2×C4311yescharacteristic, complemented
307#1554C2×C4311yescharacteristic, complemented
308#1540C2×C4311yescharacteristic, complemented
309C2×C43—41no—
310C2×C43—81no—
311C2×C43—81no—
312C2×C43—161no—
313C2×C43#304211yescharacteristic
314C2×C43#306211yescharacteristic
315C2×C43#306711yescharacteristic
316#533C22×C4311yescharacteristic
317#532C22×C4311yescharacteristic
318#532C22×C4311yescharacteristic
319#500C22×C4311yescharacteristic
320#498C22×C4311yescharacteristic
321#496—21no—
322#489—21no—
323#486C22×C4311yescharacteristic
324#486C22×C4311yescharacteristic
325#482—21no—
326#482—21no—
327#478—21no—
328#478—21no—
329#476C22×C4311yescharacteristic
330#476C22×C4311yescharacteristic
331#475—21no—
332#465—21no—
333#465—21no—
334#461C22×C4311yescharacteristic
335#461C22×C4311yescharacteristic
336#461C22×C4311yescharacteristic
337#461C22×C4311yescharacteristic
338#460—21no—
339#459C22×C4311yescharacteristic
340#459C22×C4311yescharacteristic
341#449—21no—
342#449—21no—
343#436—21no—
344#436C22×C4311yescharacteristic
345#436C22×C4311yescharacteristic
346C8×D4—21no—
347C8×D4C22×C4311yescharacteristic
348C8×D4C22×C4311yescharacteristic
349#432C22×C4311yescharacteristic
350#431C22×C4311yescharacteristic
351#431C22×C4311yescharacteristic
352C2×C4⋊C8C22×C4311yescharacteristic
353#408—21no—
354#408—21no—
355#335C22×C4311yescharacteristic
356#335C22×C4311yescharacteristic
357#334C22×C4311yescharacteristic
358#334C22×C4311yescharacteristic
359#333C22×C4311yescharacteristic
360#333C22×C4311yescharacteristic
361#332C22×C4311yescharacteristic
362#332C22×C4311yescharacteristic
363#332C22×C4311yescharacteristic
364#332C22×C4311yescharacteristic
365#331C22×C4311yescharacteristic
366#331C22×C4311yescharacteristic
367C43#1956311yescharacteristic, direct product factor, Sylow
368C2×#41—21no—
369C2×#41—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×D8—21no—
375C2×D8—21no—
376C2×M16—21no—
377C2×M16—21no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—21no—
381C4⋊Q8D4×C4311yescharacteristic
382C4⋊Q8C23×C4311yescharacteristic
383C4⋊Q8C23×C4311yescharacteristic
384C4⋊Q8C23×C4311yescharacteristic
385#127D4×C4311yescharacteristic
386#127C23×C4311yescharacteristic
387#125—21no—
388#124—21no—
389#124—21no—
390C22⋊Q8—21no—
391C22⋊Q8—21no—
392#121—21no—
393#121—21no—
394#121—21no—
395#121D4×C4311yescharacteristic
396#121D4×C4311yescharacteristic
397C4×Q8—21no—
398C4×Q8—21no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4C23×C4311yescharacteristic
403C4×D4C23×C4311yescharacteristic
404#117—21no—
405C2×C42C23×C4311yescharacteristic
406#107—21no—
407#107—21no—
408#106—21no—
409#106—21no—
410#106—21no—
411#106—21no—
412C4⋊C8—21no—
413C4⋊C8D4×C4311yescharacteristic
414C4⋊C8D4×C4311yescharacteristic
415C4⋊C8C23×C4311yescharacteristic
416C4⋊C8C23×C4311yescharacteristic
417C4⋊C8C23×C4311yescharacteristic
418C4⋊C8C23×C4311yescharacteristic
419C4⋊C8C23×C4311yescharacteristic
420C4⋊C8C23×C4311yescharacteristic
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433C22⋊C8—21no—
434C22⋊C8—21no—
435C22⋊C8—21no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8D4×C4311yescharacteristic
440C22⋊C8D4×C4311yescharacteristic
441#97—21no—
442C4×C8—21no—
443C4×C8C23×C4311yescharacteristic
444C4×C8C23×C4311yescharacteristic
445#41—81no—
446#41—81no—
447#41—81no—
448#41—81no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—41no—
461C2×D4C2×D4×C4311yescharacteristic
462C2×D4C2×D4×C4311yescharacteristic
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4C2×D4×C4311yescharacteristic
467C22×C4C2×D4×C4311yescharacteristic
468C22×C4#41×C4311yescharacteristic
469SD16—81no—
470SD16—81no—
471SD16—81no—
472SD16—81no—
473D8—81no—
474D8—81no—
475M16—81no—
476M16—81no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—81no—
484C2×C8—81no—
485C2×C8—81no—
486C2×C8C2×D4×C4311yescharacteristic
487C2×C8C2×D4×C4311yescharacteristic
488C2×C8C2×D4×C4311yescharacteristic
489C2×C8C2×D4×C4311yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4C2×D4×C4311yescharacteristic
500C4⋊C4C2×D4×C4311yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C42—41no—
509C42C2×D4×C4311yescharacteristic
510C42C2×D4×C4311yescharacteristic
511C42#41×C4311yescharacteristic
512C42C24×C4311yescharacteristic
513C23—21no—
514C23—21no—
515C23—41no—
516C23#121×C4311yescharacteristic
517Q8—41no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—81no—
522Q8—81no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—42no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—81no—
533D4—81no—
534D4—81no—
535D4—81no—
536D4—82no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—82no—
552C2×C4#121×C4311yescharacteristic
553C2×C4#121×C4311yescharacteristic
554C2×C4#121×C4311yescharacteristic
555C2×C4C22×D4×C4311yescharacteristic
556C2×C4C22×D4×C4311yescharacteristic
557C2×C4C2×#41×C4311yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—41no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22C2×#121×C4311yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4C43×#57611yescharacteristic
591C4C43×#57711yescharacteristic
592C4C43×#57711yescharacteristic
593C4C43×#57711yescharacteristic
594C2—41no—
595C2—81no—
596C2—81no—
597C2—161no—
598C2C43×#304211yescharacteristic
599C2C43×#306211yescharacteristic
600C2C43×#306711yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3214C2
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×#3246C2semidirect
2. C43×#3228C2semidirect
4. C43×#2979C2semidirect
5. C43×#1701C2semidirect
6. C43×#1697C2semidirect
7. C43×#1693C2semidirect
8. C43×#1691C2semidirect
9. C43×#1681C2semidirect
10. C43×#1677C2semidirect
11. C43×#1673C2semidirect
12. C43×#1671C2semidirect
13. C43×#1573C2semidirect
14. C43×#1554C2semidirect
15. C43×#1540C2semidirect
267. #19563C43direct (N × H)
294. #3246C2×C43semidirect
295. #3228C2×C43semidirect
297. #2979C2×C43semidirect
298. #1701C2×C43semidirect
299. #1697C2×C43semidirect
300. #1693C2×C43semidirect
301. #1691C2×C43semidirect
302. #1681C2×C43semidirect
303. #1677C2×C43semidirect
304. #1673C2×C43semidirect
305. #1671C2×C43semidirect
306. #1573C2×C43semidirect
307. #1554C2×C43semidirect
308. #1540C2×C43semidirect
367. C43#19563direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32462
C43×#32282
C43×#32142
C43×#29792
C43×#17012
C43×#16972
C43×#16932
C43×#16912
C43×#16812
C43×#16772
C43×#16732
C43×#16712
C43×#15732
C43×#15542
C43×#15402
#1956343