Finite Group Databasebeta

← C43×#19576 #24939593

Subgroups — C43×#19576 #24939593

Order 11008.

618 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3251C211yesmaximal, characteristic, complemented
2C43×#3212C211yesmaximal, characteristic, complemented
3C43×#3207C211yesmaximal, characteristic, complemented
4C43×#2994C211yesmaximal, characteristic, complemented
5C43×#1702C211yesmaximal, characteristic, complemented
6C43×#1699C211yesmaximal, characteristic, complemented
7C43×#1687C211yesmaximal, characteristic, complemented
8C43×#1686C211yesmaximal, characteristic, complemented
9C43×#1681C211yesmaximal, characteristic, complemented
10C43×#1680C211yesmaximal, characteristic, complemented
11C43×#1668C211yesmaximal, characteristic, complemented
12C43×#1665C211yesmaximal, characteristic, complemented
13C43×#1574C211yesmaximal, characteristic, complemented
14C43×#1547C211yesmaximal, characteristic, complemented
15C43×#1540C211yesmaximal, characteristic, complemented
16C43×#532C2211yescharacteristic
17C43×#532C2211yescharacteristic
18C43×#529C2211yescharacteristic
19C43×#495—21no—
20C43×#493C2211yescharacteristic
21C43×#492C2211yescharacteristic
22C43×#488—21no—
23C43×#487C2211yescharacteristic
24C43×#486C2211yescharacteristic
25C43×#478—21no—
26C43×#475C2211yescharacteristic
27C43×#474C2211yescharacteristic
28C43×#469—21no—
29C43×#468—21no—
30C43×#463—21no—
31C43×#463—21no—
32C43×#463—21no—
33C43×#462C2211yescharacteristic
34C43×#461C2211yescharacteristic
35C43×#460C2211yescharacteristic
36C43×#460C2211yescharacteristic
37C43×#459C2211yescharacteristic
38C43×#459C2211yescharacteristic
39C43×#452—21no—
40C43×#449—21no—
41C43×#449—21no—
42C43×#449—21no—
43C43×#446C2211yescharacteristic
44C8×Q8×C43C2211yescharacteristic
45C43×#436C2211yescharacteristic
46C43×#435—21no—
47C8×D4×C43—21no—
48C8×D4×C43C2211yescharacteristic
49C43×#433—21no—
50C43×#431C2211yescharacteristic
51C43×#431C2211yescharacteristic
52C43×#424—21no—
53C43×#423C2211yescharacteristic
54C2×C4⋊C8×C43C2211yescharacteristic
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×Q16×C43—21no—
70C2×SD16×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—21no—
75C2×D8×C43—21no—
76C2×D8×C43—21no—
77C2×D8×C43—21no—
78C2×D8×C43—21no—
79C2×M16×C43—21no—
80C2×M16×C43—21no—
81C22×C8×C43—21no—
82C22×C8×C43—21no—
83C4⋊Q8×C43C2311yescharacteristic
84C4⋊Q8×C43C2311yescharacteristic
85#127×C43C2311yescharacteristic
86#127×C43C2311yescharacteristic
87#126×C43—21no—
88#125×C43D411yescharacteristic
89#124×C43—21no—
90#124×C43—21no—
91#124×C43D411yescharacteristic
92#123×C43—21no—
93C22⋊Q8×C43D411yescharacteristic
94#121×C43—21no—
95#121×C43—21no—
96#121×C43—21no—
97#121×C43—21no—
98#121×C43D411yescharacteristic
99C4×Q8×C43C2311yescharacteristic
100C4×D4×C43—21no—
101C4×D4×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43C2311yescharacteristic
106#117×C43—21no—
107C2×C42×C43C2311yescharacteristic
108#107×C43—21no—
109#106×C43—21no—
110C4⋊C8×C43—21no—
111C4⋊C8×C43—21no—
112C4⋊C8×C43—21no—
113C4⋊C8×C43—21no—
114C4⋊C8×C43D411yescharacteristic
115C4⋊C8×C43D411yescharacteristic
116C4⋊C8×C43C2311yescharacteristic
117C4⋊C8×C43C2311yescharacteristic
118C4⋊C8×C43C2311yescharacteristic
119C4⋊C8×C43C2311yescharacteristic
120C4⋊C8×C43C2311yescharacteristic
121C4⋊C8×C43C2311yescharacteristic
122#103×C43—21no—
123#103×C43—21no—
124#103×C43—21no—
125#103×C43—21no—
126#103×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—
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43D411yescharacteristic
138C22⋊C8×C43D411yescharacteristic
139#97×C43—21no—
140C4×C8×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×C43C2×D411yescharacteristic
151C2×D4×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—41no—
159C2×D4×C43—41no—
160C2×D4×C43C2×D411yescharacteristic
161C22×C4×C43—21no—
162C22×C4×C43—41no—
163C22×C4×C43—41no—
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43#4111yescharacteristic
167Q16×C43—81no—
168SD16×C43—81no—
169SD16×C43—81no—
170SD16×C43—81no—
171SD16×C43—81no—
172SD16×C43—81no—
173D8×C43—81no—
174D8×C43—81no—
175D8×C43—81no—
176D8×C43—81no—
177M16×C43—81no—
178M16×C43—81no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—81no—
186C2×C8×C43—81no—
187C2×C8×C43C2×D411yescharacteristic
188C2×C8×C43C2×D411yescharacteristic
189C2×C8×C43C2×D411yescharacteristic
190C2×C8×C43C2×D411yescharacteristic
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
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×C43C2×D411yescharacteristic
200C4⋊C4×C43C2×D411yescharacteristic
201C22⋊C4×C43—21no—
202C22⋊C4×C43—21no—
203C22⋊C4×C43—21no—
204C22⋊C4×C43—21no—
205C22⋊C4×C43—21no—
206C22⋊C4×C43—41no—
207C22⋊C4×C43—41no—
208C22⋊C4×C43—41no—
209C22⋊C4×C43—41no—
210C42×C43—21no—
211C42×C43C2×D411yescharacteristic
212C42×C43C2×D411yescharacteristic
213C42×C43#4111yescharacteristic
214C42×C43C2411yescharacteristic
215C23×C43—21no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43#12111yescharacteristic
219Q8×C43—21no—
220Q8×C43—21no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—41no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43—42no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—81no—
237D4×C43—81no—
238D4×C43—82no—
239D4×C43—82no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—82no—
253C2×C4×C43—82no—
254C2×C4×C43#12111yescharacteristic
255C2×C4×C43#12111yescharacteristic
256C2×C4×C43#12111yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C8×C43—21no—
261C8×C43—21no—
262C8×C43—21no—
263C8×C43—21no—
264C8×C43—41no—
265C8×C43—41no—
266C8×C43—41no—
267C8×C43—41no—
268C8×C43—41no—
269C8×C43—41no—
270#19576C4311yesmaximal, characteristic, direct product factor, Sylow
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—21no—
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×C43C2×#12111yescharacteristic
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43#57611yescharacteristic
294C4×C43#57611yescharacteristic
295C4×C43#57711yescharacteristic
296C4×C43#57711yescharacteristic
297#3251C2×C4311yescharacteristic, complemented
298#3212C2×C4311yescharacteristic, complemented
299#3207C2×C4311yescharacteristic, complemented
300#2994C2×C4311yescharacteristic, complemented
301#1702C2×C4311yescharacteristic, complemented
302#1699C2×C4311yescharacteristic, complemented
303#1687C2×C4311yescharacteristic, complemented
304#1686C2×C4311yescharacteristic, complemented
305#1681C2×C4311yescharacteristic, complemented
306#1680C2×C4311yescharacteristic, complemented
307#1668C2×C4311yescharacteristic, complemented
308#1665C2×C4311yescharacteristic, complemented
309#1574C2×C4311yescharacteristic, complemented
310#1547C2×C4311yescharacteristic, complemented
311#1540C2×C4311yescharacteristic, complemented
312C2×C43—41no—
313C2×C43—81no—
314C2×C43—161no—
315C2×C43—161no—
316C2×C43#304511yescharacteristic
317C2×C43#306211yescharacteristic
318C2×C43#306711yescharacteristic
319#532C22×C4311yescharacteristic
320#532C22×C4311yescharacteristic
321#529C22×C4311yescharacteristic
322#495—21no—
323#493C22×C4311yescharacteristic
324#492C22×C4311yescharacteristic
325#488—21no—
326#487C22×C4311yescharacteristic
327#486C22×C4311yescharacteristic
328#478—21no—
329#475C22×C4311yescharacteristic
330#474C22×C4311yescharacteristic
331#469—21no—
332#468—21no—
333#463—21no—
334#463—21no—
335#463—21no—
336#462C22×C4311yescharacteristic
337#461C22×C4311yescharacteristic
338#460C22×C4311yescharacteristic
339#460C22×C4311yescharacteristic
340#459C22×C4311yescharacteristic
341#459C22×C4311yescharacteristic
342#452—21no—
343#449—21no—
344#449—21no—
345#449—21no—
346#446C22×C4311yescharacteristic
347C8×Q8C22×C4311yescharacteristic
348#436C22×C4311yescharacteristic
349#435—21no—
350C8×D4—21no—
351C8×D4C22×C4311yescharacteristic
352#433—21no—
353#431C22×C4311yescharacteristic
354#431C22×C4311yescharacteristic
355#424—21no—
356#423C22×C4311yescharacteristic
357C2×C4⋊C8C22×C4311yescharacteristic
358#335C22×C4311yescharacteristic
359#335C22×C4311yescharacteristic
360#334C22×C4311yescharacteristic
361#334C22×C4311yescharacteristic
362#332C22×C4311yescharacteristic
363#332C22×C4311yescharacteristic
364#332C22×C4311yescharacteristic
365#332C22×C4311yescharacteristic
366#331C22×C4311yescharacteristic
367#331C22×C4311yescharacteristic
368#331C22×C4311yescharacteristic
369#331C22×C4311yescharacteristic
370C43#1957611yescharacteristic, direct product factor, Sylow
371C2×#41—21no—
372C2×#41—21no—
373C2×Q16—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×D8—21no—
380C2×D8—21no—
381C2×D8—21no—
382C2×D8—21no—
383C2×M16—21no—
384C2×M16—21no—
385C22×C8—21no—
386C22×C8—21no—
387C4⋊Q8C23×C4311yescharacteristic
388C4⋊Q8C23×C4311yescharacteristic
389#127C23×C4311yescharacteristic
390#127C23×C4311yescharacteristic
391#126—21no—
392#125D4×C4311yescharacteristic
393#124—21no—
394#124—21no—
395#124D4×C4311yescharacteristic
396#123—21no—
397C22⋊Q8D4×C4311yescharacteristic
398#121—21no—
399#121—21no—
400#121—21no—
401#121—21no—
402#121D4×C4311yescharacteristic
403C4×Q8C23×C4311yescharacteristic
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4—21no—
409C4×D4C23×C4311yescharacteristic
410#117—21no—
411C2×C42C23×C4311yescharacteristic
412#107—21no—
413#106—21no—
414C4⋊C8—21no—
415C4⋊C8—21no—
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8D4×C4311yescharacteristic
419C4⋊C8D4×C4311yescharacteristic
420C4⋊C8C23×C4311yescharacteristic
421C4⋊C8C23×C4311yescharacteristic
422C4⋊C8C23×C4311yescharacteristic
423C4⋊C8C23×C4311yescharacteristic
424C4⋊C8C23×C4311yescharacteristic
425C4⋊C8C23×C4311yescharacteristic
426#103—21no—
427#103—21no—
428#103—21no—
429#103—21no—
430#103—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438C22⋊C8—21no—
439C22⋊C8—21no—
440C22⋊C8—21no—
441C22⋊C8D4×C4311yescharacteristic
442C22⋊C8D4×C4311yescharacteristic
443#97—21no—
444C4×C8—21no—
445C4×C8—21no—
446C4×C8C23×C4311yescharacteristic
447C4×C8C23×C4311yescharacteristic
448#41—81no—
449#41—81no—
450#41—81no—
451#41—81no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8C2×D4×C4311yescharacteristic
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4C2×D4×C4311yescharacteristic
465C22×C4—21no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4C2×D4×C4311yescharacteristic
469C22×C4C2×D4×C4311yescharacteristic
470C22×C4#41×C4311yescharacteristic
471Q16—81no—
472SD16—81no—
473SD16—81no—
474SD16—81no—
475SD16—81no—
476SD16—81no—
477D8—81no—
478D8—81no—
479D8—81no—
480D8—81no—
481M16—81no—
482M16—81no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—81no—
490C2×C8—81no—
491C2×C8C2×D4×C4311yescharacteristic
492C2×C8C2×D4×C4311yescharacteristic
493C2×C8C2×D4×C4311yescharacteristic
494C2×C8C2×D4×C4311yescharacteristic
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4C2×D4×C4311yescharacteristic
504C4⋊C4C2×D4×C4311yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C42—21no—
515C42C2×D4×C4311yescharacteristic
516C42C2×D4×C4311yescharacteristic
517C42#41×C4311yescharacteristic
518C42C24×C4311yescharacteristic
519C23—21no—
520C23—41no—
521C23—41no—
522C23#121×C4311yescharacteristic
523Q8—21no—
524Q8—21no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529D4—21no—
530D4—21no—
531D4—42no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—81no—
541D4—81no—
542D4—82no—
543D4—82no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—82no—
557C2×C4—82no—
558C2×C4#121×C4311yescharacteristic
559C2×C4#121×C4311yescharacteristic
560C2×C4#121×C4311yescharacteristic
561C2×C4C22×D4×C4311yescharacteristic
562C2×C4C22×D4×C4311yescharacteristic
563C2×C4C2×#41×C4311yescharacteristic
564C8—21no—
565C8—21no—
566C8—21no—
567C8—21no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—41no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22C2×#121×C4311yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—81no—
595C4—81no—
596C4C43×#57611yescharacteristic
597C4C43×#57611yescharacteristic
598C4C43×#57711yescharacteristic
599C4C43×#57711yescharacteristic
600C2—41no—
601C2—81no—
602C2—161no—
603C2—161no—
604C2C43×#304511yescharacteristic
605C2C43×#306211yescharacteristic
606C2C43×#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×#3251C2semidirect
2. C43×#3212C2semidirect
3. C43×#3207C2semidirect
4. C43×#2994C2semidirect
5. C43×#1702C2semidirect
6. C43×#1699C2semidirect
7. C43×#1687C2semidirect
8. C43×#1686C2semidirect
9. C43×#1681C2semidirect
10. C43×#1680C2semidirect
11. C43×#1668C2semidirect
12. C43×#1665C2semidirect
13. C43×#1574C2semidirect
14. C43×#1547C2semidirect
15. C43×#1540C2semidirect
270. #19576C43direct (N × H)
297. #3251C2×C43semidirect
298. #3212C2×C43semidirect
299. #3207C2×C43semidirect
300. #2994C2×C43semidirect
301. #1702C2×C43semidirect
302. #1699C2×C43semidirect
303. #1687C2×C43semidirect
304. #1686C2×C43semidirect
305. #1681C2×C43semidirect
306. #1680C2×C43semidirect
307. #1668C2×C43semidirect
308. #1665C2×C43semidirect
309. #1574C2×C43semidirect
310. #1547C2×C43semidirect
311. #1540C2×C43semidirect
370. C43#19576direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32512
C43×#32122
C43×#32072
C43×#29942
C43×#17022
C43×#16992
C43×#16872
C43×#16862
C43×#16812
C43×#16802
C43×#16682
C43×#16652
C43×#15742
C43×#15472
C43×#15402
#1957643