Finite Group Databasebeta

← C43×#20256 #24940273

Subgroups — C43×#20256 #24940273

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3399C211yesmaximal, characteristic, complemented
2C43×#3399C211yesmaximal, characteristic, complemented
3C43×#3332C211yesmaximal, characteristic, complemented
4C43×#3284C211yesmaximal, characteristic, complemented
5C43×#1721C211yesmaximal, characteristic, complemented
6C43×#1702C211yesmaximal, characteristic, complemented
7C43×#1687C211yesmaximal, characteristic, complemented
8C43×#1686C211yesmaximal, characteristic, complemented
9C43×#1667C211yesmaximal, characteristic, complemented
10C43×#1640C211yesmaximal, characteristic, complemented
11C43×#1625C211yesmaximal, characteristic, complemented
12C43×#1621C211yesmaximal, characteristic, complemented
13C43×#1621C211yesmaximal, characteristic, complemented
14C43×#1592C211yesmaximal, characteristic, complemented
15C43×#1582C211yesmaximal, characteristic, complemented
16C2×#135×C43—21no—
17C43×#559C2211yescharacteristic
18C43×#550C2211yescharacteristic
19C43×#550C2211yescharacteristic
20C43×#547C2211yescharacteristic
21C43×#496—21no—
22C43×#496—21no—
23C43×#493C2211yescharacteristic
24C43×#493C2211yescharacteristic
25C43×#493C2211yescharacteristic
26C43×#492C2211yescharacteristic
27C43×#486C2211yescharacteristic
28C43×#486C2211yescharacteristic
29C43×#481—21no—
30C43×#475C2211yescharacteristic
31C43×#469—21no—
32C43×#465—21no—
33C43×#463—21no—
34C43×#463—21no—
35C43×#462C2211yescharacteristic
36C43×#460C2211yescharacteristic
37C43×#460C2211yescharacteristic
38C43×#459—21no—
39C43×#459—21no—
40C43×#459C2211yescharacteristic
41C43×#459C2211yescharacteristic
42C43×#459C2211yescharacteristic
43C43×#459C2211yescharacteristic
44C43×#452—21no—
45C43×#449—21no—
46C43×#449—21no—
47C43×#446C2211yescharacteristic
48C43×#446C2211yescharacteristic
49C43×#442—21no—
50C43×#442—21no—
51C4×SD16×C43C2211yescharacteristic
52C4×SD16×C43C2211yescharacteristic
53C43×#436C2211yescharacteristic
54C8×D4×C43C2211yescharacteristic
55C43×#417—21no—
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#332C2211yescharacteristic
59C43×#331C2211yescharacteristic
60C43×#331C2211yescharacteristic
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#41×C43—21no—
68C2×#41×C43—21no—
69C2×#41×C43—21no—
70#135×C43—44no—
71C2×Q16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—21no—
75C2×SD16×C43—21no—
76C2×SD16×C43D411yescharacteristic
77C2×SD16×C43D411yescharacteristic
78C2×D8×C43—21no—
79C2×D8×C43—21no—
80C2×D8×C43—21no—
81C2×D8×C43—21no—
82C2×D8×C43—21no—
83C2×D8×C43—21no—
84C2×D8×C43—21no—
85C2×D8×C43—21no—
86C2×D8×C43—41no—
87C2×M16×C43—21no—
88C22×C8×C43—21no—
89C4⋊Q8×C43C2311yescharacteristic
90#127×C43—21no—
91#127×C43—21no—
92#127×C43C2311yescharacteristic
93#127×C43C2311yescharacteristic
94#127×C43C2311yescharacteristic
95#124×C43—21no—
96#124×C43—21no—
97#123×C43—41no—
98#123×C43—41no—
99C22⋊Q8×C43—21no—
100#121×C43—21no—
101#121×C43—21no—
102#121×C43—21no—
103#121×C43—41no—
104#121×C43—41no—
105C4×Q8×C43C2311yescharacteristic
106C4×Q8×C43C2311yescharacteristic
107C4×D4×C43—21no—
108C4×D4×C43—21no—
109C4×D4×C43—21no—
110C4×D4×C43—21no—
111C4×D4×C43C2311yescharacteristic
112C4×D4×C43C2311yescharacteristic
113C2×C4⋊C4×C43—21no—
114#106×C43—21no—
115#106×C43D411yescharacteristic
116#106×C43D411yescharacteristic
117C4⋊C8×C43—21no—
118C4⋊C8×C43—21no—
119C4⋊C8×C43C2311yescharacteristic
120C4⋊C8×C43C2311yescharacteristic
121C4⋊C8×C43C2311yescharacteristic
122C4⋊C8×C43C2311yescharacteristic
123#103×C43—21no—
124#103×C43—21no—
125#103×C43D411yescharacteristic
126#103×C43D411yescharacteristic
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×C43—41no—
136#102×C43D411yescharacteristic
137#102×C43D411yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140#97×C43—21no—
141#97×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145#41×C43—42no—
146#41×C43—42no—
147#41×C43—42no—
148#41×C43—81no—
149#41×C43—81no—
150#41×C43—81no—
151C2×Q8×C43—21no—
152C2×Q8×C43C2×D411yescharacteristic
153C2×Q8×C43C2×D411yescharacteristic
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×C43—41no—
166C2×D4×C43—41no—
167C2×D4×C43—41no—
168C2×D4×C43C2×D411yescharacteristic
169C2×D4×C43C2×D411yescharacteristic
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—41no—
173C22×C4×C43—41no—
174C22×C4×C43—41no—
175C22×C4×C43—41no—
176Q16×C43—42no—
177SD16×C43—22no—
178SD16×C43—41no—
179SD16×C43—42no—
180SD16×C43—81no—
181SD16×C43—81no—
182SD16×C43—81no—
183D8×C43—42no—
184D8×C43—42no—
185D8×C43—42no—
186D8×C43—81no—
187D8×C43—81no—
188D8×C43—81no—
189D8×C43—81no—
190D8×C43—81no—
191D8×C43—82no—
192M16×C43—81no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—42no—
199C2×C8×C43C2×D411yescharacteristic
200C2×C8×C43C2×D411yescharacteristic
201C2×C8×C43C2×D411yescharacteristic
202C2×C8×C43C2×D411yescharacteristic
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—41no—
208C4⋊C4×C43C2×D411yescharacteristic
209C4⋊C4×C43C2×D411yescharacteristic
210C4⋊C4×C43C2×D411yescharacteristic
211C4⋊C4×C43C2×D411yescharacteristic
212C22⋊C4×C43—21no—
213C22⋊C4×C43—21no—
214C22⋊C4×C43—41no—
215C22⋊C4×C43—41no—
216C22⋊C4×C43—41no—
217C22⋊C4×C43—41no—
218C22⋊C4×C43—41no—
219C22⋊C4×C43—41no—
220C42×C43—21no—
221C42×C43—21no—
222C42×C43C2411yescharacteristic
223C23×C43—21no—
224C23×C43—21no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228Q8×C43—21no—
229Q8×C43—21no—
230Q8×C43—21no—
231Q8×C43—21no—
232Q8×C43—41no—
233Q8×C43—41no—
234D4×C43—21no—
235D4×C43—21no—
236D4×C43—21no—
237D4×C43—21no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—41no—
245D4×C43—41no—
246D4×C43—41no—
247D4×C43—41no—
248D4×C43—41no—
249D4×C43—41no—
250D4×C43—81no—
251D4×C43—81no—
252D4×C43—81no—
253D4×C43—82no—
254D4×C43—82no—
255D4×C43—82no—
256D4×C43—161no—
257D4×C43—161no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—82no—
270C2×C4×C43—82no—
271C2×C4×C43—82no—
272C2×C4×C43—161no—
273C2×C4×C43C22×D411yescharacteristic
274C2×C4×C43C22×D411yescharacteristic
275C2×C4×C43H(5,𝔽2)11yescharacteristic
276C8×C43—21no—
277C8×C43—21no—
278C8×C43—21no—
279C8×C43—41no—
280C8×C43—41no—
281C8×C43—41no—
282C8×C43—41no—
283C8×C43—41no—
284C8×C43AGL(1,ℤ/8)12yes—
285#20256C4311yesmaximal, characteristic, direct product factor, Sylow
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43D4211yescharacteristic
302C4×C43—21no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—41no—
307C4×C43—41no—
308C4×C43—41no—
309C4×C43—81no—
310C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
311C4×C43#57511yescharacteristic
312C4×C43#57611yescharacteristic
313C4×C43#57611yescharacteristic
314#3399C2×C4311yescharacteristic, complemented
315#3399C2×C4311yescharacteristic, complemented
316#3332C2×C4311yescharacteristic, complemented
317#3284C2×C4311yescharacteristic, complemented
318#1721C2×C4311yescharacteristic, complemented
319#1702C2×C4311yescharacteristic, complemented
320#1687C2×C4311yescharacteristic, complemented
321#1686C2×C4311yescharacteristic, complemented
322#1667C2×C4311yescharacteristic, complemented
323#1640C2×C4311yescharacteristic, complemented
324#1625C2×C4311yescharacteristic, complemented
325#1621C2×C4311yescharacteristic, complemented
326#1621C2×C4311yescharacteristic, complemented
327#1592C2×C4311yescharacteristic, complemented
328#1582C2×C4311yescharacteristic, complemented
329C2×C43—81no—
330C2×C43—81no—
331C2×C43—161no—
332C2×C43—161no—
333C2×C43—161no—
334C2×C43#326811yescharacteristic
335C2×C43#327411yescharacteristic
336C2×C43#328811yescharacteristic
337C2×#135—21no—
338#559C22×C4311yescharacteristic
339#550C22×C4311yescharacteristic
340#550C22×C4311yescharacteristic
341#547C22×C4311yescharacteristic
342#496—21no—
343#496—21no—
344#493C22×C4311yescharacteristic
345#493C22×C4311yescharacteristic
346#493C22×C4311yescharacteristic
347#492C22×C4311yescharacteristic
348#486C22×C4311yescharacteristic
349#486C22×C4311yescharacteristic
350#481—21no—
351#475C22×C4311yescharacteristic
352#469—21no—
353#465—21no—
354#463—21no—
355#463—21no—
356#462C22×C4311yescharacteristic
357#460C22×C4311yescharacteristic
358#460C22×C4311yescharacteristic
359#459—21no—
360#459—21no—
361#459C22×C4311yescharacteristic
362#459C22×C4311yescharacteristic
363#459C22×C4311yescharacteristic
364#459C22×C4311yescharacteristic
365#452—21no—
366#449—21no—
367#449—21no—
368#446C22×C4311yescharacteristic
369#446C22×C4311yescharacteristic
370#442—21no—
371#442—21no—
372C4×SD16C22×C4311yescharacteristic
373C4×SD16C22×C4311yescharacteristic
374#436C22×C4311yescharacteristic
375C8×D4C22×C4311yescharacteristic
376#417—21no—
377#335C22×C4311yescharacteristic
378#334C22×C4311yescharacteristic
379#332C22×C4311yescharacteristic
380#331C22×C4311yescharacteristic
381#331C22×C4311yescharacteristic
382#331C22×C4311yescharacteristic
383Q8⋊C8C22×C4311yescharacteristic
384Q8⋊C8C22×C4311yescharacteristic
385D4⋊C8C22×C4311yescharacteristic
386D4⋊C8C22×C4311yescharacteristic
387#322C22×C4311yescharacteristic
388C43#2025611yescharacteristic, direct product factor, Sylow
389C2×#41—21no—
390C2×#41—21no—
391C2×#41—21no—
392#135—44no—
393C2×Q16—21no—
394C2×SD16—21no—
395C2×SD16—21no—
396C2×SD16—21no—
397C2×SD16—21no—
398C2×SD16D4×C4311yescharacteristic
399C2×SD16D4×C4311yescharacteristic
400C2×D8—21no—
401C2×D8—21no—
402C2×D8—21no—
403C2×D8—21no—
404C2×D8—21no—
405C2×D8—21no—
406C2×D8—21no—
407C2×D8—21no—
408C2×D8—41no—
409C2×M16—21no—
410C22×C8—21no—
411C4⋊Q8C23×C4311yescharacteristic
412#127—21no—
413#127—21no—
414#127C23×C4311yescharacteristic
415#127C23×C4311yescharacteristic
416#127C23×C4311yescharacteristic
417#124—21no—
418#124—21no—
419#123—41no—
420#123—41no—
421C22⋊Q8—21no—
422#121—21no—
423#121—21no—
424#121—21no—
425#121—41no—
426#121—41no—
427C4×Q8C23×C4311yescharacteristic
428C4×Q8C23×C4311yescharacteristic
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4C23×C4311yescharacteristic
434C4×D4C23×C4311yescharacteristic
435C2×C4⋊C4—21no—
436#106—21no—
437#106D4×C4311yescharacteristic
438#106D4×C4311yescharacteristic
439C4⋊C8—21no—
440C4⋊C8—21no—
441C4⋊C8C23×C4311yescharacteristic
442C4⋊C8C23×C4311yescharacteristic
443C4⋊C8C23×C4311yescharacteristic
444C4⋊C8C23×C4311yescharacteristic
445#103—21no—
446#103—21no—
447#103D4×C4311yescharacteristic
448#103D4×C4311yescharacteristic
449#102—21no—
450#102—21no—
451#102—21no—
452#102—21no—
453#102—21no—
454#102—21no—
455#102—21no—
456#102—21no—
457#102—41no—
458#102D4×C4311yescharacteristic
459#102D4×C4311yescharacteristic
460C22⋊C8—21no—
461C22⋊C8—21no—
462#97—21no—
463#97—21no—
464C4×C8C23×C4311yescharacteristic
465C4×C8C23×C4311yescharacteristic
466C4×C8C23×C4311yescharacteristic
467#41—42no—
468#41—42no—
469#41—42no—
470#41—81no—
471#41—81no—
472#41—81no—
473C2×Q8—21no—
474C2×Q8C2×D4×C4311yescharacteristic
475C2×Q8C2×D4×C4311yescharacteristic
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4C2×D4×C4311yescharacteristic
491C2×D4C2×D4×C4311yescharacteristic
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498Q16—42no—
499SD16—22no—
500SD16—41no—
501SD16—42no—
502SD16—81no—
503SD16—81no—
504SD16—81no—
505D8—42no—
506D8—42no—
507D8—42no—
508D8—81no—
509D8—81no—
510D8—81no—
511D8—81no—
512D8—81no—
513D8—82no—
514M16—81no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—42no—
521C2×C8C2×D4×C4311yescharacteristic
522C2×C8C2×D4×C4311yescharacteristic
523C2×C8C2×D4×C4311yescharacteristic
524C2×C8C2×D4×C4311yescharacteristic
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—41no—
530C4⋊C4C2×D4×C4311yescharacteristic
531C4⋊C4C2×D4×C4311yescharacteristic
532C4⋊C4C2×D4×C4311yescharacteristic
533C4⋊C4C2×D4×C4311yescharacteristic
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—41no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C22⋊C4—41no—
542C42—21no—
543C42—21no—
544C42C24×C4311yescharacteristic
545C23—21no—
546C23—21no—
547C23—41no—
548C23—41no—
549C23—41no—
550Q8—21no—
551Q8—21no—
552Q8—21no—
553Q8—21no—
554Q8—41no—
555Q8—41no—
556D4—21no—
557D4—21no—
558D4—21no—
559D4—21no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—41no—
570D4—41no—
571D4—41no—
572D4—81no—
573D4—81no—
574D4—81no—
575D4—82no—
576D4—82no—
577D4—82no—
578D4—161no—
579D4—161no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—82no—
592C2×C4—82no—
593C2×C4—82no—
594C2×C4—161no—
595C2×C4C22×D4×C4311yescharacteristic
596C2×C4C22×D4×C4311yescharacteristic
597C2×C4H(5,𝔽2)×C4311yescharacteristic
598C8—21no—
599C8—21no—
600C8—21no—
601C8—41no—
602C8—41no—
603C8—41no—
604C8—41no—
605C8—41no—
606C8AGL(1,ℤ/8)×C4312yes—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22D42×C4311yescharacteristic
623C4—21no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—41no—
630C4—81no—
631C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
632C4C43×#57511yescharacteristic
633C4C43×#57611yescharacteristic
634C4C43×#57611yescharacteristic
635C2—81no—
636C2—81no—
637C2—161no—
638C2—161no—
639C2—161no—
640C2C43×#326811yescharacteristic
641C2C43×#327411yescharacteristic
642C2C43×#328811yescharacteristic
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×#3399C2semidirect
2. C43×#3399C2semidirect
3. C43×#3332C2semidirect
4. C43×#3284C2semidirect
5. C43×#1721C2semidirect
6. C43×#1702C2semidirect
7. C43×#1687C2semidirect
8. C43×#1686C2semidirect
9. C43×#1667C2semidirect
10. C43×#1640C2semidirect
11. C43×#1625C2semidirect
12. C43×#1621C2semidirect
13. C43×#1621C2semidirect
14. C43×#1592C2semidirect
15. C43×#1582C2semidirect
285. #20256C43direct (N × H)
314. #3399C2×C43semidirect
315. #3399C2×C43semidirect
316. #3332C2×C43semidirect
317. #3284C2×C43semidirect
318. #1721C2×C43semidirect
319. #1702C2×C43semidirect
320. #1687C2×C43semidirect
321. #1686C2×C43semidirect
322. #1667C2×C43semidirect
323. #1640C2×C43semidirect
324. #1625C2×C43semidirect
325. #1621C2×C43semidirect
326. #1621C2×C43semidirect
327. #1592C2×C43semidirect
328. #1582C2×C43semidirect
388. C43#20256direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33992
C43×#33322
C43×#32842
C43×#17212
C43×#17022
C43×#16872
C43×#16862
C43×#16672
C43×#16402
C43×#16252
C43×#16212
C43×#15922
C43×#15822
#2025643