Finite Group Databasebeta

← C43×#20203 #24940220

Subgroups — C43×#20203 #24940220

Order 11008.

670 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3369C211yesmaximal, characteristic, complemented
2C43×#3362C211yesmaximal, characteristic, complemented
3C43×#3324C211yesmaximal, characteristic, complemented
4C43×#3274C211yesmaximal, characteristic
5C43×#1717C211yesmaximal, characteristic, complemented
6C43×#1703C211yesmaximal, characteristic, complemented
7C43×#1697C211yesmaximal, characteristic, complemented
8C43×#1688C211yesmaximal, characteristic, complemented
9C43×#1682C211yesmaximal, characteristic, complemented
10C43×#1641C211yesmaximal, characteristic, complemented
11C43×#1629C211yesmaximal, characteristic, complemented
12C43×#1628C211yesmaximal, characteristic, complemented
13C43×#1623C211yesmaximal, characteristic, complemented
14C43×#1592C211yesmaximal, characteristic, complemented
15C43×#1583C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C43—21no—
17Q82×C43C2211yescharacteristic, complemented
18C43×#556C2211yescharacteristic
19C43×#550C2211yescharacteristic
20D42×C43C2211yescharacteristic
21C43×#493C2211yescharacteristic
22C43×#492C2211yescharacteristic
23C43×#489—21no—
24C43×#487C2211yescharacteristic, complemented
25C43×#486—21no—
26C43×#486C2211yescharacteristic
27C43×#486C2211yescharacteristic, complemented
28C43×#486C2211yescharacteristic, complemented
29C43×#482—21no—
30C43×#476—21no—
31C43×#476C2211yescharacteristic
32C43×#476C2211yescharacteristic
33C43×#475—21no—
34C43×#474C2211yescharacteristic
35C43×#469—21no—
36C43×#468—21no—
37C43×#464—21no—
38C43×#462C2211yescharacteristic, complemented
39C43×#460—21no—
40C43×#460C2211yescharacteristic
41C43×#460C2211yescharacteristic
42C43×#460C2211yescharacteristic, complemented
43C43×#459C2211yescharacteristic
44C43×#450—21no—
45C43×#449—21no—
46C43×#447—21no—
47C43×#446C2211yescharacteristic, complemented
48C8×Q8×C43C2211yescharacteristic, complemented
49C43×#441—21no—
50C4×SD16×C43—21no—
51C4×SD16×C43C2211yescharacteristic
52C4×SD16×C43C2211yescharacteristic
53C43×#436C2211yescharacteristic
54C43×#436C2211yescharacteristic
55C43×#418—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
67C2×#41×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70AGL(1,ℤ/8)×C43—44no—
71C2×Q16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—21no—
75C2×SD16×C43—41no—
76C2×SD16×C43D411yescharacteristic
77C2×SD16×C43D411yescharacteristic
78C2×D8×C43—21no—
79C2×D8×C43—21no—
80C2×D8×C43—21no—
81C2×M16×C43—21no—
82C2×M16×C43—21no—
83C4⋊Q8×C43—21no—
84C4⋊Q8×C43—21no—
85C4⋊Q8×C43—41no—
86C4⋊Q8×C43C2311yescharacteristic
87C4⋊Q8×C43C2311yescharacteristic
88#127×C43—21no—
89#127×C43C2311yescharacteristic
90#127×C43C2311yescharacteristic
91#126×C43—41no—
92#124×C43—21no—
93C22⋊Q8×C43—21no—
94#121×C43—21no—
95#121×C43—21no—
96#121×C43—21no—
97#121×C43—41no—
98#120×C43—41no—
99C4×Q8×C43—21no—
100C4×Q8×C43—21no—
101C4×Q8×C43—21no—
102C4×Q8×C43C2311yescharacteristic
103C4×Q8×C43C2311yescharacteristic
104C4×D4×C43—21no—
105C4×D4×C43C2311yescharacteristic
106C4×D4×C43C2311yescharacteristic
107#117×C43—21no—
108#107×C43—21no—
109#106×C43—21no—
110#106×C43—21no—
111#106×C43D411yescharacteristic
112#106×C43D411yescharacteristic
113C4⋊C8×C43—21no—
114C4⋊C8×C43—21no—
115C4⋊C8×C43C2311yescharacteristic
116C4⋊C8×C43C2311yescharacteristic
117C4⋊C8×C43C2311yescharacteristic
118C4⋊C8×C43C2311yescharacteristic
119#103×C43—21no—
120#103×C43—21no—
121#103×C43—21no—
122#103×C43D411yescharacteristic
123#103×C43D411yescharacteristic
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×C43—41no—
136#102×C43D411yescharacteristic
137#102×C43D411yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140#97×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C24×C43—41no—
146#41×C43—42no—
147#41×C43—81no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—41no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×Q8×C43C2×D411yescharacteristic
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×C43—41no—
161C2×D4×C43—41no—
162C2×D4×C43—41no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43—81no—
166C2×D4×C43—81no—
167C2×D4×C43C2×D411yescharacteristic
168C2×D4×C43C2×D411yescharacteristic
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—41no—
172Q16×C43—42no—
173SD16×C43—22no—
174SD16×C43—41no—
175SD16×C43—42no—
176SD16×C43—42no—
177SD16×C43—81no—
178SD16×C43—82no—
179D8×C43—42no—
180D8×C43—42no—
181D8×C43—81no—
182M16×C43—42no—
183M16×C43—81no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
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×C43—41no—
202C4⋊C4×C43C2×D411yescharacteristic
203C4⋊C4×C43C2×D411yescharacteristic
204C4⋊C4×C43C2×D411yescharacteristic
205C4⋊C4×C43C2×D411yescharacteristic
206C22⋊C4×C43—21no—
207C22⋊C4×C43—21no—
208C22⋊C4×C43—41no—
209C22⋊C4×C43—41no—
210C22⋊C4×C43—41no—
211C22⋊C4×C43—41no—
212C42×C43—21no—
213C42×C43—21no—
214C42×C43—41no—
215C42×C43—41no—
216C42×C43C2411yescharacteristic
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—82no—
222C23×C43—82no—
223C23×C43—161no—
224Q8×C43—21no—
225Q8×C43—21no—
226Q8×C43—21no—
227Q8×C43—41no—
228Q8×C43—41no—
229Q8×C43—81no—
230Q8×C43—161no—
231Q8×C43AGL(1,ℤ/8)12yes—
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—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—82no—
245D4×C43—81no—
246D4×C43—81no—
247D4×C43—82no—
248D4×C43—82no—
249D4×C43—161no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
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×C43C22×D411yescharacteristic
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C8×C43—21no—
267C8×C43—21no—
268C8×C43—21no—
269C8×C43—21no—
270C8×C43—41no—
271C8×C43—41no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43—41no—
275#20203C4311yesmaximal, characteristic, direct product factor, Sylow
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—164no—
289C22×C43D4211yescharacteristic
290C4×C43—22no—
291C4×C43—21no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—81no—
298C4×C43—81no—
299C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
300C4×C43#57511yescharacteristic
301C4×C43#57711yescharacteristic
302C4×C43#57711yescharacteristic
303#3369C2×C4311yescharacteristic, complemented
304#3362C2×C4311yescharacteristic, complemented
305#3324C2×C4311yescharacteristic, complemented
306#3274C2×C4311yescharacteristic
307#1717C2×C4311yescharacteristic, complemented
308#1703C2×C4311yescharacteristic, complemented
309#1697C2×C4311yescharacteristic, complemented
310#1688C2×C4311yescharacteristic, complemented
311#1682C2×C4311yescharacteristic, complemented
312#1641C2×C4311yescharacteristic, complemented
313#1629C2×C4311yescharacteristic, complemented
314#1628C2×C4311yescharacteristic, complemented
315#1623C2×C4311yescharacteristic, complemented
316#1592C2×C4311yescharacteristic, complemented
317#1583C2×C4311yescharacteristic, complemented
318C2×C43—81no—
319C2×C43—81no—
320C2×C43—161no—
321C2×C43—161no—
322C2×C43#326511yescharacteristic
323C2×C43#327511yescharacteristic
324C2×C43#328811yescharacteristic
325C2×AGL(1,ℤ/8)—21no—
326Q82C22×C4311yescharacteristic, complemented
327#556C22×C4311yescharacteristic
328#550C22×C4311yescharacteristic
329D42C22×C4311yescharacteristic
330#493C22×C4311yescharacteristic
331#492C22×C4311yescharacteristic
332#489—21no—
333#487C22×C4311yescharacteristic, complemented
334#486—21no—
335#486C22×C4311yescharacteristic
336#486C22×C4311yescharacteristic, complemented
337#486C22×C4311yescharacteristic, complemented
338#482—21no—
339#476—21no—
340#476C22×C4311yescharacteristic
341#476C22×C4311yescharacteristic
342#475—21no—
343#474C22×C4311yescharacteristic
344#469—21no—
345#468—21no—
346#464—21no—
347#462C22×C4311yescharacteristic, complemented
348#460—21no—
349#460C22×C4311yescharacteristic
350#460C22×C4311yescharacteristic
351#460C22×C4311yescharacteristic, complemented
352#459C22×C4311yescharacteristic
353#450—21no—
354#449—21no—
355#447—21no—
356#446C22×C4311yescharacteristic, complemented
357C8×Q8C22×C4311yescharacteristic, complemented
358#441—21no—
359C4×SD16—21no—
360C4×SD16C22×C4311yescharacteristic
361C4×SD16C22×C4311yescharacteristic
362#436C22×C4311yescharacteristic
363#436C22×C4311yescharacteristic
364#418—21no—
365#335C22×C4311yescharacteristic, complemented
366#334C22×C4311yescharacteristic, complemented
367#333C22×C4311yescharacteristic, complemented
368#332C22×C4311yescharacteristic, complemented
369#331C22×C4311yescharacteristic
370#331C22×C4311yescharacteristic, complemented
371Q8⋊C8C22×C4311yescharacteristic, complemented
372Q8⋊C8C22×C4311yescharacteristic, complemented
373D4⋊C8C22×C4311yescharacteristic
374D4⋊C8C22×C4311yescharacteristic
375#322C22×C4311yescharacteristic, complemented
376C43#2020311yescharacteristic, direct product factor, Sylow
377C2×#41—21no—
378C22×D4—21no—
379C22×D4—21no—
380AGL(1,ℤ/8)—44no—
381C2×Q16—21no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—41no—
386C2×SD16D4×C4311yescharacteristic
387C2×SD16D4×C4311yescharacteristic
388C2×D8—21no—
389C2×D8—21no—
390C2×D8—21no—
391C2×M16—21no—
392C2×M16—21no—
393C4⋊Q8—21no—
394C4⋊Q8—21no—
395C4⋊Q8—41no—
396C4⋊Q8C23×C4311yescharacteristic
397C4⋊Q8C23×C4311yescharacteristic
398#127—21no—
399#127C23×C4311yescharacteristic
400#127C23×C4311yescharacteristic
401#126—41no—
402#124—21no—
403C22⋊Q8—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—41no—
408#120—41no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—21no—
412C4×Q8C23×C4311yescharacteristic
413C4×Q8C23×C4311yescharacteristic
414C4×D4—21no—
415C4×D4C23×C4311yescharacteristic
416C4×D4C23×C4311yescharacteristic
417#117—21no—
418#107—21no—
419#106—21no—
420#106—21no—
421#106D4×C4311yescharacteristic
422#106D4×C4311yescharacteristic
423C4⋊C8—21no—
424C4⋊C8—21no—
425C4⋊C8C23×C4311yescharacteristic
426C4⋊C8C23×C4311yescharacteristic
427C4⋊C8C23×C4311yescharacteristic
428C4⋊C8C23×C4311yescharacteristic
429#103—21no—
430#103—21no—
431#103—21no—
432#103D4×C4311yescharacteristic
433#103D4×C4311yescharacteristic
434#102—21no—
435#102—21no—
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—41no—
446#102D4×C4311yescharacteristic
447#102D4×C4311yescharacteristic
448C22⋊C8—21no—
449C22⋊C8—21no—
450#97—21no—
451C4×C8—21no—
452C4×C8C23×C4311yescharacteristic
453C4×C8C23×C4311yescharacteristic
454C4×C8C23×C4311yescharacteristic
455C24—41no—
456#41—42no—
457#41—81no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—41no—
461C2×Q8C2×D4×C4311yescharacteristic
462C2×Q8C2×D4×C4311yescharacteristic
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—81no—
476C2×D4—81no—
477C2×D4C2×D4×C4311yescharacteristic
478C2×D4C2×D4×C4311yescharacteristic
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—41no—
482Q16—42no—
483SD16—22no—
484SD16—41no—
485SD16—42no—
486SD16—42no—
487SD16—81no—
488SD16—82no—
489D8—42no—
490D8—42no—
491D8—81no—
492M16—42no—
493M16—81no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8C2×D4×C4311yescharacteristic
500C2×C8C2×D4×C4311yescharacteristic
501C2×C8C2×D4×C4311yescharacteristic
502C2×C8C2×D4×C4311yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4C2×D4×C4311yescharacteristic
513C4⋊C4C2×D4×C4311yescharacteristic
514C4⋊C4C2×D4×C4311yescharacteristic
515C4⋊C4C2×D4×C4311yescharacteristic
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C42—21no—
523C42—21no—
524C42—41no—
525C42—41no—
526C42C24×C4311yescharacteristic
527C23—21no—
528C23—21no—
529C23—41no—
530C23—41no—
531C23—82no—
532C23—82no—
533C23—161no—
534Q8—21no—
535Q8—21no—
536Q8—21no—
537Q8—41no—
538Q8—41no—
539Q8—81no—
540Q8—161no—
541Q8AGL(1,ℤ/8)×C4312yes—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—82no—
555D4—81no—
556D4—81no—
557D4—82no—
558D4—82no—
559D4—161no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—82no—
573C2×C4C22×D4×C4311yescharacteristic
574C2×C4C22×D4×C4311yescharacteristic
575C2×C4H(5,𝔽2)×C4311yescharacteristic
576C8—21no—
577C8—21no—
578C8—21no—
579C8—21no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8—41no—
584C8—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—164no—
598C22D42×C4311yescharacteristic
599C4—22no—
600C4—21no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—81no—
607C4—81no—
608C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
609C4C43×#57511yescharacteristic
610C4C43×#57711yescharacteristic
611C4C43×#57711yescharacteristic
612C2—81no—
613C2—81no—
614C2—161no—
615C2—161no—
616C2C43×#326511yescharacteristic
617C2C43×#327511yescharacteristic
618C2C43×#328811yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3274C2
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×#3369C2semidirect
2. C43×#3362C2semidirect
3. C43×#3324C2semidirect
5. C43×#1717C2semidirect
6. C43×#1703C2semidirect
7. C43×#1697C2semidirect
8. C43×#1688C2semidirect
9. C43×#1682C2semidirect
10. C43×#1641C2semidirect
11. C43×#1629C2semidirect
12. C43×#1628C2semidirect
13. C43×#1623C2semidirect
14. C43×#1592C2semidirect
15. C43×#1583C2semidirect
17. Q82×C43C22semidirect
24. C43×#487C22semidirect
27. C43×#486C22semidirect
28. C43×#486C22semidirect
38. C43×#462C22semidirect
42. C43×#460C22semidirect
47. C43×#446C22semidirect
48. 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
275. #20203C43direct (N × H)
303. #3369C2×C43semidirect
304. #3362C2×C43semidirect
305. #3324C2×C43semidirect
307. #1717C2×C43semidirect
308. #1703C2×C43semidirect
309. #1697C2×C43semidirect
310. #1688C2×C43semidirect
311. #1682C2×C43semidirect
312. #1641C2×C43semidirect
313. #1629C2×C43semidirect
314. #1628C2×C43semidirect
315. #1623C2×C43semidirect
316. #1592C2×C43semidirect
317. #1583C2×C43semidirect
326. Q82C22×C43semidirect
333. #487C22×C43semidirect
336. #486C22×C43semidirect
337. #486C22×C43semidirect
347. #462C22×C43semidirect
351. #460C22×C43semidirect
356. #446C22×C43semidirect
357. C8×Q8C22×C43semidirect
365. #335C22×C43semidirect
366. #334C22×C43semidirect
367. #333C22×C43semidirect
368. #332C22×C43semidirect
370. #331C22×C43semidirect
371. Q8⋊C8C22×C43semidirect
372. Q8⋊C8C22×C43semidirect
375. #322C22×C43semidirect
376. C43#20203direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33692
C43×#33622
C43×#33242
C43×#32742
C43×#17172
C43×#17032
C43×#16972
C43×#16882
C43×#16822
C43×#16412
C43×#16292
C43×#16282
C43×#16232
C43×#15922
C43×#15832
#2020343