Finite Group Databasebeta

← C43×#20211 #24940228

Subgroups — C43×#20211 #24940228

Order 11008.

636 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3384C211yesmaximal, characteristic, complemented
2C43×#3366C211yesmaximal, characteristic
3C43×#3338C211yesmaximal, characteristic, complemented
4C43×#3278C211yesmaximal, characteristic, complemented
5C43×#1714C211yesmaximal, characteristic, complemented
6C43×#1698C211yesmaximal, characteristic, complemented
7C43×#1695C211yesmaximal, characteristic, complemented
8C43×#1692C211yesmaximal, characteristic, complemented
9C43×#1665C211yesmaximal, characteristic, complemented
10C43×#1644C211yesmaximal, characteristic, complemented
11C43×#1637C211yesmaximal, characteristic, complemented
12C43×#1631C211yesmaximal, characteristic, complemented
13C43×#1622C211yesmaximal, characteristic, complemented
14C43×#1593C211yesmaximal, characteristic, complemented
15C43×#1581C211yesmaximal, characteristic, complemented
16C2×#137×C43—21no—
17C43×#554C2211yescharacteristic
18C43×#554C2211yescharacteristic
19C43×#550C2211yescharacteristic
20D4×Q8×C43C2211yescharacteristic
21C43×#501—21no—
22C43×#500C2211yescharacteristic
23C43×#498C2211yescharacteristic
24C43×#492C2211yescharacteristic
25C43×#492C2211yescharacteristic
26C43×#490—21no—
27C43×#487C2211yescharacteristic
28C43×#486C2211yescharacteristic
29C43×#484—21no—
30C43×#484—21no—
31C43×#478—21no—
32C43×#478—21no—
33C43×#477C2211yescharacteristic
34C43×#477C2211yescharacteristic
35C43×#476—21no—
36C43×#476C2211yescharacteristic
37C43×#476C2211yescharacteristic
38C43×#474C2211yescharacteristic
39C43×#468—21no—
40C43×#467—21no—
41C43×#462C2211yescharacteristic
42C43×#460C2211yescharacteristic
43C43×#459—21no—
44C43×#459C2211yescharacteristic
45C43×#452—21no—
46C43×#448—21no—
47C43×#446C2211yescharacteristic
48C43×#446C2211yescharacteristic
49C43×#442—21no—
50C43×#442—21no—
51C4×Q16×C43C2211yescharacteristic
52C4×D8×C43C2211yescharacteristic
53C43×#436C2211yescharacteristic
54C8×D4×C43C2211yescharacteristic
55C2×#107×C43—21no—
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#333C2211yescharacteristic
59C43×#333C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#41×C43—21no—
68C22×Q8×C43—21no—
69#137×C43—44no—
70C2×Q16×C43—21no—
71C2×Q16×C43D411yescharacteristic
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—21no—
75C2×SD16×C43—41no—
76C2×D8×C43—21no—
77C2×D8×C43D411yescharacteristic
78C2×M16×C43—21no—
79C22×C8×C43—21no—
80C4⋊Q8×C43—21no—
81C4⋊Q8×C43C2311yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83C4⋊Q8×C43C2311yescharacteristic
84#127×C43—21no—
85#127×C43C2311yescharacteristic
86#125×C43—21no—
87#125×C43—21no—
88C22⋊Q8×C43—21no—
89C22⋊Q8×C43—21no—
90C22⋊Q8×C43—21no—
91C22⋊Q8×C43—41no—
92C22⋊Q8×C43—41no—
93C22⋊Q8×C43—41no—
94#121×C43—21no—
95#121×C43—41no—
96C4×Q8×C43C2311yescharacteristic
97C4×Q8×C43C2311yescharacteristic
98C4×D4×C43—21no—
99C4×D4×C43—21no—
100C4×D4×C43—21no—
101C4×D4×C43—21no—
102C4×D4×C43C2311yescharacteristic
103C4×D4×C43C2311yescharacteristic
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106#107×C43—21no—
107#107×C43—21no—
108#107×C43—21no—
109#107×C43—21no—
110#107×C43—21no—
111#107×C43D411yescharacteristic
112#107×C43D411yescharacteristic
113#106×C43—21no—
114#106×C43—21no—
115#106×C43—21no—
116#106×C43—21no—
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×C43—21no—
126#103×C43—41no—
127#103×C43D411yescharacteristic
128#103×C43D411yescharacteristic
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—21no—
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—81no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—41no—
151C2×Q8×C43—42no—
152C2×Q8×C43—81no—
153C2×Q8×C43C2×D411yescharacteristic
154C2×Q8×C43C2×D411yescharacteristic
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—41no—
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×C43—41no—
166C22×C4×C43—41no—
167C22×C4×C43—41no—
168Q16×C43—22no—
169Q16×C43—42no—
170SD16×C43—42no—
171SD16×C43—42no—
172SD16×C43—81no—
173SD16×C43—82no—
174D8×C43—22no—
175D8×C43—42no—
176M16×C43—42no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—42no—
183C2×C8×C43C2×D411yescharacteristic
184C2×C8×C43C2×D411yescharacteristic
185C2×C8×C43C2×D411yescharacteristic
186C2×C8×C43C2×D411yescharacteristic
187C4⋊C4×C43—21no—
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—21no—
195C4⋊C4×C43—41no—
196C4⋊C4×C43—41no—
197C4⋊C4×C43—41no—
198C4⋊C4×C43—41no—
199C4⋊C4×C43—41no—
200C4⋊C4×C43C2×D411yescharacteristic
201C4⋊C4×C43C2×D411yescharacteristic
202C4⋊C4×C43C2×D411yescharacteristic
203C4⋊C4×C43C2×D411yescharacteristic
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×C43—21no—
212C42×C43C2411yescharacteristic
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—41no—
216Q8×C43—21no—
217Q8×C43—21no—
218Q8×C43—21no—
219Q8×C43—21no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—81no—
223Q8×C43—81no—
224Q8×C43—82no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—81no—
233D4×C43—82no—
234D4×C43—161no—
235D4×C43#13712yescomplemented
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—82no—
250C2×C4×C43—82no—
251C2×C4×C43—161no—
252C2×C4×C43—161no—
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—41no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43—41no—
263C8×C43—41no—
264C8×C43AGL(1,ℤ/8)12yes—
265#20211C4311yesmaximal, characteristic, direct product factor, Sylow
266C22×C43—22no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43D4211yescharacteristic
276C4×C43—21no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43—41no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43—81no—
286C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
287C4×C43C2×#13711yescharacteristic
288C4×C43#57711yescharacteristic
289C4×C43#57811yescharacteristic
290#3384C2×C4311yescharacteristic, complemented
291#3366C2×C4311yescharacteristic
292#3338C2×C4311yescharacteristic, complemented
293#3278C2×C4311yescharacteristic, complemented
294#1714C2×C4311yescharacteristic, complemented
295#1698C2×C4311yescharacteristic, complemented
296#1695C2×C4311yescharacteristic, complemented
297#1692C2×C4311yescharacteristic, complemented
298#1665C2×C4311yescharacteristic, complemented
299#1644C2×C4311yescharacteristic, complemented
300#1637C2×C4311yescharacteristic, complemented
301#1631C2×C4311yescharacteristic, complemented
302#1622C2×C4311yescharacteristic, complemented
303#1593C2×C4311yescharacteristic, complemented
304#1581C2×C4311yescharacteristic, complemented
305C2×C43—42no—
306C2×C43—81no—
307C2×C43—161no—
308C2×C43#327011yescharacteristic
309C2×C43#327211yescharacteristic
310C2×C43#328811yescharacteristic
311C2×#137—21no—
312#554C22×C4311yescharacteristic
313#554C22×C4311yescharacteristic
314#550C22×C4311yescharacteristic
315D4×Q8C22×C4311yescharacteristic
316#501—21no—
317#500C22×C4311yescharacteristic
318#498C22×C4311yescharacteristic
319#492C22×C4311yescharacteristic
320#492C22×C4311yescharacteristic
321#490—21no—
322#487C22×C4311yescharacteristic
323#486C22×C4311yescharacteristic
324#484—21no—
325#484—21no—
326#478—21no—
327#478—21no—
328#477C22×C4311yescharacteristic
329#477C22×C4311yescharacteristic
330#476—21no—
331#476C22×C4311yescharacteristic
332#476C22×C4311yescharacteristic
333#474C22×C4311yescharacteristic
334#468—21no—
335#467—21no—
336#462C22×C4311yescharacteristic
337#460C22×C4311yescharacteristic
338#459—21no—
339#459C22×C4311yescharacteristic
340#452—21no—
341#448—21no—
342#446C22×C4311yescharacteristic
343#446C22×C4311yescharacteristic
344#442—21no—
345#442—21no—
346C4×Q16C22×C4311yescharacteristic
347C4×D8C22×C4311yescharacteristic
348#436C22×C4311yescharacteristic
349C8×D4C22×C4311yescharacteristic
350C2×#107—21no—
351#335C22×C4311yescharacteristic
352#334C22×C4311yescharacteristic
353#333C22×C4311yescharacteristic
354#333C22×C4311yescharacteristic
355#332C22×C4311yescharacteristic
356#331C22×C4311yescharacteristic
357Q8⋊C8C22×C4311yescharacteristic
358Q8⋊C8C22×C4311yescharacteristic
359D4⋊C8C22×C4311yescharacteristic
360D4⋊C8C22×C4311yescharacteristic
361#322C22×C4311yescharacteristic
362C43#2021111yescharacteristic, direct product factor, Sylow
363C2×#41—21no—
364C22×Q8—21no—
365#137—44no—
366C2×Q16—21no—
367C2×Q16D4×C4311yescharacteristic
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×SD16—41no—
372C2×D8—21no—
373C2×D8D4×C4311yescharacteristic
374C2×M16—21no—
375C22×C8—21no—
376C4⋊Q8—21no—
377C4⋊Q8C23×C4311yescharacteristic
378C4⋊Q8C23×C4311yescharacteristic
379C4⋊Q8C23×C4311yescharacteristic
380#127—21no—
381#127C23×C4311yescharacteristic
382#125—21no—
383#125—21no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—41no—
388C22⋊Q8—41no—
389C22⋊Q8—41no—
390#121—21no—
391#121—41no—
392C4×Q8C23×C4311yescharacteristic
393C4×Q8C23×C4311yescharacteristic
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4C23×C4311yescharacteristic
399C4×D4C23×C4311yescharacteristic
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402#107—21no—
403#107—21no—
404#107—21no—
405#107—21no—
406#107—21no—
407#107D4×C4311yescharacteristic
408#107D4×C4311yescharacteristic
409#106—21no—
410#106—21no—
411#106—21no—
412#106—21no—
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8C23×C4311yescharacteristic
416C4⋊C8C23×C4311yescharacteristic
417C4⋊C8C23×C4311yescharacteristic
418C4⋊C8C23×C4311yescharacteristic
419#103—21no—
420#103—21no—
421#103—21no—
422#103—41no—
423#103D4×C4311yescharacteristic
424#103D4×C4311yescharacteristic
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102D4×C4311yescharacteristic
433#102D4×C4311yescharacteristic
434C22⋊C8—21no—
435C22⋊C8—21no—
436#97—21no—
437#97—21no—
438C4×C8C23×C4311yescharacteristic
439C4×C8C23×C4311yescharacteristic
440C4×C8C23×C4311yescharacteristic
441#41—42no—
442#41—81no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—41no—
447C2×Q8—42no—
448C2×Q8—81no—
449C2×Q8C2×D4×C4311yescharacteristic
450C2×Q8C2×D4×C4311yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4C2×D4×C4311yescharacteristic
457C2×D4C2×D4×C4311yescharacteristic
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464Q16—22no—
465Q16—42no—
466SD16—42no—
467SD16—42no—
468SD16—81no—
469SD16—82no—
470D8—22no—
471D8—42no—
472M16—42no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—42no—
479C2×C8C2×D4×C4311yescharacteristic
480C2×C8C2×D4×C4311yescharacteristic
481C2×C8C2×D4×C4311yescharacteristic
482C2×C8C2×D4×C4311yescharacteristic
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4C2×D4×C4311yescharacteristic
497C4⋊C4C2×D4×C4311yescharacteristic
498C4⋊C4C2×D4×C4311yescharacteristic
499C4⋊C4C2×D4×C4311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C42—21no—
507C42—21no—
508C42C24×C4311yescharacteristic
509C23—21no—
510C23—21no—
511C23—41no—
512Q8—21no—
513Q8—21no—
514Q8—21no—
515Q8—21no—
516Q8—41no—
517Q8—41no—
518Q8—81no—
519Q8—81no—
520Q8—82no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—81no—
529D4—82no—
530D4—161no—
531D4#137×C4312yescomplemented
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—82no—
546C2×C4—82no—
547C2×C4—161no—
548C2×C4—161no—
549C2×C4C22×D4×C4311yescharacteristic
550C2×C4C22×D4×C4311yescharacteristic
551C2×C4H(5,𝔽2)×C4311yescharacteristic
552C8—21no—
553C8—21no—
554C8—21no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8AGL(1,ℤ/8)×C4312yes—
561C22—22no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22D42×C4311yescharacteristic
571C4—21no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
582C4C2×#137×C4311yescharacteristic
583C4C43×#57711yescharacteristic
584C4C43×#57811yescharacteristic
585C2—42no—
586C2—81no—
587C2—161no—
588C2C43×#327011yescharacteristic
589C2C43×#327211yescharacteristic
590C2C43×#328811yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3366C2
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×#3384C2semidirect
3. C43×#3338C2semidirect
4. C43×#3278C2semidirect
5. C43×#1714C2semidirect
6. C43×#1698C2semidirect
7. C43×#1695C2semidirect
8. C43×#1692C2semidirect
9. C43×#1665C2semidirect
10. C43×#1644C2semidirect
11. C43×#1637C2semidirect
12. C43×#1631C2semidirect
13. C43×#1622C2semidirect
14. C43×#1593C2semidirect
15. C43×#1581C2semidirect
235. D4×C43#137semidirect
265. #20211C43direct (N × H)
290. #3384C2×C43semidirect
292. #3338C2×C43semidirect
293. #3278C2×C43semidirect
294. #1714C2×C43semidirect
295. #1698C2×C43semidirect
296. #1695C2×C43semidirect
297. #1692C2×C43semidirect
298. #1665C2×C43semidirect
299. #1644C2×C43semidirect
300. #1637C2×C43semidirect
301. #1631C2×C43semidirect
302. #1622C2×C43semidirect
303. #1593C2×C43semidirect
304. #1581C2×C43semidirect
362. C43#20211direct (N × H)
531. D4#137×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#33842
C43×#33662
C43×#33382
C43×#32782
C43×#17142
C43×#16982
C43×#16952
C43×#16922
C43×#16652
C43×#16442
C43×#16372
C43×#16312
C43×#16222
C43×#15932
C43×#15812
#2021143