Finite Group Databasebeta

← C43×#20205 #24940222

Subgroups — C43×#20205 #24940222

Order 11008.

638 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3375C211yesmaximal, characteristic, complemented
2C43×#3373C211yesmaximal, characteristic, complemented
3C43×#3362C211yesmaximal, characteristic, complemented
4C43×#3278C211yesmaximal, characteristic, complemented
5C43×#1717C211yesmaximal, characteristic, complemented
6C43×#1698C211yesmaximal, characteristic, complemented
7C43×#1697C211yesmaximal, characteristic, complemented
8C43×#1686C211yesmaximal, characteristic, complemented
9C43×#1682C211yesmaximal, characteristic, complemented
10C43×#1645C211yesmaximal, characteristic, complemented
11C43×#1637C211yesmaximal, characteristic, complemented
12C43×#1621C211yesmaximal, characteristic
13C43×#1620C211yesmaximal, characteristic, complemented
14C43×#1592C211yesmaximal, characteristic, complemented
15C43×#1584C211yesmaximal, characteristic, complemented
16C2×#137×C43—21no—
17C43×#559C2211yescharacteristic
18Q82×C43C2211yescharacteristic
19C43×#550C2211yescharacteristic
20D4×Q8×C43C2211yescharacteristic
21C43×#493C2211yescharacteristic
22C43×#492C2211yescharacteristic
23C43×#489—21no—
24C43×#489—21no—
25C43×#487C2211yescharacteristic
26C43×#486—21no—
27C43×#486C2211yescharacteristic
28C43×#486C2211yescharacteristic
29C43×#486C2211yescharacteristic
30C43×#477C2211yescharacteristic
31C43×#476—21no—
32C43×#476—21no—
33C43×#476C2211yescharacteristic
34C43×#475C2211yescharacteristic
35C43×#474—21no—
36C43×#468—21no—
37C43×#464—21no—
38C43×#463—21no—
39C43×#462C2211yescharacteristic
40C43×#460—21no—
41C43×#460C2211yescharacteristic
42C43×#460C2211yescharacteristic
43C43×#460C2211yescharacteristic
44C43×#459C2211yescharacteristic
45C43×#452—21no—
46C43×#448—21no—
47C43×#446C2211yescharacteristic
48C43×#446C2211yescharacteristic
49C8×Q8×C43C2211yescharacteristic
50C43×#442—21no—
51C43×#440—21no—
52C4×Q16×C43C2211yescharacteristic
53C4×SD16×C43—21no—
54C4×SD16×C43C2211yescharacteristic
55C43×#436C2211yescharacteristic
56C43×#335C2211yescharacteristic
57C43×#335C2211yescharacteristic
58C43×#333C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#331C2211yescharacteristic
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊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—21no—
76C2×SD16×C43—21no—
77C2×SD16×C43D411yescharacteristic
78C2×D8×C43—21no—
79C2×D8×C43—41no—
80C2×M16×C43—21no—
81C4⋊Q8×C43—21no—
82C4⋊Q8×C43—21no—
83C4⋊Q8×C43—21no—
84C4⋊Q8×C43—41no—
85C4⋊Q8×C43C2311yescharacteristic
86C4⋊Q8×C43C2311yescharacteristic
87#127×C43—21no—
88#127×C43C2311yescharacteristic
89#127×C43C2311yescharacteristic
90#124×C43—21no—
91#124×C43—21no—
92#123×C43—41no—
93C22⋊Q8×C43—21no—
94C22⋊Q8×C43—41no—
95#121×C43—21no—
96#121×C43—41no—
97C4×Q8×C43—21no—
98C4×Q8×C43—21no—
99C4×Q8×C43C2311yescharacteristic
100C4×Q8×C43C2311yescharacteristic
101C4×Q8×C43C2311yescharacteristic
102C4×D4×C43—21no—
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43—21no—
106C4×D4×C43C2311yescharacteristic
107#107×C43—21no—
108#107×C43D411yescharacteristic
109#106×C43—21no—
110#106×C43—21no—
111#106×C43D411yescharacteristic
112C4⋊C8×C43—21no—
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×C43—41no—
123#103×C43D411yescharacteristic
124#103×C43D411yescharacteristic
125#103×C43D411yescharacteristic
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—21no—
136#102×C43—21no—
137#102×C43D411yescharacteristic
138C22⋊C8×C43—21no—
139#97×C43—21no—
140#97×C43—21no—
141C4×C8×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—41no—
150C2×Q8×C43—41no—
151C2×Q8×C43—42no—
152C2×Q8×C43—81no—
153C2×Q8×C43C2×D411yescharacteristic
154C2×Q8×C43C2×D411yescharacteristic
155C2×Q8×C43C2×D411yescharacteristic
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—41no—
163C2×D4×C43—41no—
164C2×D4×C43C2×D411yescharacteristic
165C22×C4×C43—21no—
166C22×C4×C43—41no—
167C22×C4×C43—41no—
168C22×C4×C43—41no—
169Q16×C43—22no—
170Q16×C43—42no—
171SD16×C43—41no—
172SD16×C43—42no—
173SD16×C43—42no—
174SD16×C43—42no—
175SD16×C43—42no—
176SD16×C43—81no—
177D8×C43—42no—
178D8×C43—82no—
179M16×C43—42no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
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×C43—41no—
199C4⋊C4×C43C2×D411yescharacteristic
200C4⋊C4×C43C2×D411yescharacteristic
201C4⋊C4×C43C2×D411yescharacteristic
202C4⋊C4×C43C2×D411yescharacteristic
203C22⋊C4×C43—21no—
204C22⋊C4×C43—41no—
205C22⋊C4×C43—41no—
206C22⋊C4×C43—41no—
207C22⋊C4×C43—41no—
208C22⋊C4×C43—41no—
209C42×C43—21no—
210C42×C43—21no—
211C42×C43—21no—
212C42×C43—41no—
213C42×C43C2411yescharacteristic
214C23×C43—21no—
215C23×C43—41no—
216C23×C43—41no—
217Q8×C43—21no—
218Q8×C43—21no—
219Q8×C43—21no—
220Q8×C43—21no—
221Q8×C43—21no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—81no—
225Q8×C43—82no—
226Q8×C43—161no—
227Q8×C43AGL(1,ℤ/8)12yes—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—82no—
239D4×C43—81no—
240D4×C43—81no—
241D4×C43—161no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—82no—
254C2×C4×C43—82no—
255C2×C4×C43—161no—
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43H(5,𝔽2)11yescharacteristic
259C8×C43—21no—
260C8×C43—21no—
261C8×C43—21no—
262C8×C43—21no—
263C8×C43—41no—
264C8×C43—41no—
265C8×C43—41no—
266C8×C43—41no—
267C8×C43—41no—
268#20205C4311yesmaximal, characteristic, direct product factor, Sylow
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43D4211yescharacteristic
279C4×C43—22no—
280C4×C43—21no—
281C4×C43—41no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
290C4×C43#57511yescharacteristic
291C4×C43#57711yescharacteristic
292C4×C43#57811yescharacteristic
293#3375C2×C4311yescharacteristic, complemented
294#3373C2×C4311yescharacteristic, complemented
295#3362C2×C4311yescharacteristic, complemented
296#3278C2×C4311yescharacteristic, complemented
297#1717C2×C4311yescharacteristic, complemented
298#1698C2×C4311yescharacteristic, complemented
299#1697C2×C4311yescharacteristic, complemented
300#1686C2×C4311yescharacteristic, complemented
301#1682C2×C4311yescharacteristic, complemented
302#1645C2×C4311yescharacteristic, complemented
303#1637C2×C4311yescharacteristic, complemented
304#1621C2×C4311yescharacteristic
305#1620C2×C4311yescharacteristic, complemented
306#1592C2×C4311yescharacteristic, complemented
307#1584C2×C4311yescharacteristic, complemented
308C2×C43—81no—
309C2×C43—161no—
310C2×C43—161no—
311C2×C43#326511yescharacteristic
312C2×C43#327711yescharacteristic
313C2×C43#328811yescharacteristic
314C2×#137—21no—
315#559C22×C4311yescharacteristic
316Q82C22×C4311yescharacteristic
317#550C22×C4311yescharacteristic
318D4×Q8C22×C4311yescharacteristic
319#493C22×C4311yescharacteristic
320#492C22×C4311yescharacteristic
321#489—21no—
322#489—21no—
323#487C22×C4311yescharacteristic
324#486—21no—
325#486C22×C4311yescharacteristic
326#486C22×C4311yescharacteristic
327#486C22×C4311yescharacteristic
328#477C22×C4311yescharacteristic
329#476—21no—
330#476—21no—
331#476C22×C4311yescharacteristic
332#475C22×C4311yescharacteristic
333#474—21no—
334#468—21no—
335#464—21no—
336#463—21no—
337#462C22×C4311yescharacteristic
338#460—21no—
339#460C22×C4311yescharacteristic
340#460C22×C4311yescharacteristic
341#460C22×C4311yescharacteristic
342#459C22×C4311yescharacteristic
343#452—21no—
344#448—21no—
345#446C22×C4311yescharacteristic
346#446C22×C4311yescharacteristic
347C8×Q8C22×C4311yescharacteristic
348#442—21no—
349#440—21no—
350C4×Q16C22×C4311yescharacteristic
351C4×SD16—21no—
352C4×SD16C22×C4311yescharacteristic
353#436C22×C4311yescharacteristic
354#335C22×C4311yescharacteristic
355#335C22×C4311yescharacteristic
356#333C22×C4311yescharacteristic
357#332C22×C4311yescharacteristic
358#331C22×C4311yescharacteristic
359#331C22×C4311yescharacteristic
360Q8⋊C8C22×C4311yescharacteristic
361Q8⋊C8C22×C4311yescharacteristic
362Q8⋊C8C22×C4311yescharacteristic
363D4⋊C8C22×C4311yescharacteristic
364#322C22×C4311yescharacteristic
365C43#2020511yescharacteristic, direct product factor, Sylow
366C2×#41—21no—
367C22×Q8—21no—
368#137—44no—
369C2×Q16—21no—
370C2×Q16D4×C4311yescharacteristic
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16D4×C4311yescharacteristic
377C2×D8—21no—
378C2×D8—41no—
379C2×M16—21no—
380C4⋊Q8—21no—
381C4⋊Q8—21no—
382C4⋊Q8—21no—
383C4⋊Q8—41no—
384C4⋊Q8C23×C4311yescharacteristic
385C4⋊Q8C23×C4311yescharacteristic
386#127—21no—
387#127C23×C4311yescharacteristic
388#127C23×C4311yescharacteristic
389#124—21no—
390#124—21no—
391#123—41no—
392C22⋊Q8—21no—
393C22⋊Q8—41no—
394#121—21no—
395#121—41no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8C23×C4311yescharacteristic
399C4×Q8C23×C4311yescharacteristic
400C4×Q8C23×C4311yescharacteristic
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4C23×C4311yescharacteristic
406#107—21no—
407#107D4×C4311yescharacteristic
408#106—21no—
409#106—21no—
410#106D4×C4311yescharacteristic
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8C23×C4311yescharacteristic
415C4⋊C8C23×C4311yescharacteristic
416C4⋊C8C23×C4311yescharacteristic
417C4⋊C8C23×C4311yescharacteristic
418#103—21no—
419#103—21no—
420#103—21no—
421#103—41no—
422#103D4×C4311yescharacteristic
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#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102D4×C4311yescharacteristic
437C22⋊C8—21no—
438#97—21no—
439#97—21no—
440C4×C8—21no—
441C4×C8C23×C4311yescharacteristic
442C4×C8C23×C4311yescharacteristic
443C4×C8C23×C4311yescharacteristic
444#41—42no—
445#41—81no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—41no—
449C2×Q8—41no—
450C2×Q8—42no—
451C2×Q8—81no—
452C2×Q8C2×D4×C4311yescharacteristic
453C2×Q8C2×D4×C4311yescharacteristic
454C2×Q8C2×D4×C4311yescharacteristic
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4C2×D4×C4311yescharacteristic
464C22×C4—21no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468Q16—22no—
469Q16—42no—
470SD16—41no—
471SD16—42no—
472SD16—42no—
473SD16—42no—
474SD16—42no—
475SD16—81no—
476D8—42no—
477D8—82no—
478M16—42no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8C2×D4×C4311yescharacteristic
485C2×C8C2×D4×C4311yescharacteristic
486C2×C8C2×D4×C4311yescharacteristic
487C2×C8C2×D4×C4311yescharacteristic
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4C2×D4×C4311yescharacteristic
499C4⋊C4C2×D4×C4311yescharacteristic
500C4⋊C4C2×D4×C4311yescharacteristic
501C4⋊C4C2×D4×C4311yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—41no—
512C42C24×C4311yescharacteristic
513C23—21no—
514C23—41no—
515C23—41no—
516Q8—21no—
517Q8—21no—
518Q8—21no—
519Q8—21no—
520Q8—21no—
521Q8—41no—
522Q8—41no—
523Q8—81no—
524Q8—82no—
525Q8—161no—
526Q8AGL(1,ℤ/8)×C4312yes—
527D4—21no—
528D4—21no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—82no—
538D4—81no—
539D4—81no—
540D4—161no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—82no—
553C2×C4—82no—
554C2×C4—161no—
555C2×C4C22×D4×C4311yescharacteristic
556C2×C4C22×D4×C4311yescharacteristic
557C2×C4H(5,𝔽2)×C4311yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22D42×C4311yescharacteristic
577C4—22no—
578C4—21no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—81no—
586C4—81no—
587C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
588C4C43×#57511yescharacteristic
589C4C43×#57711yescharacteristic
590C4C43×#57811yescharacteristic
591C2—81no—
592C2—161no—
593C2—161no—
594C2C43×#326511yescharacteristic
595C2C43×#327711yescharacteristic
596C2C43×#328811yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#1621C2
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×#3375C2semidirect
2. C43×#3373C2semidirect
3. C43×#3362C2semidirect
4. C43×#3278C2semidirect
5. C43×#1717C2semidirect
6. C43×#1698C2semidirect
7. C43×#1697C2semidirect
8. C43×#1686C2semidirect
9. C43×#1682C2semidirect
10. C43×#1645C2semidirect
11. C43×#1637C2semidirect
13. C43×#1620C2semidirect
14. C43×#1592C2semidirect
15. C43×#1584C2semidirect
268. #20205C43direct (N × H)
293. #3375C2×C43semidirect
294. #3373C2×C43semidirect
295. #3362C2×C43semidirect
296. #3278C2×C43semidirect
297. #1717C2×C43semidirect
298. #1698C2×C43semidirect
299. #1697C2×C43semidirect
300. #1686C2×C43semidirect
301. #1682C2×C43semidirect
302. #1645C2×C43semidirect
303. #1637C2×C43semidirect
305. #1620C2×C43semidirect
306. #1592C2×C43semidirect
307. #1584C2×C43semidirect
365. C43#20205direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33752
C43×#33732
C43×#33622
C43×#32782
C43×#17172
C43×#16982
C43×#16972
C43×#16862
C43×#16822
C43×#16452
C43×#16372
C43×#16212
C43×#16202
C43×#15922
C43×#15842
#2020543