Finite Group Databasebeta

← C43×#20267 #24940284

Subgroups — C43×#20267 #24940284

Order 11008.

616 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3398C211yesmaximal, characteristic, complemented
2C43×#3364C211yesmaximal, characteristic, complemented
3C43×#3324C211yesmaximal, characteristic
4C43×#3324C211yesmaximal, characteristic
5C43×#1720C211yesmaximal, characteristic, complemented
6C43×#1702C211yesmaximal, characteristic, complemented
7C43×#1699C211yesmaximal, characteristic, complemented
8C43×#1689C211yesmaximal, characteristic, complemented
9C43×#1682C211yesmaximal, characteristic, complemented
10C43×#1652C211yesmaximal, characteristic, complemented
11C43×#1652C211yesmaximal, characteristic, complemented
12C43×#1639C211yesmaximal, characteristic
13C43×#1626C211yesmaximal, characteristic, complemented
14C43×#1592C211yesmaximal, characteristic, complemented
15C43×#1583C211yesmaximal, characteristic, complemented
16C43×#557C2211yescharacteristic, complemented
17C43×#556C2211yescharacteristic
18C43×#556C2211yescharacteristic
19D42×C43C2211yescharacteristic
20C43×#498C2211yescharacteristic, complemented
21C43×#497—21no—
22C43×#494C2211yescharacteristic, complemented
23C43×#488—21no—
24C43×#487C2211yescharacteristic, complemented
25C43×#486C2211yescharacteristic
26C43×#486C2211yescharacteristic
27C43×#486C2211yescharacteristic
28C43×#482—21no—
29C43×#482—21no—
30C43×#479—21no—
31C43×#474C2211yescharacteristic
32C43×#474C2211yescharacteristic
33C43×#474C2211yescharacteristic
34C43×#468—21no—
35C43×#468—21no—
36C43×#464—21no—
37C43×#464—21no—
38C43×#462—21no—
39C43×#462C2211yescharacteristic, complemented
40C43×#462C2211yescharacteristic, complemented
41C43×#461C2211yescharacteristic
42C43×#460C2211yescharacteristic
43C43×#460C2211yescharacteristic
44C43×#450—21no—
45C43×#450—21no—
46C43×#446C2211yescharacteristic, complemented
47C8×Q8×C43C2211yescharacteristic, complemented
48C43×#441—21no—
49C4×Q16×C43—21no—
50C4×SD16×C43C2211yescharacteristic
51C4×SD16×C43C2211yescharacteristic
52C43×#436C2211yescharacteristic
53C43×#436C2211yescharacteristic
54C43×#418—21no—
55C43×#418—21no—
56C43×#335C2211yescharacteristic, complemented
57C43×#334C2211yescharacteristic, complemented
58C43×#332C2211yescharacteristic, complemented
59C43×#332C2211yescharacteristic, complemented
60C43×#332C2211yescharacteristic, complemented
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic, complemented
63C43×Q8⋊C8C2211yescharacteristic, complemented
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic, complemented
67C22×D4×C43—21no—
68C22×D4×C43—21no—
69C2×Q16×C43—21no—
70C2×Q16×C43—21no—
71C2×Q16×C43—21no—
72C2×Q16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—21no—
75C2×SD16×C43—21no—
76C2×SD16×C43D411yescharacteristic
77C2×SD16×C43D411yescharacteristic
78C2×M16×C43—21no—
79C2×M16×C43—21no—
80C4⋊Q8×C43—21no—
81C4⋊Q8×C43C2311yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83C4⋊Q8×C43C2311yescharacteristic
84#127×C43C2311yescharacteristic
85#126×C43—41no—
86#126×C43—41no—
87#125×C43—21no—
88#125×C43—41no—
89#124×C43—21no—
90#124×C43—21no—
91C22⋊Q8×C43—21no—
92C22⋊Q8×C43—21no—
93#121×C43—21no—
94#121×C43—21no—
95#120×C43—41no—
96C4×Q8×C43—21no—
97C4×Q8×C43—21no—
98C4×Q8×C43—21no—
99C4×Q8×C43—21no—
100C4×Q8×C43C2311yescharacteristic
101C4×Q8×C43C2311yescharacteristic
102C4×D4×C43C2311yescharacteristic
103C4×D4×C43C2311yescharacteristic
104#117×C43—21no—
105#117×C43—21no—
106#107×C43—21no—
107#107×C43—21no—
108#107×C43—21no—
109#106×C43—41no—
110#106×C43D411yescharacteristic
111#106×C43D411yescharacteristic
112C4⋊C8×C43—21no—
113C4⋊C8×C43—21no—
114C4⋊C8×C43C2311yescharacteristic
115C4⋊C8×C43C2311yescharacteristic
116C4⋊C8×C43C2311yescharacteristic
117C4⋊C8×C43C2311yescharacteristic
118#103×C43—21no—
119#103×C43—21no—
120#103×C43—21no—
121#103×C43—21no—
122#103×C43—21no—
123#103×C43D411yescharacteristic
124#103×C43D411yescharacteristic
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—41no—
135#102×C43D411yescharacteristic
136#102×C43D411yescharacteristic
137C22⋊C8×C43—21no—
138C22⋊C8×C43—21no—
139#97×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C24×C43—41no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—41no—
154C2×D4×C43—41no—
155C2×D4×C43—42no—
156C2×D4×C43—42no—
157C2×D4×C43—81no—
158C2×D4×C43—81no—
159C2×D4×C43C2×D411yescharacteristic
160C2×D4×C43C2×D411yescharacteristic
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163Q16×C43—42no—
164Q16×C43—42no—
165Q16×C43—81no—
166Q16×C43—81no—
167SD16×C43—41no—
168SD16×C43—41no—
169SD16×C43—81no—
170SD16×C43—81no—
171SD16×C43—81no—
172M16×C43—81no—
173M16×C43—81no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C2×C8×C43C2×D411yescharacteristic
182C2×C8×C43C2×D411yescharacteristic
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—41no—
192C4⋊C4×C43—41no—
193C4⋊C4×C43—41no—
194C4⋊C4×C43—41no—
195C4⋊C4×C43—41no—
196C4⋊C4×C43C2×D411yescharacteristic
197C4⋊C4×C43C2×D411yescharacteristic
198C4⋊C4×C43C2×D411yescharacteristic
199C4⋊C4×C43C2×D411yescharacteristic
200C22⋊C4×C43—21no—
201C22⋊C4×C43—21no—
202C22⋊C4×C43—41no—
203C22⋊C4×C43—41no—
204C22⋊C4×C43—41no—
205C22⋊C4×C43—41no—
206C22⋊C4×C43—41no—
207C42×C43—21no—
208C42×C43—21no—
209C42×C43—41no—
210C42×C43—41no—
211C42×C43—41no—
212C42×C43C2411yescharacteristic
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—41no—
216C23×C43—82no—
217C23×C43—82no—
218C23×C43—161no—
219Q8×C43—21no—
220Q8×C43—21no—
221Q8×C43—21no—
222Q8×C43—21no—
223Q8×C43—41no—
224Q8×C43—41no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×C43—41no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—21no—
232D4×C43—21no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
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—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
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—21no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43—41no—
263C8×C43—41no—
264C8×C43—41no—
265#20267C4311yesmaximal, characteristic, direct product factor, Sylow
266C22×C43—41no—
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×C43—164no—
276C22×C43D4211yescharacteristic
277C4×C43—21no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43—81no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43#57511yescharacteristic
288C4×C43#57511yescharacteristic
289C4×C43#57611yescharacteristic
290C4×C43#57711yescharacteristic
291#3398C2×C4311yescharacteristic, complemented
292#3364C2×C4311yescharacteristic, complemented
293#3324C2×C4311yescharacteristic
294#3324C2×C4311yescharacteristic
295#1720C2×C4311yescharacteristic, complemented
296#1702C2×C4311yescharacteristic, complemented
297#1699C2×C4311yescharacteristic, complemented
298#1689C2×C4311yescharacteristic, complemented
299#1682C2×C4311yescharacteristic, complemented
300#1652C2×C4311yescharacteristic, complemented
301#1652C2×C4311yescharacteristic, complemented
302#1639C2×C4311yescharacteristic
303#1626C2×C4311yescharacteristic, complemented
304#1592C2×C4311yescharacteristic, complemented
305#1583C2×C4311yescharacteristic, complemented
306C2×C43—81no—
307C2×C43—81no—
308C2×C43—161no—
309C2×C43#326811yescharacteristic
310C2×C43#327511yescharacteristic
311C2×C43#328911yescharacteristic
312#557C22×C4311yescharacteristic, complemented
313#556C22×C4311yescharacteristic
314#556C22×C4311yescharacteristic
315D42C22×C4311yescharacteristic
316#498C22×C4311yescharacteristic, complemented
317#497—21no—
318#494C22×C4311yescharacteristic, complemented
319#488—21no—
320#487C22×C4311yescharacteristic, complemented
321#486C22×C4311yescharacteristic
322#486C22×C4311yescharacteristic
323#486C22×C4311yescharacteristic
324#482—21no—
325#482—21no—
326#479—21no—
327#474C22×C4311yescharacteristic
328#474C22×C4311yescharacteristic
329#474C22×C4311yescharacteristic
330#468—21no—
331#468—21no—
332#464—21no—
333#464—21no—
334#462—21no—
335#462C22×C4311yescharacteristic, complemented
336#462C22×C4311yescharacteristic, complemented
337#461C22×C4311yescharacteristic
338#460C22×C4311yescharacteristic
339#460C22×C4311yescharacteristic
340#450—21no—
341#450—21no—
342#446C22×C4311yescharacteristic, complemented
343C8×Q8C22×C4311yescharacteristic, complemented
344#441—21no—
345C4×Q16—21no—
346C4×SD16C22×C4311yescharacteristic
347C4×SD16C22×C4311yescharacteristic
348#436C22×C4311yescharacteristic
349#436C22×C4311yescharacteristic
350#418—21no—
351#418—21no—
352#335C22×C4311yescharacteristic, complemented
353#334C22×C4311yescharacteristic, complemented
354#332C22×C4311yescharacteristic, complemented
355#332C22×C4311yescharacteristic, complemented
356#332C22×C4311yescharacteristic, complemented
357#331C22×C4311yescharacteristic
358Q8⋊C8C22×C4311yescharacteristic, complemented
359Q8⋊C8C22×C4311yescharacteristic, complemented
360D4⋊C8C22×C4311yescharacteristic
361D4⋊C8C22×C4311yescharacteristic
362#322C22×C4311yescharacteristic, complemented
363C43#2026711yescharacteristic, direct product factor, Sylow
364C22×D4—21no—
365C22×D4—21no—
366C2×Q16—21no—
367C2×Q16—21no—
368C2×Q16—21no—
369C2×Q16—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16D4×C4311yescharacteristic
374C2×SD16D4×C4311yescharacteristic
375C2×M16—21no—
376C2×M16—21no—
377C4⋊Q8—21no—
378C4⋊Q8C23×C4311yescharacteristic
379C4⋊Q8C23×C4311yescharacteristic
380C4⋊Q8C23×C4311yescharacteristic
381#127C23×C4311yescharacteristic
382#126—41no—
383#126—41no—
384#125—21no—
385#125—41no—
386#124—21no—
387#124—21no—
388C22⋊Q8—21no—
389C22⋊Q8—21no—
390#121—21no—
391#121—21no—
392#120—41no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8C23×C4311yescharacteristic
398C4×Q8C23×C4311yescharacteristic
399C4×D4C23×C4311yescharacteristic
400C4×D4C23×C4311yescharacteristic
401#117—21no—
402#117—21no—
403#107—21no—
404#107—21no—
405#107—21no—
406#106—41no—
407#106D4×C4311yescharacteristic
408#106D4×C4311yescharacteristic
409C4⋊C8—21no—
410C4⋊C8—21no—
411C4⋊C8C23×C4311yescharacteristic
412C4⋊C8C23×C4311yescharacteristic
413C4⋊C8C23×C4311yescharacteristic
414C4⋊C8C23×C4311yescharacteristic
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103D4×C4311yescharacteristic
421#103D4×C4311yescharacteristic
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—41no—
432#102D4×C4311yescharacteristic
433#102D4×C4311yescharacteristic
434C22⋊C8—21no—
435C22⋊C8—21no—
436#97—21no—
437C4×C8—21no—
438C4×C8C23×C4311yescharacteristic
439C4×C8C23×C4311yescharacteristic
440C4×C8C23×C4311yescharacteristic
441C24—41no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8C2×D4×C4311yescharacteristic
446C2×Q8C2×D4×C4311yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—81no—
455C2×D4—81no—
456C2×D4C2×D4×C4311yescharacteristic
457C2×D4C2×D4×C4311yescharacteristic
458C22×C4—21no—
459C22×C4—21no—
460Q16—42no—
461Q16—42no—
462Q16—81no—
463Q16—81no—
464SD16—41no—
465SD16—41no—
466SD16—81no—
467SD16—81no—
468SD16—81no—
469M16—81no—
470M16—81no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8C2×D4×C4311yescharacteristic
477C2×C8C2×D4×C4311yescharacteristic
478C2×C8C2×D4×C4311yescharacteristic
479C2×C8C2×D4×C4311yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4C2×D4×C4311yescharacteristic
494C4⋊C4C2×D4×C4311yescharacteristic
495C4⋊C4C2×D4×C4311yescharacteristic
496C4⋊C4C2×D4×C4311yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C42—21no—
505C42—21no—
506C42—41no—
507C42—41no—
508C42—41no—
509C42C24×C4311yescharacteristic
510C23—21no—
511C23—21no—
512C23—41no—
513C23—82no—
514C23—82no—
515C23—161no—
516Q8—21no—
517Q8—21no—
518Q8—21no—
519Q8—21no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—41no—
525Q8—41no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—81no—
535D4—82no—
536D4—82no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4C22×D4×C4311yescharacteristic
551C2×C4C22×D4×C4311yescharacteristic
552C2×C4H(5,𝔽2)×C4311yescharacteristic
553C8—21no—
554C8—21no—
555C8—21no—
556C8—21no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—164no—
572C22D42×C4311yescharacteristic
573C4—21no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4C43×#57511yescharacteristic
584C4C43×#57511yescharacteristic
585C4C43×#57611yescharacteristic
586C4C43×#57711yescharacteristic
587C2—81no—
588C2—81no—
589C2—161no—
590C2C43×#326811yescharacteristic
591C2C43×#327511yescharacteristic
592C2C43×#328911yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalD42×C43C22
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×#3398C2semidirect
2. C43×#3364C2semidirect
5. C43×#1720C2semidirect
6. C43×#1702C2semidirect
7. C43×#1699C2semidirect
8. C43×#1689C2semidirect
9. C43×#1682C2semidirect
10. C43×#1652C2semidirect
11. C43×#1652C2semidirect
13. C43×#1626C2semidirect
14. C43×#1592C2semidirect
15. C43×#1583C2semidirect
16. C43×#557C22semidirect
20. C43×#498C22semidirect
22. C43×#494C22semidirect
24. C43×#487C22semidirect
39. C43×#462C22semidirect
40. C43×#462C22semidirect
46. C43×#446C22semidirect
47. C8×Q8×C43C22semidirect
56. C43×#335C22semidirect
57. C43×#334C22semidirect
58. C43×#332C22semidirect
59. C43×#332C22semidirect
60. C43×#332C22semidirect
62. C43×Q8⋊C8C22semidirect
63. C43×Q8⋊C8C22semidirect
66. C43×#322C22semidirect
265. #20267C43direct (N × H)
291. #3398C2×C43semidirect
292. #3364C2×C43semidirect
295. #1720C2×C43semidirect
296. #1702C2×C43semidirect
297. #1699C2×C43semidirect
298. #1689C2×C43semidirect
299. #1682C2×C43semidirect
300. #1652C2×C43semidirect
301. #1652C2×C43semidirect
303. #1626C2×C43semidirect
304. #1592C2×C43semidirect
305. #1583C2×C43semidirect
312. #557C22×C43semidirect
316. #498C22×C43semidirect
318. #494C22×C43semidirect
320. #487C22×C43semidirect
335. #462C22×C43semidirect
336. #462C22×C43semidirect
342. #446C22×C43semidirect
343. C8×Q8C22×C43semidirect
352. #335C22×C43semidirect
353. #334C22×C43semidirect
354. #332C22×C43semidirect
355. #332C22×C43semidirect
356. #332C22×C43semidirect
358. Q8⋊C8C22×C43semidirect
359. Q8⋊C8C22×C43semidirect
362. #322C22×C43semidirect
363. C43#20267direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33982
C43×#33642
C43×#33242
C43×#17202
C43×#17022
C43×#16992
C43×#16892
C43×#16822
C43×#16522
C43×#16392
C43×#16262
C43×#15922
C43×#15832
#2026743