Finite Group Databasebeta

← C43×#19543 #24939560

Subgroups — C43×#19543 #24939560

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3251C211yesmaximal, characteristic
2C43×#3248C211yesmaximal, characteristic, complemented
3C43×#3210C211yesmaximal, characteristic, complemented
4C43×#2993C211yesmaximal, characteristic, complemented
5C43×#1700C211yesmaximal, characteristic, complemented
6C43×#1699C211yesmaximal, characteristic, complemented
7C43×#1686C211yesmaximal, characteristic, complemented
8C43×#1685C211yesmaximal, characteristic, complemented
9C43×#1682C211yesmaximal, characteristic, complemented
10C43×#1681C211yesmaximal, characteristic, complemented
11C43×#1670C211yesmaximal, characteristic, complemented
12C43×#1669C211yesmaximal, characteristic, complemented
13C43×#1571C211yesmaximal, characteristic, complemented
14C43×#1561C211yesmaximal, characteristic, complemented
15C43×#1547C211yesmaximal, characteristic, complemented
16C43×#533C2211yescharacteristic
17C43×#532C2211yescharacteristic
18C43×#529C2211yescharacteristic
19C43×#494C2211yescharacteristic
20C43×#492C2211yescharacteristic
21C43×#487C2211yescharacteristic
22C43×#486C2211yescharacteristic
23C43×#479—21no—
24C43×#478—21no—
25C43×#475C2211yescharacteristic
26C43×#475C2211yescharacteristic
27C43×#474C2211yescharacteristic
28C43×#474C2211yescharacteristic
29C43×#469—21no—
30C43×#468—21no—
31C43×#467—21no—
32C43×#465—21no—
33C43×#464—21no—
34C43×#464—21no—
35C43×#464—21no—
36C43×#463—21no—
37C43×#462C2211yescharacteristic
38C43×#461C2211yescharacteristic
39C43×#460C2211yescharacteristic
40C43×#459C2211yescharacteristic
41C43×#452—21no—
42C43×#452—21no—
43C43×#446C2211yescharacteristic
44C8×Q8×C43C2211yescharacteristic
45C43×#436—21no—
46C43×#436C2211yescharacteristic
47C43×#435—21no—
48C8×D4×C43C2211yescharacteristic
49C43×#433—21no—
50C43×#431C2211yescharacteristic
51C43×#424—21no—
52C43×#423C2211yescharacteristic
53C43×#423C2211yescharacteristic
54C2×C4⋊C8×C43C2211yescharacteristic
55C43×#335C2211yescharacteristic
56C43×#335C2211yescharacteristic
57C43×#335C2211yescharacteristic
58C43×#335C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#332C2211yescharacteristic
62C43×#332C2211yescharacteristic
63C43×#332C2211yescharacteristic
64C43×#332C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#41×C43—21no—
68C2×Q16×C43—21no—
69C2×Q16×C43—21no—
70C2×Q16×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—21no—
75C2×D8×C43—21no—
76C2×M16×C43—21no—
77C2×M16×C43—21no—
78C2×M16×C43—21no—
79C22×C8×C43—21no—
80C22×C8×C43—21no—
81C4⋊Q8×C43C2311yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83C4⋊Q8×C43C2311yescharacteristic
84#127×C43C2311yescharacteristic
85#126×C43—21no—
86#125×C43—21no—
87#125×C43D411yescharacteristic
88#124×C43—21no—
89#124×C43D411yescharacteristic
90#123×C43—21no—
91C22⋊Q8×C43—21no—
92C22⋊Q8×C43—21no—
93C22⋊Q8×C43D411yescharacteristic
94#121×C43—21no—
95#121×C43—21no—
96#121×C43D411yescharacteristic
97C4×Q8×C43—21no—
98C4×Q8×C43—21no—
99C4×Q8×C43C2311yescharacteristic
100C4×D4×C43—21no—
101C4×D4×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43C2311yescharacteristic
104#117×C43—21no—
105#117×C43—21no—
106C2×C42×C43C2311yescharacteristic
107#107×C43—21no—
108#107×C43—21no—
109#106×C43—21no—
110#106×C43—21no—
111C4⋊C8×C43—21no—
112C4⋊C8×C43—21no—
113C4⋊C8×C43—21no—
114C4⋊C8×C43—21no—
115C4⋊C8×C43—21no—
116C4⋊C8×C43D411yescharacteristic
117C4⋊C8×C43D411yescharacteristic
118C4⋊C8×C43C2311yescharacteristic
119C4⋊C8×C43C2311yescharacteristic
120C4⋊C8×C43C2311yescharacteristic
121C4⋊C8×C43C2311yescharacteristic
122C4⋊C8×C43C2311yescharacteristic
123C4⋊C8×C43C2311yescharacteristic
124#103×C43—21no—
125#103×C43—21no—
126#103×C43—21no—
127#103×C43—21no—
128#103×C43—21no—
129#103×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—
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43D411yescharacteristic
139C22⋊C8×C43D411yescharacteristic
140#97×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—81no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—41no—
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—41no—
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43#4111yescharacteristic
161Q16×C43—81no—
162Q16×C43—81no—
163Q16×C43—81no—
164SD16×C43—81no—
165SD16×C43—81no—
166SD16×C43—81no—
167SD16×C43—81no—
168D8×C43—81no—
169M16×C43—81no—
170M16×C43—81no—
171M16×C43—81no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—81no—
179C2×C8×C43—81no—
180C2×C8×C43C2×D411yescharacteristic
181C2×C8×C43C2×D411yescharacteristic
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
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—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—41no—
195C4⋊C4×C43—41no—
196C4⋊C4×C43C2×D411yescharacteristic
197C4⋊C4×C43C2×D411yescharacteristic
198C22⋊C4×C43—21no—
199C22⋊C4×C43—21no—
200C22⋊C4×C43—21no—
201C22⋊C4×C43—21no—
202C22⋊C4×C43—21no—
203C22⋊C4×C43—41no—
204C22⋊C4×C43—41no—
205C22⋊C4×C43—41no—
206C42×C43—21no—
207C42×C43—41no—
208C42×C43C2×D411yescharacteristic
209C42×C43C2×D411yescharacteristic
210C42×C43#4111yescharacteristic
211C42×C43C2411yescharacteristic
212C23×C43—21no—
213C23×C43—41no—
214C23×C43#12111yescharacteristic
215Q8×C43—21no—
216Q8×C43—21no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—41no—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—81no—
230D4×C43—81no—
231D4×C43—82no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—82no—
246C2×C4×C43#12111yescharacteristic
247C2×C4×C43#12111yescharacteristic
248C2×C4×C43#12111yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—41no—
257C8×C43—41no—
258C8×C43—41no—
259C8×C43—41no—
260C8×C43—41no—
261C8×C43—41no—
262#19543C4311yesmaximal, characteristic, direct product factor, Sylow
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43C2×#12111yescharacteristic
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43#57611yescharacteristic
284C4×C43#57611yescharacteristic
285C4×C43#57711yescharacteristic
286C4×C43#57811yescharacteristic
287#3251C2×C4311yescharacteristic
288#3248C2×C4311yescharacteristic, complemented
289#3210C2×C4311yescharacteristic, complemented
290#2993C2×C4311yescharacteristic, complemented
291#1700C2×C4311yescharacteristic, complemented
292#1699C2×C4311yescharacteristic, complemented
293#1686C2×C4311yescharacteristic, complemented
294#1685C2×C4311yescharacteristic, complemented
295#1682C2×C4311yescharacteristic, complemented
296#1681C2×C4311yescharacteristic, complemented
297#1670C2×C4311yescharacteristic, complemented
298#1669C2×C4311yescharacteristic, complemented
299#1571C2×C4311yescharacteristic, complemented
300#1561C2×C4311yescharacteristic, complemented
301#1547C2×C4311yescharacteristic, complemented
302C2×C43—41no—
303C2×C43—81no—
304C2×C43—161no—
305C2×C43#304511yescharacteristic
306C2×C43#306111yescharacteristic
307C2×C43#306911yescharacteristic
308#533C22×C4311yescharacteristic
309#532C22×C4311yescharacteristic
310#529C22×C4311yescharacteristic
311#494C22×C4311yescharacteristic
312#492C22×C4311yescharacteristic
313#487C22×C4311yescharacteristic
314#486C22×C4311yescharacteristic
315#479—21no—
316#478—21no—
317#475C22×C4311yescharacteristic
318#475C22×C4311yescharacteristic
319#474C22×C4311yescharacteristic
320#474C22×C4311yescharacteristic
321#469—21no—
322#468—21no—
323#467—21no—
324#465—21no—
325#464—21no—
326#464—21no—
327#464—21no—
328#463—21no—
329#462C22×C4311yescharacteristic
330#461C22×C4311yescharacteristic
331#460C22×C4311yescharacteristic
332#459C22×C4311yescharacteristic
333#452—21no—
334#452—21no—
335#446C22×C4311yescharacteristic
336C8×Q8C22×C4311yescharacteristic
337#436—21no—
338#436C22×C4311yescharacteristic
339#435—21no—
340C8×D4C22×C4311yescharacteristic
341#433—21no—
342#431C22×C4311yescharacteristic
343#424—21no—
344#423C22×C4311yescharacteristic
345#423C22×C4311yescharacteristic
346C2×C4⋊C8C22×C4311yescharacteristic
347#335C22×C4311yescharacteristic
348#335C22×C4311yescharacteristic
349#335C22×C4311yescharacteristic
350#335C22×C4311yescharacteristic
351#332C22×C4311yescharacteristic
352#332C22×C4311yescharacteristic
353#332C22×C4311yescharacteristic
354#332C22×C4311yescharacteristic
355#332C22×C4311yescharacteristic
356#332C22×C4311yescharacteristic
357#331C22×C4311yescharacteristic
358#331C22×C4311yescharacteristic
359C43#1954311yescharacteristic, direct product factor, Sylow
360C2×#41—21no—
361C2×Q16—21no—
362C2×Q16—21no—
363C2×Q16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×D8—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C22×C8—21no—
373C22×C8—21no—
374C4⋊Q8C23×C4311yescharacteristic
375C4⋊Q8C23×C4311yescharacteristic
376C4⋊Q8C23×C4311yescharacteristic
377#127C23×C4311yescharacteristic
378#126—21no—
379#125—21no—
380#125D4×C4311yescharacteristic
381#124—21no—
382#124D4×C4311yescharacteristic
383#123—21no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8D4×C4311yescharacteristic
387#121—21no—
388#121—21no—
389#121D4×C4311yescharacteristic
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8C23×C4311yescharacteristic
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4C23×C4311yescharacteristic
397#117—21no—
398#117—21no—
399C2×C42C23×C4311yescharacteristic
400#107—21no—
401#107—21no—
402#106—21no—
403#106—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8D4×C4311yescharacteristic
410C4⋊C8D4×C4311yescharacteristic
411C4⋊C8C23×C4311yescharacteristic
412C4⋊C8C23×C4311yescharacteristic
413C4⋊C8C23×C4311yescharacteristic
414C4⋊C8C23×C4311yescharacteristic
415C4⋊C8C23×C4311yescharacteristic
416C4⋊C8C23×C4311yescharacteristic
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8D4×C4311yescharacteristic
432C22⋊C8D4×C4311yescharacteristic
433#97—21no—
434C4×C8—21no—
435C4×C8C23×C4311yescharacteristic
436C4×C8C23×C4311yescharacteristic
437#41—81no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×D4×C4311yescharacteristic
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4C2×D4×C4311yescharacteristic
449C22×C4—21no—
450C22×C4—41no—
451C22×C4C2×D4×C4311yescharacteristic
452C22×C4C2×D4×C4311yescharacteristic
453C22×C4#41×C4311yescharacteristic
454Q16—81no—
455Q16—81no—
456Q16—81no—
457SD16—81no—
458SD16—81no—
459SD16—81no—
460SD16—81no—
461D8—81no—
462M16—81no—
463M16—81no—
464M16—81no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—81no—
472C2×C8—81no—
473C2×C8C2×D4×C4311yescharacteristic
474C2×C8C2×D4×C4311yescharacteristic
475C2×C8C2×D4×C4311yescharacteristic
476C2×C8C2×D4×C4311yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4C2×D4×C4311yescharacteristic
490C4⋊C4C2×D4×C4311yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—21no—
500C42—41no—
501C42C2×D4×C4311yescharacteristic
502C42C2×D4×C4311yescharacteristic
503C42#41×C4311yescharacteristic
504C42C24×C4311yescharacteristic
505C23—21no—
506C23—41no—
507C23#121×C4311yescharacteristic
508Q8—21no—
509Q8—21no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516D4—21no—
517D4—21no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—81no—
523D4—81no—
524D4—82no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4#121×C4311yescharacteristic
540C2×C4#121×C4311yescharacteristic
541C2×C4#121×C4311yescharacteristic
542C2×C4C22×D4×C4311yescharacteristic
543C2×C4C22×D4×C4311yescharacteristic
544C2×C4C2×#41×C4311yescharacteristic
545C8—21no—
546C8—21no—
547C8—21no—
548C8—21no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22C2×#121×C4311yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C43×#57611yescharacteristic
576C4C43×#57611yescharacteristic
577C4C43×#57711yescharacteristic
578C4C43×#57811yescharacteristic
579C2—41no—
580C2—81no—
581C2—161no—
582C2C43×#304511yescharacteristic
583C2C43×#306111yescharacteristic
584C2C43×#306911yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3251C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C43×#3248C2semidirect
3. C43×#3210C2semidirect
4. C43×#2993C2semidirect
5. C43×#1700C2semidirect
6. C43×#1699C2semidirect
7. C43×#1686C2semidirect
8. C43×#1685C2semidirect
9. C43×#1682C2semidirect
10. C43×#1681C2semidirect
11. C43×#1670C2semidirect
12. C43×#1669C2semidirect
13. C43×#1571C2semidirect
14. C43×#1561C2semidirect
15. C43×#1547C2semidirect
262. #19543C43direct (N × H)
288. #3248C2×C43semidirect
289. #3210C2×C43semidirect
290. #2993C2×C43semidirect
291. #1700C2×C43semidirect
292. #1699C2×C43semidirect
293. #1686C2×C43semidirect
294. #1685C2×C43semidirect
295. #1682C2×C43semidirect
296. #1681C2×C43semidirect
297. #1670C2×C43semidirect
298. #1669C2×C43semidirect
299. #1571C2×C43semidirect
300. #1561C2×C43semidirect
301. #1547C2×C43semidirect
359. C43#19543direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32512
C43×#32482
C43×#32102
C43×#29932
C43×#17002
C43×#16992
C43×#16862
C43×#16852
C43×#16822
C43×#16812
C43×#16702
C43×#16692
C43×#15712
C43×#15612
C43×#15472
#1954343