Finite Group Databasebeta

← C43×#19862 #24939879

Subgroups — C43×#19862 #24939879

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3354C211yesmaximal, characteristic, complemented
2C43×#3341C211yesmaximal, characteristic, complemented
3C43×#3341C211yesmaximal, characteristic, complemented
4C43×#3303C211yesmaximal, characteristic, complemented
5C43×#1723C211yesmaximal, characteristic, complemented
6C43×#1695C211yesmaximal, characteristic, complemented
7C43×#1683C211yesmaximal, characteristic, complemented
8C43×#1675C211yesmaximal, characteristic, complemented
9C43×#1671C211yesmaximal, characteristic, complemented
10C43×#1646C211yesmaximal, characteristic, complemented
11C43×#1635C211yesmaximal, characteristic, complemented
12C43×#1634C211yesmaximal, characteristic, complemented
13C43×#1634C211yesmaximal, characteristic, complemented
14C43×#1581C211yesmaximal, characteristic, complemented
15C43×#1580C211yesmaximal, characteristic, complemented
16C43×#555C2211yescharacteristic
17C43×#555C2211yescharacteristic
18C43×#555C2211yescharacteristic
19C43×#547C2211yescharacteristic
20C43×#500C2211yescharacteristic
21C43×#500C2211yescharacteristic
22C43×#498C2211yescharacteristic
23C43×#494C2211yescharacteristic
24C43×#487C2211yescharacteristic
25C43×#487C2211yescharacteristic
26C43×#485—21no—
27C43×#482—21no—
28C43×#482—21no—
29C43×#482—21no—
30C43×#482—21no—
31C43×#482—21no—
32C43×#481—21no—
33C43×#476C2211yescharacteristic
34C43×#476C2211yescharacteristic
35C43×#476C2211yescharacteristic
36C43×#476C2211yescharacteristic
37C43×#476C2211yescharacteristic
38C43×#476C2211yescharacteristic
39C43×#474C2211yescharacteristic
40C43×#469—21no—
41C43×#466—21no—
42C43×#466—21no—
43C43×#465—21no—
44C43×#461C2211yescharacteristic
45C43×#449—21no—
46C4×D8×C43C2211yescharacteristic
47C4×D8×C43C2211yescharacteristic
48C43×#436C2211yescharacteristic
49C8×D4×C43C2211yescharacteristic
50C8×D4×C43C2211yescharacteristic
51C8×D4×C43C2211yescharacteristic
52C43×#428—21no—
53C43×#427—21no—
54C43×#427—21no—
55C43×#416—21no—
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#333C2211yescharacteristic
59C43×#333C2211yescharacteristic
60C43×#333C2211yescharacteristic
61C43×#332C2211yescharacteristic
62C43×D4⋊C8C2211yescharacteristic
63C43×D4⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#41×C43—21no—
68C2×Q16×C43—41no—
69C2×SD16×C43—21no—
70C2×D8×C43D411yescharacteristic
71C2×D8×C43D411yescharacteristic
72C2×M16×C43—21no—
73C22×C8×C43—21no—
74C22×C8×C43—21no—
75C22×C8×C43—21no—
76C4⋊Q8×C43C2311yescharacteristic
77C4⋊Q8×C43C2311yescharacteristic
78C4⋊Q8×C43C2311yescharacteristic
79C4⋊Q8×C43C2311yescharacteristic
80#124×C43—41no—
81#124×C43—41no—
82#124×C43—41no—
83#123×C43—41no—
84C22⋊Q8×C43—21no—
85#121×C43—21no—
86#121×C43—21no—
87#121×C43—21no—
88#121×C43—21no—
89#121×C43—21no—
90#121×C43—21no—
91#121×C43—21no—
92C4×D4×C43C2311yescharacteristic
93C4×D4×C43C2311yescharacteristic
94C4×D4×C43C2311yescharacteristic
95C4×D4×C43C2311yescharacteristic
96#117×C43—21no—
97#117×C43—21no—
98#117×C43—21no—
99#117×C43—21no—
100#117×C43—21no—
101#117×C43—21no—
102C2×C4⋊C4×C43—21no—
103#107×C43—21no—
104#107×C43—21no—
105#107×C43—21no—
106#107×C43—21no—
107#107×C43—21no—
108#107×C43D411yescharacteristic
109#107×C43D411yescharacteristic
110#106×C43—21no—
111#106×C43—21no—
112#106×C43—21no—
113#106×C43—21no—
114#106×C43—21no—
115#106×C43—21no—
116#106×C43—21no—
117#106×C43—21no—
118C4⋊C8×C43C2311yescharacteristic
119C4⋊C8×C43C2311yescharacteristic
120C4⋊C8×C43C2311yescharacteristic
121C4⋊C8×C43C2311yescharacteristic
122#103×C43—21no—
123#103×C43—21no—
124#103×C43—21no—
125#103×C43—41no—
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×C43D411yescharacteristic
134#102×C43D411yescharacteristic
135#102×C43D411yescharacteristic
136#102×C43D411yescharacteristic
137C22⋊C8×C43—21no—
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—42no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×D4×C43—41no—
151C2×D4×C43—41no—
152C2×D4×C43—41no—
153C2×D4×C43—41no—
154C2×D4×C43C2×D411yescharacteristic
155C2×D4×C43C2×D411yescharacteristic
156C2×D4×C43C2×D411yescharacteristic
157C2×D4×C43C2×D411yescharacteristic
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—41no—
163Q16×C43—82no—
164SD16×C43—81no—
165D8×C43—22no—
166D8×C43—41no—
167M16×C43—42no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—42no—
174C2×C8×C43—42no—
175C2×C8×C43—81no—
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—41no—
189C4⋊C4×C43C2×D411yescharacteristic
190C4⋊C4×C43C2×D411yescharacteristic
191C4⋊C4×C43C2×D411yescharacteristic
192C4⋊C4×C43C2×D411yescharacteristic
193C22⋊C4×C43—21no—
194C22⋊C4×C43—21no—
195C22⋊C4×C43—21no—
196C22⋊C4×C43—21no—
197C22⋊C4×C43—41no—
198C22⋊C4×C43—41no—
199C22⋊C4×C43—41no—
200C22⋊C4×C43—41no—
201C22⋊C4×C43—41no—
202C22⋊C4×C43—41no—
203C22⋊C4×C43—41no—
204C42×C43—41no—
205C42×C43—41no—
206C42×C43—41no—
207C42×C43C2411yescharacteristic
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—81no—
215Q8×C43—81no—
216Q8×C43—81no—
217D4×C43—21no—
218D4×C43—21no—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43—82no—
226D4×C43—161no—
227D4×C43—161no—
228D4×C43—161no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43H(5,𝔽2)11yescharacteristic
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—21no—
252C8×C43—41no—
253C8×C43—41no—
254C8×C43—41no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43#13512yes—
258#19862C4311yesmaximal, characteristic, direct product factor, Sylow
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43D4211yescharacteristic
272C4×C43—21no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—81no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43C2×#13511yescharacteristic
282C4×C43#57511yescharacteristic
283C4×C43#57711yescharacteristic
284C4×C43#57811yescharacteristic
285#3354C2×C4311yescharacteristic, complemented
286#3341C2×C4311yescharacteristic, complemented
287#3341C2×C4311yescharacteristic, complemented
288#3303C2×C4311yescharacteristic, complemented
289#1723C2×C4311yescharacteristic, complemented
290#1695C2×C4311yescharacteristic, complemented
291#1683C2×C4311yescharacteristic, complemented
292#1675C2×C4311yescharacteristic, complemented
293#1671C2×C4311yescharacteristic, complemented
294#1646C2×C4311yescharacteristic, complemented
295#1635C2×C4311yescharacteristic, complemented
296#1634C2×C4311yescharacteristic, complemented
297#1634C2×C4311yescharacteristic, complemented
298#1581C2×C4311yescharacteristic, complemented
299#1580C2×C4311yescharacteristic, complemented
300C2×C43—81no—
301C2×C43—81no—
302C2×C43—81no—
303C2×C43—81no—
304C2×C43#326711yescharacteristic
305C2×C43#328311yescharacteristic
306C2×C43#328811yescharacteristic
307#555C22×C4311yescharacteristic
308#555C22×C4311yescharacteristic
309#555C22×C4311yescharacteristic
310#547C22×C4311yescharacteristic
311#500C22×C4311yescharacteristic
312#500C22×C4311yescharacteristic
313#498C22×C4311yescharacteristic
314#494C22×C4311yescharacteristic
315#487C22×C4311yescharacteristic
316#487C22×C4311yescharacteristic
317#485—21no—
318#482—21no—
319#482—21no—
320#482—21no—
321#482—21no—
322#482—21no—
323#481—21no—
324#476C22×C4311yescharacteristic
325#476C22×C4311yescharacteristic
326#476C22×C4311yescharacteristic
327#476C22×C4311yescharacteristic
328#476C22×C4311yescharacteristic
329#476C22×C4311yescharacteristic
330#474C22×C4311yescharacteristic
331#469—21no—
332#466—21no—
333#466—21no—
334#465—21no—
335#461C22×C4311yescharacteristic
336#449—21no—
337C4×D8C22×C4311yescharacteristic
338C4×D8C22×C4311yescharacteristic
339#436C22×C4311yescharacteristic
340C8×D4C22×C4311yescharacteristic
341C8×D4C22×C4311yescharacteristic
342C8×D4C22×C4311yescharacteristic
343#428—21no—
344#427—21no—
345#427—21no—
346#416—21no—
347#335C22×C4311yescharacteristic
348#334C22×C4311yescharacteristic
349#333C22×C4311yescharacteristic
350#333C22×C4311yescharacteristic
351#333C22×C4311yescharacteristic
352#332C22×C4311yescharacteristic
353D4⋊C8C22×C4311yescharacteristic
354D4⋊C8C22×C4311yescharacteristic
355D4⋊C8C22×C4311yescharacteristic
356D4⋊C8C22×C4311yescharacteristic
357#322C22×C4311yescharacteristic
358C43#1986211yescharacteristic, direct product factor, Sylow
359C2×#41—21no—
360C2×Q16—41no—
361C2×SD16—21no—
362C2×D8D4×C4311yescharacteristic
363C2×D8D4×C4311yescharacteristic
364C2×M16—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C4⋊Q8C23×C4311yescharacteristic
369C4⋊Q8C23×C4311yescharacteristic
370C4⋊Q8C23×C4311yescharacteristic
371C4⋊Q8C23×C4311yescharacteristic
372#124—41no—
373#124—41no—
374#124—41no—
375#123—41no—
376C22⋊Q8—21no—
377#121—21no—
378#121—21no—
379#121—21no—
380#121—21no—
381#121—21no—
382#121—21no—
383#121—21no—
384C4×D4C23×C4311yescharacteristic
385C4×D4C23×C4311yescharacteristic
386C4×D4C23×C4311yescharacteristic
387C4×D4C23×C4311yescharacteristic
388#117—21no—
389#117—21no—
390#117—21no—
391#117—21no—
392#117—21no—
393#117—21no—
394C2×C4⋊C4—21no—
395#107—21no—
396#107—21no—
397#107—21no—
398#107—21no—
399#107—21no—
400#107D4×C4311yescharacteristic
401#107D4×C4311yescharacteristic
402#106—21no—
403#106—21no—
404#106—21no—
405#106—21no—
406#106—21no—
407#106—21no—
408#106—21no—
409#106—21no—
410C4⋊C8C23×C4311yescharacteristic
411C4⋊C8C23×C4311yescharacteristic
412C4⋊C8C23×C4311yescharacteristic
413C4⋊C8C23×C4311yescharacteristic
414#103—21no—
415#103—21no—
416#103—21no—
417#103—41no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102D4×C4311yescharacteristic
426#102D4×C4311yescharacteristic
427#102D4×C4311yescharacteristic
428#102D4×C4311yescharacteristic
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—21no—
432C22⋊C8—21no—
433C4×C8C23×C4311yescharacteristic
434C4×C8C23×C4311yescharacteristic
435C4×C8C23×C4311yescharacteristic
436#41—42no—
437#41—81no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4C2×D4×C4311yescharacteristic
447C2×D4C2×D4×C4311yescharacteristic
448C2×D4C2×D4×C4311yescharacteristic
449C2×D4C2×D4×C4311yescharacteristic
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—41no—
455Q16—82no—
456SD16—81no—
457D8—22no—
458D8—41no—
459M16—42no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—42no—
466C2×C8—42no—
467C2×C8—81no—
468C2×C8C2×D4×C4311yescharacteristic
469C2×C8C2×D4×C4311yescharacteristic
470C2×C8C2×D4×C4311yescharacteristic
471C2×C8C2×D4×C4311yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4C2×D4×C4311yescharacteristic
482C4⋊C4C2×D4×C4311yescharacteristic
483C4⋊C4C2×D4×C4311yescharacteristic
484C4⋊C4C2×D4×C4311yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C42—41no—
497C42—41no—
498C42—41no—
499C42C24×C4311yescharacteristic
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504Q8—41no—
505Q8—41no—
506Q8—81no—
507Q8—81no—
508Q8—81no—
509D4—21no—
510D4—21no—
511D4—21no—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—21no—
517D4—82no—
518D4—161no—
519D4—161no—
520D4—161no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—82no—
538C2×C4C22×D4×C4311yescharacteristic
539C2×C4C22×D4×C4311yescharacteristic
540C2×C4H(5,𝔽2)×C4311yescharacteristic
541C8—21no—
542C8—21no—
543C8—21no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8#135×C4312yes—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22D42×C4311yescharacteristic
563C4—21no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4C2×#135×C4311yescharacteristic
573C4C43×#57511yescharacteristic
574C4C43×#57711yescharacteristic
575C4C43×#57811yescharacteristic
576C2—81no—
577C2—81no—
578C2—81no—
579C2—81no—
580C2C43×#326711yescharacteristic
581C2C43×#328311yescharacteristic
582C2C43×#328811yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
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×#3354C2semidirect
2. C43×#3341C2semidirect
3. C43×#3341C2semidirect
4. C43×#3303C2semidirect
5. C43×#1723C2semidirect
6. C43×#1695C2semidirect
7. C43×#1683C2semidirect
8. C43×#1675C2semidirect
9. C43×#1671C2semidirect
10. C43×#1646C2semidirect
11. C43×#1635C2semidirect
12. C43×#1634C2semidirect
13. C43×#1634C2semidirect
14. C43×#1581C2semidirect
15. C43×#1580C2semidirect
258. #19862C43direct (N × H)
285. #3354C2×C43semidirect
286. #3341C2×C43semidirect
287. #3341C2×C43semidirect
288. #3303C2×C43semidirect
289. #1723C2×C43semidirect
290. #1695C2×C43semidirect
291. #1683C2×C43semidirect
292. #1675C2×C43semidirect
293. #1671C2×C43semidirect
294. #1646C2×C43semidirect
295. #1635C2×C43semidirect
296. #1634C2×C43semidirect
297. #1634C2×C43semidirect
298. #1581C2×C43semidirect
299. #1580C2×C43semidirect
358. C43#19862direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33542
C43×#33412
C43×#33032
C43×#17232
C43×#16952
C43×#16832
C43×#16752
C43×#16712
C43×#16462
C43×#16352
C43×#16342
C43×#15812
C43×#15802
#1986243