Finite Group Databasebeta

← C43×#18320 #24938337

Subgroups — C43×#18320 #24938337

Order 11008.

1008 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#539C211yesmaximal, characteristic, complemented
2C43×#3193C211yesmaximal, characteristic, complemented
3C43×#3192C211yesmaximal, characteristic
4C43×#2591C211yesmaximal, characteristic, complemented
5C43×#1615C214yesmaximal, complemented
6C43×#1597C214yesmaximal, complemented
7C43×#1508C211yesmaximal, characteristic, complemented
8C43×#1507C211yesmaximal, characteristic, complemented
9C43×#1463C211yesmaximal, characteristic, complemented
10C43×#539—22no—
11C43×#539—22no—
12C43×#539—22no—
13C43×#539C2214yes—
14C2×#126×C43—21no—
15C2×#125×C43—21no—
16C2×#123×C43—21no—
17C2×#123×C43—21no—
18C2×C22⋊Q8×C43—21no—
19C2×C22⋊Q8×C43C2211yescharacteristic
20C2×#121×C43C2211yescharacteristic
21C2×#121×C43C2211yescharacteristic
22C2×C4×D4×C43—21no—
23C22×C4⋊C4×C43C2211yescharacteristic
24C43×#484C2212yescomplemented
25C43×#481—21no—
26C43×#481C2212yes—
27C43×#480—21no—
28C43×#469—22no—
29C43×#468—22no—
30C43×#450C2212yescomplemented
31C43×#448—21no—
32C43×#447—21no—
33C43×#447C2212yes—
34C43×#407C2211yescharacteristic
35C43×#407C2211yescharacteristic
36C43×#400C2212yescomplemented
37C43×#394C2212yescomplemented
38C43×#388—22no—
39C43×#386—21no—
40C43×#386—21no—
41C4×C22⋊C4×C43C2211yescharacteristic
42C43×#328C2214yescomplemented
43C43×#327C2214yes—
44C43×#324C2214yescomplemented
45C22×Q8×C43D411yescharacteristic
46C22×D4×C43—21no—
47C22×D4×C43—21no—
48C22×D4×C43D411yescharacteristic
49C22×D4×C43C2311yescharacteristic
50C23×C4×C43—21no—
51C23×C4×C43D411yescharacteristic
52C23×C4×C43D411yescharacteristic
53C23×C4×C43C2311yescharacteristic
54C2×SD16×C43—22no—
55C2×D8×C43—22no—
56C2×M16×C43—21no—
57C2×M16×C43—21no—
58#126×C43—24no—
59#126×C43—24no—
60#125×C43—24no—
61#125×C43—24no—
62#123×C43—24no—
63#123×C43—24no—
64#123×C43—24no—
65#123×C43—24no—
66C22⋊Q8×C43—24no—
67C22⋊Q8×C43—24no—
68C22⋊Q8×C43—21no—
69C22⋊Q8×C43—21no—
70C22⋊Q8×C43D412yes—
71C22⋊Q8×C43C2312yes—
72#121×C43—21no—
73#121×C43—21no—
74#121×C43—21no—
75#121×C43—21no—
76#121×C43—21no—
77#121×C43—21no—
78#121×C43D412yes—
79#121×C43C2312yes—
80C4×D4×C43—24no—
81C4×D4×C43—24no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43—21no—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43—21no—
86C2×C4⋊C4×C43—21no—
87C2×C4⋊C4×C43—21no—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43D412yes—
91C2×C4⋊C4×C43D411yescharacteristic
92C2×C4⋊C4×C43D411yescharacteristic
93C2×C4⋊C4×C43C2311yescharacteristic
94C2×C4⋊C4×C43C2312yes—
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C22⋊C4×C43—21no—
98C2×C22⋊C4×C43—21no—
99C2×C22⋊C4×C43—21no—
100C2×C22⋊C4×C43—21no—
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—22no—
103C2×C22⋊C4×C43—22no—
104C2×C42×C43—21no—
105C2×C42×C43—21no—
106#107×C43—22no—
107#106×C43—22no—
108#103×C43—22no—
109#102×C43—22no—
110#102×C43—22no—
111#102×C43—22no—
112C22⋊C8×C43—21no—
113C22⋊C8×C43—21no—
114C22⋊C8×C43C2312yes—
115C22⋊C8×C43C2312yes—
116#95×C43—22no—
117#95×C43—22no—
118#95×C43C2312yes—
119C24×C43—21no—
120C24×C43—21no—
121C24×C43C2×D411yescharacteristic
122C2×Q8×C43—21no—
123C2×Q8×C43—81no—
124C2×Q8×C43C2×D412yes—
125C2×D4×C43—21no—
126C2×D4×C43—22no—
127C2×D4×C43—22no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—44no—
131C2×D4×C43—44no—
132C2×D4×C43—41no—
133C2×D4×C43—41no—
134C2×D4×C43—81no—
135C2×D4×C43—81no—
136C2×D4×C43C2×D412yes—
137C22×C4×C43—24no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—22no—
147C22×C4×C43—42no—
148C22×C4×C43—81no—
149C22×C4×C43—81no—
150C22×C4×C43—82no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D412yes—
156C22×C4×C43C2×D412yes—
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2411yescharacteristic
159SD16×C43—82no—
160D8×C43—82no—
161M16×C43—81no—
162M16×C43—81no—
163C2×C8×C43—22no—
164C2×C8×C43—22no—
165C4⋊C4×C43—24no—
166C4⋊C4×C43—24no—
167C4⋊C4×C43—24no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43—22no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—22no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43C2×D412yes—
179C4⋊C4×C43C2×D412yes—
180C22⋊C4×C43—24no—
181C22⋊C4×C43—24no—
182C22⋊C4×C43—24no—
183C22⋊C4×C43—22no—
184C22⋊C4×C43—22no—
185C22⋊C4×C43—22no—
186C22⋊C4×C43—22no—
187C22⋊C4×C43—42no—
188C22⋊C4×C43—44no—
189C22⋊C4×C43—41no—
190C22⋊C4×C43—41no—
191C22⋊C4×C43—82no—
192C42×C43—24no—
193C42×C43—81no—
194C23×C43—22no—
195C23×C43—22no—
196C23×C43—22no—
197C23×C43—41no—
198C23×C43—42no—
199C23×C43—42no—
200C23×C43—42no—
201C23×C43—42no—
202C23×C43—42no—
203C23×C43—41no—
204C23×C43—42no—
205C23×C43#12011yescharacteristic
206C23×C43#12011yescharacteristic
207C23×C43C22×D411yescharacteristic
208Q8×C43—42no—
209Q8×C43—81no—
210D4×C43—42no—
211D4×C43—42no—
212D4×C43—42no—
213D4×C43—44no—
214D4×C43—44no—
215D4×C43—81no—
216D4×C43—82no—
217D4×C43—82no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—41no—
242C2×C4×C43—42no—
243C2×C4×C43—81no—
244C2×C4×C43—84no—
245C2×C4×C43#12011yescharacteristic
246C2×C4×C43#12011yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C8×C43—42no—
250C8×C43—42no—
251#18320C4311yesmaximal, characteristic, direct product factor, Sylow
252C22×C43—21no—
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—44no—
260C22×C43—42no—
261C22×C43—42no—
262C22×C43—42no—
263C22×C43—84no—
264C22×C43—84no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43#45412yes—
269C22×C43C2×#12011yescharacteristic
270C22×C43#57512yes—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—42no—
276C4×C43—42no—
277C4×C43—42no—
278C4×C43—42no—
279C4×C43—42no—
280C4×C43—82no—
281C4×C43—81no—
282C2×#539C2×C4311yescharacteristic, complemented
283#3193C2×C4311yescharacteristic, complemented
284#3192C2×C4311yescharacteristic
285#2591C2×C4311yescharacteristic, complemented
286#1615C2×C4314yescomplemented
287#1597C2×C4314yescomplemented
288#1508C2×C4311yescharacteristic, complemented
289#1507C2×C4311yescharacteristic, complemented
290#1463C2×C4311yescharacteristic, complemented
291C2×C43—22no—
292C2×C43—22no—
293C2×C43—41no—
294C2×C43—82no—
295C2×C43—161no—
296C2×C43#300511yescharacteristic
297C2×C43C2×#45411yescharacteristic
298C2×C43#302611yescharacteristic
299#539—22no—
300#539—22no—
301#539—22no—
302#539C22×C4314yes—
303C2×#126—21no—
304C2×#125—21no—
305C2×#123—21no—
306C2×#123—21no—
307C2×C22⋊Q8—21no—
308C2×C22⋊Q8C22×C4311yescharacteristic
309C2×#121C22×C4311yescharacteristic
310C2×#121C22×C4311yescharacteristic
311C2×C4×D4—21no—
312C22×C4⋊C4C22×C4311yescharacteristic
313#484C22×C4312yescomplemented
314#481—21no—
315#481C22×C4312yes—
316#480—21no—
317#469—22no—
318#468—22no—
319#450C22×C4312yescomplemented
320#448—21no—
321#447—21no—
322#447C22×C4312yes—
323#407C22×C4311yescharacteristic
324#407C22×C4311yescharacteristic
325#400C22×C4312yescomplemented
326#394C22×C4312yescomplemented
327#388—22no—
328#386—21no—
329#386—21no—
330C4×C22⋊C4C22×C4311yescharacteristic
331#328C22×C4314yescomplemented
332#327C22×C4314yes—
333#324C22×C4314yescomplemented
334C43#1832011yescharacteristic, direct product factor, Sylow
335C22×Q8D4×C4311yescharacteristic
336C22×D4—21no—
337C22×D4—21no—
338C22×D4D4×C4311yescharacteristic
339C22×D4C23×C4311yescharacteristic
340C23×C4—21no—
341C23×C4D4×C4311yescharacteristic
342C23×C4D4×C4311yescharacteristic
343C23×C4C23×C4311yescharacteristic
344C2×SD16—22no—
345C2×D8—22no—
346C2×M16—21no—
347C2×M16—21no—
348#126—24no—
349#126—24no—
350#125—24no—
351#125—24no—
352#123—24no—
353#123—24no—
354#123—24no—
355#123—24no—
356C22⋊Q8—24no—
357C22⋊Q8—24no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8D4×C4312yes—
361C22⋊Q8C23×C4312yes—
362#121—21no—
363#121—21no—
364#121—21no—
365#121—21no—
366#121—21no—
367#121—21no—
368#121D4×C4312yes—
369#121C23×C4312yes—
370C4×D4—24no—
371C4×D4—24no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4D4×C4312yes—
381C2×C4⋊C4D4×C4311yescharacteristic
382C2×C4⋊C4D4×C4311yescharacteristic
383C2×C4⋊C4C23×C4311yescharacteristic
384C2×C4⋊C4C23×C4312yes—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C42—21no—
395C2×C42—21no—
396#107—22no—
397#106—22no—
398#103—22no—
399#102—22no—
400#102—22no—
401#102—22no—
402C22⋊C8—21no—
403C22⋊C8—21no—
404C22⋊C8C23×C4312yes—
405C22⋊C8C23×C4312yes—
406#95—22no—
407#95—22no—
408#95C23×C4312yes—
409C24—21no—
410C24—21no—
411C24C2×D4×C4311yescharacteristic
412C2×Q8—21no—
413C2×Q8—81no—
414C2×Q8C2×D4×C4312yes—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—44no—
421C2×D4—44no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—81no—
425C2×D4—81no—
426C2×D4C2×D4×C4312yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—24no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—42no—
438C22×C4—81no—
439C22×C4—81no—
440C22×C4—82no—
441C22×C4C2×D4×C4312yes—
442C22×C4C2×D4×C4312yes—
443C22×C4C2×D4×C4311yescharacteristic
444C22×C4C2×D4×C4311yescharacteristic
445C22×C4C2×D4×C4311yescharacteristic
446C22×C4C2×D4×C4311yescharacteristic
447C22×C4C2×D4×C4311yescharacteristic
448C22×C4C24×C4311yescharacteristic
449SD16—82no—
450D8—82no—
451M16—81no—
452M16—81no—
453C2×C8—22no—
454C2×C8—22no—
455C4⋊C4—24no—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4C2×D4×C4312yes—
469C4⋊C4C2×D4×C4312yes—
470C22⋊C4—24no—
471C22⋊C4—24no—
472C22⋊C4—24no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—44no—
478C22⋊C4—42no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—82no—
482C42—24no—
483C42—81no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23—41no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—41no—
494C23—42no—
495C23#120×C4311yescharacteristic
496C23#120×C4311yescharacteristic
497C23C22×D4×C4311yescharacteristic
498Q8—42no—
499Q8—81no—
500D4—42no—
501D4—42no—
502D4—42no—
503D4—44no—
504D4—44no—
505D4—81no—
506D4—82no—
507D4—82no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—81no—
534C2×C4—84no—
535C2×C4#120×C4311yescharacteristic
536C2×C4#120×C4311yescharacteristic
537C2×C4C22×D4×C4311yescharacteristic
538C2×C4C22×D4×C4311yescharacteristic
539C8—42no—
540C8—42no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—44no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—84no—
553C22—84no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C43×#45412yes—
558C22C2×#120×C4311yescharacteristic
559C22C43×#57512yes—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—21no—
564C4—42no—
565C4—42no—
566C4—42no—
567C4—42no—
568C4—42no—
569C4—82no—
570C4—81no—
571C2—22no—
572C2—22no—
573C2—41no—
574C2—82no—
575C2—161no—
576C2C43×#300511yescharacteristic
577C2C2×C43×#45411yescharacteristic
578C2C43×#302611yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#3192C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#539C2semidirect
2. C43×#3193C2semidirect
4. C43×#2591C2semidirect
5. C43×#1615C2semidirect
6. C43×#1597C2semidirect
7. C43×#1508C2semidirect
8. C43×#1507C2semidirect
9. C43×#1463C2semidirect
24. C43×#484C22semidirect
30. C43×#450C22semidirect
36. C43×#400C22semidirect
37. C43×#394C22semidirect
42. C43×#328C22semidirect
44. C43×#324C22semidirect
251. #18320C43direct (N × H)
282. C2×#539C2×C43semidirect
283. #3193C2×C43semidirect
285. #2591C2×C43semidirect
286. #1615C2×C43semidirect
287. #1597C2×C43semidirect
288. #1508C2×C43semidirect
289. #1507C2×C43semidirect
290. #1463C2×C43semidirect
313. #484C22×C43semidirect
319. #450C22×C43semidirect
325. #400C22×C43semidirect
326. #394C22×C43semidirect
331. #328C22×C43semidirect
333. #324C22×C43semidirect
334. C43#18320direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5392
C43×#31932
C43×#31922
C43×#25912
C43×#16152
C43×#15972
C43×#15082
C43×#15072
C43×#14632
#1832043