Finite Group Databasebeta

← C43×#29634 #24949651

Subgroups — C43×#29634 #24949651

Order 11008.

1908 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
1C2×C43×#534C211yesmaximal, characteristic, complemented
2C43×#2405C211yesmaximal, characteristic, complemented
3C43×#2403C212yesmaximal, complemented
4C43×#2044C214yesmaximal, complemented
5C43×#2021C214yesmaximal, complemented
6C43×#1819C211yesmaximal, characteristic, complemented
7C43×#1781C212yesmaximal, complemented
8C23×D4×C43C2212yes—
9C23×D4×C43C2211yescharacteristic
10C43×#534—24no—
11C43×#534—22no—
12C43×#534C2214yes—
13C2×#123×C43—22no—
14C2×#123×C43—21no—
15C2×#121×C43—21no—
16C2×#121×C43—21no—
17C2×#120×C43—22no—
18C2×#120×C43—22no—
19C2×#120×C43C2214yescomplemented
20C22×C22⋊C4×C43C2211yescharacteristic
21C2×#99×C43C2218yescomplemented
22C43×#394—22no—
23C43×#392—24no—
24C43×#386—22no—
25C43×#386—21no—
26C43×#386C2214yescomplemented
27C43×#385C2212yescomplemented
28C43×#379C2212yes—
29C43×#379C2211yescharacteristic
30C43×#379C2212yescomplemented
31C43×#342C2214yescomplemented
32C25×C43D412yescomplemented
33C25×C43C2311yescharacteristic
34C25×C43C2311yescharacteristic
35C22×D4×C43—22no—
36C22×D4×C43—22no—
37C22×D4×C43—22no—
38C22×D4×C43—21no—
39C22×D4×C43—22no—
40C22×D4×C43—22no—
41C22×D4×C43—21no—
42C22×D4×C43—21no—
43C22×D4×C43—22no—
44C22×D4×C43—21no—
45C22×D4×C43—24no—
46C22×D4×C43—44no—
47C22×D4×C43—48no—
48C22×D4×C43D414yescomplemented
49C22×D4×C43C2314yes—
50C23×C4×C43D411yescharacteristic, complemented
51C23×C4×C43D412yescomplemented
52C23×C4×C43D411yescharacteristic, complemented
53C23×C4×C43C2311yescharacteristic
54#123×C43—28no—
55#123×C43—28no—
56#123×C43—44no—
57#121×C43—24no—
58#121×C43—24no—
59#121×C43—24no—
60#121×C43—24no—
61#120×C43—28no—
62#120×C43—28no—
63#120×C43—48no—
64#120×C43—48no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—22no—
68C2×C22⋊C4×C43—22no—
69C2×C22⋊C4×C43—22no—
70C2×C22⋊C4×C43—22no—
71C2×C22⋊C4×C43—22no—
72C2×C22⋊C4×C43—22no—
73C2×C22⋊C4×C43—24no—
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—24no—
76C2×C22⋊C4×C43—22no—
77C2×C22⋊C4×C43—22no—
78C2×C22⋊C4×C43—21no—
79C2×C22⋊C4×C43—22no—
80C2×C22⋊C4×C43D412yescomplemented
81C2×C22⋊C4×C43C2314yes—
82C2×C22⋊C4×C43C2312yes—
83C2×C22⋊C4×C43C2312yes—
84#99×C43—48no—
85#95×C43—22no—
86#95×C43—24no—
87C24×C43—24no—
88C24×C43—22no—
89C24×C43—21no—
90C24×C43—22no—
91C24×C43—22no—
92C24×C43—24no—
93C24×C43—44no—
94C24×C43—42no—
95C24×C43—42no—
96C24×C43—44no—
97C24×C43—81no—
98C24×C43—81no—
99C24×C43—82no—
100C24×C43C2×D412yes—
101C24×C43C2×D411yescharacteristic
102C24×C43C2×D414yes—
103C24×C43C2×D412yes—
104C24×C43C2×D411yescharacteristic
105C24×C43C2411yescharacteristic
106C2×D4×C43—28no—
107C2×D4×C43—24no—
108C2×D4×C43—24no—
109C2×D4×C43—24no—
110C2×D4×C43—24no—
111C2×D4×C43—24no—
112C2×D4×C43—24no—
113C2×D4×C43—24no—
114C2×D4×C43—28no—
115C2×D4×C43—28no—
116C2×D4×C43—44no—
117C2×D4×C43—44no—
118C2×D4×C43—48no—
119C2×D4×C43—48no—
120C2×D4×C43—42no—
121C2×D4×C43—44no—
122C2×D4×C43—48no—
123C2×D4×C43—48no—
124C2×D4×C43—42no—
125C2×D4×C43—44no—
126C2×D4×C43—48no—
127C2×D4×C43—48no—
128C2×D4×C43—44no—
129C2×D4×C43—42no—
130C2×D4×C43—42no—
131C2×D4×C43—41no—
132C2×D4×C43—41no—
133C2×D4×C43—84no—
134C2×D4×C43—82no—
135C2×D4×C43—82no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—22no—
143C22×C4×C43—21no—
144C22×C4×C43—22no—
145C22×C4×C43—24no—
146C22×C4×C43—44no—
147C22×C4×C43—42no—
148C22×C4×C43—42no—
149C22×C4×C43—81no—
150C22×C4×C43C2×D414yes—
151C22×C4×C43C2×D412yes—
152C22×C4×C43C2×D412yes—
153C4⋊C4×C43—24no—
154C4⋊C4×C43—24no—
155C4⋊C4×C43—44no—
156C22⋊C4×C43—28no—
157C22⋊C4×C43—28no—
158C22⋊C4×C43—24no—
159C22⋊C4×C43—24no—
160C22⋊C4×C43—24no—
161C22⋊C4×C43—28no—
162C22⋊C4×C43—44no—
163C22⋊C4×C43—42no—
164C22⋊C4×C43—44no—
165C22⋊C4×C43—48no—
166C22⋊C4×C43—48no—
167C22⋊C4×C43—81no—
168C22⋊C4×C43—82no—
169C22⋊C4×C43—82no—
170C23×C43—24no—
171C23×C43—22no—
172C23×C43—22no—
173C23×C43—24no—
174C23×C43—24no—
175C23×C43—22no—
176C23×C43—22no—
177C23×C43—24no—
178C23×C43—24no—
179C23×C43—24no—
180C23×C43—24no—
181C23×C43—41no—
182C23×C43—41no—
183C23×C43—42no—
184C23×C43—41no—
185C23×C43—42no—
186C23×C43—41no—
187C23×C43—42no—
188C23×C43—41no—
189C23×C43—44no—
190C23×C43—44no—
191C23×C43—42no—
192C23×C43—44no—
193C23×C43—42no—
194C23×C43—41no—
195C23×C43—44no—
196C23×C43—44no—
197C23×C43—44no—
198C23×C43—41no—
199C23×C43—44no—
200C23×C43—42no—
201C23×C43—44no—
202C23×C43—82no—
203C23×C43—82no—
204C23×C43—88no—
205C23×C43—88no—
206C23×C43—816no—
207C23×C43#12012yes—
208C23×C43#12011yescharacteristic
209C23×C43#12011yescharacteristic
210C23×C43C22×D412yes—
211C23×C43C22×D411yescharacteristic
212C23×C43H(5,𝔽2)14yes—
213D4×C43—48no—
214D4×C43—48no—
215D4×C43—48no—
216D4×C43—44no—
217D4×C43—48no—
218D4×C43—48no—
219D4×C43—44no—
220D4×C43—84no—
221D4×C43—84no—
222D4×C43—816no—
223C2×C4×C43—24no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—24no—
228C2×C4×C43—24no—
229C2×C4×C43—24no—
230C2×C4×C43—44no—
231C2×C4×C43—44no—
232C2×C4×C43—42no—
233C2×C4×C43—41no—
234C2×C4×C43—42no—
235C2×C4×C43—41no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—44no—
241C2×C4×C43—42no—
242C2×C4×C43—44no—
243C2×C4×C43—44no—
244C2×C4×C43—42no—
245C2×C4×C43—81no—
246C2×C4×C43—81no—
247#29634C4311yesmaximal, characteristic, direct product factor, Sylow
248C22×C43—21no—
249C22×C43—22no—
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—22no—
253C22×C43—21no—
254C22×C43—22no—
255C22×C43—21no—
256C22×C43—22no—
257C22×C43—21no—
258C22×C43—22no—
259C22×C43—21no—
260C22×C43—44no—
261C22×C43—44no—
262C22×C43—48no—
263C22×C43—44no—
264C22×C43—48no—
265C22×C43—48no—
266C22×C43—44no—
267C22×C43—42no—
268C22×C43—44no—
269C22×C43—44no—
270C22×C43—84no—
271C22×C43—82no—
272C22×C43—84no—
273C22×C43—84no—
274C22×C43—82no—
275C22×C43—88no—
276C22×C43—88no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43B(4,𝔽2)12yes—
280C22×C43C2×#12011yescharacteristic
281C22×C43#53414yes—
282C22×C43#53512yes—
283C4×C43—44no—
284C4×C43—42no—
285C4×C43—42no—
286C4×C43—42no—
287C4×C43—82no—
288C4×C43—84no—
289C2×#534C2×C4311yescharacteristic, complemented
290#2405C2×C4311yescharacteristic, complemented
291#2403C2×C4312yescomplemented
292#2044C2×C4314yescomplemented
293#2021C2×C4314yescomplemented
294#1819C2×C4311yescharacteristic, complemented
295#1781C2×C4312yescomplemented
296C2×C43—24no—
297C2×C43—22no—
298C2×C43—22no—
299C2×C43—41no—
300C2×C43—42no—
301C2×C43—82no—
302C2×C43—84no—
303C2×C43#261311yescharacteristic
304C2×C43C2×B(4,𝔽2)11yescharacteristic
305C2×C43#302611yescharacteristic
306C23×D4C22×C4311yescharacteristic
307C23×D4C22×C4312yes—
308#534—24no—
309#534—22no—
310#534C22×C4314yes—
311C2×#123—22no—
312C2×#123—21no—
313C2×#121—21no—
314C2×#121—21no—
315C2×#120—22no—
316C2×#120—22no—
317C2×#120C22×C4314yescomplemented
318C22×C22⋊C4C22×C4311yescharacteristic
319C2×#99C22×C4318yescomplemented
320#394—22no—
321#392—24no—
322#386—22no—
323#386—21no—
324#386C22×C4314yescomplemented
325#385C22×C4312yescomplemented
326#379C22×C4312yes—
327#379C22×C4311yescharacteristic
328#379C22×C4312yescomplemented
329#342C22×C4314yescomplemented
330C43#2963411yescharacteristic, direct product factor, Sylow
331C25D4×C4312yescomplemented
332C25C23×C4311yescharacteristic
333C25C23×C4311yescharacteristic
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—21no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4—22no—
343C22×D4—21no—
344C22×D4—24no—
345C22×D4—44no—
346C22×D4—48no—
347C22×D4D4×C4314yescomplemented
348C22×D4C23×C4314yes—
349C23×C4D4×C4311yescharacteristic, complemented
350C23×C4D4×C4312yescomplemented
351C23×C4D4×C4311yescharacteristic, complemented
352C23×C4C23×C4311yescharacteristic
353#123—28no—
354#123—28no—
355#123—44no—
356#121—24no—
357#121—24no—
358#121—24no—
359#121—24no—
360#120—28no—
361#120—28no—
362#120—48no—
363#120—48no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4D4×C4312yescomplemented
380C2×C22⋊C4C23×C4314yes—
381C2×C22⋊C4C23×C4312yes—
382C2×C22⋊C4C23×C4312yes—
383#99—48no—
384#95—22no—
385#95—24no—
386C24—24no—
387C24—22no—
388C24—21no—
389C24—22no—
390C24—22no—
391C24—24no—
392C24—42no—
393C24—42no—
394C24—44no—
395C24—44no—
396C24—81no—
397C24—81no—
398C24—82no—
399C24C2×D4×C4312yes—
400C24C2×D4×C4311yescharacteristic
401C24C2×D4×C4314yes—
402C24C2×D4×C4312yes—
403C24C2×D4×C4311yescharacteristic
404C24C24×C4311yescharacteristic
405C2×D4—28no—
406C2×D4—24no—
407C2×D4—24no—
408C2×D4—24no—
409C2×D4—24no—
410C2×D4—24no—
411C2×D4—28no—
412C2×D4—28no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—44no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—44no—
421C2×D4—48no—
422C2×D4—48no—
423C2×D4—48no—
424C2×D4—48no—
425C2×D4—42no—
426C2×D4—44no—
427C2×D4—42no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—48no—
431C2×D4—48no—
432C2×D4—82no—
433C2×D4—82no—
434C2×D4—84no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—24no—
445C22×C4—42no—
446C22×C4—44no—
447C22×C4—42no—
448C22×C4—81no—
449C22×C4C2×D4×C4314yes—
450C22×C4C2×D4×C4312yes—
451C22×C4C2×D4×C4312yes—
452C4⋊C4—24no—
453C4⋊C4—24no—
454C4⋊C4—44no—
455C22⋊C4—28no—
456C22⋊C4—28no—
457C22⋊C4—24no—
458C22⋊C4—24no—
459C22⋊C4—24no—
460C22⋊C4—28no—
461C22⋊C4—48no—
462C22⋊C4—48no—
463C22⋊C4—44no—
464C22⋊C4—44no—
465C22⋊C4—42no—
466C22⋊C4—82no—
467C22⋊C4—81no—
468C22⋊C4—82no—
469C23—24no—
470C23—22no—
471C23—22no—
472C23—24no—
473C23—24no—
474C23—22no—
475C23—22no—
476C23—24no—
477C23—24no—
478C23—24no—
479C23—24no—
480C23—41no—
481C23—41no—
482C23—42no—
483C23—41no—
484C23—41no—
485C23—42no—
486C23—41no—
487C23—42no—
488C23—44no—
489C23—44no—
490C23—42no—
491C23—44no—
492C23—41no—
493C23—42no—
494C23—44no—
495C23—44no—
496C23—44no—
497C23—41no—
498C23—44no—
499C23—42no—
500C23—44no—
501C23—82no—
502C23—82no—
503C23—88no—
504C23—88no—
505C23—816no—
506C23#120×C4312yes—
507C23#120×C4311yescharacteristic
508C23#120×C4311yescharacteristic
509C23C22×D4×C4312yes—
510C23C22×D4×C4311yescharacteristic
511C23H(5,𝔽2)×C4314yes—
512D4—48no—
513D4—48no—
514D4—44no—
515D4—48no—
516D4—48no—
517D4—48no—
518D4—44no—
519D4—84no—
520D4—84no—
521D4—816no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—44no—
530C2×C4—44no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—44no—
540C2×C4—42no—
541C2×C4—44no—
542C2×C4—44no—
543C2×C4—42no—
544C2×C4—81no—
545C2×C4—81no—
546C22—21no—
547C22—21no—
548C22—22no—
549C22—21no—
550C22—21no—
551C22—22no—
552C22—22no—
553C22—21no—
554C22—21no—
555C22—22no—
556C22—21no—
557C22—22no—
558C22—44no—
559C22—48no—
560C22—44no—
561C22—48no—
562C22—48no—
563C22—44no—
564C22—44no—
565C22—42no—
566C22—44no—
567C22—44no—
568C22—84no—
569C22—82no—
570C22—84no—
571C22—84no—
572C22—82no—
573C22—88no—
574C22—88no—
575C22—81no—
576C22—81no—
577C22C43×B(4,𝔽2)12yes—
578C22C2×#120×C4311yescharacteristic
579C22C43×#53414yes—
580C22C43×#53512yes—
581C4—44no—
582C4—42no—
583C4—42no—
584C4—42no—
585C4—84no—
586C4—82no—
587C2—24no—
588C2—22no—
589C2—22no—
590C2—42no—
591C2—41no—
592C2—82no—
593C2—84no—
594C2C43×#261311yescharacteristic
595C2C2×C43×B(4,𝔽2)11yescharacteristic
596C2C43×#302611yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC24C24×C43
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C25×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#534C2semidirect
2. C43×#2405C2semidirect
3. C43×#2403C2semidirect
4. C43×#2044C2semidirect
5. C43×#2021C2semidirect
6. C43×#1819C2semidirect
7. C43×#1781C2semidirect
19. C2×#120×C43C22semidirect
21. C2×#99×C43C22semidirect
26. C43×#386C22semidirect
27. C43×#385C22semidirect
30. C43×#379C22semidirect
31. C43×#342C22semidirect
32. C25×C43D4semidirect
48. C22×D4×C43D4semidirect
50. C23×C4×C43D4semidirect
51. C23×C4×C43D4semidirect
52. C23×C4×C43D4semidirect
80. C2×C22⋊C4×C43D4semidirect
247. #29634C43direct (N × H)
289. C2×#534C2×C43semidirect
290. #2405C2×C43semidirect
291. #2403C2×C43semidirect
292. #2044C2×C43semidirect
293. #2021C2×C43semidirect
294. #1819C2×C43semidirect
295. #1781C2×C43semidirect
317. C2×#120C22×C43semidirect
319. C2×#99C22×C43semidirect
324. #386C22×C43semidirect
325. #385C22×C43semidirect
328. #379C22×C43semidirect
329. #342C22×C43semidirect
330. C43#29634direct (N × H)
331. C25D4×C43semidirect
347. C22×D4D4×C43semidirect
349. C23×C4D4×C43semidirect
350. C23×C4D4×C43semidirect
351. C23×C4D4×C43semidirect
379. C2×C22⋊C4D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5342
C43×#24052
C43×#24032
C43×#20442
C43×#20212
C43×#18192
C43×#17812
#2963443