Finite Group Databasebeta

← C43×#9954 #24929971

Subgroups — C43×#9954 #24929971

Order 11008.

1018 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3187C211yesmaximal, characteristic, complemented
2C2×C43×#450C211yesmaximal, characteristic, complemented
3C43×#2433C211yesmaximal, characteristic
4C43×#1996C211yesmaximal, characteristic, complemented
5C43×#1786C211yesmaximal, characteristic, complemented
6C43×#1519C211yesmaximal, characteristic, complemented
7C43×#1282C211yesmaximal, characteristic, complemented
8C23×D4×C43C2211yescharacteristic
9C22×SD16×C43—21no—
10C2×#127×C43—21no—
11C2×C22⋊Q8×C43C2211yescharacteristic
12C2×#121×C43C2211yescharacteristic
13C2×#120×C43—22no—
14C43×#483—21no—
15C43×#481—21no—
16C43×#465—22no—
17C43×#450—21no—
18C43×#450—22no—
19C43×#450—22no—
20C43×#448—21no—
21C2×#102×C43—21no—
22C2×#102×C43—22no—
23C2×C22⋊C8×C43C2211yescharacteristic
24C2×C22⋊C8×C43C2211yescharacteristic
25C43×#392—22no—
26C43×#390—21no—
27C43×#380C2211yescharacteristic
28C4×C22⋊C4×C43C2211yescharacteristic
29C43×#342—22no—
30C43×#327—22no—
31C25×C43—21no—
32C22×Q8×C43D411yescharacteristic, complemented
33C22×D4×C43—21no—
34C22×D4×C43—24no—
35C22×D4×C43—21no—
36C22×D4×C43—21no—
37C22×D4×C43—21no—
38C22×D4×C43—21no—
39C22×D4×C43—21no—
40C22×D4×C43—44no—
41C22×D4×C43D411yescharacteristic
42C22×D4×C43D412yes—
43C23×C4×C43C2311yescharacteristic
44C2×SD16×C43—24no—
45C2×SD16×C43—22no—
46C2×SD16×C43—44no—
47C22×C8×C43—21no—
48C22×C8×C43D412yescomplemented
49#127×C43—44no—
50C22⋊Q8×C43—21no—
51C22⋊Q8×C43—21no—
52C22⋊Q8×C43—21no—
53C22⋊Q8×C43—21no—
54#121×C43—21no—
55#121×C43—21no—
56#121×C43—21no—
57#121×C43—21no—
58#120×C43—44no—
59#120×C43—44no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43D411yescharacteristic
63C2×C4⋊C4×C43D411yescharacteristic, complemented
64C2×C22⋊C4×C43—24no—
65C2×C22⋊C4×C43—21no—
66C2×C22⋊C4×C43—21no—
67C2×C22⋊C4×C43—21no—
68C2×C22⋊C4×C43D412yes—
69C2×C42×C43—21no—
70#106×C43—22no—
71#103×C43—22no—
72#102×C43—24no—
73#102×C43—22no—
74#102×C43—44no—
75C22⋊C8×C43—21no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43—21no—
78C22⋊C8×C43D412yescomplemented
79#95×C43—21no—
80#95×C43—21no—
81C24×C43—22no—
82C24×C43—21no—
83C24×C43—44no—
84C24×C43—41no—
85C24×C43—41no—
86C24×C43—42no—
87C24×C43—42no—
88C24×C43—82no—
89C24×C43C2×D411yescharacteristic
90C2×Q8×C43—21no—
91C2×Q8×C43—21no—
92C2×Q8×C43—42no—
93C2×D4×C43—24no—
94C2×D4×C43—24no—
95C2×D4×C43—24no—
96C2×D4×C43—22no—
97C2×D4×C43—21no—
98C2×D4×C43—22no—
99C2×D4×C43—21no—
100C2×D4×C43—44no—
101C2×D4×C43—48no—
102C2×D4×C43—42no—
103C2×D4×C43—42no—
104C2×D4×C43—42no—
105C2×D4×C43—42no—
106C2×D4×C43—48no—
107C2×D4×C43—44no—
108C2×D4×C43—44no—
109C2×D4×C43—41no—
110C2×D4×C43—41no—
111C2×D4×C43—41no—
112C2×D4×C43—41no—
113C2×D4×C43—42no—
114C2×D4×C43—42no—
115C2×D4×C43—84no—
116C22×C4×C43—22no—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—42no—
121C22×C4×C43—41no—
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43#4111yescharacteristic
128SD16×C43—48no—
129SD16×C43—82no—
130C2×C8×C43—22no—
131C2×C8×C43—22no—
132C2×C8×C43—42no—
133C2×C8×C43—42no—
134C4⋊C4×C43—21no—
135C4⋊C4×C43—21no—
136C4⋊C4×C43—21no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—42no—
139C4⋊C4×C43—41no—
140C4⋊C4×C43—41no—
141C22⋊C4×C43—22no—
142C22⋊C4×C43—48no—
143C22⋊C4×C43—41no—
144C22⋊C4×C43—41no—
145C22⋊C4×C43—41no—
146C22⋊C4×C43—41no—
147C22⋊C4×C43—42no—
148C22⋊C4×C43SD1614yescomplemented
149C42×C43—42no—
150C23×C43—24no—
151C23×C43—41no—
152C23×C43—41no—
153C23×C43—44no—
154C23×C43—44no—
155C23×C43—42no—
156C23×C43—44no—
157C23×C43—42no—
158C23×C43—42no—
159C23×C43—42no—
160C23×C43—44no—
161C23×C43—41no—
162C23×C43—42no—
163C23×C43—82no—
164C23×C43—82no—
165C23×C43—88no—
166C23×C43—88no—
167C23×C43—82no—
168C23×C43—81no—
169C23×C43—81no—
170C23×C43#12011yescharacteristic
171C23×C43#12111yescharacteristic
172C23×C43#12711yescharacteristic
173C23×C43C2×SD1612yes—
174C23×C43AGL(1,ℤ/8)12yes—
175Q8×C43—42no—
176Q8×C43—42no—
177D4×C43—24no—
178D4×C43—24no—
179D4×C43—42no—
180D4×C43—42no—
181D4×C43—44no—
182D4×C43—44no—
183D4×C43—42no—
184D4×C43—81no—
185D4×C43—816no—
186D4×C43—82no—
187D4×C43—81no—
188D4×C43—81no—
189C2×C4×C43—22no—
190C2×C4×C43—22no—
191C2×C4×C43—22no—
192C2×C4×C43—24no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—42no—
197C2×C4×C43—42no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—42no—
202C2×C4×C43—81no—
203C2×C4×C43—81no—
204C2×C4×C43—81no—
205C2×C4×C43—81no—
206C2×C4×C43—81no—
207C2×C4×C43#12011yescharacteristic
208C2×C4×C43#12011yescharacteristic
209C2×C4×C43#12111yescharacteristic
210C2×C4×C43#12111yescharacteristic
211C8×C43—42no—
212C8×C43—42no—
213#9954C4311yesmaximal, characteristic, direct product factor, Sylow
214C22×C43—21no—
215C22×C43—21no—
216C22×C43—21no—
217C22×C43—21no—
218C22×C43—21no—
219C22×C43—21no—
220C22×C43—42no—
221C22×C43—42no—
222C22×C43—48no—
223C22×C43—44no—
224C22×C43—84no—
225C22×C43—84no—
226C22×C43—88no—
227C22×C43—84no—
228C22×C43—84no—
229C22×C43—82no—
230C22×C43—82no—
231C22×C43—81no—
232C22×C43—81no—
233C22×C43—81no—
234C22×C43#39211yescharacteristic
235C22×C43#45012yes—
236C22×C43#46012yes—
237C22×C43#49211yescharacteristic
238C22×C43#49611yescharacteristic
239C4×C43—21no—
240C4×C43—21no—
241C4×C43—21no—
242C4×C43—44no—
243C4×C43—81no—
244C4×C43—81no—
245C4×C43—81no—
246C4×C43—161no—
247C4×C43B(4,𝔽2)12yes—
248#3187C2×C4311yescharacteristic, complemented
249C2×#450C2×C4311yescharacteristic, complemented
250#2433C2×C4311yescharacteristic
251#1996C2×C4311yescharacteristic, complemented
252#1786C2×C4311yescharacteristic, complemented
253#1519C2×C4311yescharacteristic, complemented
254#1282C2×C4311yescharacteristic, complemented
255C2×C43—22no—
256C2×C43—21no—
257C2×C43—22no—
258C2×C43—21no—
259C2×C43—84no—
260C2×C43—161no—
261C2×C43#200811yescharacteristic
262C2×C43#201411yescharacteristic
263C2×C43#202111yescharacteristic
264C23×D4C22×C4311yescharacteristic
265C22×SD16—21no—
266C2×#127—21no—
267C2×C22⋊Q8C22×C4311yescharacteristic
268C2×#121C22×C4311yescharacteristic
269C2×#120—22no—
270#483—21no—
271#481—21no—
272#465—22no—
273#450—21no—
274#450—22no—
275#450—22no—
276#448—21no—
277C2×#102—21no—
278C2×#102—22no—
279C2×C22⋊C8C22×C4311yescharacteristic
280C2×C22⋊C8C22×C4311yescharacteristic
281#392—22no—
282#390—21no—
283#380C22×C4311yescharacteristic
284C4×C22⋊C4C22×C4311yescharacteristic
285#342—22no—
286#327—22no—
287C43#995411yescharacteristic, direct product factor, Sylow
288C25—21no—
289C22×Q8D4×C4311yescharacteristic, complemented
290C22×D4—21no—
291C22×D4—24no—
292C22×D4—21no—
293C22×D4—21no—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4—21no—
297C22×D4—44no—
298C22×D4D4×C4311yescharacteristic
299C22×D4D4×C4312yes—
300C23×C4C23×C4311yescharacteristic
301C2×SD16—24no—
302C2×SD16—22no—
303C2×SD16—44no—
304C22×C8—21no—
305C22×C8D4×C4312yescomplemented
306#127—44no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311#121—21no—
312#121—21no—
313#121—21no—
314#121—21no—
315#120—44no—
316#120—44no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4D4×C4311yescharacteristic
320C2×C4⋊C4D4×C4311yescharacteristic, complemented
321C2×C22⋊C4—24no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4D4×C4312yes—
326C2×C42—21no—
327#106—22no—
328#103—22no—
329#102—24no—
330#102—22no—
331#102—44no—
332C22⋊C8—21no—
333C22⋊C8—21no—
334C22⋊C8—21no—
335C22⋊C8D4×C4312yescomplemented
336#95—21no—
337#95—21no—
338C24—22no—
339C24—21no—
340C24—44no—
341C24—41no—
342C24—41no—
343C24—42no—
344C24—42no—
345C24—82no—
346C24C2×D4×C4311yescharacteristic
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—42no—
350C2×D4—24no—
351C2×D4—24no—
352C2×D4—24no—
353C2×D4—22no—
354C2×D4—21no—
355C2×D4—22no—
356C2×D4—21no—
357C2×D4—42no—
358C2×D4—42no—
359C2×D4—42no—
360C2×D4—42no—
361C2×D4—48no—
362C2×D4—44no—
363C2×D4—44no—
364C2×D4—44no—
365C2×D4—48no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—42no—
369C2×D4—42no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—84no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—42no—
378C22×C4—41no—
379C22×C4C2×D4×C4311yescharacteristic
380C22×C4C2×D4×C4311yescharacteristic
381C22×C4C2×D4×C4311yescharacteristic
382C22×C4C2×D4×C4311yescharacteristic
383C22×C4C2×D4×C4311yescharacteristic
384C22×C4#41×C4311yescharacteristic
385SD16—48no—
386SD16—82no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—42no—
390C2×C8—42no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—42no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C22⋊C4—22no—
399C22⋊C4—48no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—42no—
405C22⋊C4SD16×C4314yescomplemented
406C42—42no—
407C23—24no—
408C23—41no—
409C23—41no—
410C23—44no—
411C23—44no—
412C23—42no—
413C23—44no—
414C23—42no—
415C23—42no—
416C23—42no—
417C23—44no—
418C23—41no—
419C23—42no—
420C23—82no—
421C23—82no—
422C23—88no—
423C23—88no—
424C23—82no—
425C23—81no—
426C23—81no—
427C23#120×C4311yescharacteristic
428C23#121×C4311yescharacteristic
429C23#127×C4311yescharacteristic
430C23C2×SD16×C4312yes—
431C23AGL(1,ℤ/8)×C4312yes—
432Q8—42no—
433Q8—42no—
434D4—24no—
435D4—24no—
436D4—42no—
437D4—42no—
438D4—44no—
439D4—44no—
440D4—42no—
441D4—81no—
442D4—816no—
443D4—82no—
444D4—81no—
445D4—81no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—81no—
460C2×C4—81no—
461C2×C4—81no—
462C2×C4—81no—
463C2×C4—81no—
464C2×C4#120×C4311yescharacteristic
465C2×C4#120×C4311yescharacteristic
466C2×C4#121×C4311yescharacteristic
467C2×C4#121×C4311yescharacteristic
468C8—42no—
469C8—42no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—42no—
477C22—42no—
478C22—48no—
479C22—44no—
480C22—84no—
481C22—84no—
482C22—88no—
483C22—84no—
484C22—84no—
485C22—82no—
486C22—82no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22C43×#39211yescharacteristic
491C22C43×#45012yes—
492C22C43×#46012yes—
493C22C43×#49211yescharacteristic
494C22C43×#49611yescharacteristic
495C4—21no—
496C4—21no—
497C4—21no—
498C4—44no—
499C4—81no—
500C4—81no—
501C4—81no—
502C4—161no—
503C4C43×B(4,𝔽2)12yes—
504C2—22no—
505C2—21no—
506C2—22no—
507C2—21no—
508C2—84no—
509C2—161no—
510C2C43×#200811yescharacteristic
511C2C43×#201411yescharacteristic
512C2C43×#202111yescharacteristic
subgroupG/H
center, socleC22×C43#392
commutator, Frattini, cosocleC23×C4C23×C43
prime radicalC43×#2433C2
LCSG ▷ C23×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. C43×#3187C2semidirect
2. C2×C43×#450C2semidirect
4. C43×#1996C2semidirect
5. C43×#1786C2semidirect
6. C43×#1519C2semidirect
7. C43×#1282C2semidirect
32. C22×Q8×C43D4semidirect
48. C22×C8×C43D4semidirect
63. C2×C4⋊C4×C43D4semidirect
78. C22⋊C8×C43D4semidirect
148. C22⋊C4×C43SD16semidirect
213. #9954C43direct (N × H)
248. #3187C2×C43semidirect
249. C2×#450C2×C43semidirect
251. #1996C2×C43semidirect
252. #1786C2×C43semidirect
253. #1519C2×C43semidirect
254. #1282C2×C43semidirect
287. C43#9954direct (N × H)
289. C22×Q8D4×C43semidirect
305. C22×C8D4×C43semidirect
320. C2×C4⋊C4D4×C43semidirect
335. C22⋊C8D4×C43semidirect
405. C22⋊C4SD16×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#31872
C2×C43×#4502
C43×#24332
C43×#19962
C43×#17862
C43×#15192
C43×#12822
#995443