Finite Group Databasebeta

← C43×#29683 #24949700

Subgroups — C43×#29683 #24949700

Order 11008.

1056 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3461C211yesmaximal, characteristic, complemented
2C43×#3040C212yesmaximal, complemented
3C43×#2545C211yesmaximal, characteristic, complemented
4C43×#2028C211yesmaximal, characteristic, complemented
5C43×#2027C211yesmaximal, characteristic, complemented
6C43×#2007C211yesmaximal, characteristic, complemented
7C43×#2006C211yesmaximal, characteristic
8C43×#2005C212yesmaximal, complemented
9C43×#2003C212yesmaximal, complemented
10C43×#1806C212yesmaximal, complemented
11C43×#1801C211yesmaximal, characteristic, complemented
12C2×#137×C43C2212yes—
13C2×AGL(1,ℤ/8)×C43C2212yes—
14C43×#544C2211yescharacteristic
15C43×#542—22no—
16C43×#541—22no—
17C43×#539—22no—
18C43×#537C2211yescharacteristic
19C43×#536C2212yes—
20C43×#533—22no—
21C2×C4⋊Q8×C43C2211yescharacteristic
22C43×#529—22no—
23C43×#529—22no—
24C2×#124×C43C2211yescharacteristic
25C2×#124×C43C2211yescharacteristic
26C4×#41×C43C2212yes—
27C2×C4×Q8×C43C2211yescharacteristic
28C43×#464—22no—
29C43×#464—22no—
30C43×#463—22no—
31C43×#463—22no—
32C43×#423C2212yes—
33C2×#104×C43C2212yes—
34C2×#104×C43C2212yes—
35C43×#419C2212yes—
36C43×#418C2212yes—
37C2×#101×C43C2212yes—
38C43×#396—22no—
39C43×#391C2211yescharacteristic
40C43×#390C2211yescharacteristic
41C43×#388—22no—
42C4×C4⋊C4×C43C2211yescharacteristic
43C43×#343C2211yescharacteristic
44C43×#343C2211yescharacteristic
45C43×#339C2212yes—
46C43×#339C2212yes—
47C2×#41×C43C2312yes—
48C22×Q8×C43C2311yescharacteristic
49C22×Q8×C43C2311yescharacteristic
50C22×D4×C43C2311yescharacteristic
51#137×C43—42no—
52#137×C43—42no—
53AGL(1,ℤ/8)×C43—42no—
54AGL(1,ℤ/8)×C43—42no—
55C2×Q16×C43—22no—
56C2×SD16×C43—22no—
57C2×SD16×C43—22no—
58C2×D8×C43—22no—
59C2×M16×C43C2312yes—
60C2×M16×C43C2312yes—
61C4⋊Q8×C43—22no—
62C4⋊Q8×C43—22no—
63C4⋊Q8×C43—42no—
64#126×C43—24no—
65#126×C43—24no—
66#125×C43—22no—
67#125×C43—24no—
68#125×C43—22no—
69#124×C43—22no—
70#124×C43—22no—
71#124×C43—22no—
72#124×C43—22no—
73#124×C43—42no—
74#123×C43—24no—
75#123×C43—24no—
76C22⋊Q8×C43—24no—
77C22⋊Q8×C43—22no—
78C22⋊Q8×C43—22no—
79C22⋊Q8×C43—22no—
80C22⋊Q8×C43—22no—
81#121×C43—22no—
82#121×C43—22no—
83C4×Q8×C43—22no—
84C4×Q8×C43—22no—
85C4×Q8×C43—22no—
86C4×Q8×C43D412yes—
87C4×Q8×C43D412yes—
88C4×D4×C43—22no—
89C4×D4×C43—22no—
90C4×D4×C43—22no—
91C4×D4×C43D412yes—
92C4×D4×C43D412yes—
93#117×C43—24no—
94#117×C43—22no—
95#117×C43C2312yes—
96C2×C4⋊C4×C43—22no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43D412yes—
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C22⋊C4×C43—21no—
101C2×C22⋊C4×C43—22no—
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43—22no—
104C2×C42×C43—22no—
105C2×C42×C43D412yes—
106C2×C42×C43C2311yescharacteristic
107C2×C42×C43C2311yescharacteristic
108C2×C42×C43C2311yescharacteristic
109C4⋊C8×C43—22no—
110C4⋊C8×C43—22no—
111#104×C43—42no—
112#104×C43—42no—
113#103×C43—22no—
114#103×C43—22no—
115#102×C43—22no—
116#102×C43—22no—
117#101×C43—42no—
118#95×C43—21no—
119#95×C43—22no—
120C24×C43—21no—
121#41×C43—22no—
122#41×C43—22no—
123#41×C43—22no—
124#41×C43—22no—
125C2×Q8×C43—22no—
126C2×Q8×C43—22no—
127C2×Q8×C43—21no—
128C2×Q8×C43—22no—
129C2×Q8×C43—21no—
130C2×Q8×C43—22no—
131C2×Q8×C43—22no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43C2×D412yes—
135C2×D4×C43—22no—
136C2×D4×C43—22no—
137C2×D4×C43—22no—
138C2×D4×C43—22no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43C2×D412yes—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D412yes—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2411yescharacteristic
153Q16×C43—44no—
154SD16×C43—44no—
155SD16×C43—44no—
156D8×C43—44no—
157M16×C43—22no—
158M16×C43—22no—
159M16×C43—22no—
160M16×C43—22no—
161C2×C8×C43—22no—
162C2×C8×C43—22no—
163C4⋊C4×C43—24no—
164C4⋊C4×C43—24no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—24no—
168C4⋊C4×C43—24no—
169C4⋊C4×C43—22no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—42no—
173C4⋊C4×C43—44no—
174C4⋊C4×C43C2×D412yes—
175C4⋊C4×C43C2×D412yes—
176C22⋊C4×C43—24no—
177C22⋊C4×C43—24no—
178C22⋊C4×C43—24no—
179C22⋊C4×C43—22no—
180C22⋊C4×C43—22no—
181C22⋊C4×C43—22no—
182C22⋊C4×C43—44no—
183C22⋊C4×C43—44no—
184C22⋊C4×C43—41no—
185C22⋊C4×C43—41no—
186C22⋊C4×C43—42no—
187C42×C43—22no—
188C42×C43—22no—
189C42×C43—22no—
190C42×C43—22no—
191C42×C43—22no—
192C42×C43—22no—
193C42×C43—22no—
194C42×C43C2×D412yes—
195C42×C43C2×D412yes—
196C23×C43—22no—
197C23×C43—42no—
198C23×C43—42no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43C22×D411yescharacteristic
203Q8×C43—22no—
204Q8×C43—22no—
205Q8×C43—42no—
206Q8×C43—42no—
207Q8×C43—42no—
208Q8×C43—42no—
209Q8×C43—82no—
210D4×C43—22no—
211D4×C43—22no—
212D4×C43—42no—
213D4×C43—42no—
214D4×C43—42no—
215D4×C43—42no—
216D4×C43—82no—
217C2×C4×C43—22no—
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—44no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
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—82no—
240C2×C4×C43#12011yescharacteristic
241C2×C4×C43#12011yescharacteristic
242C2×C4×C43#12012yes—
243C2×C4×C43C22×D412yes—
244C2×C4×C43H(5,𝔽2)11yescharacteristic
245C2×C4×C43H(5,𝔽2)12yes—
246C2×C4×C432−1+411yescharacteristic
247C8×C43—42no—
248C8×C43—42no—
249#29683C4311yesmaximal, characteristic, direct product factor, Sylow
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—42no—
253C22×C43—42no—
254C22×C43—42no—
255C22×C43—82no—
256C22×C43—82no—
257C22×C43—81no—
258C22×C43—81no—
259C22×C43—81no—
260C22×C43C2×#12011yescharacteristic
261C22×C43#53511yescharacteristic
262C22×C43#53711yescharacteristic
263C4×C43—22no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—42no—
267C4×C43—42no—
268C4×C43—42no—
269C4×C43—42no—
270C4×C43—42no—
271C4×C43—42no—
272C4×C43—81no—
273C4×C43—81no—
274C4×C43#53512yes—
275C4×C43#53712yes—
276#3461C2×C4311yescharacteristic, complemented
277#3040C2×C4312yescomplemented
278#2545C2×C4311yescharacteristic, complemented
279#2028C2×C4311yescharacteristic, complemented
280#2027C2×C4311yescharacteristic, complemented
281#2007C2×C4311yescharacteristic, complemented
282#2006C2×C4311yescharacteristic
283#2005C2×C4312yescomplemented
284#2003C2×C4312yescomplemented
285#1806C2×C4312yescomplemented
286#1801C2×C4311yescharacteristic, complemented
287C2×C43—21no—
288C2×C43—21no—
289C2×C43—82no—
290C2×C43—161no—
291C2×C43#261511yescharacteristic
292C2×C43#301811yescharacteristic
293C2×C43#302011yescharacteristic
294C2×#137C22×C4312yes—
295C2×AGL(1,ℤ/8)C22×C4312yes—
296#544C22×C4311yescharacteristic
297#542—22no—
298#541—22no—
299#539—22no—
300#537C22×C4311yescharacteristic
301#536C22×C4312yes—
302#533—22no—
303C2×C4⋊Q8C22×C4311yescharacteristic
304#529—22no—
305#529—22no—
306C2×#124C22×C4311yescharacteristic
307C2×#124C22×C4311yescharacteristic
308C4×#41C22×C4312yes—
309C2×C4×Q8C22×C4311yescharacteristic
310#464—22no—
311#464—22no—
312#463—22no—
313#463—22no—
314#423C22×C4312yes—
315C2×#104C22×C4312yes—
316C2×#104C22×C4312yes—
317#419C22×C4312yes—
318#418C22×C4312yes—
319C2×#101C22×C4312yes—
320#396—22no—
321#391C22×C4311yescharacteristic
322#390C22×C4311yescharacteristic
323#388—22no—
324C4×C4⋊C4C22×C4311yescharacteristic
325#343C22×C4311yescharacteristic
326#343C22×C4311yescharacteristic
327#339C22×C4312yes—
328#339C22×C4312yes—
329C43#2968311yescharacteristic, direct product factor, Sylow
330C2×#41C23×C4312yes—
331C22×Q8C23×C4311yescharacteristic
332C22×Q8C23×C4311yescharacteristic
333C22×D4C23×C4311yescharacteristic
334#137—42no—
335#137—42no—
336AGL(1,ℤ/8)—42no—
337AGL(1,ℤ/8)—42no—
338C2×Q16—22no—
339C2×SD16—22no—
340C2×SD16—22no—
341C2×D8—22no—
342C2×M16C23×C4312yes—
343C2×M16C23×C4312yes—
344C4⋊Q8—22no—
345C4⋊Q8—22no—
346C4⋊Q8—42no—
347#126—24no—
348#126—24no—
349#125—22no—
350#125—24no—
351#125—22no—
352#124—22no—
353#124—22no—
354#124—22no—
355#124—22no—
356#124—42no—
357#123—24no—
358#123—24no—
359C22⋊Q8—24no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364#121—22no—
365#121—22no—
366C4×Q8—22no—
367C4×Q8—22no—
368C4×Q8—22no—
369C4×Q8D4×C4312yes—
370C4×Q8D4×C4312yes—
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4D4×C4312yes—
375C4×D4D4×C4312yes—
376#117—24no—
377#117—22no—
378#117C23×C4312yes—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4D4×C4312yes—
382C2×C4⋊C4C23×C4311yescharacteristic
383C2×C22⋊C4—21no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—22no—
387C2×C42—22no—
388C2×C42D4×C4312yes—
389C2×C42C23×C4311yescharacteristic
390C2×C42C23×C4311yescharacteristic
391C2×C42C23×C4311yescharacteristic
392C4⋊C8—22no—
393C4⋊C8—22no—
394#104—42no—
395#104—42no—
396#103—22no—
397#103—22no—
398#102—22no—
399#102—22no—
400#101—42no—
401#95—21no—
402#95—22no—
403C24—21no—
404#41—22no—
405#41—22no—
406#41—22no—
407#41—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—21no—
411C2×Q8—22no—
412C2×Q8—21no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8C2×D4×C4312yes—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4C2×D4×C4312yes—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4C2×D4×C4312yes—
432C22×C4C2×D4×C4312yes—
433C22×C4C2×D4×C4311yescharacteristic
434C22×C4C2×D4×C4311yescharacteristic
435C22×C4C24×C4311yescharacteristic
436Q16—44no—
437SD16—44no—
438SD16—44no—
439D8—44no—
440M16—22no—
441M16—22no—
442M16—22no—
443M16—22no—
444C2×C8—22no—
445C2×C8—22no—
446C4⋊C4—24no—
447C4⋊C4—24no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—24no—
451C4⋊C4—24no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—44no—
456C4⋊C4—42no—
457C4⋊C4C2×D4×C4312yes—
458C4⋊C4C2×D4×C4312yes—
459C22⋊C4—24no—
460C22⋊C4—24no—
461C22⋊C4—24no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—44no—
466C22⋊C4—44no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C22⋊C4—42no—
470C42—22no—
471C42—22no—
472C42—22no—
473C42—22no—
474C42—22no—
475C42—22no—
476C42—22no—
477C42C2×D4×C4312yes—
478C42C2×D4×C4312yes—
479C23—22no—
480C23—42no—
481C23—42no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23C22×D4×C4311yescharacteristic
486Q8—22no—
487Q8—22no—
488Q8—42no—
489Q8—42no—
490Q8—42no—
491Q8—42no—
492Q8—82no—
493D4—22no—
494D4—22no—
495D4—42no—
496D4—42no—
497D4—42no—
498D4—42no—
499D4—82no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—44no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—82no—
523C2×C4#120×C4311yescharacteristic
524C2×C4#120×C4311yescharacteristic
525C2×C4#120×C4312yes—
526C2×C4C22×D4×C4312yes—
527C2×C4H(5,𝔽2)×C4311yescharacteristic
528C2×C4H(5,𝔽2)×C4312yes—
529C2×C42−1+4×C4311yescharacteristic
530C8—42no—
531C8—42no—
532C22—21no—
533C22—21no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—82no—
538C22—82no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22C2×#120×C4311yescharacteristic
543C22C43×#53511yescharacteristic
544C22C43×#53711yescharacteristic
545C4—22no—
546C4—21no—
547C4—21no—
548C4—42no—
549C4—42no—
550C4—42no—
551C4—42no—
552C4—42no—
553C4—42no—
554C4—81no—
555C4—81no—
556C4C43×#53512yes—
557C4C43×#53712yes—
558C2—21no—
559C2—21no—
560C2—82no—
561C2—161no—
562C2C43×#261511yescharacteristic
563C2C43×#301811yescharacteristic
564C2C43×#302011yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#2006C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3461C2semidirect
2. C43×#3040C2semidirect
3. C43×#2545C2semidirect
4. C43×#2028C2semidirect
5. C43×#2027C2semidirect
6. C43×#2007C2semidirect
8. C43×#2005C2semidirect
9. C43×#2003C2semidirect
10. C43×#1806C2semidirect
11. C43×#1801C2semidirect
249. #29683C43direct (N × H)
276. #3461C2×C43semidirect
277. #3040C2×C43semidirect
278. #2545C2×C43semidirect
279. #2028C2×C43semidirect
280. #2027C2×C43semidirect
281. #2007C2×C43semidirect
283. #2005C2×C43semidirect
284. #2003C2×C43semidirect
285. #1806C2×C43semidirect
286. #1801C2×C43semidirect
329. C43#29683direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#34612
C43×#30402
C43×#25452
C43×#20282
C43×#20272
C43×#20072
C43×#20062
C43×#20052
C43×#20032
C43×#18062
C43×#18012
#2968343