Finite Group Databasebeta

← C43×#19156 #24939173

Subgroups — C43×#19156 #24939173

Order 11008.

650 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3167C211yesmaximal, characteristic, complemented
2C43×#3076C211yesmaximal, characteristic, complemented
3C43×#3035C211yesmaximal, characteristic
4C43×#2965C211yesmaximal, characteristic, complemented
5C43×#1700C211yesmaximal, characteristic, complemented
6C43×#1699C211yesmaximal, characteristic, complemented
7C43×#1698C211yesmaximal, characteristic, complemented
8C43×#1697C211yesmaximal, characteristic, complemented
9C43×#1692C211yesmaximal, characteristic, complemented
10C43×#1691C211yesmaximal, characteristic, complemented
11C43×#1686C211yesmaximal, characteristic, complemented
12C43×#1685C211yesmaximal, characteristic, complemented
13C2×C43×#335C211yesmaximal, characteristic, complemented
14C43×#1542C211yesmaximal, characteristic, complemented
15C43×#1540C211yesmaximal, characteristic, complemented
16C2×#135×C43—21no—
17C43×#533C2211yescharacteristic
18C43×#532C2211yescharacteristic
19C4×#41×C43C2211yescharacteristic
20C43×#498C2211yescharacteristic
21C43×#492C2211yescharacteristic
22C43×#487C2211yescharacteristic
23C43×#486C2211yescharacteristic
24C43×#479—21no—
25C43×#478—21no—
26C43×#477C2211yescharacteristic
27C43×#476C2211yescharacteristic
28C43×#475C2211yescharacteristic
29C43×#474C2211yescharacteristic
30C43×#465—21no—
31C43×#465—21no—
32C43×#464—21no—
33C43×#463—21no—
34C43×#462C2211yescharacteristic
35C43×#461C2211yescharacteristic
36C43×#460C2211yescharacteristic
37C43×#459C2211yescharacteristic
38C43×#446C2211yescharacteristic
39C43×#446C2211yescharacteristic
40C4×SD16×C43—21no—
41C4×SD16×C43—21no—
42C43×#436C2211yescharacteristic
43C43×#436C2211yescharacteristic
44C43×#435—21no—
45C43×#435—21no—
46C43×#431—21no—
47C43×#431C2211yescharacteristic
48C43×#427—21no—
49C2×C4⋊C8×C43C2211yescharacteristic
50C2×C4⋊C8×C43C2211yescharacteristic
51C43×#416—21no—
52C43×#416—21no—
53C4×M16×C43—21no—
54C2×C4×C8×C43C2211yescharacteristic
55C43×#335C2211yescharacteristic
56C43×#335C2211yescharacteristic
57C43×#335C2211yescharacteristic
58C43×#335C2211yescharacteristic
59C43×#333C2211yescharacteristic
60C43×#333C2211yescharacteristic
61C43×#332C2211yescharacteristic
62C43×#332C2211yescharacteristic
63C43×#332C2211yescharacteristic
64C43×#332C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#41×C43—21no—
68C2×#41×C43D411yescharacteristic
69#135×C43—44no—
70C2×Q16×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—21no—
75C2×D8×C43—21no—
76C2×M16×C43—21no—
77C2×M16×C43—21no—
78C22×C8×C43—21no—
79C22×C8×C43—21no—
80C22×C8×C43D411yescharacteristic
81C22×C8×C43D411yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83C4⋊Q8×C43C2311yescharacteristic
84C4⋊Q8×C43C2311yescharacteristic
85#127×C43C2311yescharacteristic
86#125×C43—21no—
87#124×C43—21no—
88C22⋊Q8×C43—21no—
89C22⋊Q8×C43—21no—
90#121×C43—21no—
91#121×C43—21no—
92C4×Q8×C43—21no—
93C4×Q8×C43—21no—
94C4×Q8×C43D411yescharacteristic
95C4×Q8×C43C2311yescharacteristic
96C4×D4×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43—21no—
100C4×D4×C43D411yescharacteristic
101C4×D4×C43C2311yescharacteristic
102#117×C43—21no—
103#117×C43—21no—
104#117×C43D411yescharacteristic
105C2×C42×C43—21no—
106C2×C42×C43C2311yescharacteristic
107#107×C43—21no—
108#107×C43—21no—
109#106×C43—21no—
110#106×C43—21no—
111#106×C43—21no—
112#106×C43—21no—
113C4⋊C8×C43—21no—
114C4⋊C8×C43—21no—
115C4⋊C8×C43—21no—
116C4⋊C8×C43—21no—
117C4⋊C8×C43C2311yescharacteristic
118C4⋊C8×C43C2311yescharacteristic
119C4⋊C8×C43C2311yescharacteristic
120C4⋊C8×C43C2311yescharacteristic
121C4⋊C8×C43C2311yescharacteristic
122C4⋊C8×C43C2311yescharacteristic
123#103×C43—21no—
124#103×C43—21no—
125#103×C43—21no—
126#103×C43—21no—
127#103×C43—21no—
128#103×C43—21no—
129#102×C43—21no—
130#102×C43—21no—
131#102×C43—21no—
132#102×C43—21no—
133#102×C43—21no—
134#102×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138#97×C43—21no—
139#97×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43D411yescharacteristic
142C4×C8×C43D411yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145#41×C43—22no—
146#41×C43—22no—
147#41×C43—42no—
148#41×C43—42no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43C2×D411yescharacteristic
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—41no—
158C2×D4×C43C2×D411yescharacteristic
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—41no—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43#4111yescharacteristic
166Q16×C43—42no—
167SD16×C43—42no—
168SD16×C43—42no—
169SD16×C43—42no—
170SD16×C43—42no—
171D8×C43—42no—
172M16×C43—42no—
173M16×C43—42no—
174C2×C8×C43—22no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—41no—
182C2×C8×C43—42no—
183C2×C8×C43—42no—
184C2×C8×C43C2×D411yescharacteristic
185C2×C8×C43C2×D411yescharacteristic
186C2×C8×C43C2×D411yescharacteristic
187C2×C8×C43C2×D411yescharacteristic
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—41no—
197C4⋊C4×C43—41no—
198C4⋊C4×C43C2×D411yescharacteristic
199C4⋊C4×C43C2×D411yescharacteristic
200C22⋊C4×C43—21no—
201C22⋊C4×C43—21no—
202C22⋊C4×C43—21no—
203C22⋊C4×C43—41no—
204C22⋊C4×C43—41no—
205C22⋊C4×C43—41no—
206C42×C43—21no—
207C42×C43—21no—
208C42×C43—21no—
209C42×C43—41no—
210C42×C43C2×D411yescharacteristic
211C42×C43C2×D411yescharacteristic
212C42×C43#4111yescharacteristic
213C42×C43C2411yescharacteristic
214C23×C43—21no—
215C23×C43—41no—
216C23×C43#12111yescharacteristic
217Q8×C43—21no—
218Q8×C43—21no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—81no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—42no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—81no—
232D4×C43—82no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—41no—
239C2×C4×C43—42no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—42no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—82no—
247C2×C4×C43#12111yescharacteristic
248C2×C4×C43#12111yescharacteristic
249C2×C4×C43#12111yescharacteristic
250C2×C4×C43AGL(1,ℤ/8)12yes—
251C2×C4×C43#13712yes—
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—41no—
259C8×C43—41no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43—41no—
263C8×C43—41no—
264C8×C43#13512yescomplemented
265#19156C4311yesmaximal, characteristic, direct product factor, Sylow
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43#46812yes—
275C22×C43C2×#12111yescharacteristic
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43#46812yes—
286C4×C43C2×#13511yescharacteristic
287C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
288C4×C43C2×#13711yescharacteristic
289C4×C43#57511yescharacteristic
290#3167C2×C4311yescharacteristic, complemented
291#3076C2×C4311yescharacteristic, complemented
292#3035C2×C4311yescharacteristic
293#2965C2×C4311yescharacteristic, complemented
294#1700C2×C4311yescharacteristic, complemented
295#1699C2×C4311yescharacteristic, complemented
296#1698C2×C4311yescharacteristic, complemented
297#1697C2×C4311yescharacteristic, complemented
298#1692C2×C4311yescharacteristic, complemented
299#1691C2×C4311yescharacteristic, complemented
300#1686C2×C4311yescharacteristic, complemented
301#1685C2×C4311yescharacteristic, complemented
302C2×#335C2×C4311yescharacteristic, complemented
303#1542C2×C4311yescharacteristic, complemented
304#1540C2×C4311yescharacteristic, complemented
305C2×C43—22no—
306C2×C43—81no—
307C2×C43—161no—
308C2×C43#303511yescharacteristic
309C2×C43C2×#46811yescharacteristic
310C2×C43#306711yescharacteristic
311C2×#135—21no—
312#533C22×C4311yescharacteristic
313#532C22×C4311yescharacteristic
314C4×#41C22×C4311yescharacteristic
315#498C22×C4311yescharacteristic
316#492C22×C4311yescharacteristic
317#487C22×C4311yescharacteristic
318#486C22×C4311yescharacteristic
319#479—21no—
320#478—21no—
321#477C22×C4311yescharacteristic
322#476C22×C4311yescharacteristic
323#475C22×C4311yescharacteristic
324#474C22×C4311yescharacteristic
325#465—21no—
326#465—21no—
327#464—21no—
328#463—21no—
329#462C22×C4311yescharacteristic
330#461C22×C4311yescharacteristic
331#460C22×C4311yescharacteristic
332#459C22×C4311yescharacteristic
333#446C22×C4311yescharacteristic
334#446C22×C4311yescharacteristic
335C4×SD16—21no—
336C4×SD16—21no—
337#436C22×C4311yescharacteristic
338#436C22×C4311yescharacteristic
339#435—21no—
340#435—21no—
341#431—21no—
342#431C22×C4311yescharacteristic
343#427—21no—
344C2×C4⋊C8C22×C4311yescharacteristic
345C2×C4⋊C8C22×C4311yescharacteristic
346#416—21no—
347#416—21no—
348C4×M16—21no—
349C2×C4×C8C22×C4311yescharacteristic
350#335C22×C4311yescharacteristic
351#335C22×C4311yescharacteristic
352#335C22×C4311yescharacteristic
353#335C22×C4311yescharacteristic
354#333C22×C4311yescharacteristic
355#333C22×C4311yescharacteristic
356#332C22×C4311yescharacteristic
357#332C22×C4311yescharacteristic
358#332C22×C4311yescharacteristic
359#332C22×C4311yescharacteristic
360#331C22×C4311yescharacteristic
361#331C22×C4311yescharacteristic
362C43#1915611yescharacteristic, direct product factor, Sylow
363C2×#41—21no—
364C2×#41D4×C4311yescharacteristic
365#135—44no—
366C2×Q16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×D8—21no—
372C2×M16—21no—
373C2×M16—21no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8D4×C4311yescharacteristic
377C22×C8D4×C4311yescharacteristic
378C4⋊Q8C23×C4311yescharacteristic
379C4⋊Q8C23×C4311yescharacteristic
380C4⋊Q8C23×C4311yescharacteristic
381#127C23×C4311yescharacteristic
382#125—21no—
383#124—21no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386#121—21no—
387#121—21no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8D4×C4311yescharacteristic
391C4×Q8C23×C4311yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4D4×C4311yescharacteristic
397C4×D4C23×C4311yescharacteristic
398#117—21no—
399#117—21no—
400#117D4×C4311yescharacteristic
401C2×C42—21no—
402C2×C42C23×C4311yescharacteristic
403#107—21no—
404#107—21no—
405#106—21no—
406#106—21no—
407#106—21no—
408#106—21no—
409C4⋊C8—21no—
410C4⋊C8—21no—
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8C23×C4311yescharacteristic
414C4⋊C8C23×C4311yescharacteristic
415C4⋊C8C23×C4311yescharacteristic
416C4⋊C8C23×C4311yescharacteristic
417C4⋊C8C23×C4311yescharacteristic
418C4⋊C8C23×C4311yescharacteristic
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431C22⋊C8—21no—
432C22⋊C8—21no—
433C22⋊C8—21no—
434#97—21no—
435#97—21no—
436C4×C8—21no—
437C4×C8D4×C4311yescharacteristic
438C4×C8D4×C4311yescharacteristic
439C4×C8C23×C4311yescharacteristic
440C4×C8C23×C4311yescharacteristic
441#41—22no—
442#41—22no—
443#41—42no—
444#41—42no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8C2×D4×C4311yescharacteristic
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—41no—
454C2×D4C2×D4×C4311yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—41no—
459C22×C4C2×D4×C4311yescharacteristic
460C22×C4C2×D4×C4311yescharacteristic
461C22×C4#41×C4311yescharacteristic
462Q16—42no—
463SD16—42no—
464SD16—42no—
465SD16—42no—
466SD16—42no—
467D8—42no—
468M16—42no—
469M16—42no—
470C2×C8—22no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—41no—
478C2×C8—42no—
479C2×C8—42no—
480C2×C8C2×D4×C4311yescharacteristic
481C2×C8C2×D4×C4311yescharacteristic
482C2×C8C2×D4×C4311yescharacteristic
483C2×C8C2×D4×C4311yescharacteristic
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4C2×D4×C4311yescharacteristic
495C4⋊C4C2×D4×C4311yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—41no—
506C42C2×D4×C4311yescharacteristic
507C42C2×D4×C4311yescharacteristic
508C42#41×C4311yescharacteristic
509C42C24×C4311yescharacteristic
510C23—21no—
511C23—41no—
512C23#121×C4311yescharacteristic
513Q8—21no—
514Q8—21no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8—41no—
519Q8—81no—
520D4—21no—
521D4—21no—
522D4—42no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—81no—
528D4—82no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—82no—
543C2×C4#121×C4311yescharacteristic
544C2×C4#121×C4311yescharacteristic
545C2×C4#121×C4311yescharacteristic
546C2×C4AGL(1,ℤ/8)×C4312yes—
547C2×C4#137×C4312yes—
548C2×C4C22×D4×C4311yescharacteristic
549C2×C4C22×D4×C4311yescharacteristic
550C2×C4C2×#41×C4311yescharacteristic
551C8—21no—
552C8—21no—
553C8—21no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8#135×C4312yescomplemented
561C22—21no—
562C22—21no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22C43×#46812yes—
570C22C2×#121×C4311yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4C43×#46812yes—
581C4C2×#135×C4311yescharacteristic
582C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
583C4C2×#137×C4311yescharacteristic
584C4C43×#57511yescharacteristic
585C2—22no—
586C2—81no—
587C2—161no—
588C2C43×#303511yescharacteristic
589C2C2×C43×#46811yescharacteristic
590C2C43×#306711yescharacteristic
subgroupG/H
centerC2×C4×C43#121
commutator, Frattini, cosocleC42C24×C43
socleC22×C43C2×#121
prime radicalC43×#3035C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3167C2semidirect
2. C43×#3076C2semidirect
4. C43×#2965C2semidirect
5. C43×#1700C2semidirect
6. C43×#1699C2semidirect
7. C43×#1698C2semidirect
8. C43×#1697C2semidirect
9. C43×#1692C2semidirect
10. C43×#1691C2semidirect
11. C43×#1686C2semidirect
12. C43×#1685C2semidirect
13. C2×C43×#335C2semidirect
14. C43×#1542C2semidirect
15. C43×#1540C2semidirect
264. C8×C43#135semidirect
265. #19156C43direct (N × H)
290. #3167C2×C43semidirect
291. #3076C2×C43semidirect
293. #2965C2×C43semidirect
294. #1700C2×C43semidirect
295. #1699C2×C43semidirect
296. #1698C2×C43semidirect
297. #1697C2×C43semidirect
298. #1692C2×C43semidirect
299. #1691C2×C43semidirect
300. #1686C2×C43semidirect
301. #1685C2×C43semidirect
302. C2×#335C2×C43semidirect
303. #1542C2×C43semidirect
304. #1540C2×C43semidirect
362. C43#19156direct (N × H)
560. C8#135×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#31672
C43×#30762
C43×#30352
C43×#29652
C43×#17002
C43×#16992
C43×#16982
C43×#16972
C43×#16922
C43×#16912
C43×#16862
C43×#16852
C2×C43×#3352
C43×#15422
C43×#15402
#1915643