Finite Group Databasebeta

← C43×#19492 #24939509

Subgroups — C43×#19492 #24939509

Order 11008.

662 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3207C211yesmaximal, characteristic, complemented
2C43×#3115C211yesmaximal, characteristic, complemented
3C43×#3035C211yesmaximal, characteristic, complemented
4C43×#2991C211yesmaximal, characteristic, complemented
5C43×#1701C211yesmaximal, characteristic, complemented
6C43×#1699C211yesmaximal, characteristic, complemented
7C43×#1687C211yesmaximal, characteristic, complemented
8C43×#1685C211yesmaximal, characteristic, complemented
9C43×#1682C211yesmaximal, characteristic, complemented
10C43×#1680C211yesmaximal, characteristic, complemented
11C43×#1668C211yesmaximal, characteristic, complemented
12C43×#1666C211yesmaximal, characteristic, complemented
13C43×#1573C211yesmaximal, characteristic, complemented
14C43×#1557C211yesmaximal, characteristic, complemented
15C43×#1547C211yesmaximal, characteristic, complemented
16C2×#135×C43—21no—
17C43×#532C2211yescharacteristic
18C43×#532C2211yescharacteristic
19C4×#41×C43C2211yescharacteristic
20C43×#493C2211yescharacteristic
21C43×#492C2211yescharacteristic
22C43×#487C2211yescharacteristic
23C43×#486C2211yescharacteristic
24C43×#482—21no—
25C43×#475C2211yescharacteristic
26C43×#474C2211yescharacteristic
27C43×#464—21no—
28C43×#463—21no—
29C43×#463—21no—
30C43×#463—21no—
31C43×#462C2211yescharacteristic
32C43×#461C2211yescharacteristic
33C43×#460C2211yescharacteristic
34C43×#460C2211yescharacteristic
35C43×#459C2211yescharacteristic
36C43×#459C2211yescharacteristic
37C43×#449—21no—
38C43×#449—21no—
39C43×#449—21no—
40C8×Q8×C43C2211yescharacteristic
41C8×Q8×C43C2211yescharacteristic
42C43×#442—21no—
43C43×#440—21no—
44C43×#436—21no—
45C43×#436—21no—
46C43×#436C2211yescharacteristic
47C43×#436C2211yescharacteristic
48C43×#432C2211yescharacteristic
49C43×#431—21no—
50C43×#431C2211yescharacteristic
51C43×#423—21no—
52C43×#423C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C43×#416—21no—
55C43×#335C2211yescharacteristic
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#334C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#332C2211yescharacteristic
62C43×#332C2211yescharacteristic
63C43×#331C2211yescharacteristic
64C43×#331C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#41×C43—21no—
68C2×#41×C43—21no—
69C2×#41×C43D411yescharacteristic
70#135×C43—44no—
71C2×Q16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—21no—
75C2×SD16×C43—21no—
76C2×SD16×C43—21no—
77C2×D8×C43—21no—
78C2×D8×C43—21no—
79C2×D8×C43—21no—
80C2×D8×C43—21no—
81C2×M16×C43—21no—
82C2×M16×C43—21no—
83C2×M16×C43—21no—
84C22×C8×C43—21no—
85C4⋊Q8×C43C2311yescharacteristic
86C4⋊Q8×C43C2311yescharacteristic
87#127×C43C2311yescharacteristic
88#127×C43C2311yescharacteristic
89#124×C43—21no—
90#124×C43—21no—
91#121×C43—21no—
92#121×C43—21no—
93#121×C43—21no—
94#121×C43—21no—
95C4×Q8×C43D411yescharacteristic
96C4×Q8×C43C2311yescharacteristic
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43—21no—
100C4×D4×C43—21no—
101C4×D4×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43D411yescharacteristic
104C4×D4×C43C2311yescharacteristic
105#117×C43—21no—
106#117×C43D411yescharacteristic
107C2×C42×C43—21no—
108C2×C42×C43C2311yescharacteristic
109#107×C43—21no—
110#106×C43—21no—
111C4⋊C8×C43—21no—
112C4⋊C8×C43—21no—
113C4⋊C8×C43—21no—
114C4⋊C8×C43—21no—
115C4⋊C8×C43D411yescharacteristic
116C4⋊C8×C43D411yescharacteristic
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#102×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—
138C22⋊C8×C43D411yescharacteristic
139C22⋊C8×C43D411yescharacteristic
140#97×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145#41×C43—22no—
146#41×C43—41no—
147#41×C43—42no—
148#41×C43—42no—
149#41×C43—81no—
150#41×C43—81no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43C2×D411yescharacteristic
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—41no—
162C2×D4×C43—41no—
163C2×D4×C43C2×D411yescharacteristic
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—41no—
168C22×C4×C43—41no—
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43#4111yescharacteristic
172Q16×C43—42no—
173SD16×C43—42no—
174SD16×C43—42no—
175SD16×C43—42no—
176SD16×C43—81no—
177SD16×C43—81no—
178D8×C43—42no—
179D8×C43—42no—
180D8×C43—81no—
181D8×C43—81no—
182M16×C43—81no—
183M16×C43—81no—
184M16×C43—81no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—42no—
192C2×C8×C43C2×D411yescharacteristic
193C2×C8×C43C2×D411yescharacteristic
194C2×C8×C43C2×D411yescharacteristic
195C2×C8×C43C2×D411yescharacteristic
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43C2×D411yescharacteristic
203C4⋊C4×C43C2×D411yescharacteristic
204C22⋊C4×C43—21no—
205C22⋊C4×C43—21no—
206C22⋊C4×C43—21no—
207C22⋊C4×C43—41no—
208C22⋊C4×C43—41no—
209C22⋊C4×C43—41no—
210C22⋊C4×C43—41no—
211C42×C43—21no—
212C42×C43—21no—
213C42×C43—21no—
214C42×C43C2×D411yescharacteristic
215C42×C43C2×D411yescharacteristic
216C42×C43#4111yescharacteristic
217C42×C43C2411yescharacteristic
218C23×C43—21no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43#12111yescharacteristic
222Q8×C43—21no—
223Q8×C43—41no—
224Q8×C43—41no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43AGL(1,ℤ/8)12yes—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—42no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—81no—
240D4×C43—81no—
241D4×C43—82no—
242D4×C43—82no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—41no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—82no—
258C2×C4×C43—82no—
259C2×C4×C43#12111yescharacteristic
260C2×C4×C43#12111yescharacteristic
261C2×C4×C43#12111yescharacteristic
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C8×C43—21no—
266C8×C43—21no—
267C8×C43—21no—
268C8×C43—21no—
269C8×C43—41no—
270C8×C43—41no—
271C8×C43—41no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43—41no—
275#19492C4311yesmaximal, characteristic, direct product factor, Sylow
276C22×C43—21no—
277C22×C43—21no—
278C22×C43—21no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43C2×#12111yescharacteristic
289C4×C43—21no—
290C4×C43—21no—
291C4×C43—22no—
292C4×C43—21no—
293C4×C43—21no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C43#57511yescharacteristic
300C4×C43#57611yescharacteristic
301C4×C43#57711yescharacteristic
302#3207C2×C4311yescharacteristic, complemented
303#3115C2×C4311yescharacteristic, complemented
304#3035C2×C4311yescharacteristic, complemented
305#2991C2×C4311yescharacteristic, complemented
306#1701C2×C4311yescharacteristic, complemented
307#1699C2×C4311yescharacteristic, complemented
308#1687C2×C4311yescharacteristic, complemented
309#1685C2×C4311yescharacteristic, complemented
310#1682C2×C4311yescharacteristic, complemented
311#1680C2×C4311yescharacteristic, complemented
312#1668C2×C4311yescharacteristic, complemented
313#1666C2×C4311yescharacteristic, complemented
314#1573C2×C4311yescharacteristic, complemented
315#1557C2×C4311yescharacteristic, complemented
316#1547C2×C4311yescharacteristic, complemented
317C2×C43—41no—
318C2×C43—81no—
319C2×C43—161no—
320C2×C43—161no—
321C2×C43#304511yescharacteristic
322C2×C43#305511yescharacteristic
323C2×C43#306711yescharacteristic
324C2×#135—21no—
325#532C22×C4311yescharacteristic
326#532C22×C4311yescharacteristic
327C4×#41C22×C4311yescharacteristic
328#493C22×C4311yescharacteristic
329#492C22×C4311yescharacteristic
330#487C22×C4311yescharacteristic
331#486C22×C4311yescharacteristic
332#482—21no—
333#475C22×C4311yescharacteristic
334#474C22×C4311yescharacteristic
335#464—21no—
336#463—21no—
337#463—21no—
338#463—21no—
339#462C22×C4311yescharacteristic
340#461C22×C4311yescharacteristic
341#460C22×C4311yescharacteristic
342#460C22×C4311yescharacteristic
343#459C22×C4311yescharacteristic
344#459C22×C4311yescharacteristic
345#449—21no—
346#449—21no—
347#449—21no—
348C8×Q8C22×C4311yescharacteristic
349C8×Q8C22×C4311yescharacteristic
350#442—21no—
351#440—21no—
352#436—21no—
353#436—21no—
354#436C22×C4311yescharacteristic
355#436C22×C4311yescharacteristic
356#432C22×C4311yescharacteristic
357#431—21no—
358#431C22×C4311yescharacteristic
359#423—21no—
360#423C22×C4311yescharacteristic
361C2×C4⋊C8C22×C4311yescharacteristic
362#416—21no—
363#335C22×C4311yescharacteristic
364#335C22×C4311yescharacteristic
365#334C22×C4311yescharacteristic
366#334C22×C4311yescharacteristic
367#332C22×C4311yescharacteristic
368#332C22×C4311yescharacteristic
369#332C22×C4311yescharacteristic
370#332C22×C4311yescharacteristic
371#331C22×C4311yescharacteristic
372#331C22×C4311yescharacteristic
373#331C22×C4311yescharacteristic
374#331C22×C4311yescharacteristic
375C43#1949211yescharacteristic, direct product factor, Sylow
376C2×#41—21no—
377C2×#41—21no—
378C2×#41D4×C4311yescharacteristic
379#135—44no—
380C2×Q16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×D8—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8—21no—
390C2×M16—21no—
391C2×M16—21no—
392C2×M16—21no—
393C22×C8—21no—
394C4⋊Q8C23×C4311yescharacteristic
395C4⋊Q8C23×C4311yescharacteristic
396#127C23×C4311yescharacteristic
397#127C23×C4311yescharacteristic
398#124—21no—
399#124—21no—
400#121—21no—
401#121—21no—
402#121—21no—
403#121—21no—
404C4×Q8D4×C4311yescharacteristic
405C4×Q8C23×C4311yescharacteristic
406C4×D4—21no—
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4—21no—
412C4×D4D4×C4311yescharacteristic
413C4×D4C23×C4311yescharacteristic
414#117—21no—
415#117D4×C4311yescharacteristic
416C2×C42—21no—
417C2×C42C23×C4311yescharacteristic
418#107—21no—
419#106—21no—
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8D4×C4311yescharacteristic
425C4⋊C8D4×C4311yescharacteristic
426C4⋊C8C23×C4311yescharacteristic
427C4⋊C8C23×C4311yescharacteristic
428C4⋊C8C23×C4311yescharacteristic
429C4⋊C8C23×C4311yescharacteristic
430C4⋊C8C23×C4311yescharacteristic
431C4⋊C8C23×C4311yescharacteristic
432#103—21no—
433#103—21no—
434#103—21no—
435#103—21no—
436#103—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444C22⋊C8—21no—
445C22⋊C8—21no—
446C22⋊C8—21no—
447C22⋊C8D4×C4311yescharacteristic
448C22⋊C8D4×C4311yescharacteristic
449#97—21no—
450C4×C8—21no—
451C4×C8—21no—
452C4×C8C23×C4311yescharacteristic
453C4×C8C23×C4311yescharacteristic
454#41—22no—
455#41—41no—
456#41—42no—
457#41—42no—
458#41—81no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8C2×D4×C4311yescharacteristic
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4C2×D4×C4311yescharacteristic
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4C2×D4×C4311yescharacteristic
479C22×C4C2×D4×C4311yescharacteristic
480C22×C4#41×C4311yescharacteristic
481Q16—42no—
482SD16—42no—
483SD16—42no—
484SD16—42no—
485SD16—81no—
486SD16—81no—
487D8—42no—
488D8—42no—
489D8—81no—
490D8—81no—
491M16—81no—
492M16—81no—
493M16—81no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—42no—
501C2×C8C2×D4×C4311yescharacteristic
502C2×C8C2×D4×C4311yescharacteristic
503C2×C8C2×D4×C4311yescharacteristic
504C2×C8C2×D4×C4311yescharacteristic
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4C2×D4×C4311yescharacteristic
512C4⋊C4C2×D4×C4311yescharacteristic
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42C2×D4×C4311yescharacteristic
524C42C2×D4×C4311yescharacteristic
525C42#41×C4311yescharacteristic
526C42C24×C4311yescharacteristic
527C23—21no—
528C23—41no—
529C23—41no—
530C23#121×C4311yescharacteristic
531Q8—21no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8AGL(1,ℤ/8)×C4312yes—
537D4—21no—
538D4—21no—
539D4—42no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—81no—
549D4—81no—
550D4—82no—
551D4—82no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—82no—
567C2×C4—82no—
568C2×C4#121×C4311yescharacteristic
569C2×C4#121×C4311yescharacteristic
570C2×C4#121×C4311yescharacteristic
571C2×C4C22×D4×C4311yescharacteristic
572C2×C4C22×D4×C4311yescharacteristic
573C2×C4C2×#41×C4311yescharacteristic
574C8—21no—
575C8—21no—
576C8—21no—
577C8—21no—
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8—41no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22C2×#121×C4311yescharacteristic
597C4—21no—
598C4—21no—
599C4—22no—
600C4—21no—
601C4—21no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
607C4C43×#57511yescharacteristic
608C4C43×#57611yescharacteristic
609C4C43×#57711yescharacteristic
610C2—41no—
611C2—81no—
612C2—161no—
613C2—161no—
614C2C43×#304511yescharacteristic
615C2C43×#305511yescharacteristic
616C2C43×#306711yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3207C2semidirect
2. C43×#3115C2semidirect
3. C43×#3035C2semidirect
4. C43×#2991C2semidirect
5. C43×#1701C2semidirect
6. C43×#1699C2semidirect
7. C43×#1687C2semidirect
8. C43×#1685C2semidirect
9. C43×#1682C2semidirect
10. C43×#1680C2semidirect
11. C43×#1668C2semidirect
12. C43×#1666C2semidirect
13. C43×#1573C2semidirect
14. C43×#1557C2semidirect
15. C43×#1547C2semidirect
275. #19492C43direct (N × H)
302. #3207C2×C43semidirect
303. #3115C2×C43semidirect
304. #3035C2×C43semidirect
305. #2991C2×C43semidirect
306. #1701C2×C43semidirect
307. #1699C2×C43semidirect
308. #1687C2×C43semidirect
309. #1685C2×C43semidirect
310. #1682C2×C43semidirect
311. #1680C2×C43semidirect
312. #1668C2×C43semidirect
313. #1666C2×C43semidirect
314. #1573C2×C43semidirect
315. #1557C2×C43semidirect
316. #1547C2×C43semidirect
375. C43#19492direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32072
C43×#31152
C43×#30352
C43×#29912
C43×#17012
C43×#16992
C43×#16872
C43×#16852
C43×#16822
C43×#16802
C43×#16682
C43×#16662
C43×#15732
C43×#15572
C43×#15472
#1949243