Finite Group Databasebeta

← C43×#20270 #24940287

Subgroups — C43×#20270 #24940287

Order 11008.

652 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3397C211yesmaximal, characteristic, complemented
2C43×#3366C211yesmaximal, characteristic, complemented
3C43×#3356C211yesmaximal, characteristic, complemented
4C43×#3287C211yesmaximal, characteristic, complemented
5C43×#1715C211yesmaximal, characteristic, complemented
6C43×#1698C211yesmaximal, characteristic, complemented
7C43×#1687C211yesmaximal, characteristic, complemented
8C43×#1686C211yesmaximal, characteristic, complemented
9C43×#1671C211yesmaximal, characteristic, complemented
10C43×#1642C211yesmaximal, characteristic, complemented
11C43×#1631C211yesmaximal, characteristic, complemented
12C43×#1628C211yesmaximal, characteristic, complemented
13C43×#1622C211yesmaximal, characteristic, complemented
14C43×#1593C211yesmaximal, characteristic, complemented
15C43×#1581C211yesmaximal, characteristic, complemented
16C2×#135×C43—21no—
17C43×#556C2211yescharacteristic
18C43×#554C2211yescharacteristic
19C43×#550C2211yescharacteristic
20C43×#550C2211yescharacteristic
21C43×#498C2211yescharacteristic
22C43×#496—21no—
23C43×#493C2211yescharacteristic
24C43×#492C2211yescharacteristic
25C43×#492C2211yescharacteristic
26C43×#490—21no—
27C43×#486C2211yescharacteristic
28C43×#486C2211yescharacteristic
29C43×#485—21no—
30C43×#483—21no—
31C43×#478—21no—
32C43×#477C2211yescharacteristic
33C43×#476C2211yescharacteristic
34C43×#475C2211yescharacteristic
35C43×#470—21no—
36C43×#466—21no—
37C43×#463—21no—
38C43×#461C2211yescharacteristic
39C43×#460—21no—
40C43×#460C2211yescharacteristic
41C43×#460C2211yescharacteristic
42C43×#459—21no—
43C43×#459C2211yescharacteristic
44C43×#459C2211yescharacteristic
45C43×#449—21no—
46C43×#449—21no—
47C43×#446C2211yescharacteristic
48C43×#446C2211yescharacteristic
49C43×#442—21no—
50C43×#440—21no—
51C4×Q16×C43C2211yescharacteristic
52C4×D8×C43C2211yescharacteristic
53C43×#436C2211yescharacteristic
54C8×D4×C43C2211yescharacteristic
55C43×#428—21no—
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#333C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#331C2211yescharacteristic
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#41×C43—21no—
68C2×#41×C43—21no—
69#135×C43—44no—
70C2×Q16×C43D411yescharacteristic
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—21no—
75C2×SD16×C43—21no—
76C2×SD16×C43—41no—
77C2×D8×C43—21no—
78C2×D8×C43—21no—
79C2×D8×C43—21no—
80C2×D8×C43—21no—
81C2×D8×C43D411yescharacteristic
82C2×M16×C43—21no—
83C22×C8×C43—21no—
84C4⋊Q8×C43C2311yescharacteristic
85C4⋊Q8×C43C2311yescharacteristic
86#127×C43—21no—
87#127×C43—21no—
88#127×C43C2311yescharacteristic
89#127×C43C2311yescharacteristic
90#126×C43—41no—
91#125×C43—21no—
92#124×C43—21no—
93C22⋊Q8×C43—21no—
94C22⋊Q8×C43—21no—
95C22⋊Q8×C43—41no—
96#121×C43—21no—
97#121×C43—21no—
98#121×C43—41no—
99#121×C43—41no—
100C4×Q8×C43—21no—
101C4×Q8×C43C2311yescharacteristic
102C4×Q8×C43C2311yescharacteristic
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43—21no—
106C4×D4×C43C2311yescharacteristic
107C4×D4×C43C2311yescharacteristic
108#117×C43—21no—
109C2×C4⋊C4×C43—21no—
110#107×C43—21no—
111#107×C43D411yescharacteristic
112#107×C43D411yescharacteristic
113#106×C43—21no—
114#106×C43—21no—
115#106×C43—21no—
116#106×C43—21no—
117C4⋊C8×C43—21no—
118C4⋊C8×C43—21no—
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×C43D411yescharacteristic
127#103×C43D411yescharacteristic
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—
135#102×C43—41no—
136#102×C43D411yescharacteristic
137#102×C43D411yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140#97×C43—21no—
141#97×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145#41×C43—42no—
146#41×C43—42no—
147#41×C43—81no—
148#41×C43—81no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×Q8×C43C2×D411yescharacteristic
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—41no—
160C2×D4×C43—41no—
161C2×D4×C43—41no—
162C2×D4×C43—41no—
163C2×D4×C43C2×D411yescharacteristic
164C2×D4×C43C2×D411yescharacteristic
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—41no—
168C22×C4×C43—41no—
169C22×C4×C43—41no—
170Q16×C43—22no—
171SD16×C43—42no—
172SD16×C43—42no—
173SD16×C43—42no—
174SD16×C43—81no—
175SD16×C43—81no—
176SD16×C43—82no—
177D8×C43—41no—
178D8×C43—42no—
179D8×C43—42no—
180D8×C43—81no—
181D8×C43—81no—
182M16×C43—42no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—42no—
189C2×C8×C43C2×D411yescharacteristic
190C2×C8×C43C2×D411yescharacteristic
191C2×C8×C43C2×D411yescharacteristic
192C2×C8×C43C2×D411yescharacteristic
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—41no—
200C4⋊C4×C43—41no—
201C4⋊C4×C43—41no—
202C4⋊C4×C43C2×D411yescharacteristic
203C4⋊C4×C43C2×D411yescharacteristic
204C4⋊C4×C43C2×D411yescharacteristic
205C4⋊C4×C43C2×D411yescharacteristic
206C22⋊C4×C43—21no—
207C22⋊C4×C43—21no—
208C22⋊C4×C43—41no—
209C22⋊C4×C43—41no—
210C22⋊C4×C43—41no—
211C22⋊C4×C43—41no—
212C22⋊C4×C43—41no—
213C42×C43—21no—
214C42×C43—21no—
215C42×C43—41no—
216C42×C43C2411yescharacteristic
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—41no—
220C23×C43—41no—
221Q8×C43—21no—
222Q8×C43—21no—
223Q8×C43—21no—
224Q8×C43—21no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—81no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—21no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—81no—
241D4×C43—81no—
242D4×C43—82no—
243D4×C43—82no—
244D4×C43—161no—
245D4×C43—161no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—82no—
259C2×C4×C43—82no—
260C2×C4×C43—161no—
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43H(5,𝔽2)11yescharacteristic
264C8×C43—21no—
265C8×C43—21no—
266C8×C43—21no—
267C8×C43—41no—
268C8×C43—41no—
269C8×C43—41no—
270C8×C43—41no—
271C8×C43—41no—
272C8×C43AGL(1,ℤ/8)12yes—
273#20270C4311yesmaximal, characteristic, direct product factor, Sylow
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43D4211yescharacteristic
287C4×C43—21no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—81no—
295C4×C43—81no—
296C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
297C4×C43#57511yescharacteristic
298C4×C43#57711yescharacteristic
299C4×C43#57711yescharacteristic
300#3397C2×C4311yescharacteristic, complemented
301#3366C2×C4311yescharacteristic, complemented
302#3356C2×C4311yescharacteristic, complemented
303#3287C2×C4311yescharacteristic, complemented
304#1715C2×C4311yescharacteristic, complemented
305#1698C2×C4311yescharacteristic, complemented
306#1687C2×C4311yescharacteristic, complemented
307#1686C2×C4311yescharacteristic, complemented
308#1671C2×C4311yescharacteristic, complemented
309#1642C2×C4311yescharacteristic, complemented
310#1631C2×C4311yescharacteristic, complemented
311#1628C2×C4311yescharacteristic, complemented
312#1622C2×C4311yescharacteristic, complemented
313#1593C2×C4311yescharacteristic, complemented
314#1581C2×C4311yescharacteristic, complemented
315C2×C43—81no—
316C2×C43—81no—
317C2×C43—161no—
318C2×C43—161no—
319C2×C43#327111yescharacteristic
320C2×C43#327211yescharacteristic
321C2×C43#328811yescharacteristic
322C2×#135—21no—
323#556C22×C4311yescharacteristic
324#554C22×C4311yescharacteristic
325#550C22×C4311yescharacteristic
326#550C22×C4311yescharacteristic
327#498C22×C4311yescharacteristic
328#496—21no—
329#493C22×C4311yescharacteristic
330#492C22×C4311yescharacteristic
331#492C22×C4311yescharacteristic
332#490—21no—
333#486C22×C4311yescharacteristic
334#486C22×C4311yescharacteristic
335#485—21no—
336#483—21no—
337#478—21no—
338#477C22×C4311yescharacteristic
339#476C22×C4311yescharacteristic
340#475C22×C4311yescharacteristic
341#470—21no—
342#466—21no—
343#463—21no—
344#461C22×C4311yescharacteristic
345#460—21no—
346#460C22×C4311yescharacteristic
347#460C22×C4311yescharacteristic
348#459—21no—
349#459C22×C4311yescharacteristic
350#459C22×C4311yescharacteristic
351#449—21no—
352#449—21no—
353#446C22×C4311yescharacteristic
354#446C22×C4311yescharacteristic
355#442—21no—
356#440—21no—
357C4×Q16C22×C4311yescharacteristic
358C4×D8C22×C4311yescharacteristic
359#436C22×C4311yescharacteristic
360C8×D4C22×C4311yescharacteristic
361#428—21no—
362#335C22×C4311yescharacteristic
363#334C22×C4311yescharacteristic
364#333C22×C4311yescharacteristic
365#332C22×C4311yescharacteristic
366#331C22×C4311yescharacteristic
367#331C22×C4311yescharacteristic
368Q8⋊C8C22×C4311yescharacteristic
369Q8⋊C8C22×C4311yescharacteristic
370D4⋊C8C22×C4311yescharacteristic
371D4⋊C8C22×C4311yescharacteristic
372#322C22×C4311yescharacteristic
373C43#2027011yescharacteristic, direct product factor, Sylow
374C2×#41—21no—
375C2×#41—21no—
376#135—44no—
377C2×Q16D4×C4311yescharacteristic
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16—41no—
384C2×D8—21no—
385C2×D8—21no—
386C2×D8—21no—
387C2×D8—21no—
388C2×D8D4×C4311yescharacteristic
389C2×M16—21no—
390C22×C8—21no—
391C4⋊Q8C23×C4311yescharacteristic
392C4⋊Q8C23×C4311yescharacteristic
393#127—21no—
394#127—21no—
395#127C23×C4311yescharacteristic
396#127C23×C4311yescharacteristic
397#126—41no—
398#125—21no—
399#124—21no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—41no—
403#121—21no—
404#121—21no—
405#121—41no—
406#121—41no—
407C4×Q8—21no—
408C4×Q8C23×C4311yescharacteristic
409C4×Q8C23×C4311yescharacteristic
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4C23×C4311yescharacteristic
414C4×D4C23×C4311yescharacteristic
415#117—21no—
416C2×C4⋊C4—21no—
417#107—21no—
418#107D4×C4311yescharacteristic
419#107D4×C4311yescharacteristic
420#106—21no—
421#106—21no—
422#106—21no—
423#106—21no—
424C4⋊C8—21no—
425C4⋊C8—21no—
426C4⋊C8C23×C4311yescharacteristic
427C4⋊C8C23×C4311yescharacteristic
428C4⋊C8C23×C4311yescharacteristic
429C4⋊C8C23×C4311yescharacteristic
430#103—21no—
431#103—21no—
432#103—21no—
433#103D4×C4311yescharacteristic
434#103D4×C4311yescharacteristic
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—41no—
443#102D4×C4311yescharacteristic
444#102D4×C4311yescharacteristic
445C22⋊C8—21no—
446C22⋊C8—21no—
447#97—21no—
448#97—21no—
449C4×C8C23×C4311yescharacteristic
450C4×C8C23×C4311yescharacteristic
451C4×C8C23×C4311yescharacteristic
452#41—42no—
453#41—42no—
454#41—81no—
455#41—81no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8C2×D4×C4311yescharacteristic
459C2×Q8C2×D4×C4311yescharacteristic
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4C2×D4×C4311yescharacteristic
471C2×D4C2×D4×C4311yescharacteristic
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477Q16—22no—
478SD16—42no—
479SD16—42no—
480SD16—42no—
481SD16—81no—
482SD16—81no—
483SD16—82no—
484D8—41no—
485D8—42no—
486D8—42no—
487D8—81no—
488D8—81no—
489M16—42no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—42no—
496C2×C8C2×D4×C4311yescharacteristic
497C2×C8C2×D4×C4311yescharacteristic
498C2×C8C2×D4×C4311yescharacteristic
499C2×C8C2×D4×C4311yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4C2×D4×C4311yescharacteristic
510C4⋊C4C2×D4×C4311yescharacteristic
511C4⋊C4C2×D4×C4311yescharacteristic
512C4⋊C4C2×D4×C4311yescharacteristic
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C42—21no—
521C42—21no—
522C42—41no—
523C42C24×C4311yescharacteristic
524C23—21no—
525C23—21no—
526C23—41no—
527C23—41no—
528Q8—21no—
529Q8—21no—
530Q8—21no—
531Q8—21no—
532Q8—41no—
533Q8—41no—
534Q8—81no—
535D4—21no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—81no—
548D4—81no—
549D4—82no—
550D4—82no—
551D4—161no—
552D4—161no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—82no—
566C2×C4—82no—
567C2×C4—161no—
568C2×C4C22×D4×C4311yescharacteristic
569C2×C4C22×D4×C4311yescharacteristic
570C2×C4H(5,𝔽2)×C4311yescharacteristic
571C8—21no—
572C8—21no—
573C8—21no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C8—41no—
579C8AGL(1,ℤ/8)×C4312yes—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22D42×C4311yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—81no—
601C4—81no—
602C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
603C4C43×#57511yescharacteristic
604C4C43×#57711yescharacteristic
605C4C43×#57711yescharacteristic
606C2—81no—
607C2—81no—
608C2—161no—
609C2—161no—
610C2C43×#327111yescharacteristic
611C2C43×#327211yescharacteristic
612C2C43×#328811yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3397C2semidirect
2. C43×#3366C2semidirect
3. C43×#3356C2semidirect
4. C43×#3287C2semidirect
5. C43×#1715C2semidirect
6. C43×#1698C2semidirect
7. C43×#1687C2semidirect
8. C43×#1686C2semidirect
9. C43×#1671C2semidirect
10. C43×#1642C2semidirect
11. C43×#1631C2semidirect
12. C43×#1628C2semidirect
13. C43×#1622C2semidirect
14. C43×#1593C2semidirect
15. C43×#1581C2semidirect
273. #20270C43direct (N × H)
300. #3397C2×C43semidirect
301. #3366C2×C43semidirect
302. #3356C2×C43semidirect
303. #3287C2×C43semidirect
304. #1715C2×C43semidirect
305. #1698C2×C43semidirect
306. #1687C2×C43semidirect
307. #1686C2×C43semidirect
308. #1671C2×C43semidirect
309. #1642C2×C43semidirect
310. #1631C2×C43semidirect
311. #1628C2×C43semidirect
312. #1622C2×C43semidirect
313. #1593C2×C43semidirect
314. #1581C2×C43semidirect
373. C43#20270direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33972
C43×#33662
C43×#33562
C43×#32872
C43×#17152
C43×#16982
C43×#16872
C43×#16862
C43×#16712
C43×#16422
C43×#16312
C43×#16282
C43×#16222
C43×#15932
C43×#15812
#2027043