Finite Group Databasebeta

← C43×#19827 #24939844

Subgroups — C43×#19827 #24939844

Order 11008.

668 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×#3362C211yesmaximal, characteristic, complemented
2C43×#3362C211yesmaximal, characteristic, complemented
3C43×#3332C211yesmaximal, characteristic, complemented
4C43×#3284C211yesmaximal, characteristic, complemented
5C43×#1717C211yesmaximal, characteristic, complemented
6C43×#1697C211yesmaximal, characteristic, complemented
7C43×#1682C211yesmaximal, characteristic, complemented
8C43×#1677C211yesmaximal, characteristic, complemented
9C43×#1666C211yesmaximal, characteristic, complemented
10C43×#1645C211yesmaximal, characteristic, complemented
11C43×#1635C211yesmaximal, characteristic, complemented
12C43×#1621C211yesmaximal, characteristic, complemented
13C43×#1621C211yesmaximal, characteristic, complemented
14C43×#1583C211yesmaximal, characteristic, complemented
15C43×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×#135×C43—21no—
17Q82×C43C2211yescharacteristic
18C43×#550C2211yescharacteristic
19C43×#550C2211yescharacteristic
20C43×#547C2211yescharacteristic
21C43×#493C2211yescharacteristic
22C43×#492C2211yescharacteristic
23C43×#487C2211yescharacteristic
24C43×#486—21no—
25C43×#486—21no—
26C43×#486C2211yescharacteristic
27C43×#486C2211yescharacteristic
28C43×#486C2211yescharacteristic
29C43×#481—21no—
30C43×#476—21no—
31C43×#476—21no—
32C43×#476C2211yescharacteristic
33C43×#476C2211yescharacteristic
34C43×#475C2211yescharacteristic
35C43×#469—21no—
36C43×#465—21no—
37C43×#462C2211yescharacteristic
38C43×#460—21no—
39C43×#460—21no—
40C43×#460C2211yescharacteristic
41C43×#460C2211yescharacteristic
42C43×#459C2211yescharacteristic
43C43×#459C2211yescharacteristic
44C43×#452—21no—
45C43×#449—21no—
46C43×#449—21no—
47C8×Q8×C43C2211yescharacteristic
48C8×Q8×C43C2211yescharacteristic
49C4×SD16×C43—21no—
50C4×SD16×C43—21no—
51C4×SD16×C43C2211yescharacteristic
52C4×SD16×C43C2211yescharacteristic
53C43×#436C2211yescharacteristic
54C8×D4×C43C2211yescharacteristic
55C43×#417—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—
69C2×#41×C43—21no—
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×C43D411yescharacteristic
77C2×SD16×C43D411yescharacteristic
78C2×D8×C43—21no—
79C2×D8×C43—21no—
80C2×D8×C43—41no—
81C2×M16×C43—21no—
82C22×C8×C43—21no—
83C4⋊Q8×C43—21no—
84C4⋊Q8×C43—21no—
85C4⋊Q8×C43—41no—
86C4⋊Q8×C43C2311yescharacteristic
87C4⋊Q8×C43C2311yescharacteristic
88#127×C43—21no—
89#127×C43—21no—
90#127×C43C2311yescharacteristic
91#127×C43C2311yescharacteristic
92#123×C43—41no—
93C22⋊Q8×C43—21no—
94#121×C43—21no—
95#121×C43—21no—
96#121×C43—21no—
97#121×C43—41no—
98#121×C43—41no—
99C4×Q8×C43—21no—
100C4×Q8×C43—21no—
101C4×Q8×C43C2311yescharacteristic
102C4×Q8×C43C2311yescharacteristic
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43C2311yescharacteristic
106C4×D4×C43C2311yescharacteristic
107C2×C4⋊C4×C43—21no—
108#106×C43—21no—
109#106×C43—21no—
110#106×C43—21no—
111#106×C43D411yescharacteristic
112#106×C43D411yescharacteristic
113C4⋊C8×C43—21no—
114C4⋊C8×C43—21no—
115C4⋊C8×C43C2311yescharacteristic
116C4⋊C8×C43C2311yescharacteristic
117C4⋊C8×C43C2311yescharacteristic
118C4⋊C8×C43C2311yescharacteristic
119#103×C43—21no—
120#103×C43—21no—
121#103×C43—41no—
122#103×C43D411yescharacteristic
123#103×C43D411yescharacteristic
124#102×C43—21no—
125#102×C43—21no—
126#102×C43—21no—
127#102×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—
135#102×C43—21no—
136#102×C43D411yescharacteristic
137#102×C43D411yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145#41×C43—42no—
146#41×C43—42no—
147#41×C43—42no—
148#41×C43—81no—
149#41×C43—81no—
150#41×C43—81no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—41no—
154C2×Q8×C43C2×D411yescharacteristic
155C2×Q8×C43C2×D411yescharacteristic
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—41no—
163C2×D4×C43—41no—
164C2×D4×C43—41no—
165C2×D4×C43—41no—
166C2×D4×C43—41no—
167C2×D4×C43C2×D411yescharacteristic
168C2×D4×C43C2×D411yescharacteristic
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—41no—
172C22×C4×C43—41no—
173C22×C4×C43—41no—
174Q16×C43—42no—
175SD16×C43—22no—
176SD16×C43—22no—
177SD16×C43—42no—
178SD16×C43—42no—
179SD16×C43—42no—
180SD16×C43—81no—
181D8×C43—42no—
182D8×C43—81no—
183D8×C43—82no—
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—42no—
191C2×C8×C43C2×D411yescharacteristic
192C2×C8×C43C2×D411yescharacteristic
193C2×C8×C43C2×D411yescharacteristic
194C2×C8×C43C2×D411yescharacteristic
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—41no—
202C4⋊C4×C43—41no—
203C4⋊C4×C43—41no—
204C4⋊C4×C43C2×D411yescharacteristic
205C4⋊C4×C43C2×D411yescharacteristic
206C4⋊C4×C43C2×D411yescharacteristic
207C4⋊C4×C43C2×D411yescharacteristic
208C22⋊C4×C43—21no—
209C22⋊C4×C43—21no—
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—41no—
224Q8×C43—41no—
225Q8×C43—81no—
226Q8×C43—161no—
227Q8×C43#13512yescomplemented
228Q8×C43AGL(1,ℤ/8)12yes—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—21no—
232D4×C43—21no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—82no—
242D4×C43—82no—
243D4×C43—81no—
244D4×C43—81no—
245D4×C43—82no—
246D4×C43—161no—
247D4×C43—161no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—82no—
261C2×C4×C43—82no—
262C2×C4×C43—82no—
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C8×C43—21no—
267C8×C43—21no—
268C8×C43—21no—
269C8×C43—21no—
270C8×C43—41no—
271C8×C43—41no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43—41no—
275#19827C4311yesmaximal, characteristic, direct product factor, Sylow
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
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×C43D4211yescharacteristic
289C4×C43—22no—
290C4×C43—22no—
291C4×C43—21no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43C2×#13511yescharacteristic
299C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
300C4×C43#57711yescharacteristic
301C4×C43#57711yescharacteristic
302#3362C2×C4311yescharacteristic, complemented
303#3362C2×C4311yescharacteristic, complemented
304#3332C2×C4311yescharacteristic, complemented
305#3284C2×C4311yescharacteristic, complemented
306#1717C2×C4311yescharacteristic, complemented
307#1697C2×C4311yescharacteristic, complemented
308#1682C2×C4311yescharacteristic, complemented
309#1677C2×C4311yescharacteristic, complemented
310#1666C2×C4311yescharacteristic, complemented
311#1645C2×C4311yescharacteristic, complemented
312#1635C2×C4311yescharacteristic, complemented
313#1621C2×C4311yescharacteristic, complemented
314#1621C2×C4311yescharacteristic, complemented
315#1583C2×C4311yescharacteristic, complemented
316SD16⋊C8C2×C4311yescharacteristic, complemented
317C2×C43—81no—
318C2×C43—81no—
319C2×C43—161no—
320C2×C43—161no—
321C2×C43#326511yescharacteristic
322C2×C43#328211yescharacteristic
323C2×C43#328811yescharacteristic
324C2×#135—21no—
325Q82C22×C4311yescharacteristic
326#550C22×C4311yescharacteristic
327#550C22×C4311yescharacteristic
328#547C22×C4311yescharacteristic
329#493C22×C4311yescharacteristic
330#492C22×C4311yescharacteristic
331#487C22×C4311yescharacteristic
332#486—21no—
333#486—21no—
334#486C22×C4311yescharacteristic
335#486C22×C4311yescharacteristic
336#486C22×C4311yescharacteristic
337#481—21no—
338#476—21no—
339#476—21no—
340#476C22×C4311yescharacteristic
341#476C22×C4311yescharacteristic
342#475C22×C4311yescharacteristic
343#469—21no—
344#465—21no—
345#462C22×C4311yescharacteristic
346#460—21no—
347#460—21no—
348#460C22×C4311yescharacteristic
349#460C22×C4311yescharacteristic
350#459C22×C4311yescharacteristic
351#459C22×C4311yescharacteristic
352#452—21no—
353#449—21no—
354#449—21no—
355C8×Q8C22×C4311yescharacteristic
356C8×Q8C22×C4311yescharacteristic
357C4×SD16—21no—
358C4×SD16—21no—
359C4×SD16C22×C4311yescharacteristic
360C4×SD16C22×C4311yescharacteristic
361#436C22×C4311yescharacteristic
362C8×D4C22×C4311yescharacteristic
363#417—21no—
364#335C22×C4311yescharacteristic
365#334C22×C4311yescharacteristic
366#333C22×C4311yescharacteristic
367#332C22×C4311yescharacteristic
368#331C22×C4311yescharacteristic
369#331C22×C4311yescharacteristic
370Q8⋊C8C22×C4311yescharacteristic
371Q8⋊C8C22×C4311yescharacteristic
372D4⋊C8C22×C4311yescharacteristic
373D4⋊C8C22×C4311yescharacteristic
374#322C22×C4311yescharacteristic
375C43#1982711yescharacteristic, direct product factor, Sylow
376C2×#41—21no—
377C2×#41—21no—
378C2×#41—21no—
379#135—44no—
380C2×Q16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16D4×C4311yescharacteristic
386C2×SD16D4×C4311yescharacteristic
387C2×D8—21no—
388C2×D8—21no—
389C2×D8—41no—
390C2×M16—21no—
391C22×C8—21no—
392C4⋊Q8—21no—
393C4⋊Q8—21no—
394C4⋊Q8—41no—
395C4⋊Q8C23×C4311yescharacteristic
396C4⋊Q8C23×C4311yescharacteristic
397#127—21no—
398#127—21no—
399#127C23×C4311yescharacteristic
400#127C23×C4311yescharacteristic
401#123—41no—
402C22⋊Q8—21no—
403#121—21no—
404#121—21no—
405#121—21no—
406#121—41no—
407#121—41no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8C23×C4311yescharacteristic
411C4×Q8C23×C4311yescharacteristic
412C4×D4—21no—
413C4×D4—21no—
414C4×D4C23×C4311yescharacteristic
415C4×D4C23×C4311yescharacteristic
416C2×C4⋊C4—21no—
417#106—21no—
418#106—21no—
419#106—21no—
420#106D4×C4311yescharacteristic
421#106D4×C4311yescharacteristic
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8C23×C4311yescharacteristic
425C4⋊C8C23×C4311yescharacteristic
426C4⋊C8C23×C4311yescharacteristic
427C4⋊C8C23×C4311yescharacteristic
428#103—21no—
429#103—21no—
430#103—41no—
431#103D4×C4311yescharacteristic
432#103D4×C4311yescharacteristic
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102D4×C4311yescharacteristic
446#102D4×C4311yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—21no—
449C4×C8—21no—
450C4×C8—21no—
451C4×C8C23×C4311yescharacteristic
452C4×C8C23×C4311yescharacteristic
453C4×C8C23×C4311yescharacteristic
454#41—42no—
455#41—42no—
456#41—42no—
457#41—81no—
458#41—81no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—41no—
463C2×Q8C2×D4×C4311yescharacteristic
464C2×Q8C2×D4×C4311yescharacteristic
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4C2×D4×C4311yescharacteristic
477C2×D4C2×D4×C4311yescharacteristic
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483Q16—42no—
484SD16—22no—
485SD16—22no—
486SD16—42no—
487SD16—42no—
488SD16—42no—
489SD16—81no—
490D8—42no—
491D8—81no—
492D8—82no—
493M16—81no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—42no—
500C2×C8C2×D4×C4311yescharacteristic
501C2×C8C2×D4×C4311yescharacteristic
502C2×C8C2×D4×C4311yescharacteristic
503C2×C8C2×D4×C4311yescharacteristic
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4C2×D4×C4311yescharacteristic
514C4⋊C4C2×D4×C4311yescharacteristic
515C4⋊C4C2×D4×C4311yescharacteristic
516C4⋊C4C2×D4×C4311yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C42—21no—
523C42—21no—
524C42—41no—
525C42C24×C4311yescharacteristic
526C23—21no—
527C23—21no—
528C23—41no—
529C23—41no—
530Q8—21no—
531Q8—21no—
532Q8—41no—
533Q8—41no—
534Q8—81no—
535Q8—161no—
536Q8#135×C4312yescomplemented
537Q8AGL(1,ℤ/8)×C4312yes—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—82no—
551D4—82no—
552D4—81no—
553D4—81no—
554D4—82no—
555D4—161no—
556D4—161no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4—82no—
572C2×C4C22×D4×C4311yescharacteristic
573C2×C4C22×D4×C4311yescharacteristic
574C2×C4H(5,𝔽2)×C4311yescharacteristic
575C8—21no—
576C8—21no—
577C8—21no—
578C8—21no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22D42×C4311yescharacteristic
597C4—22no—
598C4—22no—
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4C2×#135×C4311yescharacteristic
607C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
608C4C43×#57711yescharacteristic
609C4C43×#57711yescharacteristic
610C2—81no—
611C2—81no—
612C2—161no—
613C2—161no—
614C2C43×#326511yescharacteristic
615C2C43×#328211yescharacteristic
616C2C43×#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×#3362C2semidirect
2. C43×#3362C2semidirect
3. C43×#3332C2semidirect
4. C43×#3284C2semidirect
5. C43×#1717C2semidirect
6. C43×#1697C2semidirect
7. C43×#1682C2semidirect
8. C43×#1677C2semidirect
9. C43×#1666C2semidirect
10. C43×#1645C2semidirect
11. C43×#1635C2semidirect
12. C43×#1621C2semidirect
13. C43×#1621C2semidirect
14. C43×#1583C2semidirect
15. C43×SD16⋊C8C2semidirect
227. Q8×C43#135semidirect
275. #19827C43direct (N × H)
302. #3362C2×C43semidirect
303. #3362C2×C43semidirect
304. #3332C2×C43semidirect
305. #3284C2×C43semidirect
306. #1717C2×C43semidirect
307. #1697C2×C43semidirect
308. #1682C2×C43semidirect
309. #1677C2×C43semidirect
310. #1666C2×C43semidirect
311. #1645C2×C43semidirect
312. #1635C2×C43semidirect
313. #1621C2×C43semidirect
314. #1621C2×C43semidirect
315. #1583C2×C43semidirect
316. SD16⋊C8C2×C43semidirect
375. C43#19827direct (N × H)
536. Q8#135×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#33622
C43×#33322
C43×#32842
C43×#17172
C43×#16972
C43×#16822
C43×#16772
C43×#16662
C43×#16452
C43×#16352
C43×#16212
C43×#15832
C43×SD16⋊C82
#1982743