Finite Group Databasebeta

← C43×#19851 #24939868

Subgroups — C43×#19851 #24939868

Order 11008.

666 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×#3397C211yesmaximal, characteristic, complemented
2C43×#3334C211yesmaximal, characteristic, complemented
3C43×#3302C211yesmaximal, characteristic, complemented
4C43×#3284C211yesmaximal, characteristic, complemented
5C43×#1714C211yesmaximal, characteristic, complemented
6C43×#1694C211yesmaximal, characteristic, complemented
7C43×#1679C211yesmaximal, characteristic, complemented
8C43×#1665C211yesmaximal, characteristic, complemented
9C43×#1665C211yesmaximal, characteristic, complemented
10C43×#1654C211yesmaximal, characteristic, complemented
11C43×#1652C211yesmaximal, characteristic, complemented
12C43×#1641C211yesmaximal, characteristic, complemented
13C43×#1625C211yesmaximal, characteristic, complemented
14C43×#1582C211yesmaximal, characteristic, complemented
15C43×#1580C211yesmaximal, characteristic, complemented
16C2×#135×C43—21no—
17C43×#556C2211yescharacteristic
18C43×#550C2211yescharacteristic
19C43×#547C2211yescharacteristic
20C43×#547C2211yescharacteristic
21C43×#500C2211yescharacteristic
22C43×#498C2211yescharacteristic
23C43×#496—21no—
24C43×#492C2211yescharacteristic
25C43×#492C2211yescharacteristic
26C43×#487C2211yescharacteristic
27C43×#486C2211yescharacteristic
28C43×#485—21no—
29C43×#480—21no—
30C43×#480—21no—
31C43×#474C2211yescharacteristic
32C43×#474C2211yescharacteristic
33C43×#474C2211yescharacteristic
34C43×#467—21no—
35C43×#466—21no—
36C43×#465—21no—
37C43×#463—21no—
38C43×#462C2211yescharacteristic
39C43×#462C2211yescharacteristic
40C43×#461C2211yescharacteristic
41C43×#460—21no—
42C43×#459C2211yescharacteristic
43C43×#459C2211yescharacteristic
44C43×#452—21no—
45C43×#452—21no—
46C43×#449—21no—
47C43×#446C2211yescharacteristic
48C43×#440—21no—
49C4×SD16×C43C2211yescharacteristic
50C4×D8×C43C2211yescharacteristic
51C8×D4×C43C2211yescharacteristic
52C8×D4×C43C2211yescharacteristic
53C8×D4×C43C2211yescharacteristic
54C2×#107×C43—21no—
55C43×#416—21no—
56C43×#334C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#332C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×D4⋊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×Q16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—21no—
75C2×SD16×C43—21no—
76C2×SD16×C43—21no—
77C2×SD16×C43—21no—
78C2×SD16×C43D411yescharacteristic
79C2×D8×C43—21no—
80C2×D8×C43—21no—
81C2×D8×C43D411yescharacteristic
82C22×C8×C43—21no—
83C22×C8×C43—21no—
84C22×C8×C43—21no—
85C4⋊Q8×C43C2311yescharacteristic
86C4⋊Q8×C43C2311yescharacteristic
87C4⋊Q8×C43C2311yescharacteristic
88#127×C43—21no—
89#127×C43C2311yescharacteristic
90#126×C43—41no—
91#124×C43—21no—
92#123×C43—41no—
93#123×C43—41no—
94C22⋊Q8×C43—21no—
95C22⋊Q8×C43—21no—
96C22⋊Q8×C43—21no—
97#121×C43—21no—
98#121×C43—21no—
99#121×C43—21no—
100#121×C43—41no—
101C4×Q8×C43—21no—
102C4×Q8×C43C2311yescharacteristic
103C4×D4×C43—21no—
104C4×D4×C43C2311yescharacteristic
105C4×D4×C43C2311yescharacteristic
106C4×D4×C43C2311yescharacteristic
107#117×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110#107×C43—21no—
111#107×C43—21no—
112#107×C43—21no—
113#107×C43—21no—
114#107×C43—21no—
115#107×C43D411yescharacteristic
116#106×C43—41no—
117#106×C43D411yescharacteristic
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×C43—21no—
127#103×C43—21no—
128#103×C43D411yescharacteristic
129#102×C43—21no—
130#102×C43—21no—
131#102×C43—21no—
132#102×C43—21no—
133#102×C43—21no—
134#102×C43—41no—
135#102×C43D411yescharacteristic
136#102×C43D411yescharacteristic
137#102×C43D411yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140C22⋊C8×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—42no—
148#41×C43—81no—
149#41×C43—81no—
150#41×C43—81no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43C2×D411yescharacteristic
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—41no—
159C2×D4×C43—41no—
160C2×D4×C43—41no—
161C2×D4×C43—41no—
162C2×D4×C43C2×D411yescharacteristic
163C2×D4×C43C2×D411yescharacteristic
164C2×D4×C43C2×D411yescharacteristic
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—41no—
169C22×C4×C43—41no—
170C22×C4×C43—41no—
171Q16×C43—42no—
172Q16×C43—81no—
173SD16×C43—22no—
174SD16×C43—42no—
175SD16×C43—42no—
176SD16×C43—81no—
177SD16×C43—81no—
178SD16×C43—81no—
179D8×C43—22no—
180D8×C43—42no—
181D8×C43—81no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—42no—
188C2×C8×C43—42no—
189C2×C8×C43—81no—
190C2×C8×C43C2×D411yescharacteristic
191C2×C8×C43C2×D411yescharacteristic
192C2×C8×C43C2×D411yescharacteristic
193C2×C8×C43C2×D411yescharacteristic
194C4⋊C4×C43—21no—
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—21no—
211C22⋊C4×C43—41no—
212C22⋊C4×C43—41no—
213C22⋊C4×C43—41no—
214C22⋊C4×C43—41no—
215C22⋊C4×C43—41no—
216C42×C43—21no—
217C42×C43—41no—
218C42×C43C2411yescharacteristic
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—41no—
223Q8×C43—21no—
224Q8×C43—21no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×C43—41no—
229Q8×C43—41no—
230Q8×C43—41no—
231D4×C43—21no—
232D4×C43—21no—
233D4×C43—21no—
234D4×C43—21no—
235D4×C43—21no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—81no—
241D4×C43—82no—
242D4×C43—82no—
243D4×C43—82no—
244D4×C43—161no—
245D4×C43AGL(1,ℤ/8)12yes—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—41no—
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—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—41no—
270C8×C43—41no—
271C8×C43—41no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43#13512yescomplemented
275#19851C4311yesmaximal, characteristic, direct product factor, Sylow
276C22×C43—22no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43D4211yescharacteristic
289C4×C43—21no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—81no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43C2×#13511yescharacteristic
299C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
300C4×C43#57611yescharacteristic
301C4×C43#57711yescharacteristic
302#3397C2×C4311yescharacteristic, complemented
303#3334C2×C4311yescharacteristic, complemented
304#3302C2×C4311yescharacteristic, complemented
305#3284C2×C4311yescharacteristic, complemented
306#1714C2×C4311yescharacteristic, complemented
307#1694C2×C4311yescharacteristic, complemented
308#1679C2×C4311yescharacteristic, complemented
309#1665C2×C4311yescharacteristic, complemented
310#1665C2×C4311yescharacteristic, complemented
311#1654C2×C4311yescharacteristic, complemented
312#1652C2×C4311yescharacteristic, complemented
313#1641C2×C4311yescharacteristic, complemented
314#1625C2×C4311yescharacteristic, complemented
315#1582C2×C4311yescharacteristic, complemented
316#1580C2×C4311yescharacteristic, complemented
317C2×C43—42no—
318C2×C43—81no—
319C2×C43—81no—
320C2×C43—161no—
321C2×C43#326411yescharacteristic
322C2×C43#328411yescharacteristic
323C2×C43#328911yescharacteristic
324C2×#135—21no—
325#556C22×C4311yescharacteristic
326#550C22×C4311yescharacteristic
327#547C22×C4311yescharacteristic
328#547C22×C4311yescharacteristic
329#500C22×C4311yescharacteristic
330#498C22×C4311yescharacteristic
331#496—21no—
332#492C22×C4311yescharacteristic
333#492C22×C4311yescharacteristic
334#487C22×C4311yescharacteristic
335#486C22×C4311yescharacteristic
336#485—21no—
337#480—21no—
338#480—21no—
339#474C22×C4311yescharacteristic
340#474C22×C4311yescharacteristic
341#474C22×C4311yescharacteristic
342#467—21no—
343#466—21no—
344#465—21no—
345#463—21no—
346#462C22×C4311yescharacteristic
347#462C22×C4311yescharacteristic
348#461C22×C4311yescharacteristic
349#460—21no—
350#459C22×C4311yescharacteristic
351#459C22×C4311yescharacteristic
352#452—21no—
353#452—21no—
354#449—21no—
355#446C22×C4311yescharacteristic
356#440—21no—
357C4×SD16C22×C4311yescharacteristic
358C4×D8C22×C4311yescharacteristic
359C8×D4C22×C4311yescharacteristic
360C8×D4C22×C4311yescharacteristic
361C8×D4C22×C4311yescharacteristic
362C2×#107—21no—
363#416—21no—
364#334C22×C4311yescharacteristic
365#334C22×C4311yescharacteristic
366#332C22×C4311yescharacteristic
367#332C22×C4311yescharacteristic
368#332C22×C4311yescharacteristic
369#331C22×C4311yescharacteristic
370Q8⋊C8C22×C4311yescharacteristic
371D4⋊C8C22×C4311yescharacteristic
372D4⋊C8C22×C4311yescharacteristic
373D4⋊C8C22×C4311yescharacteristic
374#322C22×C4311yescharacteristic
375C43#1985111yescharacteristic, direct product factor, Sylow
376C2×#41—21no—
377C2×#41—21no—
378C2×#41—21no—
379#135—44no—
380C2×Q16—21no—
381C2×Q16—21no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16D4×C4311yescharacteristic
388C2×D8—21no—
389C2×D8—21no—
390C2×D8D4×C4311yescharacteristic
391C22×C8—21no—
392C22×C8—21no—
393C22×C8—21no—
394C4⋊Q8C23×C4311yescharacteristic
395C4⋊Q8C23×C4311yescharacteristic
396C4⋊Q8C23×C4311yescharacteristic
397#127—21no—
398#127C23×C4311yescharacteristic
399#126—41no—
400#124—21no—
401#123—41no—
402#123—41no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—21no—
406#121—21no—
407#121—21no—
408#121—21no—
409#121—41no—
410C4×Q8—21no—
411C4×Q8C23×C4311yescharacteristic
412C4×D4—21no—
413C4×D4C23×C4311yescharacteristic
414C4×D4C23×C4311yescharacteristic
415C4×D4C23×C4311yescharacteristic
416#117—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419#107—21no—
420#107—21no—
421#107—21no—
422#107—21no—
423#107—21no—
424#107D4×C4311yescharacteristic
425#106—41no—
426#106D4×C4311yescharacteristic
427C4⋊C8—21no—
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#103D4×C4311yescharacteristic
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—41no—
444#102D4×C4311yescharacteristic
445#102D4×C4311yescharacteristic
446#102D4×C4311yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—21no—
449C22⋊C8—21no—
450#97—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—21no—
463C2×Q8C2×D4×C4311yescharacteristic
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4C2×D4×C4311yescharacteristic
472C2×D4C2×D4×C4311yescharacteristic
473C2×D4C2×D4×C4311yescharacteristic
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480Q16—42no—
481Q16—81no—
482SD16—22no—
483SD16—42no—
484SD16—42no—
485SD16—81no—
486SD16—81no—
487SD16—81no—
488D8—22no—
489D8—42no—
490D8—81no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—42no—
497C2×C8—42no—
498C2×C8—81no—
499C2×C8C2×D4×C4311yescharacteristic
500C2×C8C2×D4×C4311yescharacteristic
501C2×C8C2×D4×C4311yescharacteristic
502C2×C8C2×D4×C4311yescharacteristic
503C4⋊C4—21no—
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—21no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C42—21no—
526C42—41no—
527C42C24×C4311yescharacteristic
528C23—21no—
529C23—21no—
530C23—21no—
531C23—41no—
532Q8—21no—
533Q8—21no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537Q8—41no—
538Q8—41no—
539Q8—41no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—81no—
550D4—82no—
551D4—82no—
552D4—82no—
553D4—161no—
554D4AGL(1,ℤ/8)×C4312yes—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
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—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8#135×C4312yescomplemented
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22D42×C4311yescharacteristic
597C4—21no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—81no—
604C4—81no—
605C4—81no—
606C4C2×#135×C4311yescharacteristic
607C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
608C4C43×#57611yescharacteristic
609C4C43×#57711yescharacteristic
610C2—42no—
611C2—81no—
612C2—81no—
613C2—161no—
614C2C43×#326411yescharacteristic
615C2C43×#328411yescharacteristic
616C2C43×#328911yescharacteristic
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×#3334C2semidirect
3. C43×#3302C2semidirect
4. C43×#3284C2semidirect
5. C43×#1714C2semidirect
6. C43×#1694C2semidirect
7. C43×#1679C2semidirect
8. C43×#1665C2semidirect
9. C43×#1665C2semidirect
10. C43×#1654C2semidirect
11. C43×#1652C2semidirect
12. C43×#1641C2semidirect
13. C43×#1625C2semidirect
14. C43×#1582C2semidirect
15. C43×#1580C2semidirect
274. C8×C43#135semidirect
275. #19851C43direct (N × H)
302. #3397C2×C43semidirect
303. #3334C2×C43semidirect
304. #3302C2×C43semidirect
305. #3284C2×C43semidirect
306. #1714C2×C43semidirect
307. #1694C2×C43semidirect
308. #1679C2×C43semidirect
309. #1665C2×C43semidirect
310. #1665C2×C43semidirect
311. #1654C2×C43semidirect
312. #1652C2×C43semidirect
313. #1641C2×C43semidirect
314. #1625C2×C43semidirect
315. #1582C2×C43semidirect
316. #1580C2×C43semidirect
375. C43#19851direct (N × H)
583. C8#135×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#33972
C43×#33342
C43×#33022
C43×#32842
C43×#17142
C43×#16942
C43×#16792
C43×#16652
C43×#16542
C43×#16522
C43×#16412
C43×#16252
C43×#15822
C43×#15802
#1985143