Finite Group Databasebeta

← C43×#19823 #24939840

Subgroups — C43×#19823 #24939840

Order 11008.

632 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3360C211yesmaximal, characteristic, complemented
2C43×#3340C211yesmaximal, characteristic, complemented
3C43×#3325C211yesmaximal, characteristic
4C43×#3295C211yesmaximal, characteristic, complemented
5C43×#1720C211yesmaximal, characteristic, complemented
6C43×#1703C211yesmaximal, characteristic, complemented
7C43×#1678C211yesmaximal, characteristic, complemented
8C43×#1677C211yesmaximal, characteristic, complemented
9C43×#1671C211yesmaximal, characteristic, complemented
10C43×#1639C211yesmaximal, characteristic, complemented
11C43×#1634C211yesmaximal, characteristic, complemented
12C43×#1632C211yesmaximal, characteristic, complemented
13C43×#1628C211yesmaximal, characteristic, complemented
14C43×#1583C211yesmaximal, characteristic, complemented
15C43×#1580C211yesmaximal, characteristic, complemented
16C43×#556C2211yescharacteristic, complemented
17C43×#555C2211yescharacteristic
18C43×#554C2211yescharacteristic
19D42×C43C2211yescharacteristic
20C43×#498C2211yescharacteristic, complemented
21C43×#494C2211yescharacteristic, complemented
22C43×#488—21no—
23C43×#487C2211yescharacteristic, complemented
24C43×#486C2211yescharacteristic
25C43×#486C2211yescharacteristic
26C43×#486C2211yescharacteristic
27C43×#485—21no—
28C43×#482—21no—
29C43×#482—21no—
30C43×#481—21no—
31C43×#479—21no—
32C43×#477C2211yescharacteristic, complemented
33C43×#476C2211yescharacteristic
34C43×#476C2211yescharacteristic
35C43×#476C2211yescharacteristic, complemented
36C43×#474C2211yescharacteristic
37C43×#469—21no—
38C43×#465—21no—
39C43×#465—21no—
40C43×#463—21no—
41C43×#461C2211yescharacteristic
42C43×#460C2211yescharacteristic
43C43×#459C2211yescharacteristic
44C43×#450—21no—
45C43×#447—21no—
46C8×Q8×C43C2211yescharacteristic, complemented
47C4×SD16×C43—21no—
48C4×SD16×C43C2211yescharacteristic
49C4×D8×C43C2211yescharacteristic
50C43×#436C2211yescharacteristic
51C8×D4×C43C2211yescharacteristic
52C8×D4×C43C2211yescharacteristic, complemented
53C43×#427—21no—
54C43×#418—21no—
55C2×#102×C43—21no—
56C43×#334C2211yescharacteristic, complemented
57C43×#334C2211yescharacteristic, complemented
58C43×#333C2211yescharacteristic, complemented
59C43×#333C2211yescharacteristic, complemented
60C43×#332C2211yescharacteristic, complemented
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic, complemented
63C43×D4⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic, complemented
66C43×#322C2211yescharacteristic, complemented
67C22×D4×C43—21no—
68C22×D4×C43—21no—
69C2×Q16×C43—41no—
70C2×SD16×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43D411yescharacteristic
73C2×D8×C43—21no—
74C2×D8×C43D411yescharacteristic
75C2×M16×C43—21no—
76C22×C8×C43—21no—
77C22×C8×C43—21no—
78C4⋊Q8×C43C2311yescharacteristic
79C4⋊Q8×C43C2311yescharacteristic
80C4⋊Q8×C43C2311yescharacteristic
81#127×C43C2311yescharacteristic
82#126×C43—41no—
83#125×C43—21no—
84#124×C43—21no—
85#124×C43—41no—
86C22⋊Q8×C43—21no—
87C22⋊Q8×C43—21no—
88C22⋊Q8×C43—41no—
89#121×C43—21no—
90#121×C43—21no—
91#121×C43—21no—
92#121×C43—21no—
93#120×C43—41no—
94C4×Q8×C43—21no—
95C4×Q8×C43C2311yescharacteristic
96C4×D4×C43—21no—
97C4×D4×C43C2311yescharacteristic
98C4×D4×C43C2311yescharacteristic
99C4×D4×C43C2311yescharacteristic
100#117×C43—21no—
101#117×C43—21no—
102#117×C43—21no—
103C2×C4⋊C4×C43—21no—
104#107×C43—21no—
105#107×C43—21no—
106#107×C43D411yescharacteristic
107#106×C43—21no—
108#106×C43—21no—
109#106×C43—21no—
110#106×C43—21no—
111#106×C43—21no—
112#106×C43D411yescharacteristic
113C4⋊C8×C43—21no—
114C4⋊C8×C43C2311yescharacteristic
115C4⋊C8×C43C2311yescharacteristic
116C4⋊C8×C43C2311yescharacteristic
117C4⋊C8×C43C2311yescharacteristic
118#103×C43—21no—
119#103×C43—21no—
120#103×C43—21no—
121#103×C43—21no—
122#103×C43D411yescharacteristic
123#102×C43—21no—
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—41no—
134#102×C43D411yescharacteristic
135#102×C43D411yescharacteristic
136#102×C43D411yescharacteristic
137C22⋊C8×C43—21no—
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C24×C43—41no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—41no—
153C2×D4×C43—41no—
154C2×D4×C43—41no—
155C2×D4×C43—42no—
156C2×D4×C43—42no—
157C2×D4×C43—81no—
158C2×D4×C43—81no—
159C2×D4×C43C2×D411yescharacteristic
160C2×D4×C43C2×D411yescharacteristic
161C2×D4×C43C2×D411yescharacteristic
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—41no—
166Q16×C43—82no—
167SD16×C43—41no—
168SD16×C43—42no—
169SD16×C43—81no—
170D8×C43—22no—
171D8×C43—81no—
172M16×C43—81no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—42no—
179C2×C8×C43—81no—
180C2×C8×C43C2×D411yescharacteristic
181C2×C8×C43C2×D411yescharacteristic
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—41no—
192C4⋊C4×C43—41no—
193C4⋊C4×C43—41no—
194C4⋊C4×C43C2×D411yescharacteristic
195C4⋊C4×C43C2×D411yescharacteristic
196C4⋊C4×C43C2×D411yescharacteristic
197C4⋊C4×C43C2×D411yescharacteristic
198C22⋊C4×C43—21no—
199C22⋊C4×C43—21no—
200C22⋊C4×C43—21no—
201C22⋊C4×C43—41no—
202C22⋊C4×C43—41no—
203C22⋊C4×C43—41no—
204C22⋊C4×C43—41no—
205C22⋊C4×C43—41no—
206C22⋊C4×C43—41no—
207C42×C43—21no—
208C42×C43—41no—
209C42×C43—41no—
210C42×C43C2411yescharacteristic
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—41no—
215C23×C43—82no—
216C23×C43—82no—
217C23×C43—161no—
218Q8×C43—21no—
219Q8×C43—21no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—81no—
223Q8×C43—81no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—81no—
234D4×C43—82no—
235D4×C43—82no—
236D4×C43—161no—
237D4×C43#13512yes—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—161no—
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43—41no—
263C8×C43—41no—
264C8×C43—41no—
265#19823C4311yesmaximal, characteristic, direct product factor, Sylow
266C22×C43—22no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43—164no—
279C22×C43D4211yescharacteristic
280C4×C43—21no—
281C4×C43—41no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43C2×#13511yescharacteristic
290C4×C43#57511yescharacteristic
291C4×C43#57711yescharacteristic
292C4×C43#57711yescharacteristic
293#3360C2×C4311yescharacteristic, complemented
294#3340C2×C4311yescharacteristic, complemented
295#3325C2×C4311yescharacteristic
296#3295C2×C4311yescharacteristic, complemented
297#1720C2×C4311yescharacteristic, complemented
298#1703C2×C4311yescharacteristic, complemented
299#1678C2×C4311yescharacteristic, complemented
300#1677C2×C4311yescharacteristic, complemented
301#1671C2×C4311yescharacteristic, complemented
302#1639C2×C4311yescharacteristic, complemented
303#1634C2×C4311yescharacteristic, complemented
304#1632C2×C4311yescharacteristic, complemented
305#1628C2×C4311yescharacteristic, complemented
306#1583C2×C4311yescharacteristic, complemented
307#1580C2×C4311yescharacteristic, complemented
308C2×C43—42no—
309C2×C43—81no—
310C2×C43—81no—
311C2×C43—161no—
312C2×C43#326711yescharacteristic
313C2×C43#328211yescharacteristic
314C2×C43#328811yescharacteristic
315#556C22×C4311yescharacteristic, complemented
316#555C22×C4311yescharacteristic
317#554C22×C4311yescharacteristic
318D42C22×C4311yescharacteristic
319#498C22×C4311yescharacteristic, complemented
320#494C22×C4311yescharacteristic, complemented
321#488—21no—
322#487C22×C4311yescharacteristic, complemented
323#486C22×C4311yescharacteristic
324#486C22×C4311yescharacteristic
325#486C22×C4311yescharacteristic
326#485—21no—
327#482—21no—
328#482—21no—
329#481—21no—
330#479—21no—
331#477C22×C4311yescharacteristic, complemented
332#476C22×C4311yescharacteristic
333#476C22×C4311yescharacteristic
334#476C22×C4311yescharacteristic, complemented
335#474C22×C4311yescharacteristic
336#469—21no—
337#465—21no—
338#465—21no—
339#463—21no—
340#461C22×C4311yescharacteristic
341#460C22×C4311yescharacteristic
342#459C22×C4311yescharacteristic
343#450—21no—
344#447—21no—
345C8×Q8C22×C4311yescharacteristic, complemented
346C4×SD16—21no—
347C4×SD16C22×C4311yescharacteristic
348C4×D8C22×C4311yescharacteristic
349#436C22×C4311yescharacteristic
350C8×D4C22×C4311yescharacteristic
351C8×D4C22×C4311yescharacteristic, complemented
352#427—21no—
353#418—21no—
354C2×#102—21no—
355#334C22×C4311yescharacteristic, complemented
356#334C22×C4311yescharacteristic, complemented
357#333C22×C4311yescharacteristic, complemented
358#333C22×C4311yescharacteristic, complemented
359#332C22×C4311yescharacteristic, complemented
360#331C22×C4311yescharacteristic
361Q8⋊C8C22×C4311yescharacteristic, complemented
362D4⋊C8C22×C4311yescharacteristic
363D4⋊C8C22×C4311yescharacteristic
364D4⋊C8C22×C4311yescharacteristic, complemented
365#322C22×C4311yescharacteristic, complemented
366C43#1982311yescharacteristic, direct product factor, Sylow
367C22×D4—21no—
368C22×D4—21no—
369C2×Q16—41no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16D4×C4311yescharacteristic
373C2×D8—21no—
374C2×D8D4×C4311yescharacteristic
375C2×M16—21no—
376C22×C8—21no—
377C22×C8—21no—
378C4⋊Q8C23×C4311yescharacteristic
379C4⋊Q8C23×C4311yescharacteristic
380C4⋊Q8C23×C4311yescharacteristic
381#127C23×C4311yescharacteristic
382#126—41no—
383#125—21no—
384#124—21no—
385#124—41no—
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8—41no—
389#121—21no—
390#121—21no—
391#121—21no—
392#121—21no—
393#120—41no—
394C4×Q8—21no—
395C4×Q8C23×C4311yescharacteristic
396C4×D4—21no—
397C4×D4C23×C4311yescharacteristic
398C4×D4C23×C4311yescharacteristic
399C4×D4C23×C4311yescharacteristic
400#117—21no—
401#117—21no—
402#117—21no—
403C2×C4⋊C4—21no—
404#107—21no—
405#107—21no—
406#107D4×C4311yescharacteristic
407#106—21no—
408#106—21no—
409#106—21no—
410#106—21no—
411#106—21no—
412#106D4×C4311yescharacteristic
413C4⋊C8—21no—
414C4⋊C8C23×C4311yescharacteristic
415C4⋊C8C23×C4311yescharacteristic
416C4⋊C8C23×C4311yescharacteristic
417C4⋊C8C23×C4311yescharacteristic
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103D4×C4311yescharacteristic
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—41no—
434#102D4×C4311yescharacteristic
435#102D4×C4311yescharacteristic
436#102D4×C4311yescharacteristic
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—21no—
440C4×C8—21no—
441C4×C8C23×C4311yescharacteristic
442C4×C8C23×C4311yescharacteristic
443C4×C8C23×C4311yescharacteristic
444C24—41no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8C2×D4×C4311yescharacteristic
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—42no—
455C2×D4—42no—
456C2×D4—41no—
457C2×D4—81no—
458C2×D4—81no—
459C2×D4C2×D4×C4311yescharacteristic
460C2×D4C2×D4×C4311yescharacteristic
461C2×D4C2×D4×C4311yescharacteristic
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466Q16—82no—
467SD16—41no—
468SD16—42no—
469SD16—81no—
470D8—22no—
471D8—81no—
472M16—81no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—42no—
479C2×C8—81no—
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—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4C2×D4×C4311yescharacteristic
495C4⋊C4C2×D4×C4311yescharacteristic
496C4⋊C4C2×D4×C4311yescharacteristic
497C4⋊C4C2×D4×C4311yescharacteristic
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C42—21no—
508C42—41no—
509C42—41no—
510C42C24×C4311yescharacteristic
511C23—21no—
512C23—21no—
513C23—21no—
514C23—41no—
515C23—82no—
516C23—82no—
517C23—161no—
518Q8—21no—
519Q8—21no—
520Q8—41no—
521Q8—41no—
522Q8—81no—
523Q8—81no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—81no—
534D4—82no—
535D4—82no—
536D4—161no—
537D4#135×C4312yes—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—161no—
553C2×C4C22×D4×C4311yescharacteristic
554C2×C4C22×D4×C4311yescharacteristic
555C2×C4H(5,𝔽2)×C4311yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—41no—
565C22—22no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—164no—
578C22D42×C4311yescharacteristic
579C4—21no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4C2×#135×C4311yescharacteristic
589C4C43×#57511yescharacteristic
590C4C43×#57711yescharacteristic
591C4C43×#57711yescharacteristic
592C2—42no—
593C2—81no—
594C2—81no—
595C2—161no—
596C2C43×#326711yescharacteristic
597C2C43×#328211yescharacteristic
598C2C43×#328811yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3325C2
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×#3360C2semidirect
2. C43×#3340C2semidirect
4. C43×#3295C2semidirect
5. C43×#1720C2semidirect
6. C43×#1703C2semidirect
7. C43×#1678C2semidirect
8. C43×#1677C2semidirect
9. C43×#1671C2semidirect
10. C43×#1639C2semidirect
11. C43×#1634C2semidirect
12. C43×#1632C2semidirect
13. C43×#1628C2semidirect
14. C43×#1583C2semidirect
15. C43×#1580C2semidirect
16. C43×#556C22semidirect
20. C43×#498C22semidirect
21. C43×#494C22semidirect
23. C43×#487C22semidirect
32. C43×#477C22semidirect
35. C43×#476C22semidirect
46. C8×Q8×C43C22semidirect
52. C8×D4×C43C22semidirect
56. C43×#334C22semidirect
57. C43×#334C22semidirect
58. C43×#333C22semidirect
59. C43×#333C22semidirect
60. C43×#332C22semidirect
62. C43×Q8⋊C8C22semidirect
65. C43×D4⋊C8C22semidirect
66. C43×#322C22semidirect
265. #19823C43direct (N × H)
293. #3360C2×C43semidirect
294. #3340C2×C43semidirect
296. #3295C2×C43semidirect
297. #1720C2×C43semidirect
298. #1703C2×C43semidirect
299. #1678C2×C43semidirect
300. #1677C2×C43semidirect
301. #1671C2×C43semidirect
302. #1639C2×C43semidirect
303. #1634C2×C43semidirect
304. #1632C2×C43semidirect
305. #1628C2×C43semidirect
306. #1583C2×C43semidirect
307. #1580C2×C43semidirect
315. #556C22×C43semidirect
319. #498C22×C43semidirect
320. #494C22×C43semidirect
322. #487C22×C43semidirect
331. #477C22×C43semidirect
334. #476C22×C43semidirect
345. C8×Q8C22×C43semidirect
351. C8×D4C22×C43semidirect
355. #334C22×C43semidirect
356. #334C22×C43semidirect
357. #333C22×C43semidirect
358. #333C22×C43semidirect
359. #332C22×C43semidirect
361. Q8⋊C8C22×C43semidirect
364. D4⋊C8C22×C43semidirect
365. #322C22×C43semidirect
366. C43#19823direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33602
C43×#33402
C43×#33252
C43×#32952
C43×#17202
C43×#17032
C43×#16782
C43×#16772
C43×#16712
C43×#16392
C43×#16342
C43×#16322
C43×#16282
C43×#15832
C43×#15802
#1982343