Finite Group Databasebeta

← C43×#20287 #24940304

Subgroups — C43×#20287 #24940304

Order 11008.

634 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3367C211yesmaximal, characteristic, complemented
2C43×#3329C211yesmaximal, characteristic, complemented
3C43×#3325C211yesmaximal, characteristic
4C43×#3324C211yesmaximal, characteristic, complemented
5C43×#1711C211yesmaximal, characteristic, complemented
6C43×#1703C211yesmaximal, characteristic, complemented
7C43×#1701C211yesmaximal, characteristic, complemented
8C43×#1699C211yesmaximal, characteristic, complemented
9C43×#1698C211yesmaximal, characteristic, complemented
10C43×#1646C211yesmaximal, characteristic, complemented
11C43×#1639C211yesmaximal, characteristic, complemented
12C43×#1638C211yesmaximal, characteristic, complemented
13C43×#1627C211yesmaximal, characteristic, complemented
14C43×#1590C211yesmaximal, characteristic, complemented
15C43×#1589C211yesmaximal, characteristic, complemented
16C43×#556C2211yescharacteristic
17C43×#555C2211yescharacteristic
18D4×Q8×C43C2211yescharacteristic, complemented
19D42×C43C2211yescharacteristic
20C43×#489—21no—
21C43×#487C2211yescharacteristic, complemented
22C43×#487C2211yescharacteristic, complemented
23C43×#487C2211yescharacteristic, complemented
24C43×#486C2211yescharacteristic
25C43×#486C2211yescharacteristic
26C43×#486C2211yescharacteristic
27C43×#485—21no—
28C43×#482—21no—
29C43×#482—21no—
30C43×#477—21no—
31C43×#477C2211yescharacteristic, complemented
32C43×#476C2211yescharacteristic
33C43×#474C2211yescharacteristic
34C43×#474C2211yescharacteristic
35C43×#469—21no—
36C43×#468—21no—
37C43×#468—21no—
38C43×#463—21no—
39C43×#461C2211yescharacteristic
40C43×#461C2211yescharacteristic, complemented
41C43×#460C2211yescharacteristic
42C43×#459C2211yescharacteristic
43C43×#450—21no—
44C43×#448—21no—
45C43×#447—21no—
46C43×#446C2211yescharacteristic, complemented
47C43×#440—21no—
48C4×SD16×C43C2211yescharacteristic
49C4×D8×C43C2211yescharacteristic
50C43×#436C2211yescharacteristic
51C43×#436C2211yescharacteristic
52C43×#436C2211yescharacteristic, complemented
53C43×#419—21no—
54C43×#418—21no—
55C43×#418—21no—
56C43×#335C2211yescharacteristic, complemented
57C43×#334C2211yescharacteristic, complemented
58C43×#333C2211yescharacteristic, complemented
59C43×#332C2211yescharacteristic, complemented
60C43×#332C2211yescharacteristic, complemented
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic, complemented
63C43×D4⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic, complemented
66C82×C43C2211yescharacteristic, complemented
67C22×Q8×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70C2×SD16×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43D411yescharacteristic
74C2×D8×C43—21no—
75C2×D8×C43D411yescharacteristic
76C2×M16×C43—21no—
77C2×M16×C43—21no—
78C2×M16×C43—21no—
79C4⋊Q8×C43—21no—
80C4⋊Q8×C43C2311yescharacteristic
81C4⋊Q8×C43C2311yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83#127×C43C2311yescharacteristic
84#126×C43—41no—
85#124×C43—21no—
86#124×C43—41no—
87C22⋊Q8×C43—21no—
88C22⋊Q8×C43—21no—
89C22⋊Q8×C43—41no—
90#121×C43—21no—
91#121×C43—21no—
92#121×C43—21no—
93#121×C43—21no—
94#120×C43—41no—
95C4×Q8×C43—21no—
96C4×Q8×C43C2311yescharacteristic
97C4×D4×C43—21no—
98C4×D4×C43C2311yescharacteristic
99C4×D4×C43C2311yescharacteristic
100C4×D4×C43C2311yescharacteristic
101#117×C43—21no—
102#117×C43—21no—
103#117×C43—21no—
104#107×C43—21no—
105#107×C43—21no—
106#107×C43—21no—
107#107×C43D411yescharacteristic
108#106×C43—21no—
109#106×C43D411yescharacteristic
110C4⋊C8×C43—21no—
111C4⋊C8×C43C2311yescharacteristic
112C4⋊C8×C43C2311yescharacteristic
113C4⋊C8×C43C2311yescharacteristic
114C4⋊C8×C43C2311yescharacteristic
115#103×C43—21no—
116#103×C43—21no—
117#103×C43—21no—
118#103×C43—21no—
119#103×C43—21no—
120#103×C43—21no—
121#103×C43—21no—
122#103×C43—41no—
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—41no—
134#102×C43D411yescharacteristic
135#102×C43D411yescharacteristic
136#102×C43D411yescharacteristic
137C22⋊C8×C43—21no—
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140#97×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×C43—41no—
149C2×Q8×C43—42no—
150C2×Q8×C43—81no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43—42no—
159C2×D4×C43—42no—
160C2×D4×C43—81no—
161C2×D4×C43—81no—
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—
169SD16×C43—41no—
170SD16×C43—42no—
171SD16×C43—81no—
172SD16×C43—81no—
173D8×C43—41no—
174D8×C43—81no—
175M16×C43—81no—
176M16×C43—81no—
177M16×C43—81no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43C2×D411yescharacteristic
184C2×C8×C43C2×D411yescharacteristic
185C2×C8×C43C2×D411yescharacteristic
186C2×C8×C43C2×D411yescharacteristic
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—41no—
195C4⋊C4×C43—41no—
196C4⋊C4×C43C2×D411yescharacteristic
197C4⋊C4×C43C2×D411yescharacteristic
198C4⋊C4×C43C2×D411yescharacteristic
199C4⋊C4×C43C2×D411yescharacteristic
200C22⋊C4×C43—21no—
201C22⋊C4×C43—21no—
202C22⋊C4×C43—21no—
203C22⋊C4×C43—41no—
204C22⋊C4×C43—41no—
205C22⋊C4×C43—41no—
206C22⋊C4×C43—41no—
207C22⋊C4×C43—41no—
208C22⋊C4×C43—41no—
209C42×C43—21no—
210C42×C43—41no—
211C42×C43—41no—
212C42×C43C2411yescharacteristic
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—41no—
217C23×C43—82no—
218C23×C43—82no—
219C23×C43—161no—
220Q8×C43—21no—
221Q8×C43—21no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—41no—
225Q8×C43—41no—
226Q8×C43—81no—
227Q8×C43—82no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—21no—
232D4×C43—21no—
233D4×C43—21no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—81no—
239D4×C43—82no—
240D4×C43—82no—
241D4×C43—161no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—82no—
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C8×C43—21no—
261C8×C43—21no—
262C8×C43—21no—
263C8×C43—21no—
264C8×C43—41no—
265C8×C43—41no—
266C8×C43—41no—
267C8×C43—41no—
268C8×C43—41no—
269#20287C4311yesmaximal, characteristic, direct product factor, Sylow
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—164no—
283C22×C43D4211yescharacteristic
284C4×C43—21no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—81no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43#57511yescharacteristic
294C4×C43#57511yescharacteristic
295C4×C43#57611yescharacteristic
296C4×C43#57711yescharacteristic
297#3367C2×C4311yescharacteristic, complemented
298#3329C2×C4311yescharacteristic, complemented
299#3325C2×C4311yescharacteristic
300#3324C2×C4311yescharacteristic, complemented
301#1711C2×C4311yescharacteristic, complemented
302#1703C2×C4311yescharacteristic, complemented
303#1701C2×C4311yescharacteristic, complemented
304#1699C2×C4311yescharacteristic, complemented
305#1698C2×C4311yescharacteristic, complemented
306#1646C2×C4311yescharacteristic, complemented
307#1639C2×C4311yescharacteristic, complemented
308#1638C2×C4311yescharacteristic, complemented
309#1627C2×C4311yescharacteristic, complemented
310#1590C2×C4311yescharacteristic, complemented
311#1589C2×C4311yescharacteristic, complemented
312C2×C43—81no—
313C2×C43—81no—
314C2×C43—81no—
315C2×C43—161no—
316C2×C43#327311yescharacteristic
317C2×C43#327511yescharacteristic
318C2×C43#329011yescharacteristic
319#556C22×C4311yescharacteristic
320#555C22×C4311yescharacteristic
321D4×Q8C22×C4311yescharacteristic, complemented
322D42C22×C4311yescharacteristic
323#489—21no—
324#487C22×C4311yescharacteristic, complemented
325#487C22×C4311yescharacteristic, complemented
326#487C22×C4311yescharacteristic, complemented
327#486C22×C4311yescharacteristic
328#486C22×C4311yescharacteristic
329#486C22×C4311yescharacteristic
330#485—21no—
331#482—21no—
332#482—21no—
333#477—21no—
334#477C22×C4311yescharacteristic, complemented
335#476C22×C4311yescharacteristic
336#474C22×C4311yescharacteristic
337#474C22×C4311yescharacteristic
338#469—21no—
339#468—21no—
340#468—21no—
341#463—21no—
342#461C22×C4311yescharacteristic
343#461C22×C4311yescharacteristic, complemented
344#460C22×C4311yescharacteristic
345#459C22×C4311yescharacteristic
346#450—21no—
347#448—21no—
348#447—21no—
349#446C22×C4311yescharacteristic, complemented
350#440—21no—
351C4×SD16C22×C4311yescharacteristic
352C4×D8C22×C4311yescharacteristic
353#436C22×C4311yescharacteristic
354#436C22×C4311yescharacteristic
355#436C22×C4311yescharacteristic, complemented
356#419—21no—
357#418—21no—
358#418—21no—
359#335C22×C4311yescharacteristic, complemented
360#334C22×C4311yescharacteristic, complemented
361#333C22×C4311yescharacteristic, complemented
362#332C22×C4311yescharacteristic, complemented
363#332C22×C4311yescharacteristic, complemented
364#331C22×C4311yescharacteristic
365Q8⋊C8C22×C4311yescharacteristic, complemented
366D4⋊C8C22×C4311yescharacteristic
367D4⋊C8C22×C4311yescharacteristic
368D4⋊C8C22×C4311yescharacteristic, complemented
369C82C22×C4311yescharacteristic, complemented
370C43#2028711yescharacteristic, direct product factor, Sylow
371C22×Q8—21no—
372C22×D4—21no—
373C22×D4—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16D4×C4311yescharacteristic
378C2×D8—21no—
379C2×D8D4×C4311yescharacteristic
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C4⋊Q8—21no—
384C4⋊Q8C23×C4311yescharacteristic
385C4⋊Q8C23×C4311yescharacteristic
386C4⋊Q8C23×C4311yescharacteristic
387#127C23×C4311yescharacteristic
388#126—41no—
389#124—21no—
390#124—41no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8—41no—
394#121—21no—
395#121—21no—
396#121—21no—
397#121—21no—
398#120—41no—
399C4×Q8—21no—
400C4×Q8C23×C4311yescharacteristic
401C4×D4—21no—
402C4×D4C23×C4311yescharacteristic
403C4×D4C23×C4311yescharacteristic
404C4×D4C23×C4311yescharacteristic
405#117—21no—
406#117—21no—
407#117—21no—
408#107—21no—
409#107—21no—
410#107—21no—
411#107D4×C4311yescharacteristic
412#106—21no—
413#106D4×C4311yescharacteristic
414C4⋊C8—21no—
415C4⋊C8C23×C4311yescharacteristic
416C4⋊C8C23×C4311yescharacteristic
417C4⋊C8C23×C4311yescharacteristic
418C4⋊C8C23×C4311yescharacteristic
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103—41no—
427#103D4×C4311yescharacteristic
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—41no—
438#102D4×C4311yescharacteristic
439#102D4×C4311yescharacteristic
440#102D4×C4311yescharacteristic
441C22⋊C8—21no—
442C22⋊C8—21no—
443C22⋊C8—21no—
444#97—21no—
445C4×C8C23×C4311yescharacteristic
446C4×C8C23×C4311yescharacteristic
447C4×C8C23×C4311yescharacteristic
448C24—41no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—41no—
453C2×Q8—42no—
454C2×Q8—81no—
455C2×Q8C2×D4×C4311yescharacteristic
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—41no—
464C2×D4—81no—
465C2×D4—81no—
466C2×D4C2×D4×C4311yescharacteristic
467C2×D4C2×D4×C4311yescharacteristic
468C2×D4C2×D4×C4311yescharacteristic
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—41no—
473SD16—41no—
474SD16—42no—
475SD16—81no—
476SD16—81no—
477D8—41no—
478D8—81no—
479M16—81no—
480M16—81no—
481M16—81no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8C2×D4×C4311yescharacteristic
488C2×C8C2×D4×C4311yescharacteristic
489C2×C8C2×D4×C4311yescharacteristic
490C2×C8C2×D4×C4311yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4C2×D4×C4311yescharacteristic
501C4⋊C4C2×D4×C4311yescharacteristic
502C4⋊C4C2×D4×C4311yescharacteristic
503C4⋊C4C2×D4×C4311yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C42—21no—
514C42—41no—
515C42—41no—
516C42C24×C4311yescharacteristic
517C23—21no—
518C23—21no—
519C23—21no—
520C23—41no—
521C23—82no—
522C23—82no—
523C23—161no—
524Q8—21no—
525Q8—21no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—81no—
531Q8—82no—
532D4—21no—
533D4—21no—
534D4—21no—
535D4—21no—
536D4—21no—
537D4—21no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—81no—
543D4—82no—
544D4—82no—
545D4—161no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—82no—
561C2×C4C22×D4×C4311yescharacteristic
562C2×C4C22×D4×C4311yescharacteristic
563C2×C4H(5,𝔽2)×C4311yescharacteristic
564C8—21no—
565C8—21no—
566C8—21no—
567C8—21no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—164no—
586C22D42×C4311yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—81no—
594C4—81no—
595C4—81no—
596C4C43×#57511yescharacteristic
597C4C43×#57511yescharacteristic
598C4C43×#57611yescharacteristic
599C4C43×#57711yescharacteristic
600C2—81no—
601C2—81no—
602C2—81no—
603C2—161no—
604C2C43×#327311yescharacteristic
605C2C43×#327511yescharacteristic
606C2C43×#329011yescharacteristic
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×#3367C2semidirect
2. C43×#3329C2semidirect
4. C43×#3324C2semidirect
5. C43×#1711C2semidirect
6. C43×#1703C2semidirect
7. C43×#1701C2semidirect
8. C43×#1699C2semidirect
9. C43×#1698C2semidirect
10. C43×#1646C2semidirect
11. C43×#1639C2semidirect
12. C43×#1638C2semidirect
13. C43×#1627C2semidirect
14. C43×#1590C2semidirect
15. C43×#1589C2semidirect
18. D4×Q8×C43C22semidirect
21. C43×#487C22semidirect
22. C43×#487C22semidirect
23. C43×#487C22semidirect
31. C43×#477C22semidirect
40. C43×#461C22semidirect
46. C43×#446C22semidirect
52. C43×#436C22semidirect
56. C43×#335C22semidirect
57. C43×#334C22semidirect
58. C43×#333C22semidirect
59. C43×#332C22semidirect
60. C43×#332C22semidirect
62. C43×Q8⋊C8C22semidirect
65. C43×D4⋊C8C22semidirect
66. C82×C43C22semidirect
269. #20287C43direct (N × H)
297. #3367C2×C43semidirect
298. #3329C2×C43semidirect
300. #3324C2×C43semidirect
301. #1711C2×C43semidirect
302. #1703C2×C43semidirect
303. #1701C2×C43semidirect
304. #1699C2×C43semidirect
305. #1698C2×C43semidirect
306. #1646C2×C43semidirect
307. #1639C2×C43semidirect
308. #1638C2×C43semidirect
309. #1627C2×C43semidirect
310. #1590C2×C43semidirect
311. #1589C2×C43semidirect
321. D4×Q8C22×C43semidirect
324. #487C22×C43semidirect
325. #487C22×C43semidirect
326. #487C22×C43semidirect
334. #477C22×C43semidirect
343. #461C22×C43semidirect
349. #446C22×C43semidirect
355. #436C22×C43semidirect
359. #335C22×C43semidirect
360. #334C22×C43semidirect
361. #333C22×C43semidirect
362. #332C22×C43semidirect
363. #332C22×C43semidirect
365. Q8⋊C8C22×C43semidirect
368. D4⋊C8C22×C43semidirect
369. C82C22×C43semidirect
370. C43#20287direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33672
C43×#33292
C43×#33252
C43×#33242
C43×#17112
C43×#17032
C43×#17012
C43×#16992
C43×#16982
C43×#16462
C43×#16392
C43×#16382
C43×#16272
C43×#15902
C43×#15892
#2028743