Finite Group Databasebeta

← C43×#20258 #24940275

Subgroups — C43×#20258 #24940275

Order 11008.

658 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3397C211yesmaximal, characteristic, complemented
2C43×#3325C211yesmaximal, characteristic, complemented
3C43×#3324C211yesmaximal, characteristic, complemented
4C43×#3305C211yesmaximal, characteristic, complemented
5C43×#1717C211yesmaximal, characteristic, complemented
6C43×#1698C211yesmaximal, characteristic, complemented
7C43×#1697C211yesmaximal, characteristic, complemented
8C43×#1685C211yesmaximal, characteristic, complemented
9C43×#1681C211yesmaximal, characteristic, complemented
10C43×#1646C211yesmaximal, characteristic, complemented
11C43×#1638C211yesmaximal, characteristic, complemented
12C43×#1621C211yesmaximal, characteristic, complemented
13C43×#1619C211yesmaximal, characteristic, complemented
14C43×#1592C211yesmaximal, characteristic, complemented
15C43×#1581C211yesmaximal, characteristic, complemented
16C43×#556C2211yescharacteristic
17C43×#555C2211yescharacteristic
18C43×#550C2211yescharacteristic, complemented
19D42×C43C2211yescharacteristic
20C43×#496—21no—
21C43×#493C2211yescharacteristic
22C43×#492C2211yescharacteristic, complemented
23C43×#487C2211yescharacteristic, complemented
24C43×#486C2211yescharacteristic
25C43×#486C2211yescharacteristic
26C43×#486C2211yescharacteristic, complemented
27C43×#482—21no—
28C43×#482—21no—
29C43×#482—21no—
30C43×#477C2211yescharacteristic, complemented
31C43×#476C2211yescharacteristic
32C43×#474C2211yescharacteristic
33C43×#469—21no—
34C43×#468—21no—
35C43×#466—21no—
36C43×#463—21no—
37C43×#461C2211yescharacteristic, complemented
38C43×#460—21no—
39C43×#460C2211yescharacteristic
40C43×#459C2211yescharacteristic
41C43×#459C2211yescharacteristic
42C43×#459C2211yescharacteristic
43C43×#450—21no—
44C43×#449—21no—
45C43×#447—21no—
46C43×#446C2211yescharacteristic, complemented
47C43×#440—21no—
48C4×SD16×C43C2211yescharacteristic
49C4×D8×C43C2211yescharacteristic
50C43×#436C2211yescharacteristic
51C43×#436C2211yescharacteristic
52C8×D4×C43C2211yescharacteristic, complemented
53C43×#418—21no—
54C43×#418—21no—
55C43×#416—21no—
56C43×#335C2211yescharacteristic, complemented
57C43×#335C2211yescharacteristic, complemented
58C43×#333C2211yescharacteristic, complemented
59C43×#332C2211yescharacteristic, complemented
60C43×#331C2211yescharacteristic
61C43×#331C2211yescharacteristic, complemented
62C43×Q8⋊C8C2211yescharacteristic, complemented
63C43×D4⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic, complemented
66C43×#322C2211yescharacteristic, complemented
67C2×#41×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70C2×SD16×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43D411yescharacteristic
75C2×D8×C43—21no—
76C2×D8×C43—21no—
77C2×D8×C43—21no—
78C2×D8×C43—41no—
79C2×D8×C43D411yescharacteristic
80C2×M16×C43—21no—
81C2×M16×C43—21no—
82C22×C8×C43—21no—
83C4⋊Q8×C43C2311yescharacteristic
84C4⋊Q8×C43C2311yescharacteristic
85#127×C43—21no—
86#127×C43C2311yescharacteristic
87#127×C43C2311yescharacteristic
88#126×C43—41no—
89#124×C43—21no—
90#124×C43—41no—
91C22⋊Q8×C43—21no—
92#121×C43—21no—
93#121×C43—21no—
94#121×C43—21no—
95#121×C43—21no—
96#121×C43—21no—
97#121×C43—41no—
98#120×C43—41no—
99C4×Q8×C43—21no—
100C4×Q8×C43C2311yescharacteristic
101C4×D4×C43—21no—
102C4×D4×C43C2311yescharacteristic
103C4×D4×C43C2311yescharacteristic
104C4×D4×C43C2311yescharacteristic
105#117×C43—21no—
106#117×C43—21no—
107#117×C43—21no—
108#107×C43—21no—
109#107×C43—21no—
110#107×C43D411yescharacteristic
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—41no—
121#103×C43D411yescharacteristic
122#102×C43—21no—
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—21no—
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—
145#41×C43—42no—
146#41×C43—81no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43—41no—
159C2×D4×C43—41no—
160C2×D4×C43—41no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—81no—
164C2×D4×C43—81no—
165C2×D4×C43C2×D411yescharacteristic
166C2×D4×C43C2×D411yescharacteristic
167C2×D4×C43C2×D411yescharacteristic
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—41no—
172SD16×C43—41no—
173SD16×C43—42no—
174SD16×C43—81no—
175SD16×C43—81no—
176SD16×C43—81no—
177D8×C43—41no—
178D8×C43—81no—
179D8×C43—81no—
180D8×C43—81no—
181D8×C43—82no—
182M16×C43—81no—
183M16×C43—81no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
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—41no—
200C4⋊C4×C43C2×D411yescharacteristic
201C4⋊C4×C43C2×D411yescharacteristic
202C4⋊C4×C43C2×D411yescharacteristic
203C4⋊C4×C43C2×D411yescharacteristic
204C22⋊C4×C43—21no—
205C22⋊C4×C43—21no—
206C22⋊C4×C43—21no—
207C22⋊C4×C43—41no—
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—41no—
215C42×C43—41no—
216C42×C43C2411yescharacteristic
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—82no—
223C23×C43—82no—
224C23×C43—161no—
225Q8×C43—21no—
226Q8×C43—21no—
227Q8×C43—41no—
228Q8×C43—41no—
229Q8×C43—81no—
230D4×C43—21no—
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—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—81no—
245D4×C43—81no—
246D4×C43—82no—
247D4×C43—82no—
248D4×C43—82no—
249D4×C43—161no—
250D4×C43—161no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—82no—
265C2×C4×C43C22×D411yescharacteristic
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43H(5,𝔽2)11yescharacteristic
268C8×C43—21no—
269C8×C43—21no—
270C8×C43—21no—
271C8×C43—21no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43—41no—
275C8×C43—41no—
276C8×C43—41no—
277#20258C4311yesmaximal, characteristic, direct product factor, Sylow
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43—164no—
294C22×C43D4211yescharacteristic
295C4×C43—21no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—41no—
299C4×C43—41no—
300C4×C43—41no—
301C4×C43—81no—
302C4×C43—81no—
303C4×C43#57511yescharacteristic
304C4×C43#57511yescharacteristic
305C4×C43#57611yescharacteristic
306C4×C43#57611yescharacteristic
307#3397C2×C4311yescharacteristic, complemented
308#3325C2×C4311yescharacteristic, complemented
309#3324C2×C4311yescharacteristic, complemented
310#3305C2×C4311yescharacteristic, complemented
311#1717C2×C4311yescharacteristic, complemented
312#1698C2×C4311yescharacteristic, complemented
313#1697C2×C4311yescharacteristic, complemented
314#1685C2×C4311yescharacteristic, complemented
315#1681C2×C4311yescharacteristic, complemented
316#1646C2×C4311yescharacteristic, complemented
317#1638C2×C4311yescharacteristic, complemented
318#1621C2×C4311yescharacteristic, complemented
319#1619C2×C4311yescharacteristic, complemented
320#1592C2×C4311yescharacteristic, complemented
321#1581C2×C4311yescharacteristic, complemented
322C2×C43—81no—
323C2×C43—81no—
324C2×C43—81no—
325C2×C43—161no—
326C2×C43—161no—
327C2×C43#326811yescharacteristic
328C2×C43#327311yescharacteristic
329C2×C43#328811yescharacteristic
330#556C22×C4311yescharacteristic
331#555C22×C4311yescharacteristic
332#550C22×C4311yescharacteristic, complemented
333D42C22×C4311yescharacteristic
334#496—21no—
335#493C22×C4311yescharacteristic
336#492C22×C4311yescharacteristic, complemented
337#487C22×C4311yescharacteristic, complemented
338#486C22×C4311yescharacteristic
339#486C22×C4311yescharacteristic
340#486C22×C4311yescharacteristic, complemented
341#482—21no—
342#482—21no—
343#482—21no—
344#477C22×C4311yescharacteristic, complemented
345#476C22×C4311yescharacteristic
346#474C22×C4311yescharacteristic
347#469—21no—
348#468—21no—
349#466—21no—
350#463—21no—
351#461C22×C4311yescharacteristic, complemented
352#460—21no—
353#460C22×C4311yescharacteristic
354#459C22×C4311yescharacteristic
355#459C22×C4311yescharacteristic
356#459C22×C4311yescharacteristic
357#450—21no—
358#449—21no—
359#447—21no—
360#446C22×C4311yescharacteristic, complemented
361#440—21no—
362C4×SD16C22×C4311yescharacteristic
363C4×D8C22×C4311yescharacteristic
364#436C22×C4311yescharacteristic
365#436C22×C4311yescharacteristic
366C8×D4C22×C4311yescharacteristic, complemented
367#418—21no—
368#418—21no—
369#416—21no—
370#335C22×C4311yescharacteristic, complemented
371#335C22×C4311yescharacteristic, complemented
372#333C22×C4311yescharacteristic, complemented
373#332C22×C4311yescharacteristic, complemented
374#331C22×C4311yescharacteristic
375#331C22×C4311yescharacteristic, complemented
376Q8⋊C8C22×C4311yescharacteristic, complemented
377D4⋊C8C22×C4311yescharacteristic
378D4⋊C8C22×C4311yescharacteristic
379D4⋊C8C22×C4311yescharacteristic, complemented
380#322C22×C4311yescharacteristic, complemented
381C43#2025811yescharacteristic, direct product factor, Sylow
382C2×#41—21no—
383C22×D4—21no—
384C22×D4—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16—21no—
388C2×SD16—21no—
389C2×SD16D4×C4311yescharacteristic
390C2×D8—21no—
391C2×D8—21no—
392C2×D8—21no—
393C2×D8—41no—
394C2×D8D4×C4311yescharacteristic
395C2×M16—21no—
396C2×M16—21no—
397C22×C8—21no—
398C4⋊Q8C23×C4311yescharacteristic
399C4⋊Q8C23×C4311yescharacteristic
400#127—21no—
401#127C23×C4311yescharacteristic
402#127C23×C4311yescharacteristic
403#126—41no—
404#124—21no—
405#124—41no—
406C22⋊Q8—21no—
407#121—21no—
408#121—21no—
409#121—21no—
410#121—21no—
411#121—21no—
412#121—41no—
413#120—41no—
414C4×Q8—21no—
415C4×Q8C23×C4311yescharacteristic
416C4×D4—21no—
417C4×D4C23×C4311yescharacteristic
418C4×D4C23×C4311yescharacteristic
419C4×D4C23×C4311yescharacteristic
420#117—21no—
421#117—21no—
422#117—21no—
423#107—21no—
424#107—21no—
425#107D4×C4311yescharacteristic
426#106—21no—
427#106D4×C4311yescharacteristic
428C4⋊C8—21no—
429C4⋊C8C23×C4311yescharacteristic
430C4⋊C8C23×C4311yescharacteristic
431C4⋊C8C23×C4311yescharacteristic
432C4⋊C8C23×C4311yescharacteristic
433#103—21no—
434#103—21no—
435#103—41no—
436#103D4×C4311yescharacteristic
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#102—21no—
446#102—21no—
447#102—21no—
448#102—21no—
449#102D4×C4311yescharacteristic
450#102D4×C4311yescharacteristic
451#102D4×C4311yescharacteristic
452C22⋊C8—21no—
453C22⋊C8—21no—
454C22⋊C8—21no—
455#97—21no—
456C4×C8C23×C4311yescharacteristic
457C4×C8C23×C4311yescharacteristic
458C4×C8C23×C4311yescharacteristic
459C24—41no—
460#41—42no—
461#41—81no—
462C2×Q8—21no—
463C2×Q8—21no—
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—42no—
476C2×D4—42no—
477C2×D4—41no—
478C2×D4—81no—
479C2×D4—81no—
480C2×D4C2×D4×C4311yescharacteristic
481C2×D4C2×D4×C4311yescharacteristic
482C2×D4C2×D4×C4311yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—41no—
487SD16—41no—
488SD16—42no—
489SD16—81no—
490SD16—81no—
491SD16—81no—
492D8—41no—
493D8—81no—
494D8—81no—
495D8—81no—
496D8—82no—
497M16—81no—
498M16—81no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—81no—
505C2×C8C2×D4×C4311yescharacteristic
506C2×C8C2×D4×C4311yescharacteristic
507C2×C8C2×D4×C4311yescharacteristic
508C2×C8C2×D4×C4311yescharacteristic
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—41no—
515C4⋊C4C2×D4×C4311yescharacteristic
516C4⋊C4C2×D4×C4311yescharacteristic
517C4⋊C4C2×D4×C4311yescharacteristic
518C4⋊C4C2×D4×C4311yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C42—21no—
529C42—41no—
530C42—41no—
531C42C24×C4311yescharacteristic
532C23—21no—
533C23—21no—
534C23—21no—
535C23—41no—
536C23—41no—
537C23—82no—
538C23—82no—
539C23—161no—
540Q8—21no—
541Q8—21no—
542Q8—41no—
543Q8—41no—
544Q8—81no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—21no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—41no—
559D4—81no—
560D4—81no—
561D4—82no—
562D4—82no—
563D4—82no—
564D4—161no—
565D4—161no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—82no—
580C2×C4C22×D4×C4311yescharacteristic
581C2×C4C22×D4×C4311yescharacteristic
582C2×C4H(5,𝔽2)×C4311yescharacteristic
583C8—21no—
584C8—21no—
585C8—21no—
586C8—21no—
587C8—41no—
588C8—41no—
589C8—41no—
590C8—41no—
591C8—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—164no—
608C22D42×C4311yescharacteristic
609C4—21no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—81no—
616C4—81no—
617C4C43×#57511yescharacteristic
618C4C43×#57511yescharacteristic
619C4C43×#57611yescharacteristic
620C4C43×#57611yescharacteristic
621C2—81no—
622C2—81no—
623C2—81no—
624C2—161no—
625C2—161no—
626C2C43×#326811yescharacteristic
627C2C43×#327311yescharacteristic
628C2C43×#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×#3325C2semidirect
3. C43×#3324C2semidirect
4. C43×#3305C2semidirect
5. C43×#1717C2semidirect
6. C43×#1698C2semidirect
7. C43×#1697C2semidirect
8. C43×#1685C2semidirect
9. C43×#1681C2semidirect
10. C43×#1646C2semidirect
11. C43×#1638C2semidirect
12. C43×#1621C2semidirect
13. C43×#1619C2semidirect
14. C43×#1592C2semidirect
15. C43×#1581C2semidirect
18. C43×#550C22semidirect
22. C43×#492C22semidirect
23. C43×#487C22semidirect
26. C43×#486C22semidirect
30. C43×#477C22semidirect
37. C43×#461C22semidirect
46. C43×#446C22semidirect
52. C8×D4×C43C22semidirect
56. C43×#335C22semidirect
57. C43×#335C22semidirect
58. C43×#333C22semidirect
59. C43×#332C22semidirect
61. C43×#331C22semidirect
62. C43×Q8⋊C8C22semidirect
65. C43×D4⋊C8C22semidirect
66. C43×#322C22semidirect
277. #20258C43direct (N × H)
307. #3397C2×C43semidirect
308. #3325C2×C43semidirect
309. #3324C2×C43semidirect
310. #3305C2×C43semidirect
311. #1717C2×C43semidirect
312. #1698C2×C43semidirect
313. #1697C2×C43semidirect
314. #1685C2×C43semidirect
315. #1681C2×C43semidirect
316. #1646C2×C43semidirect
317. #1638C2×C43semidirect
318. #1621C2×C43semidirect
319. #1619C2×C43semidirect
320. #1592C2×C43semidirect
321. #1581C2×C43semidirect
332. #550C22×C43semidirect
336. #492C22×C43semidirect
337. #487C22×C43semidirect
340. #486C22×C43semidirect
344. #477C22×C43semidirect
351. #461C22×C43semidirect
360. #446C22×C43semidirect
366. C8×D4C22×C43semidirect
370. #335C22×C43semidirect
371. #335C22×C43semidirect
372. #333C22×C43semidirect
373. #332C22×C43semidirect
375. #331C22×C43semidirect
376. Q8⋊C8C22×C43semidirect
379. D4⋊C8C22×C43semidirect
380. #322C22×C43semidirect
381. C43#20258direct (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×#33252
C43×#33242
C43×#33052
C43×#17172
C43×#16982
C43×#16972
C43×#16852
C43×#16812
C43×#16462
C43×#16382
C43×#16212
C43×#16192
C43×#15922
C43×#15812
#2025843