Finite Group Databasebeta

← C43×#19761 #24939778

Subgroups — C43×#19761 #24939778

Order 11008.

694 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×D8×C43C211yesmaximal, characteristic, complemented
2C43×#3358C211yesmaximal, characteristic
3D4×Q16×C43C211yesmaximal, characteristic, complemented
4C43×#3278C211yesmaximal, characteristic, complemented
5C43×#1722C211yesmaximal, characteristic, complemented
6C43×#1689C211yesmaximal, characteristic, complemented
7C43×#1682C211yesmaximal, characteristic, complemented
8C43×#1674C211yesmaximal, characteristic, complemented
9C43×#1665C211yesmaximal, characteristic, complemented
10C43×#1649C211yesmaximal, characteristic, complemented
11C43×#1649C211yesmaximal, characteristic, complemented
12C43×#1641C211yesmaximal, characteristic, complemented
13C43×#1627C211yesmaximal, characteristic, complemented
14C43×#1581C211yesmaximal, characteristic, complemented
15C43×#1579C211yesmaximal, characteristic, complemented
16C2×#137×C43—21no—
17C22×Q16×C43—21no—
18C43×#550C2211yescharacteristic
19D4×Q8×C43C2211yescharacteristic
20D4×Q8×C43C2211yescharacteristic
21D4×Q8×C43C2211yescharacteristic
22C43×#500—21no—
23C43×#500C2211yescharacteristic
24C43×#500C2211yescharacteristic
25C43×#494C2211yescharacteristic
26C43×#492C2211yescharacteristic
27C43×#486—21no—
28C43×#486C2211yescharacteristic
29C43×#486C2211yescharacteristic
30C43×#474—21no—
31C43×#474—21no—
32C43×#474—21no—
33C43×#474C2211yescharacteristic
34C43×#474C2211yescharacteristic
35C43×#474C2211yescharacteristic
36C43×#468—21no—
37C43×#467—21no—
38C43×#462C2211yescharacteristic
39C43×#462C2211yescharacteristic
40C43×#462C2211yescharacteristic
41C43×#460C2211yescharacteristic
42C43×#459—21no—
43C43×#459C2211yescharacteristic
44C43×#452—21no—
45C43×#451—21no—
46C43×#451—21no—
47C43×#448—21no—
48C8×Q8×C43C2211yescharacteristic
49C8×Q8×C43C2211yescharacteristic
50C4×Q16×C43C2211yescharacteristic
51C4×D8×C43—21no—
52C4×D8×C43—21no—
53C4×D8×C43C2211yescharacteristic
54C43×#436C2211yescharacteristic
55C8×D4×C43C2211yescharacteristic
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#332C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#41×C43—21no—
68C22×Q8×C43—21no—
69C22×Q8×C43—21no—
70C22×Q8×C43—21no—
71#137×C43—44no—
72C2×Q16×C43—21no—
73C2×Q16×C43—21no—
74C2×Q16×C43—21no—
75C2×Q16×C43—21no—
76C2×Q16×C43—21no—
77C2×Q16×C43—44no—
78C2×Q16×C43D411yescharacteristic
79C2×SD16×C43—21no—
80C2×SD16×C43—21no—
81C2×SD16×C43—21no—
82C2×D8×C43—21no—
83C2×D8×C43D411yescharacteristic
84C2×M16×C43—21no—
85C22×C8×C43—21no—
86C4⋊Q8×C43—21no—
87C4⋊Q8×C43—21no—
88C4⋊Q8×C43—21no—
89C4⋊Q8×C43C2311yescharacteristic
90C4⋊Q8×C43C2311yescharacteristic
91C4⋊Q8×C43C2311yescharacteristic
92#127×C43—21no—
93#127×C43C2311yescharacteristic
94C22⋊Q8×C43—21no—
95C22⋊Q8×C43—21no—
96C22⋊Q8×C43—21no—
97C22⋊Q8×C43—41no—
98C22⋊Q8×C43—41no—
99C22⋊Q8×C43—41no—
100#121×C43—21no—
101#121×C43—41no—
102C4×Q8×C43C2311yescharacteristic
103C4×Q8×C43C2311yescharacteristic
104C4×D4×C43—21no—
105C4×D4×C43—21no—
106C4×D4×C43—21no—
107C4×D4×C43—21no—
108C4×D4×C43C2311yescharacteristic
109C4×D4×C43C2311yescharacteristic
110#107×C43—21no—
111#107×C43—21no—
112#107×C43—21no—
113#107×C43—21no—
114#107×C43—21no—
115#107×C43—41no—
116#107×C43D411yescharacteristic
117#107×C43D411yescharacteristic
118C4⋊C8×C43—21no—
119C4⋊C8×C43—21no—
120C4⋊C8×C43C2311yescharacteristic
121C4⋊C8×C43C2311yescharacteristic
122C4⋊C8×C43C2311yescharacteristic
123C4⋊C8×C43C2311yescharacteristic
124#103×C43—21no—
125#103×C43—21no—
126#103×C43—21no—
127#103×C43D411yescharacteristic
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—21no—
135#102×C43—21no—
136#102×C43—41no—
137#102×C43D411yescharacteristic
138#102×C43D411yescharacteristic
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C4×C8×C43C2311yescharacteristic
146#41×C43—42no—
147#41×C43—81no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—41no—
152C2×Q8×C43—41no—
153C2×Q8×C43—41no—
154C2×Q8×C43—42no—
155C2×Q8×C43—42no—
156C2×Q8×C43—42no—
157C2×Q8×C43—81no—
158C2×Q8×C43—81no—
159C2×Q8×C43—81no—
160C2×Q8×C43C2×D411yescharacteristic
161C2×Q8×C43C2×D411yescharacteristic
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
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—
174C22×C4×C43—41no—
175Q16×C43—42no—
176Q16×C43—42no—
177Q16×C43—42no—
178Q16×C43—42no—
179Q16×C43—81no—
180Q16×C43D814yescomplemented
181SD16×C43—42no—
182SD16×C43—42no—
183SD16×C43—81no—
184D8×C43—22no—
185D8×C43—42no—
186M16×C43—42no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—42no—
193C2×C8×C43C2×D411yescharacteristic
194C2×C8×C43C2×D411yescharacteristic
195C2×C8×C43C2×D411yescharacteristic
196C2×C8×C43C2×D411yescharacteristic
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—41no—
206C4⋊C4×C43—41no—
207C4⋊C4×C43—41no—
208C4⋊C4×C43C2×D411yescharacteristic
209C4⋊C4×C43C2×D411yescharacteristic
210C4⋊C4×C43C2×D411yescharacteristic
211C4⋊C4×C43C2×D411yescharacteristic
212C22⋊C4×C43—21no—
213C22⋊C4×C43—21no—
214C22⋊C4×C43—41no—
215C22⋊C4×C43—41no—
216C22⋊C4×C43—41no—
217C22⋊C4×C43—41no—
218C42×C43—21no—
219C42×C43—21no—
220C42×C43C2411yescharacteristic
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—41no—
224Q8×C43—21no—
225Q8×C43—21no—
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×C43—41no—
229Q8×C43—41no—
230Q8×C43—41no—
231Q8×C43—41no—
232Q8×C43—82no—
233Q8×C43—82no—
234Q8×C43—82no—
235Q8×C43C2×D812yes—
236Q8×C43C2×D812yes—
237D4×C43—21no—
238D4×C43—21no—
239D4×C43—21no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—82no—
245D4×C43—81no—
246D4×C43—161no—
247D4×C43#13712yescomplemented
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—41no—
261C2×C4×C43—82no—
262C2×C4×C43—82no—
263C2×C4×C43—82no—
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—41no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43—41no—
275C8×C43—41no—
276C8×C43C2×D812yes—
277#19761C4311yesmaximal, characteristic, direct product factor, Sylow
278C22×C43—22no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43D4211yescharacteristic
288C4×C43—22no—
289C4×C43—22no—
290C4×C43—21no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—81no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43C22×D811yescharacteristic
299C4×C43C2×#13711yescharacteristic
300C4×C43#57611yescharacteristic
301C4×C43#57811yescharacteristic
302Q8×D8C2×C4311yescharacteristic, complemented
303#3358C2×C4311yescharacteristic
304D4×Q16C2×C4311yescharacteristic, complemented
305#3278C2×C4311yescharacteristic, complemented
306#1722C2×C4311yescharacteristic, complemented
307#1689C2×C4311yescharacteristic, complemented
308#1682C2×C4311yescharacteristic, complemented
309#1674C2×C4311yescharacteristic, complemented
310#1665C2×C4311yescharacteristic, complemented
311#1649C2×C4311yescharacteristic, complemented
312#1649C2×C4311yescharacteristic, complemented
313#1641C2×C4311yescharacteristic, complemented
314#1627C2×C4311yescharacteristic, complemented
315#1581C2×C4311yescharacteristic, complemented
316#1579C2×C4311yescharacteristic, complemented
317C2×C43—42no—
318C2×C43—81no—
319C2×C43—161no—
320C2×C43#327011yescharacteristic
321C2×C43D4×D811yescharacteristic
322C2×C43#328911yescharacteristic
323C2×#137—21no—
324C22×Q16—21no—
325#550C22×C4311yescharacteristic
326D4×Q8C22×C4311yescharacteristic
327D4×Q8C22×C4311yescharacteristic
328D4×Q8C22×C4311yescharacteristic
329#500—21no—
330#500C22×C4311yescharacteristic
331#500C22×C4311yescharacteristic
332#494C22×C4311yescharacteristic
333#492C22×C4311yescharacteristic
334#486—21no—
335#486C22×C4311yescharacteristic
336#486C22×C4311yescharacteristic
337#474—21no—
338#474—21no—
339#474—21no—
340#474C22×C4311yescharacteristic
341#474C22×C4311yescharacteristic
342#474C22×C4311yescharacteristic
343#468—21no—
344#467—21no—
345#462C22×C4311yescharacteristic
346#462C22×C4311yescharacteristic
347#462C22×C4311yescharacteristic
348#460C22×C4311yescharacteristic
349#459—21no—
350#459C22×C4311yescharacteristic
351#452—21no—
352#451—21no—
353#451—21no—
354#448—21no—
355C8×Q8C22×C4311yescharacteristic
356C8×Q8C22×C4311yescharacteristic
357C4×Q16C22×C4311yescharacteristic
358C4×D8—21no—
359C4×D8—21no—
360C4×D8C22×C4311yescharacteristic
361#436C22×C4311yescharacteristic
362C8×D4C22×C4311yescharacteristic
363#335C22×C4311yescharacteristic
364#334C22×C4311yescharacteristic
365#332C22×C4311yescharacteristic
366#332C22×C4311yescharacteristic
367#332C22×C4311yescharacteristic
368#331C22×C4311yescharacteristic
369Q8⋊C8C22×C4311yescharacteristic
370Q8⋊C8C22×C4311yescharacteristic
371D4⋊C8C22×C4311yescharacteristic
372D4⋊C8C22×C4311yescharacteristic
373#322C22×C4311yescharacteristic
374C43#1976111yescharacteristic, direct product factor, Sylow
375C2×#41—21no—
376C22×Q8—21no—
377C22×Q8—21no—
378C22×Q8—21no—
379#137—44no—
380C2×Q16—21no—
381C2×Q16—21no—
382C2×Q16—21no—
383C2×Q16—21no—
384C2×Q16—21no—
385C2×Q16—44no—
386C2×Q16D4×C4311yescharacteristic
387C2×SD16—21no—
388C2×SD16—21no—
389C2×SD16—21no—
390C2×D8—21no—
391C2×D8D4×C4311yescharacteristic
392C2×M16—21no—
393C22×C8—21no—
394C4⋊Q8—21no—
395C4⋊Q8—21no—
396C4⋊Q8—21no—
397C4⋊Q8C23×C4311yescharacteristic
398C4⋊Q8C23×C4311yescharacteristic
399C4⋊Q8C23×C4311yescharacteristic
400#127—21no—
401#127C23×C4311yescharacteristic
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—41no—
406C22⋊Q8—41no—
407C22⋊Q8—41no—
408#121—21no—
409#121—41no—
410C4×Q8C23×C4311yescharacteristic
411C4×Q8C23×C4311yescharacteristic
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4C23×C4311yescharacteristic
417C4×D4C23×C4311yescharacteristic
418#107—21no—
419#107—21no—
420#107—21no—
421#107—21no—
422#107—21no—
423#107—41no—
424#107D4×C4311yescharacteristic
425#107D4×C4311yescharacteristic
426C4⋊C8—21no—
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#103D4×C4311yescharacteristic
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—41no—
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—81no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—41no—
460C2×Q8—41no—
461C2×Q8—41no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—81no—
466C2×Q8—81no—
467C2×Q8—81no—
468C2×Q8C2×D4×C4311yescharacteristic
469C2×Q8C2×D4×C4311yescharacteristic
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4C2×D4×C4311yescharacteristic
476C2×D4C2×D4×C4311yescharacteristic
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483Q16—42no—
484Q16—42no—
485Q16—42no—
486Q16—42no—
487Q16—81no—
488Q16D8×C4314yescomplemented
489SD16—42no—
490SD16—42no—
491SD16—81no—
492D8—22no—
493D8—42no—
494M16—42no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—42no—
501C2×C8C2×D4×C4311yescharacteristic
502C2×C8C2×D4×C4311yescharacteristic
503C2×C8C2×D4×C4311yescharacteristic
504C2×C8C2×D4×C4311yescharacteristic
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4C2×D4×C4311yescharacteristic
517C4⋊C4C2×D4×C4311yescharacteristic
518C4⋊C4C2×D4×C4311yescharacteristic
519C4⋊C4C2×D4×C4311yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C42—21no—
527C42—21no—
528C42C24×C4311yescharacteristic
529C23—21no—
530C23—21no—
531C23—41no—
532Q8—21no—
533Q8—21no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537Q8—41no—
538Q8—41no—
539Q8—41no—
540Q8—82no—
541Q8—82no—
542Q8—82no—
543Q8C2×D8×C4312yes—
544Q8C2×D8×C4312yes—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—82no—
553D4—81no—
554D4—161no—
555D4#137×C4312yescomplemented
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
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×C4—82no—
573C2×C4C22×D4×C4311yescharacteristic
574C2×C4C22×D4×C4311yescharacteristic
575C2×C4H(5,𝔽2)×C4311yescharacteristic
576C8—21no—
577C8—21no—
578C8—21no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8—41no—
584C8C2×D8×C4312yes—
585C22—22no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22D42×C4311yescharacteristic
595C4—22no—
596C4—22no—
597C4—21no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—81no—
603C4—81no—
604C4—81no—
605C4C22×D8×C4311yescharacteristic
606C4C2×#137×C4311yescharacteristic
607C4C43×#57611yescharacteristic
608C4C43×#57811yescharacteristic
609C2—42no—
610C2—81no—
611C2—161no—
612C2C43×#327011yescharacteristic
613C2D4×D8×C4311yescharacteristic
614C2C43×#328911yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3358C2
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. Q8×D8×C43C2semidirect
3. D4×Q16×C43C2semidirect
4. C43×#3278C2semidirect
5. C43×#1722C2semidirect
6. C43×#1689C2semidirect
7. C43×#1682C2semidirect
8. C43×#1674C2semidirect
9. C43×#1665C2semidirect
10. C43×#1649C2semidirect
11. C43×#1649C2semidirect
12. C43×#1641C2semidirect
13. C43×#1627C2semidirect
14. C43×#1581C2semidirect
15. C43×#1579C2semidirect
180. Q16×C43D8semidirect
247. D4×C43#137semidirect
277. #19761C43direct (N × H)
302. Q8×D8C2×C43semidirect
304. D4×Q16C2×C43semidirect
305. #3278C2×C43semidirect
306. #1722C2×C43semidirect
307. #1689C2×C43semidirect
308. #1682C2×C43semidirect
309. #1674C2×C43semidirect
310. #1665C2×C43semidirect
311. #1649C2×C43semidirect
312. #1649C2×C43semidirect
313. #1641C2×C43semidirect
314. #1627C2×C43semidirect
315. #1581C2×C43semidirect
316. #1579C2×C43semidirect
374. C43#19761direct (N × H)
488. Q16D8×C43semidirect
555. D4#137×C43semidirect

Maximal subgroups

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

subgroupindex
Q8×D8×C432
C43×#33582
D4×Q16×C432
C43×#32782
C43×#17222
C43×#16892
C43×#16822
C43×#16742
C43×#16652
C43×#16492
C43×#16412
C43×#16272
C43×#15812
C43×#15792
#1976143