Finite Group Databasebeta

← C43×#19762 #24939779

Subgroups — C43×#19762 #24939779

Order 11008.

728 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3391C211yesmaximal, characteristic, complemented
2C43×#3358C211yesmaximal, characteristic, complemented
3C43×#3287C211yesmaximal, characteristic, complemented
4C43×#3278C211yesmaximal, characteristic, complemented
5C43×#1721C211yesmaximal, characteristic, complemented
6C43×#1687C211yesmaximal, characteristic, complemented
7C43×#1682C211yesmaximal, characteristic, complemented
8C43×#1668C211yesmaximal, characteristic, complemented
9C43×#1665C211yesmaximal, characteristic, complemented
10C43×#1641C211yesmaximal, characteristic, complemented
11C43×#1627C211yesmaximal, characteristic, complemented
12C43×#1621C211yesmaximal, characteristic, complemented
13C43×#1621C211yesmaximal, characteristic, complemented
14C43×#1581C211yesmaximal, characteristic, complemented
15C43×#1579C211yesmaximal, characteristic, complemented
16C2×#137×C43—21no—
17C2×#135×C43—21no—
18C43×#550C2211yescharacteristic
19C43×#550C2211yescharacteristic
20C43×#550C2211yescharacteristic
21D4×Q8×C43C2211yescharacteristic
22C43×#493—21no—
23C43×#493C2211yescharacteristic
24C43×#493C2211yescharacteristic
25C43×#493C2211yescharacteristic
26C43×#492C2211yescharacteristic
27C43×#486—21no—
28C43×#486C2211yescharacteristic
29C43×#486C2211yescharacteristic
30C43×#474—21no—
31C43×#474C2211yescharacteristic
32C43×#468—21no—
33C43×#466—21no—
34C43×#462C2211yescharacteristic
35C43×#460C2211yescharacteristic
36C43×#460C2211yescharacteristic
37C43×#460C2211yescharacteristic
38C43×#459—21no—
39C43×#459—21no—
40C43×#459—21no—
41C43×#459C2211yescharacteristic
42C43×#459C2211yescharacteristic
43C43×#459C2211yescharacteristic
44C43×#452—21no—
45C43×#449—21no—
46C43×#449—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×#331C2211yescharacteristic
60C43×#331C2211yescharacteristic
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#41×C43—21no—
68C2×#41×C43—21no—
69C2×#41×C43—21no—
70C22×Q8×C43—21no—
71#137×C43—44no—
72#135×C43—44no—
73C2×Q16×C43—21no—
74C2×Q16×C43D411yescharacteristic
75C2×SD16×C43—21no—
76C2×SD16×C43—21no—
77C2×SD16×C43—21no—
78C2×SD16×C43—21no—
79C2×SD16×C43—21no—
80C2×D8×C43—21no—
81C2×D8×C43—21no—
82C2×D8×C43—21no—
83C2×D8×C43—21no—
84C2×D8×C43—21no—
85C2×D8×C43—21no—
86C2×D8×C43—21no—
87C2×D8×C43—41no—
88C2×D8×C43D411yescharacteristic
89C2×M16×C43—21no—
90C22×C8×C43—21no—
91C4⋊Q8×C43—21no—
92C4⋊Q8×C43C2311yescharacteristic
93#127×C43—21no—
94#127×C43—21no—
95#127×C43—21no—
96#127×C43C2311yescharacteristic
97#127×C43C2311yescharacteristic
98#127×C43C2311yescharacteristic
99C22⋊Q8×C43—21no—
100C22⋊Q8×C43—41no—
101#121×C43—21no—
102#121×C43—21no—
103#121×C43—21no—
104#121×C43—41no—
105#121×C43—41no—
106#121×C43—41no—
107C4×Q8×C43C2311yescharacteristic
108C4×Q8×C43C2311yescharacteristic
109C4×D4×C43—21no—
110C4×D4×C43—21no—
111C4×D4×C43—21no—
112C4×D4×C43—21no—
113C4×D4×C43C2311yescharacteristic
114C4×D4×C43C2311yescharacteristic
115#107×C43—21no—
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×C43D411yescharacteristic
126#103×C43D411yescharacteristic
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×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—42no—
148#41×C43—42no—
149#41×C43—81no—
150#41×C43—81no—
151#41×C43—81no—
152C2×Q8×C43—21no—
153C2×Q8×C43—41no—
154C2×Q8×C43—42no—
155C2×Q8×C43—81no—
156C2×Q8×C43C2×D411yescharacteristic
157C2×Q8×C43C2×D411yescharacteristic
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—41no—
168C2×D4×C43—41no—
169C2×D4×C43—41no—
170C2×D4×C43—41no—
171C2×D4×C43—41no—
172C2×D4×C43—41no—
173C2×D4×C43C2×D411yescharacteristic
174C2×D4×C43C2×D411yescharacteristic
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—41no—
178C22×C4×C43—41no—
179C22×C4×C43—41no—
180C22×C4×C43—41no—
181Q16×C43—42no—
182Q16×C43D814yescomplemented
183SD16×C43—42no—
184SD16×C43—42no—
185SD16×C43—42no—
186SD16×C43—42no—
187SD16×C43—81no—
188D8×C43—41no—
189D8×C43—42no—
190D8×C43—42no—
191D8×C43—42no—
192D8×C43—81no—
193D8×C43—81no—
194D8×C43—81no—
195D8×C43—81no—
196D8×C43—82no—
197M16×C43—42no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—42no—
204C2×C8×C43C2×D411yescharacteristic
205C2×C8×C43C2×D411yescharacteristic
206C2×C8×C43C2×D411yescharacteristic
207C2×C8×C43C2×D411yescharacteristic
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—41no—
213C4⋊C4×C43C2×D411yescharacteristic
214C4⋊C4×C43C2×D411yescharacteristic
215C4⋊C4×C43C2×D411yescharacteristic
216C4⋊C4×C43C2×D411yescharacteristic
217C22⋊C4×C43—21no—
218C22⋊C4×C43—21no—
219C22⋊C4×C43—41no—
220C22⋊C4×C43—41no—
221C22⋊C4×C43—41no—
222C22⋊C4×C43—41no—
223C42×C43—21no—
224C42×C43—21no—
225C42×C43C2411yescharacteristic
226C23×C43—21no—
227C23×C43—21no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231Q8×C43—21no—
232Q8×C43—21no—
233Q8×C43—41no—
234Q8×C43—41no—
235Q8×C43—82no—
236Q8×C43C2×D812yes—
237Q8×C43C2×D812yes—
238D4×C43—21no—
239D4×C43—21no—
240D4×C43—21no—
241D4×C43—21no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—41no—
245D4×C43—41no—
246D4×C43—41no—
247D4×C43—41no—
248D4×C43—41no—
249D4×C43—41no—
250D4×C43—41no—
251D4×C43—41no—
252D4×C43—41no—
253D4×C43—41no—
254D4×C43—82no—
255D4×C43—82no—
256D4×C43—82no—
257D4×C43—81no—
258D4×C43—81no—
259D4×C43—81no—
260D4×C43—161no—
261D4×C43—161no—
262D4×C43—161no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—82no—
275C2×C4×C43—82no—
276C2×C4×C43—82no—
277C2×C4×C43—82no—
278C2×C4×C43C22×D411yescharacteristic
279C2×C4×C43C22×D411yescharacteristic
280C2×C4×C43H(5,𝔽2)11yescharacteristic
281C8×C43—21no—
282C8×C43—21no—
283C8×C43—21no—
284C8×C43—41no—
285C8×C43—41no—
286C8×C43—41no—
287C8×C43—41no—
288C8×C43—41no—
289C8×C43C2×D812yes—
290#19762C4311yesmaximal, characteristic, direct product factor, Sylow
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—41no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43D4211yescharacteristic
307C4×C43—22no—
308C4×C43—22no—
309C4×C43—21no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43—41no—
313C4×C43—41no—
314C4×C43—81no—
315C4×C43C22×D811yescharacteristic
316C4×C43#57511yescharacteristic
317C4×C43#57611yescharacteristic
318C4×C43#57711yescharacteristic
319#3391C2×C4311yescharacteristic, complemented
320#3358C2×C4311yescharacteristic, complemented
321#3287C2×C4311yescharacteristic, complemented
322#3278C2×C4311yescharacteristic, complemented
323#1721C2×C4311yescharacteristic, complemented
324#1687C2×C4311yescharacteristic, complemented
325#1682C2×C4311yescharacteristic, complemented
326#1668C2×C4311yescharacteristic, complemented
327#1665C2×C4311yescharacteristic, complemented
328#1641C2×C4311yescharacteristic, complemented
329#1627C2×C4311yescharacteristic, complemented
330#1621C2×C4311yescharacteristic, complemented
331#1621C2×C4311yescharacteristic, complemented
332#1581C2×C4311yescharacteristic, complemented
333#1579C2×C4311yescharacteristic, complemented
334C2×C43—81no—
335C2×C43—81no—
336C2×C43—161no—
337C2×C43—161no—
338C2×C43—161no—
339C2×C43#327111yescharacteristic
340C2×C43D4×D811yescharacteristic
341C2×C43#328811yescharacteristic
342C2×#137—21no—
343C2×#135—21no—
344#550C22×C4311yescharacteristic
345#550C22×C4311yescharacteristic
346#550C22×C4311yescharacteristic
347D4×Q8C22×C4311yescharacteristic
348#493—21no—
349#493C22×C4311yescharacteristic
350#493C22×C4311yescharacteristic
351#493C22×C4311yescharacteristic
352#492C22×C4311yescharacteristic
353#486—21no—
354#486C22×C4311yescharacteristic
355#486C22×C4311yescharacteristic
356#474—21no—
357#474C22×C4311yescharacteristic
358#468—21no—
359#466—21no—
360#462C22×C4311yescharacteristic
361#460C22×C4311yescharacteristic
362#460C22×C4311yescharacteristic
363#460C22×C4311yescharacteristic
364#459—21no—
365#459—21no—
366#459—21no—
367#459C22×C4311yescharacteristic
368#459C22×C4311yescharacteristic
369#459C22×C4311yescharacteristic
370#452—21no—
371#449—21no—
372#449—21no—
373#448—21no—
374C8×Q8C22×C4311yescharacteristic
375C8×Q8C22×C4311yescharacteristic
376C4×Q16C22×C4311yescharacteristic
377C4×D8—21no—
378C4×D8—21no—
379C4×D8C22×C4311yescharacteristic
380#436C22×C4311yescharacteristic
381C8×D4C22×C4311yescharacteristic
382#335C22×C4311yescharacteristic
383#334C22×C4311yescharacteristic
384#332C22×C4311yescharacteristic
385#331C22×C4311yescharacteristic
386#331C22×C4311yescharacteristic
387#331C22×C4311yescharacteristic
388Q8⋊C8C22×C4311yescharacteristic
389Q8⋊C8C22×C4311yescharacteristic
390D4⋊C8C22×C4311yescharacteristic
391D4⋊C8C22×C4311yescharacteristic
392#322C22×C4311yescharacteristic
393C43#1976211yescharacteristic, direct product factor, Sylow
394C2×#41—21no—
395C2×#41—21no—
396C2×#41—21no—
397C22×Q8—21no—
398#137—44no—
399#135—44no—
400C2×Q16—21no—
401C2×Q16D4×C4311yescharacteristic
402C2×SD16—21no—
403C2×SD16—21no—
404C2×SD16—21no—
405C2×SD16—21no—
406C2×SD16—21no—
407C2×D8—21no—
408C2×D8—21no—
409C2×D8—21no—
410C2×D8—21no—
411C2×D8—21no—
412C2×D8—21no—
413C2×D8—21no—
414C2×D8—41no—
415C2×D8D4×C4311yescharacteristic
416C2×M16—21no—
417C22×C8—21no—
418C4⋊Q8—21no—
419C4⋊Q8C23×C4311yescharacteristic
420#127—21no—
421#127—21no—
422#127—21no—
423#127C23×C4311yescharacteristic
424#127C23×C4311yescharacteristic
425#127C23×C4311yescharacteristic
426C22⋊Q8—21no—
427C22⋊Q8—41no—
428#121—21no—
429#121—21no—
430#121—21no—
431#121—41no—
432#121—41no—
433#121—41no—
434C4×Q8C23×C4311yescharacteristic
435C4×Q8C23×C4311yescharacteristic
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4C23×C4311yescharacteristic
441C4×D4C23×C4311yescharacteristic
442#107—21no—
443#107D4×C4311yescharacteristic
444#107D4×C4311yescharacteristic
445C4⋊C8—21no—
446C4⋊C8—21no—
447C4⋊C8C23×C4311yescharacteristic
448C4⋊C8C23×C4311yescharacteristic
449C4⋊C8C23×C4311yescharacteristic
450C4⋊C8C23×C4311yescharacteristic
451#103—21no—
452#103D4×C4311yescharacteristic
453#103D4×C4311yescharacteristic
454#102—21no—
455#102—21no—
456#102—21no—
457#102—21no—
458#102—21no—
459#102—21no—
460#102—21no—
461#102—21no—
462#102—21no—
463#102—41no—
464#102D4×C4311yescharacteristic
465#102D4×C4311yescharacteristic
466C22⋊C8—21no—
467C22⋊C8—21no—
468C4×C8—21no—
469C4×C8—21no—
470C4×C8C23×C4311yescharacteristic
471C4×C8C23×C4311yescharacteristic
472C4×C8C23×C4311yescharacteristic
473#41—42no—
474#41—42no—
475#41—42no—
476#41—81no—
477#41—81no—
478#41—81no—
479C2×Q8—21no—
480C2×Q8—41no—
481C2×Q8—42no—
482C2×Q8—81no—
483C2×Q8C2×D4×C4311yescharacteristic
484C2×Q8C2×D4×C4311yescharacteristic
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—41no—
495C2×D4—41no—
496C2×D4—41no—
497C2×D4—41no—
498C2×D4—41no—
499C2×D4—41no—
500C2×D4C2×D4×C4311yescharacteristic
501C2×D4C2×D4×C4311yescharacteristic
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508Q16—42no—
509Q16D8×C4314yescomplemented
510SD16—42no—
511SD16—42no—
512SD16—42no—
513SD16—42no—
514SD16—81no—
515D8—41no—
516D8—42no—
517D8—42no—
518D8—42no—
519D8—81no—
520D8—81no—
521D8—81no—
522D8—81no—
523D8—82no—
524M16—42no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—42no—
531C2×C8C2×D4×C4311yescharacteristic
532C2×C8C2×D4×C4311yescharacteristic
533C2×C8C2×D4×C4311yescharacteristic
534C2×C8C2×D4×C4311yescharacteristic
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—41no—
540C4⋊C4C2×D4×C4311yescharacteristic
541C4⋊C4C2×D4×C4311yescharacteristic
542C4⋊C4C2×D4×C4311yescharacteristic
543C4⋊C4C2×D4×C4311yescharacteristic
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—41no—
549C22⋊C4—41no—
550C42—21no—
551C42—21no—
552C42C24×C4311yescharacteristic
553C23—21no—
554C23—21no—
555C23—41no—
556C23—41no—
557C23—41no—
558Q8—21no—
559Q8—21no—
560Q8—41no—
561Q8—41no—
562Q8—82no—
563Q8C2×D8×C4312yes—
564Q8C2×D8×C4312yes—
565D4—21no—
566D4—21no—
567D4—21no—
568D4—21no—
569D4—41no—
570D4—41no—
571D4—41no—
572D4—41no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—41no—
577D4—41no—
578D4—41no—
579D4—41no—
580D4—41no—
581D4—82no—
582D4—82no—
583D4—82no—
584D4—81no—
585D4—81no—
586D4—81no—
587D4—161no—
588D4—161no—
589D4—161no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—82no—
602C2×C4—82no—
603C2×C4—82no—
604C2×C4—82no—
605C2×C4C22×D4×C4311yescharacteristic
606C2×C4C22×D4×C4311yescharacteristic
607C2×C4H(5,𝔽2)×C4311yescharacteristic
608C8—21no—
609C8—21no—
610C8—21no—
611C8—41no—
612C8—41no—
613C8—41no—
614C8—41no—
615C8—41no—
616C8C2×D8×C4312yes—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22D42×C4311yescharacteristic
633C4—22no—
634C4—22no—
635C4—21no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—81no—
641C4C22×D8×C4311yescharacteristic
642C4C43×#57511yescharacteristic
643C4C43×#57611yescharacteristic
644C4C43×#57711yescharacteristic
645C2—81no—
646C2—81no—
647C2—161no—
648C2—161no—
649C2—161no—
650C2C43×#327111yescharacteristic
651C2D4×D8×C4311yescharacteristic
652C2C43×#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×#3391C2semidirect
2. C43×#3358C2semidirect
3. C43×#3287C2semidirect
4. C43×#3278C2semidirect
5. C43×#1721C2semidirect
6. C43×#1687C2semidirect
7. C43×#1682C2semidirect
8. C43×#1668C2semidirect
9. C43×#1665C2semidirect
10. C43×#1641C2semidirect
11. C43×#1627C2semidirect
12. C43×#1621C2semidirect
13. C43×#1621C2semidirect
14. C43×#1581C2semidirect
15. C43×#1579C2semidirect
182. Q16×C43D8semidirect
290. #19762C43direct (N × H)
319. #3391C2×C43semidirect
320. #3358C2×C43semidirect
321. #3287C2×C43semidirect
322. #3278C2×C43semidirect
323. #1721C2×C43semidirect
324. #1687C2×C43semidirect
325. #1682C2×C43semidirect
326. #1668C2×C43semidirect
327. #1665C2×C43semidirect
328. #1641C2×C43semidirect
329. #1627C2×C43semidirect
330. #1621C2×C43semidirect
331. #1621C2×C43semidirect
332. #1581C2×C43semidirect
333. #1579C2×C43semidirect
393. C43#19762direct (N × H)
509. Q16D8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#33912
C43×#33582
C43×#32872
C43×#32782
C43×#17212
C43×#16872
C43×#16822
C43×#16682
C43×#16652
C43×#16412
C43×#16272
C43×#16212
C43×#15812
C43×#15792
#1976243