Finite Group Databasebeta

← C43×#18306 #24938323

Subgroups — C43×#18306 #24938323

Order 11008.

1040 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3459C211yesmaximal, characteristic, complemented
2C43×#3211C212yesmaximal, complemented
3C43×#2631C211yesmaximal, characteristic, complemented
4C43×#1606C212yesmaximal, complemented
5C43×#1602C211yesmaximal, characteristic, complemented
6C43×#1601C211yesmaximal, characteristic, complemented
7C43×#1600C212yesmaximal, complemented
8C43×#1596C211yesmaximal, characteristic, complemented
9C43×#1595C211yesmaximal, characteristic, complemented
10C43×#1521C212yesmaximal, complemented
11C43×#1460C211yesmaximal, characteristic, complemented
12C43×#543C2211yescharacteristic
13C43×#539—22no—
14C43×#539—21no—
15C43×#538—22no—
16C43×#538C2212yes—
17C43×#534—21no—
18C43×#534C2211yescharacteristic
19C43×#529—22no—
20C43×#529C2212yes—
21C2×#124×C43C2211yescharacteristic, complemented
22C43×#525—21no—
23C43×#525—22no—
24C2×C4×D4×C43—21no—
25C2×C4×D4×C43C2211yescharacteristic
26C43×#495—22no—
27C43×#488—22no—
28C43×#464—22no—
29C43×#463—22no—
30C43×#451C2212yescomplemented
31C43×#450C2212yescomplemented
32C43×#448C2212yes—
33C43×#447C2212yes—
34C43×#431C2212yescomplemented
35C43×#397—21no—
36C43×#393C2211yescharacteristic
37C43×#393C2211yescharacteristic, complemented
38C43×#392—21no—
39C43×#392C2211yescharacteristic
40C43×#392C2211yescharacteristic, complemented
41C43×#386—21no—
42C43×#386—21no—
43C43×#383C2211yescharacteristic, complemented
44C43×#328C2212yescomplemented
45C43×#328C2212yescomplemented
46C43×#327C2212yes—
47C43×#327C2212yes—
48C43×#323C2211yescharacteristic
49C43×#323C2211yescharacteristic
50C43×#323C2212yescomplemented
51C2×#41×C43—21no—
52C22×Q8×C43C2311yescharacteristic
53C22×D4×C43—21no—
54C22×D4×C43—21no—
55C22×D4×C43—21no—
56C22×D4×C43D411yescharacteristic
57C22×D4×C43C2311yescharacteristic
58C23×C4×C43—21no—
59C23×C4×C43D411yescharacteristic
60C23×C4×C43D411yescharacteristic
61C2×Q16×C43—22no—
62C2×SD16×C43—22no—
63C2×SD16×C43—22no—
64C2×D8×C43—22no—
65#126×C43—22no—
66#126×C43—22no—
67#126×C43—22no—
68#125×C43—22no—
69#125×C43D412yescomplemented
70#124×C43—22no—
71#124×C43—22no—
72#124×C43—22no—
73#124×C43D412yescomplemented
74#123×C43—22no—
75#123×C43—22no—
76#123×C43—22no—
77#123×C43—22no—
78#123×C43—22no—
79#123×C43—22no—
80C22⋊Q8×C43—21no—
81C22⋊Q8×C43—22no—
82C22⋊Q8×C43—22no—
83C22⋊Q8×C43—21no—
84C22⋊Q8×C43—22no—
85C22⋊Q8×C43C2312yes—
86#121×C43—22no—
87#121×C43—21no—
88#121×C43—22no—
89#121×C43—22no—
90#121×C43—21no—
91#121×C43C2312yes—
92#120×C43—22no—
93#120×C43—22no—
94#120×C43—22no—
95C4×Q8×C43D412yescomplemented
96C4×D4×C43—22no—
97C4×D4×C43—22no—
98C4×D4×C43—22no—
99C4×D4×C43—22no—
100C4×D4×C43—22no—
101C4×D4×C43—22no—
102C4×D4×C43—22no—
103C4×D4×C43D412yescomplemented
104#117×C43—21no—
105#117×C43—22no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43D411yescharacteristic
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43C2311yescharacteristic
117C2×C22⋊C4×C43C2311yescharacteristic
118C2×C42×C43—21no—
119C2×C42×C43C2311yescharacteristic
120C4⋊C8×C43—22no—
121#103×C43—22no—
122#103×C43—22no—
123#102×C43—22no—
124#102×C43—22no—
125C22⋊C8×C43C2312yes—
126C22⋊C8×C43C2312yes—
127C4×C8×C43—22no—
128#95×C43—21no—
129#95×C43—21no—
130#95×C43—21no—
131#95×C43—21no—
132#95×C43C2311yescharacteristic
133#95×C43C2311yescharacteristic
134C24×C43—21no—
135C24×C43—21no—
136C24×C43C2×D411yescharacteristic
137C24×C43C2×D411yescharacteristic
138#41×C43—82no—
139C2×Q8×C43—21no—
140C2×Q8×C43—22no—
141C2×Q8×C43—81no—
142C2×Q8×C43C2×D412yes—
143C2×D4×C43—22no—
144C2×D4×C43—22no—
145C2×D4×C43—22no—
146C2×D4×C43—21no—
147C2×D4×C43—22no—
148C2×D4×C43—22no—
149C2×D4×C43—22no—
150C2×D4×C43—22no—
151C2×D4×C43—41no—
152C2×D4×C43—42no—
153C2×D4×C43—42no—
154C2×D4×C43—42no—
155C2×D4×C43—42no—
156C2×D4×C43—81no—
157C2×D4×C43—81no—
158C2×D4×C43—81no—
159C2×D4×C43—81no—
160C2×D4×C43—81no—
161C2×D4×C43C2×D412yes—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—22no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—22no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—81no—
175C22×C4×C43—81no—
176C22×C4×C43—82no—
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2411yescharacteristic
182Q16×C43—82no—
183SD16×C43—82no—
184SD16×C43—82no—
185D8×C43—82no—
186C2×C8×C43—22no—
187C2×C8×C43—22no—
188C4⋊C4×C43—22no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—22no—
192C4⋊C4×C43—22no—
193C4⋊C4×C43—22no—
194C4⋊C4×C43—22no—
195C4⋊C4×C43—22no—
196C4⋊C4×C43—22no—
197C4⋊C4×C43C2×D412yes—
198C4⋊C4×C43C2×D412yes—
199C22⋊C4×C43—22no—
200C22⋊C4×C43—22no—
201C22⋊C4×C43—22no—
202C22⋊C4×C43—22no—
203C22⋊C4×C43—22no—
204C22⋊C4×C43—22no—
205C22⋊C4×C43—22no—
206C22⋊C4×C43—22no—
207C22⋊C4×C43—22no—
208C22⋊C4×C43—22no—
209C22⋊C4×C43—22no—
210C22⋊C4×C43—22no—
211C22⋊C4×C43—41no—
212C22⋊C4×C43—42no—
213C22⋊C4×C43—41no—
214C22⋊C4×C43—81no—
215C22⋊C4×C43—81no—
216C22⋊C4×C43—81no—
217C22⋊C4×C43—81no—
218C42×C43—22no—
219C42×C43—22no—
220C42×C43C2×D412yes—
221C42×C43C2×D412yes—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—21no—
225C23×C43—22no—
226C23×C43—21no—
227C23×C43—21no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43—42no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43—81no—
241C23×C43—81no—
242C23×C43#13512yes—
243C23×C43C22×D411yescharacteristic
244Q8×C43—42no—
245Q8×C43—42no—
246Q8×C43—42no—
247Q8×C43—81no—
248D4×C43—44no—
249D4×C43—42no—
250D4×C43—42no—
251D4×C43—42no—
252D4×C43—44no—
253D4×C43—42no—
254D4×C43—42no—
255D4×C43—82no—
256D4×C43—81no—
257D4×C43—82no—
258D4×C43—84no—
259D4×C43—84no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—22no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—42no—
270C2×C4×C43—42no—
271C2×C4×C43—44no—
272C2×C4×C43—42no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—81no—
285C2×C4×C43—81no—
286C2×C4×C43—81no—
287C2×C4×C43—82no—
288C2×C4×C43—81no—
289C2×C4×C43#12011yescharacteristic
290C2×C4×C43#12012yes—
291C2×C4×C43#12011yescharacteristic
292C2×C4×C43C22×D412yes—
293C8×C43—42no—
294C8×C43—42no—
295#18306C4311yesmaximal, characteristic, direct product factor, Sylow
296C22×C43—21no—
297C22×C43—21no—
298C22×C43—22no—
299C22×C43—42no—
300C22×C43—42no—
301C22×C43—41no—
302C22×C43—41no—
303C22×C43—41no—
304C22×C43—42no—
305C22×C43—41no—
306C22×C43—42no—
307C22×C43—41no—
308C22×C43—42no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43—81no—
312C22×C43—81no—
313C22×C43—81no—
314C22×C43—81no—
315C22×C43—84no—
316C22×C43—81no—
317C22×C43—81no—
318C22×C43—81no—
319C22×C43C2×#12011yescharacteristic
320C22×C43C2×#13511yescharacteristic
321C22×C43#57511yescharacteristic
322C4×C43—22no—
323C4×C43—21no—
324C4×C43—21no—
325C4×C43—22no—
326C4×C43—42no—
327C4×C43—41no—
328C4×C43—41no—
329C4×C43—42no—
330C4×C43—42no—
331C4×C43—81no—
332C4×C43—81no—
333C4×C43—81no—
334#3459C2×C4311yescharacteristic, complemented
335#3211C2×C4312yescomplemented
336#2631C2×C4311yescharacteristic, complemented
337#1606C2×C4312yescomplemented
338#1602C2×C4311yescharacteristic, complemented
339#1601C2×C4311yescharacteristic, complemented
340#1600C2×C4312yescomplemented
341#1596C2×C4311yescharacteristic, complemented
342#1595C2×C4311yescharacteristic, complemented
343#1521C2×C4312yescomplemented
344#1460C2×C4311yescharacteristic, complemented
345C2×C43—21no—
346C2×C43—21no—
347C2×C43—42no—
348C2×C43—81no—
349C2×C43—82no—
350C2×C43—161no—
351C2×C43#300211yescharacteristic
352C2×C43#301911yescharacteristic
353C2×C43#302711yescharacteristic
354#543C22×C4311yescharacteristic
355#539—22no—
356#539—21no—
357#538—22no—
358#538C22×C4312yes—
359#534—21no—
360#534C22×C4311yescharacteristic
361#529—22no—
362#529C22×C4312yes—
363C2×#124C22×C4311yescharacteristic, complemented
364#525—21no—
365#525—22no—
366C2×C4×D4—21no—
367C2×C4×D4C22×C4311yescharacteristic
368#495—22no—
369#488—22no—
370#464—22no—
371#463—22no—
372#451C22×C4312yescomplemented
373#450C22×C4312yescomplemented
374#448C22×C4312yes—
375#447C22×C4312yes—
376#431C22×C4312yescomplemented
377#397—21no—
378#393C22×C4311yescharacteristic
379#393C22×C4311yescharacteristic, complemented
380#392—21no—
381#392C22×C4311yescharacteristic
382#392C22×C4311yescharacteristic, complemented
383#386—21no—
384#386—21no—
385#383C22×C4311yescharacteristic, complemented
386#328C22×C4312yescomplemented
387#328C22×C4312yescomplemented
388#327C22×C4312yes—
389#327C22×C4312yes—
390#323C22×C4311yescharacteristic
391#323C22×C4311yescharacteristic
392#323C22×C4312yescomplemented
393C43#1830611yescharacteristic, direct product factor, Sylow
394C2×#41—21no—
395C22×Q8C23×C4311yescharacteristic
396C22×D4—21no—
397C22×D4—21no—
398C22×D4—21no—
399C22×D4D4×C4311yescharacteristic
400C22×D4C23×C4311yescharacteristic
401C23×C4—21no—
402C23×C4D4×C4311yescharacteristic
403C23×C4D4×C4311yescharacteristic
404C2×Q16—22no—
405C2×SD16—22no—
406C2×SD16—22no—
407C2×D8—22no—
408#126—22no—
409#126—22no—
410#126—22no—
411#125—22no—
412#125D4×C4312yescomplemented
413#124—22no—
414#124—22no—
415#124—22no—
416#124D4×C4312yescomplemented
417#123—22no—
418#123—22no—
419#123—22no—
420#123—22no—
421#123—22no—
422#123—22no—
423C22⋊Q8—21no—
424C22⋊Q8—22no—
425C22⋊Q8—22no—
426C22⋊Q8—21no—
427C22⋊Q8—22no—
428C22⋊Q8C23×C4312yes—
429#121—22no—
430#121—21no—
431#121—22no—
432#121—22no—
433#121—21no—
434#121C23×C4312yes—
435#120—22no—
436#120—22no—
437#120—22no—
438C4×Q8D4×C4312yescomplemented
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—22no—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4D4×C4312yescomplemented
447#117—21no—
448#117—22no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4D4×C4311yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4C23×C4311yescharacteristic
460C2×C22⋊C4C23×C4311yescharacteristic
461C2×C42—21no—
462C2×C42C23×C4311yescharacteristic
463C4⋊C8—22no—
464#103—22no—
465#103—22no—
466#102—22no—
467#102—22no—
468C22⋊C8C23×C4312yes—
469C22⋊C8C23×C4312yes—
470C4×C8—22no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95C23×C4311yescharacteristic
476#95C23×C4311yescharacteristic
477C24—21no—
478C24—21no—
479C24C2×D4×C4311yescharacteristic
480C24C2×D4×C4311yescharacteristic
481#41—82no—
482C2×Q8—21no—
483C2×Q8—22no—
484C2×Q8—81no—
485C2×Q8C2×D4×C4312yes—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—21no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—41no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—81no—
500C2×D4—81no—
501C2×D4—81no—
502C2×D4—81no—
503C2×D4—81no—
504C2×D4C2×D4×C4312yes—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—81no—
518C22×C4—81no—
519C22×C4—82no—
520C22×C4C2×D4×C4311yescharacteristic
521C22×C4C2×D4×C4311yescharacteristic
522C22×C4C2×D4×C4311yescharacteristic
523C22×C4C2×D4×C4311yescharacteristic
524C22×C4C24×C4311yescharacteristic
525Q16—82no—
526SD16—82no—
527SD16—82no—
528D8—82no—
529C2×C8—22no—
530C2×C8—22no—
531C4⋊C4—22no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4C2×D4×C4312yes—
541C4⋊C4C2×D4×C4312yes—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—41no—
555C22⋊C4—42no—
556C22⋊C4—41no—
557C22⋊C4—81no—
558C22⋊C4—81no—
559C22⋊C4—81no—
560C22⋊C4—81no—
561C42—22no—
562C42—22no—
563C42C2×D4×C4312yes—
564C42C2×D4×C4312yes—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—22no—
569C23—21no—
570C23—21no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—42no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—81no—
584C23—81no—
585C23#135×C4312yes—
586C23C22×D4×C4311yescharacteristic
587Q8—42no—
588Q8—42no—
589Q8—42no—
590Q8—81no—
591D4—44no—
592D4—42no—
593D4—42no—
594D4—42no—
595D4—44no—
596D4—42no—
597D4—42no—
598D4—81no—
599D4—82no—
600D4—82no—
601D4—84no—
602D4—84no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—44no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—81no—
628C2×C4—81no—
629C2×C4—82no—
630C2×C4—81no—
631C2×C4—81no—
632C2×C4#120×C4311yescharacteristic
633C2×C4#120×C4312yes—
634C2×C4#120×C4311yescharacteristic
635C2×C4C22×D4×C4312yes—
636C8—42no—
637C8—42no—
638C22—21no—
639C22—21no—
640C22—22no—
641C22—42no—
642C22—42no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—42no—
647C22—41no—
648C22—42no—
649C22—42no—
650C22—41no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22—84no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22C2×#120×C4311yescharacteristic
662C22C2×#135×C4311yescharacteristic
663C22C43×#57511yescharacteristic
664C4—22no—
665C4—21no—
666C4—21no—
667C4—22no—
668C4—42no—
669C4—41no—
670C4—41no—
671C4—42no—
672C4—42no—
673C4—81no—
674C4—81no—
675C4—81no—
676C2—21no—
677C2—21no—
678C2—42no—
679C2—81no—
680C2—82no—
681C2—161no—
682C2C43×#300211yescharacteristic
683C2C43×#301911yescharacteristic
684C2C43×#302711yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C43×#3459C2semidirect
2. C43×#3211C2semidirect
3. C43×#2631C2semidirect
4. C43×#1606C2semidirect
5. C43×#1602C2semidirect
6. C43×#1601C2semidirect
7. C43×#1600C2semidirect
8. C43×#1596C2semidirect
9. C43×#1595C2semidirect
10. C43×#1521C2semidirect
11. C43×#1460C2semidirect
21. C2×#124×C43C22semidirect
30. C43×#451C22semidirect
31. C43×#450C22semidirect
34. C43×#431C22semidirect
37. C43×#393C22semidirect
40. C43×#392C22semidirect
43. C43×#383C22semidirect
44. C43×#328C22semidirect
45. C43×#328C22semidirect
50. C43×#323C22semidirect
69. #125×C43D4semidirect
73. #124×C43D4semidirect
95. C4×Q8×C43D4semidirect
103. C4×D4×C43D4semidirect
295. #18306C43direct (N × H)
334. #3459C2×C43semidirect
335. #3211C2×C43semidirect
336. #2631C2×C43semidirect
337. #1606C2×C43semidirect
338. #1602C2×C43semidirect
339. #1601C2×C43semidirect
340. #1600C2×C43semidirect
341. #1596C2×C43semidirect
342. #1595C2×C43semidirect
343. #1521C2×C43semidirect
344. #1460C2×C43semidirect
363. C2×#124C22×C43semidirect
372. #451C22×C43semidirect
373. #450C22×C43semidirect
376. #431C22×C43semidirect
379. #393C22×C43semidirect
382. #392C22×C43semidirect
385. #383C22×C43semidirect
386. #328C22×C43semidirect
387. #328C22×C43semidirect
392. #323C22×C43semidirect
393. C43#18306direct (N × H)
412. #125D4×C43semidirect
416. #124D4×C43semidirect
438. C4×Q8D4×C43semidirect
446. C4×D4D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#34592
C43×#32112
C43×#26312
C43×#16062
C43×#16022
C43×#16012
C43×#16002
C43×#15962
C43×#15952
C43×#15212
C43×#14602
#1830643