Finite Group Databasebeta

← C43×#18244 #24938261

Subgroups — C43×#18244 #24938261

Order 11008.

956 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3559C211yesmaximal, characteristic, complemented
2C43×#3114C211yesmaximal, characteristic, complemented
3C43×#3100C211yesmaximal, characteristic, complemented
4C43×#2633C211yesmaximal, characteristic, complemented
5C43×#1610C212yesmaximal, complemented
6C43×#1609C212yesmaximal, complemented
7C43×#1598C212yesmaximal, complemented
8C43×#1597C212yesmaximal, complemented
9C43×#1521C211yesmaximal, characteristic, complemented
10C43×#1514C211yesmaximal, characteristic, complemented
11C43×#1470C211yesmaximal, characteristic, complemented
12C43×#563—21no—
13C43×#562—21no—
14C43×#554—21no—
15C43×#553—21no—
16C43×#553—21no—
17C43×#547—22no—
18C43×#547—21no—
19C43×#544—21no—
20C43×#540—21no—
21C43×#539—22no—
22C43×#539C2212yes—
23C43×#537C2212yes—
24C43×#532C2211yescharacteristic
25C43×#529C2211yescharacteristic
26C2×#125×C43C2211yescharacteristic
27C2×C4×D4×C43C2211yescharacteristic
28C43×#483C2211yescharacteristic
29C43×#480C2212yes—
30C43×#480C2211yescharacteristic
31C43×#478—21no—
32C43×#474—21no—
33C43×#463—21no—
34C43×#459—21no—
35C43×#450C2211yescharacteristic
36C43×#447C2212yes—
37C43×#447C2211yescharacteristic
38C43×#442—21no—
39C43×#440—21no—
40C4×D8×C43—22no—
41C43×#432C2211yescharacteristic
42C43×#431C2211yescharacteristic
43C43×#399—21no—
44C43×#398C2212yes—
45C43×#397—21no—
46C43×#394C2212yes—
47C43×#385—22no—
48C43×#383C2211yescharacteristic
49C43×#328C2212yes—
50C43×#327C2212yes—
51C43×#327C2212yes—
52C43×#327C2212yes—
53C43×#324C2212yes—
54C43×#324C2212yes—
55C2×#41×C43—21no—
56C2×#41×C43—22no—
57C22×D4×C43C2311yescharacteristic
58C23×C4×C43—21no—
59C2×SD16×C43—21no—
60C2×D8×C43—22no—
61C2×D8×C43—21no—
62C4⋊Q8×C43—21no—
63C4⋊Q8×C43—22no—
64C4⋊Q8×C43D411yescharacteristic
65#127×C43D411yescharacteristic
66#126×C43—22no—
67#126×C43—22no—
68#126×C43—21no—
69#125×C43—21no—
70#125×C43—22no—
71#125×C43—21no—
72#125×C43—21no—
73#125×C43—21no—
74#125×C43—21no—
75#125×C43D411yescharacteristic
76#124×C43—21no—
77#124×C43D411yescharacteristic
78#123×C43—22no—
79#123×C43—22no—
80#123×C43—22no—
81#123×C43—22no—
82#123×C43—22no—
83#123×C43—21no—
84#123×C43—22no—
85C22⋊Q8×C43—22no—
86C22⋊Q8×C43—22no—
87C22⋊Q8×C43—22no—
88C22⋊Q8×C43—22no—
89C22⋊Q8×C43—22no—
90C22⋊Q8×C43—22no—
91C22⋊Q8×C43C2311yescharacteristic
92#121×C43—21no—
93#121×C43—22no—
94#121×C43—21no—
95#121×C43—22no—
96#121×C43—22no—
97#121×C43—21no—
98#121×C43—22no—
99#121×C43C2311yescharacteristic
100#121×C43C2312yes—
101C4×Q8×C43D411yescharacteristic
102C4×D4×C43—22no—
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43—21no—
106C4×D4×C43—22no—
107C4×D4×C43—21no—
108C4×D4×C43—21no—
109C4×D4×C43—21no—
110C4×D4×C43—21no—
111C4×D4×C43—21no—
112C4×D4×C43D411yescharacteristic
113C4×D4×C43D412yes—
114#117×C43—21no—
115#117×C43—21no—
116C2×C4⋊C4×C43—22no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43—22no—
119C2×C4⋊C4×C43D412yes—
120C2×C4⋊C4×C43D411yescharacteristic
121C2×C4⋊C4×C43D411yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2312yes—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—22no—
126C2×C22⋊C4×C43—22no—
127C2×C42×C43C2311yescharacteristic
128#107×C43—22no—
129#107×C43—21no—
130#106×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43—21no—
133#103×C43—21no—
134#102×C43—22no—
135#102×C43—21no—
136#102×C43—22no—
137#102×C43—21no—
138#102×C43—21no—
139C22⋊C8×C43C2311yescharacteristic
140C22⋊C8×C43C2311yescharacteristic
141C22⋊C8×C43C2312yes—
142#97×C43—21no—
143C4×C8×C43—21no—
144#95×C43—21no—
145#95×C43—21no—
146#95×C43—22no—
147#95×C43C2312yes—
148C24×C43—21no—
149#41×C43—82no—
150#41×C43—82no—
151#41×C43—82no—
152C2×Q8×C43—22no—
153C2×Q8×C43—21no—
154C2×Q8×C43C2×D411yescharacteristic
155C2×D4×C43—22no—
156C2×D4×C43—22no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—22no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—42no—
164C2×D4×C43C2×D411yescharacteristic
165C2×D4×C43C2×D412yes—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—21no—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—21no—
173C22×C4×C43—41no—
174C22×C4×C43—41no—
175C22×C4×C43—82no—
176C22×C4×C43C2×D412yes—
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D412yes—
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2411yescharacteristic
181SD16×C43—42no—
182D8×C43—44no—
183D8×C43—42no—
184C2×C8×C43—22no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C4⋊C4×C43—22no—
188C4⋊C4×C43—22no—
189C4⋊C4×C43—22no—
190C4⋊C4×C43—22no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—22no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—22no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—22no—
202C4⋊C4×C43—22no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—82no—
207C4⋊C4×C43C2×D411yescharacteristic
208C4⋊C4×C43C2×D412yes—
209C4⋊C4×C43C2×D411yescharacteristic
210C22⋊C4×C43—22no—
211C22⋊C4×C43—22no—
212C22⋊C4×C43—22no—
213C22⋊C4×C43—22no—
214C22⋊C4×C43—22no—
215C22⋊C4×C43—21no—
216C22⋊C4×C43—21no—
217C22⋊C4×C43—21no—
218C22⋊C4×C43—22no—
219C22⋊C4×C43—21no—
220C22⋊C4×C43—22no—
221C22⋊C4×C43—21no—
222C22⋊C4×C43—44no—
223C22⋊C4×C43—41no—
224C22⋊C4×C43—41no—
225C22⋊C4×C43—82no—
226C42×C43—22no—
227C42×C43—21no—
228C42×C43C2×D411yescharacteristic
229C42×C43C2×D411yescharacteristic
230C42×C43C2×D411yescharacteristic
231C42×C43C2×D411yescharacteristic
232C23×C43—22no—
233C23×C43—21no—
234C23×C43—22no—
235C23×C43—41no—
236C23×C43—42no—
237C23×C43—41no—
238C23×C43—42no—
239C23×C43C22×D411yescharacteristic
240Q8×C43—41no—
241Q8×C43—81no—
242Q8×C43—82no—
243D4×C43—22no—
244D4×C43—22no—
245D4×C43—42no—
246D4×C43—41no—
247D4×C43—42no—
248D4×C43—41no—
249D4×C43—41no—
250D4×C43—42no—
251D4×C43—42no—
252D4×C43—42no—
253D4×C43—81no—
254D4×C43—82no—
255D4×C43—82no—
256C2×C4×C43—22no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—21no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—42no—
268C2×C4×C43—42no—
269C2×C4×C43—42no—
270C2×C4×C43—42no—
271C2×C4×C43—41no—
272C2×C4×C43—42no—
273C2×C4×C43—42no—
274C2×C4×C43—82no—
275C2×C4×C43—82no—
276C2×C4×C43—82no—
277C2×C4×C43—82no—
278C2×C4×C43—82no—
279C2×C4×C43—82no—
280C2×C4×C43#12011yescharacteristic
281C2×C4×C43#12011yescharacteristic
282C2×C4×C43#12011yescharacteristic
283C2×C4×C43#12011yescharacteristic
284C2×C4×C43C22×D411yescharacteristic
285C2×C4×C43C22×D411yescharacteristic
286C8×C43—42no—
287C8×C43—41no—
288C8×C43—41no—
289#18244C4311yesmaximal, characteristic, direct product factor, Sylow
290C22×C43—21no—
291C22×C43—21no—
292C22×C43—44no—
293C22×C43—42no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—42no—
297C22×C43—42no—
298C22×C43—42no—
299C22×C43—41no—
300C22×C43—82no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43C2×#12011yescharacteristic
304C22×C43#57612yes—
305C4×C43—21no—
306C4×C43—21no—
307C4×C43—21no—
308C4×C43—21no—
309C4×C43—21no—
310C4×C43—21no—
311C4×C43—42no—
312C4×C43—42no—
313C4×C43—41no—
314C4×C43—41no—
315C4×C43—42no—
316C4×C43—41no—
317C4×C43—82no—
318C4×C43—81no—
319#3559C2×C4311yescharacteristic, complemented
320#3114C2×C4311yescharacteristic, complemented
321#3100C2×C4311yescharacteristic, complemented
322#2633C2×C4311yescharacteristic, complemented
323#1610C2×C4312yescomplemented
324#1609C2×C4312yescomplemented
325#1598C2×C4312yescomplemented
326#1597C2×C4312yescomplemented
327#1521C2×C4311yescharacteristic, complemented
328#1514C2×C4311yescharacteristic, complemented
329#1470C2×C4311yescharacteristic, complemented
330C2×C43—22no—
331C2×C43—81no—
332C2×C43—82no—
333C2×C43—82no—
334C2×C43#300811yescharacteristic
335C2×C43#302011yescharacteristic
336C2×C43#302511yescharacteristic
337#563—21no—
338#562—21no—
339#554—21no—
340#553—21no—
341#553—21no—
342#547—22no—
343#547—21no—
344#544—21no—
345#540—21no—
346#539—22no—
347#539C22×C4312yes—
348#537C22×C4312yes—
349#532C22×C4311yescharacteristic
350#529C22×C4311yescharacteristic
351C2×#125C22×C4311yescharacteristic
352C2×C4×D4C22×C4311yescharacteristic
353#483C22×C4311yescharacteristic
354#480C22×C4312yes—
355#480C22×C4311yescharacteristic
356#478—21no—
357#474—21no—
358#463—21no—
359#459—21no—
360#450C22×C4311yescharacteristic
361#447C22×C4312yes—
362#447C22×C4311yescharacteristic
363#442—21no—
364#440—21no—
365C4×D8—22no—
366#432C22×C4311yescharacteristic
367#431C22×C4311yescharacteristic
368#399—21no—
369#398C22×C4312yes—
370#397—21no—
371#394C22×C4312yes—
372#385—22no—
373#383C22×C4311yescharacteristic
374#328C22×C4312yes—
375#327C22×C4312yes—
376#327C22×C4312yes—
377#327C22×C4312yes—
378#324C22×C4312yes—
379#324C22×C4312yes—
380C43#1824411yescharacteristic, direct product factor, Sylow
381C2×#41—21no—
382C2×#41—22no—
383C22×D4C23×C4311yescharacteristic
384C23×C4—21no—
385C2×SD16—21no—
386C2×D8—22no—
387C2×D8—21no—
388C4⋊Q8—21no—
389C4⋊Q8—22no—
390C4⋊Q8D4×C4311yescharacteristic
391#127D4×C4311yescharacteristic
392#126—22no—
393#126—22no—
394#126—21no—
395#125—21no—
396#125—22no—
397#125—21no—
398#125—21no—
399#125—21no—
400#125—21no—
401#125D4×C4311yescharacteristic
402#124—21no—
403#124D4×C4311yescharacteristic
404#123—22no—
405#123—22no—
406#123—22no—
407#123—22no—
408#123—22no—
409#123—21no—
410#123—22no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—22no—
417C22⋊Q8C23×C4311yescharacteristic
418#121—21no—
419#121—22no—
420#121—21no—
421#121—22no—
422#121—22no—
423#121—21no—
424#121—22no—
425#121C23×C4311yescharacteristic
426#121C23×C4312yes—
427C4×Q8D4×C4311yescharacteristic
428C4×D4—22no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4—22no—
433C4×D4—21no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4D4×C4311yescharacteristic
439C4×D4D4×C4312yes—
440#117—21no—
441#117—21no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4D4×C4312yes—
446C2×C4⋊C4D4×C4311yescharacteristic
447C2×C4⋊C4D4×C4311yescharacteristic
448C2×C4⋊C4C23×C4311yescharacteristic
449C2×C4⋊C4C23×C4312yes—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C42C23×C4311yescharacteristic
454#107—22no—
455#107—21no—
456#106—21no—
457C4⋊C8—21no—
458C4⋊C8—21no—
459#103—21no—
460#102—22no—
461#102—21no—
462#102—22no—
463#102—21no—
464#102—21no—
465C22⋊C8C23×C4311yescharacteristic
466C22⋊C8C23×C4311yescharacteristic
467C22⋊C8C23×C4312yes—
468#97—21no—
469C4×C8—21no—
470#95—21no—
471#95—21no—
472#95—22no—
473#95C23×C4312yes—
474C24—21no—
475#41—82no—
476#41—82no—
477#41—82no—
478C2×Q8—22no—
479C2×Q8—21no—
480C2×Q8C2×D4×C4311yescharacteristic
481C2×D4—21no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—42no—
490C2×D4C2×D4×C4311yescharacteristic
491C2×D4C2×D4×C4312yes—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—82no—
502C22×C4C2×D4×C4312yes—
503C22×C4C2×D4×C4311yescharacteristic
504C22×C4C2×D4×C4312yes—
505C22×C4C2×D4×C4311yescharacteristic
506C22×C4C24×C4311yescharacteristic
507SD16—42no—
508D8—44no—
509D8—42no—
510C2×C8—22no—
511C2×C8—21no—
512C2×C8—21no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—22no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—82no—
533C4⋊C4C2×D4×C4311yescharacteristic
534C4⋊C4C2×D4×C4312yes—
535C4⋊C4C2×D4×C4311yescharacteristic
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—22no—
546C22⋊C4—21no—
547C22⋊C4—22no—
548C22⋊C4—44no—
549C22⋊C4—41no—
550C22⋊C4—41no—
551C22⋊C4—82no—
552C42—22no—
553C42—21no—
554C42C2×D4×C4311yescharacteristic
555C42C2×D4×C4311yescharacteristic
556C42C2×D4×C4311yescharacteristic
557C42C2×D4×C4311yescharacteristic
558C23—22no—
559C23—21no—
560C23—22no—
561C23—41no—
562C23—42no—
563C23—41no—
564C23—42no—
565C23C22×D4×C4311yescharacteristic
566Q8—41no—
567Q8—81no—
568Q8—82no—
569D4—22no—
570D4—22no—
571D4—42no—
572D4—41no—
573D4—41no—
574D4—41no—
575D4—42no—
576D4—42no—
577D4—42no—
578D4—42no—
579D4—81no—
580D4—82no—
581D4—82no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—82no—
601C2×C4—82no—
602C2×C4—82no—
603C2×C4—82no—
604C2×C4—82no—
605C2×C4—82no—
606C2×C4#120×C4311yescharacteristic
607C2×C4#120×C4311yescharacteristic
608C2×C4#120×C4311yescharacteristic
609C2×C4#120×C4311yescharacteristic
610C2×C4C22×D4×C4311yescharacteristic
611C2×C4C22×D4×C4311yescharacteristic
612C8—42no—
613C8—41no—
614C8—41no—
615C22—21no—
616C22—21no—
617C22—44no—
618C22—42no—
619C22—41no—
620C22—41no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—41no—
625C22—82no—
626C22—81no—
627C22—81no—
628C22C2×#120×C4311yescharacteristic
629C22C43×#57612yes—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—42no—
637C4—42no—
638C4—41no—
639C4—41no—
640C4—42no—
641C4—41no—
642C4—82no—
643C4—81no—
644C2—22no—
645C2—82no—
646C2—81no—
647C2—82no—
648C2C43×#300811yescharacteristic
649C2C43×#302011yescharacteristic
650C2C43×#302511yescharacteristic
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×#3559C2semidirect
2. C43×#3114C2semidirect
3. C43×#3100C2semidirect
4. C43×#2633C2semidirect
5. C43×#1610C2semidirect
6. C43×#1609C2semidirect
7. C43×#1598C2semidirect
8. C43×#1597C2semidirect
9. C43×#1521C2semidirect
10. C43×#1514C2semidirect
11. C43×#1470C2semidirect
289. #18244C43direct (N × H)
319. #3559C2×C43semidirect
320. #3114C2×C43semidirect
321. #3100C2×C43semidirect
322. #2633C2×C43semidirect
323. #1610C2×C43semidirect
324. #1609C2×C43semidirect
325. #1598C2×C43semidirect
326. #1597C2×C43semidirect
327. #1521C2×C43semidirect
328. #1514C2×C43semidirect
329. #1470C2×C43semidirect
380. C43#18244direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35592
C43×#31142
C43×#31002
C43×#26332
C43×#16102
C43×#16092
C43×#15982
C43×#15972
C43×#15212
C43×#15142
C43×#14702
#1824443