Finite Group Databasebeta

← C43×#26405 #24946422

Subgroups — C43×#26405 #24946422

Order 11008.

732 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3084C211yesmaximal, characteristic, complemented
2C43×#3081C211yesmaximal, characteristic, complemented
3C43×#2946C211yesmaximal, characteristic
4C43×#2913C211yesmaximal, characteristic, complemented
5C43×#2092C211yesmaximal, characteristic, complemented
6C43×#2089C211yesmaximal, characteristic, complemented
7C43×#2063C211yesmaximal, characteristic, complemented
8C43×#2061C211yesmaximal, characteristic, complemented
9C43×#1951C211yesmaximal, characteristic, complemented
10C43×#1922C211yesmaximal, characteristic, complemented
11C43×#1907C211yesmaximal, characteristic
12C43×#1883C211yesmaximal, characteristic
13C43×#1866C211yesmaximal, characteristic, complemented
14C43×#1860C211yesmaximal, characteristic, complemented
15C43×#1856C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
17C2×#131×C43C2211yescharacteristic
18C43×#544C2211yescharacteristic
19C43×#520C2211yescharacteristic
20C43×#520C2211yescharacteristic
21C43×#518C2211yescharacteristic
22C43×#479—21no—
23C43×#478—21no—
24C43×#478—21no—
25C43×#478—21no—
26C43×#476—21no—
27C43×#476—21no—
28C43×#475—21no—
29C43×#474—21no—
30C43×#442—21no—
31C43×#440—21no—
32C4×SD16×C43—21no—
33C4×D8×C43—21no—
34C2×#108×C43C2211yescharacteristic
35C43×#428—21no—
36C43×#428—21no—
37C43×#428C2211yescharacteristic
38C43×#428C2211yescharacteristic
39C43×#428C2211yescharacteristic
40C43×#428C2211yescharacteristic
41C43×#428C2211yescharacteristic
42C43×#427—21no—
43C43×#427C2211yescharacteristic
44C2×#107×C43—21no—
45C2×#107×C43C2211yescharacteristic
46C2×#106×C43C2211yescharacteristic
47C43×#424C2211yescharacteristic
48C43×#424C2211yescharacteristic
49C2×#104×C43C2211yescharacteristic
50C43×#418C2211yescharacteristic
51C43×#417C2211yescharacteristic
52C43×#416C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#100×C43C2211yescharacteristic
56C43×#405C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#382C2211yescharacteristic
59C43×#343C2211yescharacteristic
60C43×#343C2211yescharacteristic
61C43×#343C2211yescharacteristic
62C43×#341C2211yescharacteristic
63C43×#339C2211yescharacteristic
64C43×#339C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#336C2211yescharacteristic
67C2×#41×C43C2311yescharacteristic
68C22×D4×C43C2311yescharacteristic
69AGL(1,ℤ/8)×C43—22no—
70AGL(1,ℤ/8)×C43Q814yescomplemented
71C2×SD16×C43—21no—
72C2×D8×C43—21no—
73#131×C43—22no—
74#131×C43—22no—
75C2×M16×C43—21no—
76C2×M16×C43C2311yescharacteristic
77C2×M16×C43C2311yescharacteristic
78C2×M16×C43C2311yescharacteristic
79C2×M16×C43C2311yescharacteristic
80C22×C8×C43—21no—
81C22×C8×C43C2311yescharacteristic
82C22×C8×C43C2311yescharacteristic
83C4⋊Q8×C43—21no—
84C4⋊Q8×C43—21no—
85#125×C43—21no—
86#125×C43—21no—
87C22⋊Q8×C43—41no—
88C4×Q8×C43—21no—
89C4×Q8×C43—21no—
90C4×D4×C43—21no—
91C4×D4×C43—21no—
92C4×D4×C43—21no—
93C4×D4×C43—21no—
94C4×D4×C43—21no—
95C4×D4×C43—21no—
96C4×D4×C43—41no—
97C4×D4×C43—41no—
98#117×C43—21no—
99#117×C43—21no—
100#117×C43C2311yescharacteristic
101#117×C43C2311yescharacteristic
102#117×C43C2311yescharacteristic
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C22⋊C4×C43—41no—
109C2×C22⋊C4×C43—41no—
110C2×C42×C43C2311yescharacteristic
111#108×C43—22no—
112#107×C43—21no—
113#107×C43—21no—
114#107×C43—21no—
115#107×C43—21no—
116#107×C43—21no—
117#107×C43—21no—
118#107×C43—21no—
119#107×C43D411yescharacteristic
120#107×C43D411yescharacteristic
121#106×C43—21no—
122#106×C43—21no—
123#106×C43—21no—
124#106×C43—21no—
125#106×C43—21no—
126#106×C43—21no—
127#106×C43—21no—
128#106×C43D411yescharacteristic
129#106×C43D411yescharacteristic
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43—21no—
133C4⋊C8×C43—21no—
134#104×C43—22no—
135#103×C43—21no—
136#103×C43D411yescharacteristic
137#103×C43D411yescharacteristic
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143#102×C43—21no—
144#102×C43—21no—
145#102×C43D411yescharacteristic
146#102×C43D411yescharacteristic
147#100×C43—22no—
148#97×C43—21no—
149C4×C8×C43—21no—
150#95×C43—41no—
151C24×C43—21no—
152#41×C43—21no—
153#41×C43—21no—
154#41×C43C2×Q812yes—
155#41×C43#4112yes—
156C2×Q8×C43—41no—
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×C43C2×D411yescharacteristic
165C2×D4×C43C2×Q812yes—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—41no—
172C22×C4×C43—41no—
173C22×C4×C43—41no—
174C22×C4×C43—41no—
175C22×C4×C43C2411yescharacteristic
176SD16×C43—24no—
177D8×C43—24no—
178M16×C43—24no—
179M16×C43—21no—
180M16×C43—21no—
181M16×C43—21no—
182M16×C43—21no—
183M16×C43—21no—
184M16×C43—21no—
185M16×C43C2×Q812yes—
186M16×C43#4112yes—
187C2×C8×C43—24no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43C2×D411yescharacteristic
197C2×C8×C43C2×D411yescharacteristic
198C2×C8×C43C2×D411yescharacteristic
199C2×C8×C43C2×D411yescharacteristic
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—41no—
207C4⋊C4×C43—41no—
208C4⋊C4×C43—41no—
209C4⋊C4×C43—41no—
210C4⋊C4×C43—41no—
211C4⋊C4×C43C2×D411yescharacteristic
212C4⋊C4×C43C2×D411yescharacteristic
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—21no—
220C22⋊C4×C43—41no—
221C22⋊C4×C43—41no—
222C22⋊C4×C43—41no—
223C22⋊C4×C43—41no—
224C22⋊C4×C43—82no—
225C42×C43—21no—
226C42×C43—21no—
227C42×C43—21no—
228C42×C43—21no—
229C42×C43—21no—
230C42×C43—41no—
231C42×C43—41no—
232C23×C43—21no—
233C23×C43—22no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—81no—
237C23×C43—81no—
238C23×C43H(5,𝔽2)11yescharacteristic
239Q8×C43—21no—
240Q8×C43—161no—
241Q8×C43C22⋊Q812yes—
242D4×C43—22no—
243D4×C43—22no—
244D4×C43—22no—
245D4×C43—21no—
246D4×C43—22no—
247D4×C43—41no—
248D4×C43—41no—
249D4×C43C22⋊Q812yes—
250C2×C4×C43—21no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—81no—
266C2×C4×C43—81no—
267C2×C4×C43—81no—
268C2×C4×C43—161no—
269C2×C4×C43—161no—
270C2×C4×C43—161no—
271C2×C4×C43—161no—
272C2×C4×C43C22×D411yescharacteristic
273C2×C4×C43C22×D411yescharacteristic
274C2×C4×C43C22×Q811yescharacteristic
275C2×C4×C43C2×#4111yescharacteristic
276C2×C4×C43C2×#4111yescharacteristic
277C2×C4×C432−1+411yescharacteristic
278C8×C43—22no—
279C8×C43—21no—
280C8×C43—22no—
281C8×C43—21no—
282C8×C43—21no—
283C8×C43—21no—
284C8×C43—41no—
285C8×C43—41no—
286#26405C4311yesmaximal, characteristic, direct product factor, Sylow
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—22no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—42no—
293C22×C43—82no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—161no—
297C22×C43#53911yescharacteristic
298C22×C43D4211yescharacteristic
299C22×C43#55411yescharacteristic
300C4×C43—22no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—41no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43—81no—
310C4×C43—81no—
311C4×C43C2×C22⋊Q811yescharacteristic
312C4×C43#52511yescharacteristic
313C4×C43#54711yescharacteristic
314C4×C43D4×Q811yescharacteristic
315#3084C2×C4311yescharacteristic, complemented
316#3081C2×C4311yescharacteristic, complemented
317#2946C2×C4311yescharacteristic
318#2913C2×C4311yescharacteristic, complemented
319#2092C2×C4311yescharacteristic, complemented
320#2089C2×C4311yescharacteristic, complemented
321#2063C2×C4311yescharacteristic, complemented
322#2061C2×C4311yescharacteristic, complemented
323#1951C2×C4311yescharacteristic, complemented
324#1922C2×C4311yescharacteristic, complemented
325#1907C2×C4311yescharacteristic
326#1883C2×C4311yescharacteristic
327#1866C2×C4311yescharacteristic, complemented
328#1860C2×C4311yescharacteristic, complemented
329#1856C2×C4311yescharacteristic, complemented
330C2×C43—21no—
331C2×C43—21no—
332C2×C43—42no—
333C2×C43—82no—
334C2×C43#244911yescharacteristic
335C2×C43#328811yescharacteristic
336C2×C43#329011yescharacteristic
337C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
338C2×#131C22×C4311yescharacteristic
339#544C22×C4311yescharacteristic
340#520C22×C4311yescharacteristic
341#520C22×C4311yescharacteristic
342#518C22×C4311yescharacteristic
343#479—21no—
344#478—21no—
345#478—21no—
346#478—21no—
347#476—21no—
348#476—21no—
349#475—21no—
350#474—21no—
351#442—21no—
352#440—21no—
353C4×SD16—21no—
354C4×D8—21no—
355C2×#108C22×C4311yescharacteristic
356#428—21no—
357#428—21no—
358#428C22×C4311yescharacteristic
359#428C22×C4311yescharacteristic
360#428C22×C4311yescharacteristic
361#428C22×C4311yescharacteristic
362#428C22×C4311yescharacteristic
363#427—21no—
364#427C22×C4311yescharacteristic
365C2×#107—21no—
366C2×#107C22×C4311yescharacteristic
367C2×#106C22×C4311yescharacteristic
368#424C22×C4311yescharacteristic
369#424C22×C4311yescharacteristic
370C2×#104C22×C4311yescharacteristic
371#418C22×C4311yescharacteristic
372#417C22×C4311yescharacteristic
373#416C22×C4311yescharacteristic
374C2×#102C22×C4311yescharacteristic
375C2×#102C22×C4311yescharacteristic
376C2×#100C22×C4311yescharacteristic
377#405C22×C4311yescharacteristic
378#390C22×C4311yescharacteristic
379#382C22×C4311yescharacteristic
380#343C22×C4311yescharacteristic
381#343C22×C4311yescharacteristic
382#343C22×C4311yescharacteristic
383#341C22×C4311yescharacteristic
384#339C22×C4311yescharacteristic
385#339C22×C4311yescharacteristic
386#339C22×C4311yescharacteristic
387#336C22×C4311yescharacteristic
388C43#2640511yescharacteristic, direct product factor, Sylow
389C2×#41C23×C4311yescharacteristic
390C22×D4C23×C4311yescharacteristic
391AGL(1,ℤ/8)—22no—
392AGL(1,ℤ/8)Q8×C4314yescomplemented
393C2×SD16—21no—
394C2×D8—21no—
395#131—22no—
396#131—22no—
397C2×M16—21no—
398C2×M16C23×C4311yescharacteristic
399C2×M16C23×C4311yescharacteristic
400C2×M16C23×C4311yescharacteristic
401C2×M16C23×C4311yescharacteristic
402C22×C8—21no—
403C22×C8C23×C4311yescharacteristic
404C22×C8C23×C4311yescharacteristic
405C4⋊Q8—21no—
406C4⋊Q8—21no—
407#125—21no—
408#125—21no—
409C22⋊Q8—41no—
410C4×Q8—21no—
411C4×Q8—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4—21no—
418C4×D4—41no—
419C4×D4—41no—
420#117—21no—
421#117—21no—
422#117C23×C4311yescharacteristic
423#117C23×C4311yescharacteristic
424#117C23×C4311yescharacteristic
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4C23×C4311yescharacteristic
428C2×C4⋊C4C23×C4311yescharacteristic
429C2×C4⋊C4C23×C4311yescharacteristic
430C2×C22⋊C4—41no—
431C2×C22⋊C4—41no—
432C2×C42C23×C4311yescharacteristic
433#108—22no—
434#107—21no—
435#107—21no—
436#107—21no—
437#107—21no—
438#107—21no—
439#107—21no—
440#107—21no—
441#107D4×C4311yescharacteristic
442#107D4×C4311yescharacteristic
443#106—21no—
444#106—21no—
445#106—21no—
446#106—21no—
447#106—21no—
448#106—21no—
449#106—21no—
450#106D4×C4311yescharacteristic
451#106D4×C4311yescharacteristic
452C4⋊C8—21no—
453C4⋊C8—21no—
454C4⋊C8—21no—
455C4⋊C8—21no—
456#104—22no—
457#103—21no—
458#103D4×C4311yescharacteristic
459#103D4×C4311yescharacteristic
460#102—21no—
461#102—21no—
462#102—21no—
463#102—21no—
464#102—21no—
465#102—21no—
466#102—21no—
467#102D4×C4311yescharacteristic
468#102D4×C4311yescharacteristic
469#100—22no—
470#97—21no—
471C4×C8—21no—
472#95—41no—
473C24—21no—
474#41—21no—
475#41—21no—
476#41C2×Q8×C4312yes—
477#41#41×C4312yes—
478C2×Q8—41no—
479C2×Q8C2×D4×C4311yescharacteristic
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4C2×D4×C4311yescharacteristic
487C2×D4C2×Q8×C4312yes—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4C24×C4311yescharacteristic
498SD16—24no—
499D8—24no—
500M16—24no—
501M16—21no—
502M16—21no—
503M16—21no—
504M16—21no—
505M16—21no—
506M16—21no—
507M16C2×Q8×C4312yes—
508M16#41×C4312yes—
509C2×C8—24no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8C2×D4×C4311yescharacteristic
519C2×C8C2×D4×C4311yescharacteristic
520C2×C8C2×D4×C4311yescharacteristic
521C2×C8C2×D4×C4311yescharacteristic
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4C2×D4×C4311yescharacteristic
534C4⋊C4C2×D4×C4311yescharacteristic
535C4⋊C4C2×D4×C4311yescharacteristic
536C4⋊C4C2×D4×C4311yescharacteristic
537C4⋊C4C2×D4×C4311yescharacteristic
538C4⋊C4C2×D4×C4311yescharacteristic
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—41no—
543C22⋊C4—41no—
544C22⋊C4—41no—
545C22⋊C4—41no—
546C22⋊C4—82no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—41no—
553C42—41no—
554C23—21no—
555C23—22no—
556C23—41no—
557C23—41no—
558C23—81no—
559C23—81no—
560C23H(5,𝔽2)×C4311yescharacteristic
561Q8—21no—
562Q8—161no—
563Q8C22⋊Q8×C4312yes—
564D4—22no—
565D4—22no—
566D4—22no—
567D4—21no—
568D4—22no—
569D4—41no—
570D4—41no—
571D4C22⋊Q8×C4312yes—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—81no—
588C2×C4—81no—
589C2×C4—81no—
590C2×C4—161no—
591C2×C4—161no—
592C2×C4—161no—
593C2×C4—161no—
594C2×C4C22×D4×C4311yescharacteristic
595C2×C4C22×D4×C4311yescharacteristic
596C2×C4C22×Q8×C4311yescharacteristic
597C2×C4C2×#41×C4311yescharacteristic
598C2×C4C2×#41×C4311yescharacteristic
599C2×C42−1+4×C4311yescharacteristic
600C8—22no—
601C8—21no—
602C8—22no—
603C8—21no—
604C8—21no—
605C8—21no—
606C8—41no—
607C8—41no—
608C22—21no—
609C22—21no—
610C22—22no—
611C22—41no—
612C22—41no—
613C22—42no—
614C22—82no—
615C22—81no—
616C22—81no—
617C22—161no—
618C22C43×#53911yescharacteristic
619C22D42×C4311yescharacteristic
620C22C43×#55411yescharacteristic
621C4—22no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—81no—
629C4—81no—
630C4—81no—
631C4—81no—
632C4C2×C22⋊Q8×C4311yescharacteristic
633C4C43×#52511yescharacteristic
634C4C43×#54711yescharacteristic
635C4D4×Q8×C4311yescharacteristic
636C2—21no—
637C2—21no—
638C2—42no—
639C2—82no—
640C2C43×#244911yescharacteristic
641C2C43×#328811yescharacteristic
642C2C43×#329011yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×AGL(1,ℤ/8)×C43C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C22×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3084C2semidirect
2. C43×#3081C2semidirect
4. C43×#2913C2semidirect
5. C43×#2092C2semidirect
6. C43×#2089C2semidirect
7. C43×#2063C2semidirect
8. C43×#2061C2semidirect
9. C43×#1951C2semidirect
10. C43×#1922C2semidirect
13. C43×#1866C2semidirect
14. C43×#1860C2semidirect
15. C43×#1856C2semidirect
70. AGL(1,ℤ/8)×C43Q8semidirect
286. #26405C43direct (N × H)
315. #3084C2×C43semidirect
316. #3081C2×C43semidirect
318. #2913C2×C43semidirect
319. #2092C2×C43semidirect
320. #2089C2×C43semidirect
321. #2063C2×C43semidirect
322. #2061C2×C43semidirect
323. #1951C2×C43semidirect
324. #1922C2×C43semidirect
327. #1866C2×C43semidirect
328. #1860C2×C43semidirect
329. #1856C2×C43semidirect
388. C43#26405direct (N × H)
392. AGL(1,ℤ/8)Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#30842
C43×#30812
C43×#29462
C43×#29132
C43×#20922
C43×#20892
C43×#20632
C43×#20612
C43×#19512
C43×#19222
C43×#19072
C43×#18832
C43×#18662
C43×#18602
C43×#18562
#2640543