Finite Group Databasebeta

← C43×#24808 #24944825

Subgroups — C43×#24808 #24944825

Order 11008.

820 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3069C211yesmaximal, characteristic, complemented
2C43×#3068C211yesmaximal, characteristic
3C2×C43×#471C211yesmaximal, characteristic, complemented
4C2×C43×#471C211yesmaximal, characteristic, complemented
5C43×#2955C211yesmaximal, characteristic, complemented
6C43×#2916C211yesmaximal, characteristic, complemented
7C43×#2070C211yesmaximal, characteristic, complemented
8C43×#2069C211yesmaximal, characteristic, complemented
9C43×#2049C211yesmaximal, characteristic, complemented
10C43×#2048C211yesmaximal, characteristic, complemented
11C43×#1977C211yesmaximal, characteristic, complemented
12C43×#1953C211yesmaximal, characteristic, complemented
13C43×#1903C211yesmaximal, characteristic, complemented
14C43×#1902C211yesmaximal, characteristic, complemented
15C43×#1813C211yesmaximal, characteristic, complemented
16C43×#575C2211yescharacteristic
17C2×#137×C43C2211yescharacteristic
18C2×#137×C43C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
21C22×SD16×C43C2211yescharacteristic
22C43×#568C2211yescharacteristic
23C43×#568C2211yescharacteristic
24C2×#131×C43C2211yescharacteristic
25C2×#131×C43C2211yescharacteristic
26C43×#473—22no—
27C43×#472—22no—
28C43×#471—22no—
29C43×#471—22no—
30C43×#471—22no—
31C43×#471—22no—
32C43×#471—22no—
33C43×#471—22no—
34C43×#444—22no—
35C43×#443—22no—
36C43×#430—22no—
37C43×#430C2211yescharacteristic
38C43×#430C2211yescharacteristic
39C43×#430C2211yescharacteristic
40C43×#430C2211yescharacteristic
41C43×#430C2211yescharacteristic
42C2×#108×C43—22no—
43C2×#108×C43C2211yescharacteristic
44C2×#108×C43C2211yescharacteristic
45C2×#108×C43C2211yescharacteristic
46C43×#421C2211yescharacteristic
47C43×#421C2211yescharacteristic
48C43×#419C2211yescharacteristic
49C43×#418C2211yescharacteristic
50C43×#413C2211yescharacteristic
51C43×#413C2211yescharacteristic
52C2×#101×C43C2211yescharacteristic
53C2×#101×C43C2211yescharacteristic
54C2×#101×C43C2211yescharacteristic
55C2×#100×C43C2211yescharacteristic
56C2×#100×C43C2211yescharacteristic
57C2×#100×C43C2211yescharacteristic
58C43×#405C2211yescharacteristic
59C43×#344C2211yescharacteristic
60C43×#344C2211yescharacteristic
61C43×#338C2211yescharacteristic
62C43×#338C2211yescharacteristic
63C2×#41×C43C2311yescharacteristic
64C2×#41×C43C2311yescharacteristic
65C22×Q8×C43C2311yescharacteristic
66C22×D4×C43C2311yescharacteristic
67#137×C43—21no—
68#137×C43—22no—
69#137×C43—22no—
70#137×C43—22no—
71#137×C43—41no—
72#137×C43D412yes—
73AGL(1,ℤ/8)×C43—21no—
74AGL(1,ℤ/8)×C43—22no—
75AGL(1,ℤ/8)×C43—22no—
76AGL(1,ℤ/8)×C43—22no—
77AGL(1,ℤ/8)×C43—41no—
78AGL(1,ℤ/8)×C43D412yes—
79#135×C43—22no—
80C2×Q16×C43—21no—
81C2×Q16×C43—21no—
82C2×SD16×C43—21no—
83C2×SD16×C43—21no—
84C2×SD16×C43—21no—
85C2×SD16×C43—21no—
86C2×SD16×C43—21no—
87C2×SD16×C43—21no—
88C2×SD16×C43—21no—
89C2×SD16×C43—21no—
90C2×SD16×C43—21no—
91C2×SD16×C43—21no—
92C2×D8×C43—21no—
93C2×D8×C43—21no—
94#131×C43—21no—
95#131×C43—21no—
96#131×C43—22no—
97#131×C43—22no—
98#131×C43—21no—
99#131×C43—21no—
100#131×C43—21no—
101#131×C43—21no—
102#131×C43—41no—
103#131×C43—41no—
104#131×C43D412yes—
105#131×C43D412yes—
106C2×M16×C43—21no—
107C2×M16×C43—21no—
108C2×M16×C43—22no—
109C2×M16×C43—22no—
110C2×M16×C43C2311yescharacteristic
111C2×M16×C43C2311yescharacteristic
112C2×M16×C43C2311yescharacteristic
113C2×M16×C43C2311yescharacteristic
114C2×M16×C43C2311yescharacteristic
115C2×M16×C43C2311yescharacteristic
116C2×M16×C43C2311yescharacteristic
117C2×M16×C43C2311yescharacteristic
118C2×M16×C43C2311yescharacteristic
119C22×C8×C43—21no—
120C22×C8×C43—21no—
121C22×C8×C43C2311yescharacteristic
122#117×C43C2311yescharacteristic
123#108×C43—22no—
124#108×C43—22no—
125#108×C43—22no—
126#108×C43—22no—
127#108×C43—22no—
128#108×C43—21no—
129#108×C43—21no—
130#108×C43—21no—
131#108×C43—21no—
132#108×C43D412yes—
133#108×C43D412yes—
134#104×C43—22no—
135#104×C43—22no—
136#103×C43—41no—
137#102×C43—41no—
138#101×C43—21no—
139#101×C43—21no—
140#101×C43—22no—
141#101×C43—22no—
142#101×C43—22no—
143#100×C43—21no—
144#100×C43—21no—
145#100×C43—22no—
146#100×C43—22no—
147#100×C43—22no—
148#97×C43—21no—
149C4×C8×C43—21no—
150C24×C43—21no—
151#41×C43—21no—
152#41×C43—21no—
153#41×C43—21no—
154#41×C43—21no—
155#41×C43—21no—
156#41×C43—21no—
157#41×C43C2×D412yes—
158#41×C43C2×D412yes—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43C2×D411yescharacteristic
166C2×Q8×C43#4111yescharacteristic
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43C2×D411yescharacteristic
176C2×D4×C43#4111yescharacteristic
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43C2411yescharacteristic
181Q16×C43—22no—
182Q16×C43—42no—
183Q16×C43—42no—
184SD16×C43—22no—
185SD16×C43—22no—
186SD16×C43—42no—
187SD16×C43—42no—
188SD16×C43—42no—
189SD16×C43—42no—
190SD16×C43—41no—
191SD16×C43—41no—
192SD16×C43—41no—
193SD16×C43—41no—
194D8×C43—22no—
195D8×C43—42no—
196D8×C43—42no—
197M16×C43—21no—
198M16×C43—21no—
199M16×C43—21no—
200M16×C43—21no—
201M16×C43—22no—
202M16×C43—22no—
203M16×C43—21no—
204M16×C43—21no—
205M16×C43—21no—
206M16×C43—21no—
207M16×C43—21no—
208M16×C43—21no—
209M16×C43—21no—
210M16×C43—21no—
211M16×C43—21no—
212M16×C43—21no—
213M16×C43—42no—
214M16×C43—42no—
215M16×C43—41no—
216M16×C43—41no—
217M16×C43C2×D412yes—
218M16×C43C2×D412yes—
219M16×C43C2×D412yes—
220M16×C43C2×D412yes—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—22no—
226C2×C8×C43—22no—
227C2×C8×C43—21no—
228C2×C8×C43—21no—
229C2×C8×C43—21no—
230C2×C8×C43—21no—
231C2×C8×C43—21no—
232C2×C8×C43—42no—
233C2×C8×C43—42no—
234C2×C8×C43—41no—
235C2×C8×C43—41no—
236C2×C8×C43C2×D411yescharacteristic
237C2×C8×C43C2×D411yescharacteristic
238C2×C8×C43C2×D411yescharacteristic
239C2×C8×C43C2×D411yescharacteristic
240C2×C8×C43#4111yescharacteristic
241C2×C8×C43#4111yescharacteristic
242C4⋊C4×C43—21no—
243C22⋊C4×C43—21no—
244C42×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—161no—
251C23×C432−1+411yescharacteristic
252Q8×C43—21no—
253Q8×C43—21no—
254Q8×C43—21no—
255Q8×C43—41no—
256Q8×C43—41no—
257Q8×C43—41no—
258Q8×C43—41no—
259Q8×C43#12112yes—
260D4×C43—22no—
261D4×C43—22no—
262D4×C43—21no—
263D4×C43—21no—
264D4×C43—21no—
265D4×C43—41no—
266D4×C43—41no—
267D4×C43—41no—
268D4×C43—41no—
269D4×C43—41no—
270D4×C43—41no—
271D4×C43#12112yes—
272C2×C4×C43—21no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—21no—
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×C43C22×D411yescharacteristic
283C2×C4×C43C22×D411yescharacteristic
284C2×C4×C43C22×D411yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×C4×C43H(5,𝔽2)11yescharacteristic
288C8×C43—22no—
289C8×C43—22no—
290C8×C43—22no—
291C8×C43—22no—
292C8×C43—41no—
293C8×C43—41no—
294C8×C43—41no—
295C8×C43—41no—
296C8×C43—41no—
297C8×C43#12111yescharacteristic
298C8×C43#12111yescharacteristic
299C8×C43#12111yescharacteristic
300C8×C43#12111yescharacteristic
301#24808C4311yesmaximal, characteristic, direct product factor, Sylow
302C22×C43—22no—
303C22×C43—41no—
304C22×C43—41no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43—161no—
309C22×C43—161no—
310C22×C43—161no—
311C22×C43#53711yescharacteristic
312C22×C43#54711yescharacteristic
313C22×C43#54811yescharacteristic
314C4×C43—22no—
315C4×C43—41no—
316C4×C43—81no—
317C4×C43—81no—
318C4×C43C2×#12111yescharacteristic
319C4×C43C2×#12111yescharacteristic
320C4×C43D4211yescharacteristic
321C4×C43#55311yescharacteristic
322#3069C2×C4311yescharacteristic, complemented
323#3068C2×C4311yescharacteristic
324C2×#471C2×C4311yescharacteristic, complemented
325C2×#471C2×C4311yescharacteristic, complemented
326#2955C2×C4311yescharacteristic, complemented
327#2916C2×C4311yescharacteristic, complemented
328#2070C2×C4311yescharacteristic, complemented
329#2069C2×C4311yescharacteristic, complemented
330#2049C2×C4311yescharacteristic, complemented
331#2048C2×C4311yescharacteristic, complemented
332#1977C2×C4311yescharacteristic, complemented
333#1953C2×C4311yescharacteristic, complemented
334#1903C2×C4311yescharacteristic, complemented
335#1902C2×C4311yescharacteristic, complemented
336#1813C2×C4311yescharacteristic, complemented
337C2×C43—21no—
338C2×C43—21no—
339C2×C43—21no—
340C2×C43—42no—
341C2×C43—81no—
342C2×C43—161no—
343C2×C43#241611yescharacteristic
344#575C22×C4311yescharacteristic
345C2×#137C22×C4311yescharacteristic
346C2×#137C22×C4311yescharacteristic
347C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
348C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
349C22×SD16C22×C4311yescharacteristic
350#568C22×C4311yescharacteristic
351#568C22×C4311yescharacteristic
352C2×#131C22×C4311yescharacteristic
353C2×#131C22×C4311yescharacteristic
354#473—22no—
355#472—22no—
356#471—22no—
357#471—22no—
358#471—22no—
359#471—22no—
360#471—22no—
361#471—22no—
362#444—22no—
363#443—22no—
364#430—22no—
365#430C22×C4311yescharacteristic
366#430C22×C4311yescharacteristic
367#430C22×C4311yescharacteristic
368#430C22×C4311yescharacteristic
369#430C22×C4311yescharacteristic
370C2×#108—22no—
371C2×#108C22×C4311yescharacteristic
372C2×#108C22×C4311yescharacteristic
373C2×#108C22×C4311yescharacteristic
374#421C22×C4311yescharacteristic
375#421C22×C4311yescharacteristic
376#419C22×C4311yescharacteristic
377#418C22×C4311yescharacteristic
378#413C22×C4311yescharacteristic
379#413C22×C4311yescharacteristic
380C2×#101C22×C4311yescharacteristic
381C2×#101C22×C4311yescharacteristic
382C2×#101C22×C4311yescharacteristic
383C2×#100C22×C4311yescharacteristic
384C2×#100C22×C4311yescharacteristic
385C2×#100C22×C4311yescharacteristic
386#405C22×C4311yescharacteristic
387#344C22×C4311yescharacteristic
388#344C22×C4311yescharacteristic
389#338C22×C4311yescharacteristic
390#338C22×C4311yescharacteristic
391C43#2480811yescharacteristic, direct product factor, Sylow
392C2×#41C23×C4311yescharacteristic
393C2×#41C23×C4311yescharacteristic
394C22×Q8C23×C4311yescharacteristic
395C22×D4C23×C4311yescharacteristic
396#137—21no—
397#137—22no—
398#137—22no—
399#137—22no—
400#137—41no—
401#137D4×C4312yes—
402AGL(1,ℤ/8)—21no—
403AGL(1,ℤ/8)—22no—
404AGL(1,ℤ/8)—22no—
405AGL(1,ℤ/8)—22no—
406AGL(1,ℤ/8)—41no—
407AGL(1,ℤ/8)D4×C4312yes—
408#135—22no—
409C2×Q16—21no—
410C2×Q16—21no—
411C2×SD16—21no—
412C2×SD16—21no—
413C2×SD16—21no—
414C2×SD16—21no—
415C2×SD16—21no—
416C2×SD16—21no—
417C2×SD16—21no—
418C2×SD16—21no—
419C2×SD16—21no—
420C2×SD16—21no—
421C2×D8—21no—
422C2×D8—21no—
423#131—21no—
424#131—21no—
425#131—22no—
426#131—22no—
427#131—21no—
428#131—21no—
429#131—21no—
430#131—21no—
431#131—41no—
432#131—41no—
433#131D4×C4312yes—
434#131D4×C4312yes—
435C2×M16—21no—
436C2×M16—21no—
437C2×M16—22no—
438C2×M16—22no—
439C2×M16C23×C4311yescharacteristic
440C2×M16C23×C4311yescharacteristic
441C2×M16C23×C4311yescharacteristic
442C2×M16C23×C4311yescharacteristic
443C2×M16C23×C4311yescharacteristic
444C2×M16C23×C4311yescharacteristic
445C2×M16C23×C4311yescharacteristic
446C2×M16C23×C4311yescharacteristic
447C2×M16C23×C4311yescharacteristic
448C22×C8—21no—
449C22×C8—21no—
450C22×C8C23×C4311yescharacteristic
451#117C23×C4311yescharacteristic
452#108—22no—
453#108—22no—
454#108—22no—
455#108—22no—
456#108—22no—
457#108—21no—
458#108—21no—
459#108—21no—
460#108—21no—
461#108D4×C4312yes—
462#108D4×C4312yes—
463#104—22no—
464#104—22no—
465#103—41no—
466#102—41no—
467#101—21no—
468#101—21no—
469#101—22no—
470#101—22no—
471#101—22no—
472#100—21no—
473#100—21no—
474#100—22no—
475#100—22no—
476#100—22no—
477#97—21no—
478C4×C8—21no—
479C24—21no—
480#41—21no—
481#41—21no—
482#41—21no—
483#41—21no—
484#41—21no—
485#41—21no—
486#41C2×D4×C4312yes—
487#41C2×D4×C4312yes—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8C2×D4×C4311yescharacteristic
495C2×Q8#41×C4311yescharacteristic
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4C2×D4×C4311yescharacteristic
505C2×D4#41×C4311yescharacteristic
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4C24×C4311yescharacteristic
510Q16—22no—
511Q16—42no—
512Q16—42no—
513SD16—22no—
514SD16—22no—
515SD16—42no—
516SD16—42no—
517SD16—42no—
518SD16—42no—
519SD16—41no—
520SD16—41no—
521SD16—41no—
522SD16—41no—
523D8—22no—
524D8—42no—
525D8—42no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—22no—
531M16—22no—
532M16—21no—
533M16—21no—
534M16—21no—
535M16—21no—
536M16—21no—
537M16—21no—
538M16—21no—
539M16—21no—
540M16—21no—
541M16—21no—
542M16—42no—
543M16—42no—
544M16—41no—
545M16—41no—
546M16C2×D4×C4312yes—
547M16C2×D4×C4312yes—
548M16C2×D4×C4312yes—
549M16C2×D4×C4312yes—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—42no—
562C2×C8—42no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8C2×D4×C4311yescharacteristic
566C2×C8C2×D4×C4311yescharacteristic
567C2×C8C2×D4×C4311yescharacteristic
568C2×C8C2×D4×C4311yescharacteristic
569C2×C8#41×C4311yescharacteristic
570C2×C8#41×C4311yescharacteristic
571C4⋊C4—21no—
572C22⋊C4—21no—
573C42—21no—
574C23—21no—
575C23—21no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—161no—
580C232−1+4×C4311yescharacteristic
581Q8—21no—
582Q8—21no—
583Q8—21no—
584Q8—41no—
585Q8—41no—
586Q8—41no—
587Q8—41no—
588Q8#121×C4312yes—
589D4—22no—
590D4—22no—
591D4—21no—
592D4—21no—
593D4—21no—
594D4—41no—
595D4—41no—
596D4—41no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4#121×C4312yes—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4C22×D4×C4311yescharacteristic
612C2×C4C22×D4×C4311yescharacteristic
613C2×C4C22×D4×C4311yescharacteristic
614C2×C4C2×#41×C4311yescharacteristic
615C2×C4C2×#41×C4311yescharacteristic
616C2×C4H(5,𝔽2)×C4311yescharacteristic
617C8—22no—
618C8—22no—
619C8—22no—
620C8—22no—
621C8—41no—
622C8—41no—
623C8—41no—
624C8—41no—
625C8—41no—
626C8#121×C4311yescharacteristic
627C8#121×C4311yescharacteristic
628C8#121×C4311yescharacteristic
629C8#121×C4311yescharacteristic
630C22—22no—
631C22—41no—
632C22—41no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—161no—
637C22—161no—
638C22—161no—
639C22C43×#53711yescharacteristic
640C22C43×#54711yescharacteristic
641C22C43×#54811yescharacteristic
642C4—22no—
643C4—41no—
644C4—81no—
645C4—81no—
646C4C2×#121×C4311yescharacteristic
647C4C2×#121×C4311yescharacteristic
648C4D42×C4311yescharacteristic
649C4C43×#55311yescharacteristic
650C2—21no—
651C2—21no—
652C2—21no—
653C2—42no—
654C2—81no—
655C2—161no—
656C2C43×#241611yescharacteristic
subgroupG/H
center, socleC2×C43#2416
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#3068C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C43 ◁ C22×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3069C2semidirect
3. C2×C43×#471C2semidirect
4. C2×C43×#471C2semidirect
5. C43×#2955C2semidirect
6. C43×#2916C2semidirect
7. C43×#2070C2semidirect
8. C43×#2069C2semidirect
9. C43×#2049C2semidirect
10. C43×#2048C2semidirect
11. C43×#1977C2semidirect
12. C43×#1953C2semidirect
13. C43×#1903C2semidirect
14. C43×#1902C2semidirect
15. C43×#1813C2semidirect
301. #24808C43direct (N × H)
322. #3069C2×C43semidirect
324. C2×#471C2×C43semidirect
325. C2×#471C2×C43semidirect
326. #2955C2×C43semidirect
327. #2916C2×C43semidirect
328. #2070C2×C43semidirect
329. #2069C2×C43semidirect
330. #2049C2×C43semidirect
331. #2048C2×C43semidirect
332. #1977C2×C43semidirect
333. #1953C2×C43semidirect
334. #1903C2×C43semidirect
335. #1902C2×C43semidirect
336. #1813C2×C43semidirect
391. C43#24808direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#30692
C43×#30682
C2×C43×#4712
C43×#29552
C43×#29162
C43×#20702
C43×#20692
C43×#20492
C43×#20482
C43×#19772
C43×#19532
C43×#19032
C43×#19022
C43×#18132
#2480843