Finite Group Databasebeta

← C43×#19014 #24939031

Subgroups — C43×#19014 #24939031

Order 11008.

1140 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3558C211yesmaximal, characteristic, complemented
2C43×#3217C211yesmaximal, characteristic, complemented
3C43×#3151C211yesmaximal, characteristic, complemented
4C2×C43×#496C211yesmaximal, characteristic, complemented
5C43×#1656C214yesmaximal, complemented
6C43×#1655C214yesmaximal, complemented
7C43×#1530C211yesmaximal, characteristic, complemented
8C43×#1527C211yesmaximal, characteristic, complemented
9C43×#1524C211yesmaximal, characteristic, complemented
10C2×AGL(1,ℤ/8)×C43—22no—
11C22×SD16×C43—21no—
12C22×D8×C43—21no—
13C43×#562C2212yescomplemented
14C43×H(3,𝔽4)C2212yescomplemented
15C43×#559—21no—
16C43×#548—21no—
17C43×#546—22no—
18C43×#546—21no—
19D42×C43—21no—
20C43×#542—21no—
21C43×#538—22no—
22C43×#538—21no—
23C43×#535—21no—
24C43×#534—21no—
25C43×#532C2211yescharacteristic
26C2×#127×C43C2211yescharacteristic, complemented
27C43×#529C2211yescharacteristic
28C2×#124×C43C2211yescharacteristic
29C43×#496—22no—
30C43×#496C2214yescomplemented
31C43×#496C2214yescomplemented
32C43×#496C2212yescomplemented
33C43×#493—21no—
34C43×#492—21no—
35C43×#490C2212yescomplemented
36C43×#460—21no—
37C43×#459—21no—
38C43×#450—21no—
39C43×#447—21no—
40C43×#432C2211yescharacteristic, complemented
41C4×M16×C43C2211yescharacteristic, complemented
42C2×#97×C43C2211yescharacteristic, complemented
43C43×#330C2212yescomplemented
44C43×#329C2212yescomplemented
45C43×#329C2214yescomplemented
46C43×#329C2214yescomplemented
47C2×#41×C43—21no—
48C2×#41×C43D412yes—
49C22×Q8×C43D411yescharacteristic
50C22×D4×C43—22no—
51C22×D4×C43—21no—
52C22×D4×C43—21no—
53C22×D4×C43—21no—
54C22×D4×C43—21no—
55C22×D4×C43D411yescharacteristic
56AGL(1,ℤ/8)×C43—48no—
57C2×SD16×C43—24no—
58C2×SD16×C43—24no—
59C2×SD16×C43—22no—
60C2×SD16×C43—44no—
61C2×D8×C43—24no—
62C2×D8×C43—24no—
63C2×D8×C43—22no—
64C2×D8×C43—44no—
65C2×M16×C43—21no—
66C22×C8×C43—21no—
67C4⋊Q8×C43D411yescharacteristic
68#127×C43—21no—
69#127×C43—21no—
70#127×C43—21no—
71#127×C43—21no—
72#127×C43D411yescharacteristic
73#127×C43C2312yes—
74#126×C43—22no—
75#126×C43—21no—
76#125×C43C2311yescharacteristic
77#124×C43—21no—
78#124×C43—22no—
79#124×C43—22no—
80#124×C43—22no—
81#124×C43—21no—
82#124×C43—21no—
83#124×C43D412yes—
84#124×C43C2312yes—
85#124×C43C2311yescharacteristic
86#124×C43C2312yes—
87#123×C43—22no—
88#123×C43—22no—
89#123×C43—21no—
90#123×C43—22no—
91#123×C43—22no—
92C22⋊Q8×C43—21no—
93C22⋊Q8×C43—22no—
94C22⋊Q8×C43—22no—
95C22⋊Q8×C43D411yescharacteristic
96#121×C43—22no—
97#121×C43—22no—
98#121×C43—22no—
99#121×C43—21no—
100#121×C43—22no—
101#121×C43—22no—
102#121×C43—21no—
103#121×C43—21no—
104#121×C43D411yescharacteristic
105#120×C43—22no—
106#120×C43—22no—
107#120×C43—22no—
108#120×C43—22no—
109#120×C43—22no—
110C4×Q8×C43—21no—
111C4×Q8×C43D411yescharacteristic
112C4×D4×C43—22no—
113C4×D4×C43—22no—
114C4×D4×C43—21no—
115C4×D4×C43—21no—
116C4×D4×C43—21no—
117C4×D4×C43—21no—
118C4×D4×C43D411yescharacteristic
119#117×C43—21no—
120C2×C22⋊C4×C43—22no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C42×C43C2311yescharacteristic
124C4⋊C8×C43—21no—
125#102×C43—22no—
126#102×C43—22no—
127C22⋊C8×C43—21no—
128#97×C43—21no—
129#97×C43C2312yes—
130#97×C43C2312yes—
131#97×C43C2312yes—
132C4×C8×C43—21no—
133C24×C43—22no—
134C24×C43—21no—
135C24×C43—41no—
136#41×C43—44no—
137#41×C43—82no—
138C2×Q8×C43—21no—
139C2×Q8×C43—42no—
140C2×Q8×C43C2×D411yescharacteristic
141C2×Q8×C43C2×D412yes—
142C2×Q8×C43C2×D412yes—
143C2×D4×C43—22no—
144C2×D4×C43—22no—
145C2×D4×C43—22no—
146C2×D4×C43—22no—
147C2×D4×C43—22no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—22no—
152C2×D4×C43—21no—
153C2×D4×C43—22no—
154C2×D4×C43—22no—
155C2×D4×C43—22no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43—41no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43—44no—
163C2×D4×C43—84no—
164C2×D4×C43—82no—
165C2×D4×C43—82no—
166C2×D4×C43C2×D411yescharacteristic
167C2×D4×C43C2×D412yes—
168C2×D4×C43C2×D412yes—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—21no—
172C22×C4×C43—22no—
173C22×C4×C43—21no—
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177SD16×C43—48no—
178SD16×C43—48no—
179SD16×C43—82no—
180D8×C43—48no—
181D8×C43—48no—
182D8×C43—82no—
183M16×C43—24no—
184C2×C8×C43—24no—
185C2×C8×C43—22no—
186C2×C8×C43—22no—
187C2×C8×C43—22no—
188C4⋊C4×C43—22no—
189C4⋊C4×C43—22no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43C2×D411yescharacteristic
197C4⋊C4×C43C2×D411yescharacteristic
198C22⋊C4×C43—22no—
199C22⋊C4×C43—22no—
200C22⋊C4×C43—22no—
201C22⋊C4×C43—22no—
202C22⋊C4×C43—22no—
203C22⋊C4×C43—22no—
204C22⋊C4×C43—21no—
205C22⋊C4×C43—22no—
206C22⋊C4×C43—21no—
207C22⋊C4×C43—22no—
208C22⋊C4×C43—22no—
209C22⋊C4×C43—21no—
210C22⋊C4×C43—21no—
211C22⋊C4×C43—22no—
212C22⋊C4×C43—22no—
213C22⋊C4×C43—21no—
214C42×C43—22no—
215C42×C43—21no—
216C42×C43C2×D411yescharacteristic
217C42×C43C2×D411yescharacteristic
218C42×C43C2×D411yescharacteristic
219C42×C43C2411yescharacteristic
220C23×C43—22no—
221C23×C43—21no—
222C23×C43—22no—
223C23×C43—42no—
224C23×C43—42no—
225C23×C43—81no—
226C23×C43—81no—
227C23×C43—82no—
228C23×C43—82no—
229C23×C43—82no—
230C23×C43—82no—
231C23×C43—82no—
232C23×C43—82no—
233C23×C43#12011yescharacteristic
234Q8×C43—42no—
235Q8×C43—42no—
236Q8×C43—41no—
237Q8×C43—42no—
238D4×C43—42no—
239D4×C43—42no—
240D4×C43—41no—
241D4×C43—42no—
242D4×C43—44no—
243D4×C43—42no—
244D4×C43—42no—
245D4×C43—42no—
246D4×C43—42no—
247D4×C43—44no—
248D4×C43—42no—
249D4×C43—42no—
250D4×C43—81no—
251D4×C43—82no—
252D4×C43—82no—
253D4×C43—82no—
254D4×C43—82no—
255D4×C43—82no—
256D4×C43—82no—
257D4×C43—82no—
258D4×C43—82no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—21no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—41no—
267C2×C4×C43—42no—
268C2×C4×C43—82no—
269C2×C4×C43—81no—
270C2×C4×C43—82no—
271C2×C4×C43—82no—
272C2×C4×C43#12011yescharacteristic
273C2×C4×C43#12011yescharacteristic
274C2×C4×C43#12011yescharacteristic
275C2×C4×C43C22×D411yescharacteristic
276C2×C4×C43C22×D411yescharacteristic
277C2×C4×C43C22×D411yescharacteristic
278C8×C43—24no—
279C8×C43—24no—
280C8×C43—42no—
281#19014C4311yesmaximal, characteristic, direct product factor, Sylow
282C22×C43—21no—
283C22×C43—21no—
284C22×C43—42no—
285C22×C43—41no—
286C22×C43—42no—
287C22×C43—41no—
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—41no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—82no—
294C22×C43—82no—
295C22×C43—82no—
296C22×C43—162no—
297C22×C43—164no—
298C22×C43—164no—
299C22×C43#45312yes—
300C22×C43C2×#12011yescharacteristic
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—41no—
307C4×C43—41no—
308C4×C43—42no—
309C4×C43—42no—
310C4×C43—41no—
311C4×C43#45312yes—
312#3558C2×C4311yescharacteristic, complemented
313#3217C2×C4311yescharacteristic, complemented
314#3151C2×C4311yescharacteristic, complemented
315C2×#496C2×C4311yescharacteristic, complemented
316#1656C2×C4314yescomplemented
317#1655C2×C4314yescomplemented
318#1530C2×C4311yescharacteristic, complemented
319#1527C2×C4311yescharacteristic, complemented
320#1524C2×C4311yescharacteristic, complemented
321C2×C43—22no—
322C2×C43—82no—
323C2×C43—82no—
324C2×C43—81no—
325C2×C43—162no—
326C2×C43C2×#45311yescharacteristic
327C2×C43C2×#45311yescharacteristic
328C2×C43#302111yescharacteristic
329C2×AGL(1,ℤ/8)—22no—
330C22×SD16—21no—
331C22×D8—21no—
332#562C22×C4312yescomplemented
333H(3,𝔽4)C22×C4312yescomplemented
334#559—21no—
335#548—21no—
336#546—22no—
337#546—21no—
338D42—21no—
339#542—21no—
340#538—22no—
341#538—21no—
342#535—21no—
343#534—21no—
344#532C22×C4311yescharacteristic
345C2×#127C22×C4311yescharacteristic, complemented
346#529C22×C4311yescharacteristic
347C2×#124C22×C4311yescharacteristic
348#496—22no—
349#496C22×C4314yescomplemented
350#496C22×C4314yescomplemented
351#496C22×C4312yescomplemented
352#493—21no—
353#492—21no—
354#490C22×C4312yescomplemented
355#460—21no—
356#459—21no—
357#450—21no—
358#447—21no—
359#432C22×C4311yescharacteristic, complemented
360C4×M16C22×C4311yescharacteristic, complemented
361C2×#97C22×C4311yescharacteristic, complemented
362#330C22×C4312yescomplemented
363#329C22×C4312yescomplemented
364#329C22×C4314yescomplemented
365#329C22×C4314yescomplemented
366C43#1901411yescharacteristic, direct product factor, Sylow
367C2×#41—21no—
368C2×#41D4×C4312yes—
369C22×Q8D4×C4311yescharacteristic
370C22×D4—22no—
371C22×D4—21no—
372C22×D4—21no—
373C22×D4—21no—
374C22×D4—21no—
375C22×D4D4×C4311yescharacteristic
376AGL(1,ℤ/8)—48no—
377C2×SD16—24no—
378C2×SD16—24no—
379C2×SD16—22no—
380C2×SD16—44no—
381C2×D8—24no—
382C2×D8—24no—
383C2×D8—22no—
384C2×D8—44no—
385C2×M16—21no—
386C22×C8—21no—
387C4⋊Q8D4×C4311yescharacteristic
388#127—21no—
389#127—21no—
390#127—21no—
391#127—21no—
392#127D4×C4311yescharacteristic
393#127C23×C4312yes—
394#126—22no—
395#126—21no—
396#125C23×C4311yescharacteristic
397#124—21no—
398#124—22no—
399#124—22no—
400#124—22no—
401#124—21no—
402#124—21no—
403#124D4×C4312yes—
404#124C23×C4312yes—
405#124C23×C4311yescharacteristic
406#124C23×C4312yes—
407#123—22no—
408#123—22no—
409#123—21no—
410#123—22no—
411#123—22no—
412C22⋊Q8—21no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8D4×C4311yescharacteristic
416#121—22no—
417#121—22no—
418#121—22no—
419#121—21no—
420#121—22no—
421#121—22no—
422#121—21no—
423#121—21no—
424#121D4×C4311yescharacteristic
425#120—22no—
426#120—22no—
427#120—22no—
428#120—22no—
429#120—22no—
430C4×Q8—21no—
431C4×Q8D4×C4311yescharacteristic
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4D4×C4311yescharacteristic
439#117—21no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C42C23×C4311yescharacteristic
444C4⋊C8—21no—
445#102—22no—
446#102—22no—
447C22⋊C8—21no—
448#97—21no—
449#97C23×C4312yes—
450#97C23×C4312yes—
451#97C23×C4312yes—
452C4×C8—21no—
453C24—22no—
454C24—21no—
455C24—41no—
456#41—44no—
457#41—82no—
458C2×Q8—21no—
459C2×Q8—42no—
460C2×Q8C2×D4×C4311yescharacteristic
461C2×Q8C2×D4×C4312yes—
462C2×Q8C2×D4×C4312yes—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—44no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—82no—
484C2×D4—82no—
485C2×D4—84no—
486C2×D4C2×D4×C4311yescharacteristic
487C2×D4C2×D4×C4312yes—
488C2×D4C2×D4×C4312yes—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4C2×D4×C4311yescharacteristic
495C22×C4C2×D4×C4311yescharacteristic
496C22×C4C2×D4×C4311yescharacteristic
497SD16—48no—
498SD16—48no—
499SD16—82no—
500D8—48no—
501D8—48no—
502D8—82no—
503M16—24no—
504C2×C8—24no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4C2×D4×C4311yescharacteristic
517C4⋊C4C2×D4×C4311yescharacteristic
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—21no—
524C22⋊C4—22no—
525C22⋊C4—21no—
526C22⋊C4—22no—
527C22⋊C4—21no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C42—22no—
535C42—21no—
536C42C2×D4×C4311yescharacteristic
537C42C2×D4×C4311yescharacteristic
538C42C2×D4×C4311yescharacteristic
539C42C24×C4311yescharacteristic
540C23—21no—
541C23—22no—
542C23—22no—
543C23—42no—
544C23—42no—
545C23—81no—
546C23—81no—
547C23—82no—
548C23—82no—
549C23—82no—
550C23—82no—
551C23—82no—
552C23—82no—
553C23#120×C4311yescharacteristic
554Q8—42no—
555Q8—42no—
556Q8—41no—
557Q8—42no—
558D4—42no—
559D4—42no—
560D4—41no—
561D4—42no—
562D4—44no—
563D4—42no—
564D4—42no—
565D4—42no—
566D4—42no—
567D4—44no—
568D4—42no—
569D4—42no—
570D4—81no—
571D4—82no—
572D4—82no—
573D4—82no—
574D4—82no—
575D4—82no—
576D4—82no—
577D4—82no—
578D4—82no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—82no—
589C2×C4—81no—
590C2×C4—82no—
591C2×C4—82no—
592C2×C4#120×C4311yescharacteristic
593C2×C4#120×C4311yescharacteristic
594C2×C4#120×C4311yescharacteristic
595C2×C4C22×D4×C4311yescharacteristic
596C2×C4C22×D4×C4311yescharacteristic
597C2×C4C22×D4×C4311yescharacteristic
598C8—24no—
599C8—24no—
600C8—42no—
601C22—21no—
602C22—21no—
603C22—41no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—41no—
609C22—41no—
610C22—42no—
611C22—42no—
612C22—82no—
613C22—82no—
614C22—82no—
615C22—162no—
616C22—164no—
617C22—164no—
618C22C43×#45312yes—
619C22C2×#120×C4311yescharacteristic
620C4—21no—
621C4—21no—
622C4—21no—
623C4—21no—
624C4—21no—
625C4—41no—
626C4—41no—
627C4—42no—
628C4—42no—
629C4—41no—
630C4C43×#45312yes—
631C2—22no—
632C2—81no—
633C2—82no—
634C2—82no—
635C2—162no—
636C2C2×C43×#45311yescharacteristic
637C2C2×C43×#45311yescharacteristic
638C2C43×#302111yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC42C24×C43
LCSG ▷ C42 ▷ 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×#3558C2semidirect
2. C43×#3217C2semidirect
3. C43×#3151C2semidirect
4. C2×C43×#496C2semidirect
5. C43×#1656C2semidirect
6. C43×#1655C2semidirect
7. C43×#1530C2semidirect
8. C43×#1527C2semidirect
9. C43×#1524C2semidirect
13. C43×#562C22semidirect
14. C43×H(3,𝔽4)C22semidirect
26. C2×#127×C43C22semidirect
30. C43×#496C22semidirect
31. C43×#496C22semidirect
32. C43×#496C22semidirect
35. C43×#490C22semidirect
40. C43×#432C22semidirect
41. C4×M16×C43C22semidirect
42. C2×#97×C43C22semidirect
43. C43×#330C22semidirect
44. C43×#329C22semidirect
45. C43×#329C22semidirect
46. C43×#329C22semidirect
281. #19014C43direct (N × H)
312. #3558C2×C43semidirect
313. #3217C2×C43semidirect
314. #3151C2×C43semidirect
315. C2×#496C2×C43semidirect
316. #1656C2×C43semidirect
317. #1655C2×C43semidirect
318. #1530C2×C43semidirect
319. #1527C2×C43semidirect
320. #1524C2×C43semidirect
332. #562C22×C43semidirect
333. H(3,𝔽4)C22×C43semidirect
345. C2×#127C22×C43semidirect
349. #496C22×C43semidirect
350. #496C22×C43semidirect
351. #496C22×C43semidirect
354. #490C22×C43semidirect
359. #432C22×C43semidirect
360. C4×M16C22×C43semidirect
361. C2×#97C22×C43semidirect
362. #330C22×C43semidirect
363. #329C22×C43semidirect
364. #329C22×C43semidirect
365. #329C22×C43semidirect
366. C43#19014direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35582
C43×#32172
C43×#31512
C2×C43×#4962
C43×#16562
C43×#16552
C43×#15302
C43×#15272
C43×#15242
#1901443