Finite Group Databasebeta

← C43×#20199 #24940216

Subgroups — C43×#20199 #24940216

Order 11008.

616 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×SD16×C43C211yesmaximal, characteristic, complemented
2C43×#3369C211yesmaximal, characteristic, complemented
3C43×#3353C211yesmaximal, characteristic
4C43×#3276C211yesmaximal, characteristic
5C43×#1723C211yesmaximal, characteristic, complemented
6C43×#1703C211yesmaximal, characteristic, complemented
7C43×#1691C211yesmaximal, characteristic, complemented
8C43×#1690C211yesmaximal, characteristic, complemented
9C43×#1674C211yesmaximal, characteristic, complemented
10C43×#1650C211yesmaximal, characteristic, complemented
11C43×#1649C211yesmaximal, characteristic, complemented
12C43×#1645C211yesmaximal, characteristic, complemented
13C43×#1635C211yesmaximal, characteristic
14C43×#1592C211yesmaximal, characteristic, complemented
15C43×#1583C211yesmaximal, characteristic, complemented
16C2×#137×C43—21no—
17Q82×C43C2211yescharacteristic
18C43×#556C2211yescharacteristic
19D4×Q8×C43C2211yescharacteristic
20C43×#547C2211yescharacteristic
21C43×#500C2211yescharacteristic
22C43×#500C2211yescharacteristic
23C43×#498—21no—
24C43×#498C2211yescharacteristic
25C43×#494C2211yescharacteristic
26C43×#489—21no—
27C43×#487C2211yescharacteristic
28C43×#487C2211yescharacteristic
29C43×#484—21no—
30C43×#482—21no—
31C43×#476—21no—
32C43×#476C2211yescharacteristic
33C43×#476C2211yescharacteristic
34C43×#475—21no—
35C43×#475—21no—
36C43×#475C2211yescharacteristic
37C43×#475C2211yescharacteristic
38C43×#474C2211yescharacteristic
39C43×#470—21no—
40C43×#468—21no—
41C43×#464—21no—
42C43×#462C2211yescharacteristic
43C43×#462C2211yescharacteristic
44C43×#461C2211yescharacteristic
45C43×#452—21no—
46C43×#451—21no—
47C43×#446C2211yescharacteristic
48C8×Q8×C43C2211yescharacteristic
49C43×#441—21no—
50C4×SD16×C43—21no—
51C4×SD16×C43C2211yescharacteristic
52C4×SD16×C43C2211yescharacteristic
53C43×#436C2211yescharacteristic
54C43×#436C2211yescharacteristic
55C43×#428—21no—
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#333C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#332C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#41×C43—21no—
68C22×Q8×C43—21no—
69#137×C43—44no—
70C2×Q16×C43—21no—
71C2×Q16×C43—21no—
72C2×Q16×C43—21no—
73C2×Q16×C43—21no—
74C2×SD16×C43—21no—
75C2×SD16×C43D411yescharacteristic
76C2×SD16×C43D411yescharacteristic
77C2×M16×C43—21no—
78C2×M16×C43—21no—
79C4⋊Q8×C43—21no—
80C4⋊Q8×C43—21no—
81C4⋊Q8×C43—21no—
82C4⋊Q8×C43—41no—
83C4⋊Q8×C43C2311yescharacteristic
84C4⋊Q8×C43C2311yescharacteristic
85C4⋊Q8×C43C2311yescharacteristic
86C4⋊Q8×C43C2311yescharacteristic
87#126×C43—41no—
88#124×C43—21no—
89#123×C43—41no—
90C22⋊Q8×C43—21no—
91C22⋊Q8×C43—21no—
92C22⋊Q8×C43—21no—
93C22⋊Q8×C43—41no—
94#121×C43—21no—
95C4×Q8×C43—21no—
96C4×Q8×C43—21no—
97C4×Q8×C43—21no—
98C4×Q8×C43C2311yescharacteristic
99C4×Q8×C43C2311yescharacteristic
100C4×D4×C43—21no—
101C4×D4×C43C2311yescharacteristic
102C4×D4×C43C2311yescharacteristic
103#117×C43—21no—
104C2×C4⋊C4×C43—21no—
105#107×C43—21no—
106#107×C43—21no—
107#107×C43—21no—
108#107×C43—41no—
109#106×C43—21no—
110#106×C43—21no—
111#106×C43—21no—
112#106×C43—21no—
113#106×C43—21no—
114#106×C43—21no—
115#106×C43D411yescharacteristic
116#106×C43D411yescharacteristic
117C4⋊C8×C43—21no—
118C4⋊C8×C43—21no—
119C4⋊C8×C43C2311yescharacteristic
120C4⋊C8×C43C2311yescharacteristic
121C4⋊C8×C43C2311yescharacteristic
122C4⋊C8×C43C2311yescharacteristic
123#103×C43—21no—
124#103×C43—21no—
125#103×C43—21no—
126#103×C43—21no—
127#103×C43—21no—
128#103×C43—21no—
129#103×C43—21no—
130#103×C43—41no—
131#103×C43D411yescharacteristic
132#103×C43D411yescharacteristic
133#102×C43—21no—
134#102×C43—21no—
135#102×C43—21no—
136#102×C43D411yescharacteristic
137#102×C43D411yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140#97×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145#41×C43—42no—
146#41×C43—81no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—41no—
152C2×Q8×C43—41no—
153C2×Q8×C43—42no—
154C2×Q8×C43—81no—
155C2×Q8×C43C2×D411yescharacteristic
156C2×Q8×C43C2×D411yescharacteristic
157C2×D4×C43—41no—
158C2×D4×C43C2×D411yescharacteristic
159C2×D4×C43C2×D411yescharacteristic
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—41no—
163C22×C4×C43—41no—
164Q16×C43—42no—
165Q16×C43—42no—
166Q16×C43—42no—
167Q16×C43—81no—
168SD16×C43—22no—
169SD16×C43—22no—
170SD16×C43—42no—
171M16×C43—42no—
172M16×C43—42no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C2×C8×C43C2×D411yescharacteristic
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—41no—
193C4⋊C4×C43—41no—
194C4⋊C4×C43—41no—
195C4⋊C4×C43—41no—
196C4⋊C4×C43—41no—
197C4⋊C4×C43C2×D411yescharacteristic
198C4⋊C4×C43C2×D411yescharacteristic
199C4⋊C4×C43C2×D411yescharacteristic
200C4⋊C4×C43C2×D411yescharacteristic
201C22⋊C4×C43—21no—
202C22⋊C4×C43—21no—
203C22⋊C4×C43—41no—
204C22⋊C4×C43—41no—
205C22⋊C4×C43—41no—
206C22⋊C4×C43—41no—
207C42×C43—21no—
208C42×C43—21no—
209C42×C43—41no—
210C42×C43—41no—
211C42×C43C2411yescharacteristic
212C23×C43—21no—
213C23×C43—21no—
214Q8×C43—21no—
215Q8×C43—21no—
216Q8×C43—21no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—82no—
224Q8×C43—81no—
225Q8×C43—161no—
226Q8×C43AGL(1,ℤ/8)12yes—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—82no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—82no—
247C2×C4×C43—82no—
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—41no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43—41no—
258C8×C43—41no—
259C8×C43#13712yescomplemented
260#20199C4311yesmaximal, characteristic, direct product factor, Sylow
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43D4211yescharacteristic
268C4×C43—22no—
269C4×C43—21no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—81no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43—81no—
279C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
280C4×C43C2×#13711yescharacteristic
281C4×C43#57711yescharacteristic
282C4×C43#57811yescharacteristic
283Q8×SD16C2×C4311yescharacteristic, complemented
284#3369C2×C4311yescharacteristic, complemented
285#3353C2×C4311yescharacteristic
286#3276C2×C4311yescharacteristic
287#1723C2×C4311yescharacteristic, complemented
288#1703C2×C4311yescharacteristic, complemented
289#1691C2×C4311yescharacteristic, complemented
290#1690C2×C4311yescharacteristic, complemented
291#1674C2×C4311yescharacteristic, complemented
292#1650C2×C4311yescharacteristic, complemented
293#1649C2×C4311yescharacteristic, complemented
294#1645C2×C4311yescharacteristic, complemented
295#1635C2×C4311yescharacteristic
296#1592C2×C4311yescharacteristic, complemented
297#1583C2×C4311yescharacteristic, complemented
298C2×C43—81no—
299C2×C43—81no—
300C2×C43#326511yescharacteristic
301C2×C43#327611yescharacteristic
302C2×C43#328911yescharacteristic
303C2×#137—21no—
304Q82C22×C4311yescharacteristic
305#556C22×C4311yescharacteristic
306D4×Q8C22×C4311yescharacteristic
307#547C22×C4311yescharacteristic
308#500C22×C4311yescharacteristic
309#500C22×C4311yescharacteristic
310#498—21no—
311#498C22×C4311yescharacteristic
312#494C22×C4311yescharacteristic
313#489—21no—
314#487C22×C4311yescharacteristic
315#487C22×C4311yescharacteristic
316#484—21no—
317#482—21no—
318#476—21no—
319#476C22×C4311yescharacteristic
320#476C22×C4311yescharacteristic
321#475—21no—
322#475—21no—
323#475C22×C4311yescharacteristic
324#475C22×C4311yescharacteristic
325#474C22×C4311yescharacteristic
326#470—21no—
327#468—21no—
328#464—21no—
329#462C22×C4311yescharacteristic
330#462C22×C4311yescharacteristic
331#461C22×C4311yescharacteristic
332#452—21no—
333#451—21no—
334#446C22×C4311yescharacteristic
335C8×Q8C22×C4311yescharacteristic
336#441—21no—
337C4×SD16—21no—
338C4×SD16C22×C4311yescharacteristic
339C4×SD16C22×C4311yescharacteristic
340#436C22×C4311yescharacteristic
341#436C22×C4311yescharacteristic
342#428—21no—
343#335C22×C4311yescharacteristic
344#334C22×C4311yescharacteristic
345#333C22×C4311yescharacteristic
346#332C22×C4311yescharacteristic
347#332C22×C4311yescharacteristic
348#332C22×C4311yescharacteristic
349Q8⋊C8C22×C4311yescharacteristic
350Q8⋊C8C22×C4311yescharacteristic
351D4⋊C8C22×C4311yescharacteristic
352D4⋊C8C22×C4311yescharacteristic
353#322C22×C4311yescharacteristic
354C43#2019911yescharacteristic, direct product factor, Sylow
355C2×#41—21no—
356C22×Q8—21no—
357#137—44no—
358C2×Q16—21no—
359C2×Q16—21no—
360C2×Q16—21no—
361C2×Q16—21no—
362C2×SD16—21no—
363C2×SD16D4×C4311yescharacteristic
364C2×SD16D4×C4311yescharacteristic
365C2×M16—21no—
366C2×M16—21no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8—21no—
370C4⋊Q8—41no—
371C4⋊Q8C23×C4311yescharacteristic
372C4⋊Q8C23×C4311yescharacteristic
373C4⋊Q8C23×C4311yescharacteristic
374C4⋊Q8C23×C4311yescharacteristic
375#126—41no—
376#124—21no—
377#123—41no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8—41no—
382#121—21no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8C23×C4311yescharacteristic
387C4×Q8C23×C4311yescharacteristic
388C4×D4—21no—
389C4×D4C23×C4311yescharacteristic
390C4×D4C23×C4311yescharacteristic
391#117—21no—
392C2×C4⋊C4—21no—
393#107—21no—
394#107—21no—
395#107—21no—
396#107—41no—
397#106—21no—
398#106—21no—
399#106—21no—
400#106—21no—
401#106—21no—
402#106—21no—
403#106D4×C4311yescharacteristic
404#106D4×C4311yescharacteristic
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8C23×C4311yescharacteristic
408C4⋊C8C23×C4311yescharacteristic
409C4⋊C8C23×C4311yescharacteristic
410C4⋊C8C23×C4311yescharacteristic
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—41no—
419#103D4×C4311yescharacteristic
420#103D4×C4311yescharacteristic
421#102—21no—
422#102—21no—
423#102—21no—
424#102D4×C4311yescharacteristic
425#102D4×C4311yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—21no—
428#97—21no—
429C4×C8—21no—
430C4×C8C23×C4311yescharacteristic
431C4×C8C23×C4311yescharacteristic
432C4×C8C23×C4311yescharacteristic
433#41—42no—
434#41—81no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—41no—
440C2×Q8—41no—
441C2×Q8—42no—
442C2×Q8—81no—
443C2×Q8C2×D4×C4311yescharacteristic
444C2×Q8C2×D4×C4311yescharacteristic
445C2×D4—41no—
446C2×D4C2×D4×C4311yescharacteristic
447C2×D4C2×D4×C4311yescharacteristic
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—41no—
451C22×C4—41no—
452Q16—42no—
453Q16—42no—
454Q16—42no—
455Q16—81no—
456SD16—22no—
457SD16—22no—
458SD16—42no—
459M16—42no—
460M16—42no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8C2×D4×C4311yescharacteristic
467C2×C8C2×D4×C4311yescharacteristic
468C2×C8C2×D4×C4311yescharacteristic
469C2×C8C2×D4×C4311yescharacteristic
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4C2×D4×C4311yescharacteristic
486C4⋊C4C2×D4×C4311yescharacteristic
487C4⋊C4C2×D4×C4311yescharacteristic
488C4⋊C4C2×D4×C4311yescharacteristic
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C42—21no—
496C42—21no—
497C42—41no—
498C42—41no—
499C42C24×C4311yescharacteristic
500C23—21no—
501C23—21no—
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—82no—
512Q8—81no—
513Q8—161no—
514Q8AGL(1,ℤ/8)×C4312yes—
515D4—21no—
516D4—21no—
517D4—21no—
518D4—21no—
519D4—82no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—82no—
535C2×C4—82no—
536C2×C4C22×D4×C4311yescharacteristic
537C2×C4C22×D4×C4311yescharacteristic
538C2×C4H(5,𝔽2)×C4311yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8#137×C4312yescomplemented
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22D42×C4311yescharacteristic
555C4—22no—
556C4—21no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
567C4C2×#137×C4311yescharacteristic
568C4C43×#57711yescharacteristic
569C4C43×#57811yescharacteristic
570C2—81no—
571C2—81no—
572C2C43×#326511yescharacteristic
573C2C43×#327611yescharacteristic
574C2C43×#328911yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#547C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. Q8×SD16×C43C2semidirect
2. C43×#3369C2semidirect
5. C43×#1723C2semidirect
6. C43×#1703C2semidirect
7. C43×#1691C2semidirect
8. C43×#1690C2semidirect
9. C43×#1674C2semidirect
10. C43×#1650C2semidirect
11. C43×#1649C2semidirect
12. C43×#1645C2semidirect
14. C43×#1592C2semidirect
15. C43×#1583C2semidirect
259. C8×C43#137semidirect
260. #20199C43direct (N × H)
283. Q8×SD16C2×C43semidirect
284. #3369C2×C43semidirect
287. #1723C2×C43semidirect
288. #1703C2×C43semidirect
289. #1691C2×C43semidirect
290. #1690C2×C43semidirect
291. #1674C2×C43semidirect
292. #1650C2×C43semidirect
293. #1649C2×C43semidirect
294. #1645C2×C43semidirect
296. #1592C2×C43semidirect
297. #1583C2×C43semidirect
354. C43#20199direct (N × H)
547. C8#137×C43semidirect

Maximal subgroups

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

subgroupindex
Q8×SD16×C432
C43×#33692
C43×#33532
C43×#32762
C43×#17232
C43×#17032
C43×#16912
C43×#16902
C43×#16742
C43×#16502
C43×#16492
C43×#16452
C43×#16352
C43×#15922
C43×#15832
#2019943