Finite Group Databasebeta

← C43×#20206 #24940223

Subgroups — C43×#20206 #24940223

Order 11008.

618 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
1C43×#3384C211yesmaximal, characteristic
2C43×#3367C211yesmaximal, characteristic
3C43×#3356C211yesmaximal, characteristic, complemented
4D4×Q16×C43C211yesmaximal, characteristic, complemented
5C43×#1716C211yesmaximal, characteristic, complemented
6C43×#1700C211yesmaximal, characteristic, complemented
7C43×#1692C211yesmaximal, characteristic, complemented
8C43×#1689C211yesmaximal, characteristic, complemented
9C43×#1671C211yesmaximal, characteristic, complemented
10C43×#1652C211yesmaximal, characteristic, complemented
11C43×#1651C211yesmaximal, characteristic, complemented
12C43×#1644C211yesmaximal, characteristic, complemented
13C43×#1637C211yesmaximal, characteristic, complemented
14C43×#1593C211yesmaximal, characteristic, complemented
15C43×#1581C211yesmaximal, characteristic
16C22×Q16×C43—21no—
17C43×#556C2211yescharacteristic
18C43×#554C2211yescharacteristic
19D4×Q8×C43C2211yescharacteristic
20D4×Q8×C43C2211yescharacteristic
21C43×#501—21no—
22C43×#498C2211yescharacteristic
23C43×#498C2211yescharacteristic
24C43×#498C2211yescharacteristic
25C43×#494C2211yescharacteristic
26C43×#489—21no—
27C43×#487C2211yescharacteristic
28C43×#487C2211yescharacteristic
29C43×#485—21no—
30C43×#483—21no—
31C43×#478—21no—
32C43×#477—21no—
33C43×#477C2211yescharacteristic
34C43×#476—21no—
35C43×#476C2211yescharacteristic
36C43×#475C2211yescharacteristic
37C43×#474C2211yescharacteristic
38C43×#474C2211yescharacteristic
39C43×#470—21no—
40C43×#467—21no—
41C43×#463—21no—
42C43×#462C2211yescharacteristic
43C43×#462C2211yescharacteristic
44C43×#461C2211yescharacteristic
45C43×#451—21no—
46C43×#451—21no—
47C43×#446C2211yescharacteristic
48C43×#446C2211yescharacteristic
49C43×#442—21no—
50C43×#440—21no—
51C4×Q16×C43C2211yescharacteristic
52C4×D8×C43C2211yescharacteristic
53C43×#436C2211yescharacteristic
54C8×D4×C43C2211yescharacteristic
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
67C22×Q8×C43—21no—
68C22×Q8×C43—21no—
69C2×Q16×C43—21no—
70C2×Q16×C43—21no—
71C2×Q16×C43—21no—
72C2×Q16×C43—21no—
73C2×Q16×C43—44no—
74C2×Q16×C43D411yescharacteristic
75C2×SD16×C43—21no—
76C2×D8×C43D411yescharacteristic
77C2×M16×C43—21no—
78C22×C8×C43—21no—
79C4⋊Q8×C43—21no—
80C4⋊Q8×C43—21no—
81C4⋊Q8×C43C2311yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83C4⋊Q8×C43C2311yescharacteristic
84C4⋊Q8×C43C2311yescharacteristic
85#126×C43—41no—
86#125×C43—21no—
87#124×C43—21no—
88C22⋊Q8×C43—21no—
89C22⋊Q8×C43—21no—
90C22⋊Q8×C43—21no—
91C22⋊Q8×C43—21no—
92C22⋊Q8×C43—41no—
93C22⋊Q8×C43—41no—
94C22⋊Q8×C43—41no—
95C4×Q8×C43—21no—
96C4×Q8×C43C2311yescharacteristic
97C4×Q8×C43C2311yescharacteristic
98C4×D4×C43—21no—
99C4×D4×C43—21no—
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×C43D411yescharacteristic
109#107×C43D411yescharacteristic
110#106×C43—21no—
111#106×C43—21no—
112#106×C43—21no—
113#106×C43—21no—
114#106×C43—21no—
115#106×C43—21no—
116#106×C43—41no—
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—
141#97×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—41no—
150C2×Q8×C43—41no—
151C2×Q8×C43—42no—
152C2×Q8×C43—42no—
153C2×Q8×C43—81no—
154C2×Q8×C43—81no—
155C2×Q8×C43C2×D411yescharacteristic
156C2×Q8×C43C2×D411yescharacteristic
157C2×D4×C43C2×D411yescharacteristic
158C2×D4×C43C2×D411yescharacteristic
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—41no—
162C22×C4×C43—41no—
163C22×C4×C43—41no—
164Q16×C43—22no—
165Q16×C43—42no—
166Q16×C43—42no—
167Q16×C43—42no—
168Q16×C43—81no—
169SD16×C43—42no—
170D8×C43—22no—
171M16×C43—42no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—42no—
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—
207C22⋊C4×C43—41no—
208C42×C43—21no—
209C42×C43—21no—
210C42×C43—41no—
211C42×C43C2411yescharacteristic
212C23×C43—21no—
213C23×C43—21no—
214Q8×C43—21no—
215Q8×C43—21no—
216Q8×C43—21no—
217Q8×C43—21no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—81no—
225Q8×C43—82no—
226Q8×C43—82no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43#13712yes—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—41no—
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—82no—
246C2×C4×C43—82no—
247C2×C4×C43—161no—
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×C43AGL(1,ℤ/8)12yes—
260#20206C4311yesmaximal, characteristic, direct product factor, Sylow
261C22×C43—22no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43D4211yescharacteristic
268C4×C43—21no—
269C4×C43—41no—
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
283#3384C2×C4311yescharacteristic
284#3367C2×C4311yescharacteristic
285#3356C2×C4311yescharacteristic, complemented
286D4×Q16C2×C4311yescharacteristic, complemented
287#1716C2×C4311yescharacteristic, complemented
288#1700C2×C4311yescharacteristic, complemented
289#1692C2×C4311yescharacteristic, complemented
290#1689C2×C4311yescharacteristic, complemented
291#1671C2×C4311yescharacteristic, complemented
292#1652C2×C4311yescharacteristic, complemented
293#1651C2×C4311yescharacteristic, complemented
294#1644C2×C4311yescharacteristic, complemented
295#1637C2×C4311yescharacteristic, complemented
296#1593C2×C4311yescharacteristic, complemented
297#1581C2×C4311yescharacteristic
298C2×C43—42no—
299C2×C43—81no—
300C2×C43#327011yescharacteristic
301C2×C43#327211yescharacteristic
302C2×C43#328911yescharacteristic
303C22×Q16—21no—
304#556C22×C4311yescharacteristic
305#554C22×C4311yescharacteristic
306D4×Q8C22×C4311yescharacteristic
307D4×Q8C22×C4311yescharacteristic
308#501—21no—
309#498C22×C4311yescharacteristic
310#498C22×C4311yescharacteristic
311#498C22×C4311yescharacteristic
312#494C22×C4311yescharacteristic
313#489—21no—
314#487C22×C4311yescharacteristic
315#487C22×C4311yescharacteristic
316#485—21no—
317#483—21no—
318#478—21no—
319#477—21no—
320#477C22×C4311yescharacteristic
321#476—21no—
322#476C22×C4311yescharacteristic
323#475C22×C4311yescharacteristic
324#474C22×C4311yescharacteristic
325#474C22×C4311yescharacteristic
326#470—21no—
327#467—21no—
328#463—21no—
329#462C22×C4311yescharacteristic
330#462C22×C4311yescharacteristic
331#461C22×C4311yescharacteristic
332#451—21no—
333#451—21no—
334#446C22×C4311yescharacteristic
335#446C22×C4311yescharacteristic
336#442—21no—
337#440—21no—
338C4×Q16C22×C4311yescharacteristic
339C4×D8C22×C4311yescharacteristic
340#436C22×C4311yescharacteristic
341C8×D4C22×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#2020611yescharacteristic, direct product factor, Sylow
355C22×Q8—21no—
356C22×Q8—21no—
357C2×Q16—21no—
358C2×Q16—21no—
359C2×Q16—21no—
360C2×Q16—21no—
361C2×Q16—44no—
362C2×Q16D4×C4311yescharacteristic
363C2×SD16—21no—
364C2×D8D4×C4311yescharacteristic
365C2×M16—21no—
366C22×C8—21no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8C23×C4311yescharacteristic
370C4⋊Q8C23×C4311yescharacteristic
371C4⋊Q8C23×C4311yescharacteristic
372C4⋊Q8C23×C4311yescharacteristic
373#126—41no—
374#125—21no—
375#124—21no—
376C22⋊Q8—21no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380C22⋊Q8—41no—
381C22⋊Q8—41no—
382C22⋊Q8—41no—
383C4×Q8—21no—
384C4×Q8C23×C4311yescharacteristic
385C4×Q8C23×C4311yescharacteristic
386C4×D4—21no—
387C4×D4—21no—
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#107D4×C4311yescharacteristic
397#107D4×C4311yescharacteristic
398#106—21no—
399#106—21no—
400#106—21no—
401#106—21no—
402#106—21no—
403#106—21no—
404#106—41no—
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—
429#97—21no—
430C4×C8C23×C4311yescharacteristic
431C4×C8C23×C4311yescharacteristic
432C4×C8C23×C4311yescharacteristic
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—41no—
438C2×Q8—41no—
439C2×Q8—42no—
440C2×Q8—42no—
441C2×Q8—81no—
442C2×Q8—81no—
443C2×Q8C2×D4×C4311yescharacteristic
444C2×Q8C2×D4×C4311yescharacteristic
445C2×D4C2×D4×C4311yescharacteristic
446C2×D4C2×D4×C4311yescharacteristic
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452Q16—22no—
453Q16—42no—
454Q16—42no—
455Q16—42no—
456Q16—81no—
457SD16—42no—
458D8—22no—
459M16—42no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—42no—
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—
495C22⋊C4—41no—
496C42—21no—
497C42—21no—
498C42—41no—
499C42C24×C4311yescharacteristic
500C23—21no—
501C23—21no—
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8—21no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—81no—
513Q8—82no—
514Q8—82no—
515D4—21no—
516D4—21no—
517D4—21no—
518D4#137×C4312yes—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—82no—
534C2×C4—82no—
535C2×C4—161no—
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—
547C8AGL(1,ℤ/8)×C4312yes—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22D42×C4311yescharacteristic
555C4—21no—
556C4—41no—
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—42no—
571C2—81no—
572C2C43×#327011yescharacteristic
573C2C43×#327211yescharacteristic
574C2C43×#328911yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC2×D8×C43D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C43×#3356C2semidirect
4. D4×Q16×C43C2semidirect
5. C43×#1716C2semidirect
6. C43×#1700C2semidirect
7. C43×#1692C2semidirect
8. C43×#1689C2semidirect
9. C43×#1671C2semidirect
10. C43×#1652C2semidirect
11. C43×#1651C2semidirect
12. C43×#1644C2semidirect
13. C43×#1637C2semidirect
14. C43×#1593C2semidirect
260. #20206C43direct (N × H)
285. #3356C2×C43semidirect
286. D4×Q16C2×C43semidirect
287. #1716C2×C43semidirect
288. #1700C2×C43semidirect
289. #1692C2×C43semidirect
290. #1689C2×C43semidirect
291. #1671C2×C43semidirect
292. #1652C2×C43semidirect
293. #1651C2×C43semidirect
294. #1644C2×C43semidirect
295. #1637C2×C43semidirect
296. #1593C2×C43semidirect
354. C43#20206direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33842
C43×#33672
C43×#33562
D4×Q16×C432
C43×#17162
C43×#17002
C43×#16922
C43×#16892
C43×#16712
C43×#16522
C43×#16512
C43×#16442
C43×#16372
C43×#15932
C43×#15812
#2020643