Finite Group Databasebeta

← C43×#19878 #24939895

Subgroups — C43×#19878 #24939895

Order 11008.

594 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3393C211yesmaximal, characteristic, complemented
2C43×#3354C211yesmaximal, characteristic
3C43×#3340C211yesmaximal, characteristic, complemented
4C43×#3302C211yesmaximal, characteristic, complemented
5C43×#1716C211yesmaximal, characteristic, complemented
6C43×#1689C211yesmaximal, characteristic, complemented
7C43×#1679C211yesmaximal, characteristic, complemented
8C43×#1672C211yesmaximal, characteristic, complemented
9C43×#1671C211yesmaximal, characteristic, complemented
10C43×#1654C211yesmaximal, characteristic, complemented
11C43×#1652C211yesmaximal, characteristic, complemented
12C43×#1646C211yesmaximal, characteristic, complemented
13C43×#1638C211yesmaximal, characteristic, complemented
14C43×#1583C211yesmaximal, characteristic, complemented
15C43×#1580C211yesmaximal, characteristic, complemented
16C43×#556C2211yescharacteristic
17C43×#556C2211yescharacteristic
18C43×#555C2211yescharacteristic
19C43×#547C2211yescharacteristic
20C43×#498C2211yescharacteristic
21C43×#498C2211yescharacteristic
22C43×#498C2211yescharacteristic
23C43×#495—21no—
24C43×#494C2211yescharacteristic
25C43×#487C2211yescharacteristic
26C43×#487C2211yescharacteristic
27C43×#485—21no—
28C43×#485—21no—
29C43×#482—21no—
30C43×#482—21no—
31C43×#481—21no—
32C43×#477C2211yescharacteristic
33C43×#476C2211yescharacteristic
34C43×#474C2211yescharacteristic
35C43×#474C2211yescharacteristic
36C43×#474C2211yescharacteristic
37C43×#469—21no—
38C43×#467—21no—
39C43×#465—21no—
40C43×#464—21no—
41C43×#464—21no—
42C43×#462C2211yescharacteristic
43C43×#461C2211yescharacteristic
44C43×#461C2211yescharacteristic
45C43×#452—21no—
46C8×Q8×C43C2211yescharacteristic
47C4×Q16×C43—21no—
48C4×SD16×C43C2211yescharacteristic
49C4×D8×C43C2211yescharacteristic
50C43×#436C2211yescharacteristic
51C8×D4×C43C2211yescharacteristic
52C8×D4×C43C2211yescharacteristic
53C43×#428—21no—
54C43×#427—21no—
55C43×#416—21no—
56C43×#334C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#333C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#332C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×D4⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#41×C43—21no—
68C2×Q16×C43—21no—
69C2×Q16×C43—21no—
70C2×Q16×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43D411yescharacteristic
74C2×D8×C43D411yescharacteristic
75C2×M16×C43—21no—
76C22×C8×C43—21no—
77C22×C8×C43—21no—
78C4⋊Q8×C43C2311yescharacteristic
79C4⋊Q8×C43C2311yescharacteristic
80C4⋊Q8×C43C2311yescharacteristic
81C4⋊Q8×C43C2311yescharacteristic
82#126×C43—41no—
83#126×C43—41no—
84#124×C43—21no—
85#124×C43—21no—
86#124×C43—41no—
87#123×C43—41no—
88C22⋊Q8×C43—21no—
89C22⋊Q8×C43—21no—
90C22⋊Q8×C43—21no—
91#121×C43—21no—
92#121×C43—21no—
93#121×C43—21no—
94C4×Q8×C43—21no—
95C4×Q8×C43—21no—
96C4×Q8×C43C2311yescharacteristic
97C4×D4×C43C2311yescharacteristic
98C4×D4×C43C2311yescharacteristic
99C4×D4×C43C2311yescharacteristic
100#117×C43—21no—
101#117×C43—21no—
102#117×C43—21no—
103#117×C43—21no—
104C2×C4⋊C4×C43—21no—
105#107×C43—21no—
106#107×C43—21no—
107#107×C43—21no—
108#107×C43—21no—
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—41no—
116#106×C43D411yescharacteristic
117C4⋊C8×C43—21no—
118C4⋊C8×C43C2311yescharacteristic
119C4⋊C8×C43C2311yescharacteristic
120C4⋊C8×C43C2311yescharacteristic
121C4⋊C8×C43C2311yescharacteristic
122#103×C43—21no—
123#103×C43—21no—
124#103×C43—21no—
125#103×C43—21no—
126#103×C43—21no—
127#103×C43—21no—
128#103×C43—41no—
129#103×C43D411yescharacteristic
130#102×C43—21no—
131#102×C43—21no—
132#102×C43—21no—
133#102×C43—21no—
134#102×C43D411yescharacteristic
135#102×C43D411yescharacteristic
136#102×C43D411yescharacteristic
137C22⋊C8×C43—21no—
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—42no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43C2×D411yescharacteristic
151C2×D4×C43—41no—
152C2×D4×C43—41no—
153C2×D4×C43C2×D411yescharacteristic
154C2×D4×C43C2×D411yescharacteristic
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—41no—
160Q16×C43—42no—
161Q16×C43—81no—
162Q16×C43—81no—
163SD16×C43—41no—
164SD16×C43—81no—
165SD16×C43—81no—
166D8×C43—22no—
167M16×C43—42no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—42no—
174C2×C8×C43—81no—
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
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—41no—
189C4⋊C4×C43—41no—
190C4⋊C4×C43—41no—
191C4⋊C4×C43C2×D411yescharacteristic
192C4⋊C4×C43C2×D411yescharacteristic
193C4⋊C4×C43C2×D411yescharacteristic
194C4⋊C4×C43C2×D411yescharacteristic
195C22⋊C4×C43—21no—
196C22⋊C4×C43—21no—
197C22⋊C4×C43—21no—
198C22⋊C4×C43—41no—
199C22⋊C4×C43—41no—
200C22⋊C4×C43—41no—
201C22⋊C4×C43—41no—
202C22⋊C4×C43—41no—
203C22⋊C4×C43—41no—
204C22⋊C4×C43—41no—
205C42×C43—21no—
206C42×C43—41no—
207C42×C43—41no—
208C42×C43—41no—
209C42×C43C2411yescharacteristic
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213Q8×C43—21no—
214Q8×C43—21no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—81no—
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—82no—
229D4×C43—161no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43H(5,𝔽2)11yescharacteristic
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—21no—
252C8×C43—41no—
253C8×C43—41no—
254C8×C43—41no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43#13512yes—
258#19878C4311yesmaximal, characteristic, direct product factor, Sylow
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43D4211yescharacteristic
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×#13511yescharacteristic
280C4×C43#57511yescharacteristic
281C4×C43#57711yescharacteristic
282C4×C43#57711yescharacteristic
283#3393C2×C4311yescharacteristic, complemented
284#3354C2×C4311yescharacteristic
285#3340C2×C4311yescharacteristic, complemented
286#3302C2×C4311yescharacteristic, complemented
287#1716C2×C4311yescharacteristic, complemented
288#1689C2×C4311yescharacteristic, complemented
289#1679C2×C4311yescharacteristic, complemented
290#1672C2×C4311yescharacteristic, complemented
291#1671C2×C4311yescharacteristic, complemented
292#1654C2×C4311yescharacteristic, complemented
293#1652C2×C4311yescharacteristic, complemented
294#1646C2×C4311yescharacteristic, complemented
295#1638C2×C4311yescharacteristic, complemented
296#1583C2×C4311yescharacteristic, complemented
297#1580C2×C4311yescharacteristic, complemented
298C2×C43—81no—
299C2×C43—81no—
300C2×C43—81no—
301C2×C43#326711yescharacteristic
302C2×C43#328411yescharacteristic
303C2×C43#328911yescharacteristic
304#556C22×C4311yescharacteristic
305#556C22×C4311yescharacteristic
306#555C22×C4311yescharacteristic
307#547C22×C4311yescharacteristic
308#498C22×C4311yescharacteristic
309#498C22×C4311yescharacteristic
310#498C22×C4311yescharacteristic
311#495—21no—
312#494C22×C4311yescharacteristic
313#487C22×C4311yescharacteristic
314#487C22×C4311yescharacteristic
315#485—21no—
316#485—21no—
317#482—21no—
318#482—21no—
319#481—21no—
320#477C22×C4311yescharacteristic
321#476C22×C4311yescharacteristic
322#474C22×C4311yescharacteristic
323#474C22×C4311yescharacteristic
324#474C22×C4311yescharacteristic
325#469—21no—
326#467—21no—
327#465—21no—
328#464—21no—
329#464—21no—
330#462C22×C4311yescharacteristic
331#461C22×C4311yescharacteristic
332#461C22×C4311yescharacteristic
333#452—21no—
334C8×Q8C22×C4311yescharacteristic
335C4×Q16—21no—
336C4×SD16C22×C4311yescharacteristic
337C4×D8C22×C4311yescharacteristic
338#436C22×C4311yescharacteristic
339C8×D4C22×C4311yescharacteristic
340C8×D4C22×C4311yescharacteristic
341#428—21no—
342#427—21no—
343#416—21no—
344#334C22×C4311yescharacteristic
345#334C22×C4311yescharacteristic
346#333C22×C4311yescharacteristic
347#332C22×C4311yescharacteristic
348#332C22×C4311yescharacteristic
349#332C22×C4311yescharacteristic
350Q8⋊C8C22×C4311yescharacteristic
351D4⋊C8C22×C4311yescharacteristic
352D4⋊C8C22×C4311yescharacteristic
353D4⋊C8C22×C4311yescharacteristic
354#322C22×C4311yescharacteristic
355C43#1987811yescharacteristic, direct product factor, Sylow
356C2×#41—21no—
357C2×Q16—21no—
358C2×Q16—21no—
359C2×Q16—21no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×SD16D4×C4311yescharacteristic
363C2×D8D4×C4311yescharacteristic
364C2×M16—21no—
365C22×C8—21no—
366C22×C8—21no—
367C4⋊Q8C23×C4311yescharacteristic
368C4⋊Q8C23×C4311yescharacteristic
369C4⋊Q8C23×C4311yescharacteristic
370C4⋊Q8C23×C4311yescharacteristic
371#126—41no—
372#126—41no—
373#124—21no—
374#124—21no—
375#124—41no—
376#123—41no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380#121—21no—
381#121—21no—
382#121—21no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8C23×C4311yescharacteristic
386C4×D4C23×C4311yescharacteristic
387C4×D4C23×C4311yescharacteristic
388C4×D4C23×C4311yescharacteristic
389#117—21no—
390#117—21no—
391#117—21no—
392#117—21no—
393C2×C4⋊C4—21no—
394#107—21no—
395#107—21no—
396#107—21no—
397#107—21no—
398#107D4×C4311yescharacteristic
399#106—21no—
400#106—21no—
401#106—21no—
402#106—21no—
403#106—21no—
404#106—41no—
405#106D4×C4311yescharacteristic
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—41no—
418#103D4×C4311yescharacteristic
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102D4×C4311yescharacteristic
424#102D4×C4311yescharacteristic
425#102D4×C4311yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—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×Q8C2×D4×C4311yescharacteristic
440C2×D4—41no—
441C2×D4—41no—
442C2×D4C2×D4×C4311yescharacteristic
443C2×D4C2×D4×C4311yescharacteristic
444C2×D4C2×D4×C4311yescharacteristic
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—41no—
449Q16—42no—
450Q16—81no—
451Q16—81no—
452SD16—41no—
453SD16—81no—
454SD16—81no—
455D8—22no—
456M16—42no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—42no—
463C2×C8—81no—
464C2×C8C2×D4×C4311yescharacteristic
465C2×C8C2×D4×C4311yescharacteristic
466C2×C8C2×D4×C4311yescharacteristic
467C2×C8C2×D4×C4311yescharacteristic
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4C2×D4×C4311yescharacteristic
481C4⋊C4C2×D4×C4311yescharacteristic
482C4⋊C4C2×D4×C4311yescharacteristic
483C4⋊C4C2×D4×C4311yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C42—21no—
495C42—41no—
496C42—41no—
497C42—41no—
498C42C24×C4311yescharacteristic
499C23—21no—
500C23—21no—
501C23—21no—
502Q8—21no—
503Q8—21no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—81no—
511D4—21no—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—21no—
517D4—82no—
518D4—161no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
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—41no—
534C2×C4—82no—
535C2×C4C22×D4×C4311yescharacteristic
536C2×C4C22×D4×C4311yescharacteristic
537C2×C4H(5,𝔽2)×C4311yescharacteristic
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8#135×C4312yes—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22D42×C4311yescharacteristic
557C4—21no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4C2×#135×C4311yescharacteristic
568C4C43×#57511yescharacteristic
569C4C43×#57711yescharacteristic
570C4C43×#57711yescharacteristic
571C2—81no—
572C2—81no—
573C2—81no—
574C2C43×#326711yescharacteristic
575C2C43×#328411yescharacteristic
576C2C43×#328911yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3354C2
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. C43×#3393C2semidirect
3. C43×#3340C2semidirect
4. C43×#3302C2semidirect
5. C43×#1716C2semidirect
6. C43×#1689C2semidirect
7. C43×#1679C2semidirect
8. C43×#1672C2semidirect
9. C43×#1671C2semidirect
10. C43×#1654C2semidirect
11. C43×#1652C2semidirect
12. C43×#1646C2semidirect
13. C43×#1638C2semidirect
14. C43×#1583C2semidirect
15. C43×#1580C2semidirect
258. #19878C43direct (N × H)
283. #3393C2×C43semidirect
285. #3340C2×C43semidirect
286. #3302C2×C43semidirect
287. #1716C2×C43semidirect
288. #1689C2×C43semidirect
289. #1679C2×C43semidirect
290. #1672C2×C43semidirect
291. #1671C2×C43semidirect
292. #1654C2×C43semidirect
293. #1652C2×C43semidirect
294. #1646C2×C43semidirect
295. #1638C2×C43semidirect
296. #1583C2×C43semidirect
297. #1580C2×C43semidirect
355. C43#19878direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33932
C43×#33542
C43×#33402
C43×#33022
C43×#17162
C43×#16892
C43×#16792
C43×#16722
C43×#16712
C43×#16542
C43×#16522
C43×#16462
C43×#16382
C43×#15832
C43×#15802
#1987843