Finite Group Databasebeta

← C43×#20253 #24940270

Subgroups — C43×#20253 #24940270

Order 11008.

592 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×#3366C211yesmaximal, characteristic
2C43×#3360C211yesmaximal, characteristic, complemented
3C43×#3356C211yesmaximal, characteristic, complemented
4C43×#3333C211yesmaximal, characteristic, complemented
5C43×#1720C211yesmaximal, characteristic, complemented
6C43×#1704C211yesmaximal, characteristic, complemented
7C43×#1697C211yesmaximal, characteristic, complemented
8C43×#1691C211yesmaximal, characteristic, complemented
9C43×#1678C211yesmaximal, characteristic, complemented
10C43×#1642C211yesmaximal, characteristic, complemented
11C43×#1632C211yesmaximal, characteristic, complemented
12C43×#1632C211yesmaximal, characteristic, complemented
13C43×#1628C211yesmaximal, characteristic, complemented
14C43×#1594C211yesmaximal, characteristic, complemented
15C43×#1584C211yesmaximal, characteristic, complemented
16C43×#556C2211yescharacteristic
17C43×#554C2211yescharacteristic
18C43×#554C2211yescharacteristic
19C43×#550C2211yescharacteristic
20C43×#498C2211yescharacteristic
21C43×#494C2211yescharacteristic
22C43×#490—21no—
23C43×#488—21no—
24C43×#487C2211yescharacteristic
25C43×#486C2211yescharacteristic
26C43×#486C2211yescharacteristic
27C43×#486C2211yescharacteristic
28C43×#485—21no—
29C43×#483—21no—
30C43×#480—21no—
31C43×#479—21no—
32C43×#478—21no—
33C43×#477C2211yescharacteristic
34C43×#477C2211yescharacteristic
35C43×#476C2211yescharacteristic
36C43×#476C2211yescharacteristic
37C43×#475C2211yescharacteristic
38C43×#470—21no—
39C43×#468—21no—
40C43×#463—21no—
41C43×#461C2211yescharacteristic
42C43×#460C2211yescharacteristic
43C43×#459—21no—
44C43×#459C2211yescharacteristic
45C43×#452—21no—
46C43×#446C2211yescharacteristic
47C8×Q8×C43C2211yescharacteristic
48C43×#442—21no—
49C4×Q16×C43C2211yescharacteristic
50C4×SD16×C43—21no—
51C4×D8×C43C2211yescharacteristic
52C43×#436C2211yescharacteristic
53C43×#436C2211yescharacteristic
54C43×#428—21no—
55C43×#417—21no—
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#333C2211yescharacteristic
59C43×#333C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#41×C43—21no—
68C2×Q16×C43—41no—
69C2×Q16×C43D411yescharacteristic
70C2×SD16×C43—21no—
71C2×SD16×C43—21no—
72C2×D8×C43—21no—
73C2×D8×C43D411yescharacteristic
74C2×M16×C43—21no—
75C2×M16×C43—21no—
76C4⋊Q8×C43C2311yescharacteristic
77C4⋊Q8×C43C2311yescharacteristic
78C4⋊Q8×C43C2311yescharacteristic
79#127×C43—21no—
80#127×C43C2311yescharacteristic
81#126×C43—41no—
82#125×C43—21no—
83#125×C43—21no—
84#124×C43—21no—
85C22⋊Q8×C43—21no—
86C22⋊Q8×C43—21no—
87C22⋊Q8×C43—21no—
88C22⋊Q8×C43—41no—
89C22⋊Q8×C43—41no—
90#121×C43—21no—
91#121×C43—41no—
92C4×Q8×C43—21no—
93C4×Q8×C43C2311yescharacteristic
94C4×Q8×C43C2311yescharacteristic
95C4×D4×C43—21no—
96C4×D4×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43C2311yescharacteristic
99C4×D4×C43C2311yescharacteristic
100#117×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103#107×C43—21no—
104#107×C43—21no—
105#107×C43D411yescharacteristic
106#107×C43D411yescharacteristic
107#106×C43—21no—
108#106×C43—21no—
109#106×C43—21no—
110#106×C43—21no—
111#106×C43—21no—
112C4⋊C8×C43—21no—
113C4⋊C8×C43—21no—
114C4⋊C8×C43C2311yescharacteristic
115C4⋊C8×C43C2311yescharacteristic
116C4⋊C8×C43C2311yescharacteristic
117C4⋊C8×C43C2311yescharacteristic
118#103×C43—21no—
119#103×C43—21no—
120#103×C43—21no—
121#103×C43—21no—
122#103×C43—21no—
123#103×C43—21no—
124#103×C43D411yescharacteristic
125#103×C43D411yescharacteristic
126#102×C43—21no—
127#102×C43—21no—
128#102×C43—21no—
129#102×C43—21no—
130#102×C43—21no—
131#102×C43—21no—
132#102×C43—21no—
133#102×C43—21no—
134#102×C43—41no—
135#102×C43D411yescharacteristic
136#102×C43D411yescharacteristic
137C22⋊C8×C43—21no—
138C22⋊C8×C43—21no—
139#97×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×C43C2×D411yescharacteristic
150C2×Q8×C43C2×D411yescharacteristic
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—41no—
155C2×D4×C43—41no—
156C2×D4×C43C2×D411yescharacteristic
157C2×D4×C43C2×D411yescharacteristic
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—41no—
161C22×C4×C43—41no—
162C22×C4×C43—41no—
163Q16×C43—41no—
164Q16×C43—82no—
165SD16×C43—42no—
166SD16×C43—81no—
167D8×C43—41no—
168D8×C43—42no—
169M16×C43—42no—
170M16×C43—81no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
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×C43—41no—
192C4⋊C4×C43—41no—
193C4⋊C4×C43C2×D411yescharacteristic
194C4⋊C4×C43C2×D411yescharacteristic
195C4⋊C4×C43C2×D411yescharacteristic
196C4⋊C4×C43C2×D411yescharacteristic
197C22⋊C4×C43—21no—
198C22⋊C4×C43—21no—
199C22⋊C4×C43—41no—
200C22⋊C4×C43—41no—
201C22⋊C4×C43—41no—
202C22⋊C4×C43—41no—
203C22⋊C4×C43—41no—
204C42×C43—21no—
205C42×C43—21no—
206C42×C43—41no—
207C42×C43C2411yescharacteristic
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—41no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—21no—
214Q8×C43—21no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—81no—
218Q8×C43—81no—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—81no—
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—21no—
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—82no—
244C2×C4×C43—161no—
245C2×C4×C43—161no—
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—21no—
253C8×C43—41no—
254C8×C43—41no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43—41no—
258#20253C4311yesmaximal, 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—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43D4211yescharacteristic
269C4×C43—21no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43—81no—
279C4×C43#57511yescharacteristic
280C4×C43#57511yescharacteristic
281C4×C43#57711yescharacteristic
282C4×C43#57811yescharacteristic
283#3366C2×C4311yescharacteristic
284#3360C2×C4311yescharacteristic, complemented
285#3356C2×C4311yescharacteristic, complemented
286#3333C2×C4311yescharacteristic, complemented
287#1720C2×C4311yescharacteristic, complemented
288#1704C2×C4311yescharacteristic, complemented
289#1697C2×C4311yescharacteristic, complemented
290#1691C2×C4311yescharacteristic, complemented
291#1678C2×C4311yescharacteristic, complemented
292#1642C2×C4311yescharacteristic, complemented
293#1632C2×C4311yescharacteristic, complemented
294#1632C2×C4311yescharacteristic, complemented
295#1628C2×C4311yescharacteristic, complemented
296#1594C2×C4311yescharacteristic, complemented
297#1584C2×C4311yescharacteristic, complemented
298C2×C43—81no—
299C2×C43—81no—
300C2×C43—161no—
301C2×C43#326711yescharacteristic
302C2×C43#327711yescharacteristic
303C2×C43#328811yescharacteristic
304#556C22×C4311yescharacteristic
305#554C22×C4311yescharacteristic
306#554C22×C4311yescharacteristic
307#550C22×C4311yescharacteristic
308#498C22×C4311yescharacteristic
309#494C22×C4311yescharacteristic
310#490—21no—
311#488—21no—
312#487C22×C4311yescharacteristic
313#486C22×C4311yescharacteristic
314#486C22×C4311yescharacteristic
315#486C22×C4311yescharacteristic
316#485—21no—
317#483—21no—
318#480—21no—
319#479—21no—
320#478—21no—
321#477C22×C4311yescharacteristic
322#477C22×C4311yescharacteristic
323#476C22×C4311yescharacteristic
324#476C22×C4311yescharacteristic
325#475C22×C4311yescharacteristic
326#470—21no—
327#468—21no—
328#463—21no—
329#461C22×C4311yescharacteristic
330#460C22×C4311yescharacteristic
331#459—21no—
332#459C22×C4311yescharacteristic
333#452—21no—
334#446C22×C4311yescharacteristic
335C8×Q8C22×C4311yescharacteristic
336#442—21no—
337C4×Q16C22×C4311yescharacteristic
338C4×SD16—21no—
339C4×D8C22×C4311yescharacteristic
340#436C22×C4311yescharacteristic
341#436C22×C4311yescharacteristic
342#428—21no—
343#417—21no—
344#335C22×C4311yescharacteristic
345#334C22×C4311yescharacteristic
346#333C22×C4311yescharacteristic
347#333C22×C4311yescharacteristic
348#332C22×C4311yescharacteristic
349#331C22×C4311yescharacteristic
350Q8⋊C8C22×C4311yescharacteristic
351Q8⋊C8C22×C4311yescharacteristic
352D4⋊C8C22×C4311yescharacteristic
353D4⋊C8C22×C4311yescharacteristic
354#322C22×C4311yescharacteristic
355C43#2025311yescharacteristic, direct product factor, Sylow
356C2×#41—21no—
357C2×Q16—41no—
358C2×Q16D4×C4311yescharacteristic
359C2×SD16—21no—
360C2×SD16—21no—
361C2×D8—21no—
362C2×D8D4×C4311yescharacteristic
363C2×M16—21no—
364C2×M16—21no—
365C4⋊Q8C23×C4311yescharacteristic
366C4⋊Q8C23×C4311yescharacteristic
367C4⋊Q8C23×C4311yescharacteristic
368#127—21no—
369#127C23×C4311yescharacteristic
370#126—41no—
371#125—21no—
372#125—21no—
373#124—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C22⋊Q8—41no—
378C22⋊Q8—41no—
379#121—21no—
380#121—41no—
381C4×Q8—21no—
382C4×Q8C23×C4311yescharacteristic
383C4×Q8C23×C4311yescharacteristic
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4C23×C4311yescharacteristic
388C4×D4C23×C4311yescharacteristic
389#117—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392#107—21no—
393#107—21no—
394#107D4×C4311yescharacteristic
395#107D4×C4311yescharacteristic
396#106—21no—
397#106—21no—
398#106—21no—
399#106—21no—
400#106—21no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8C23×C4311yescharacteristic
404C4⋊C8C23×C4311yescharacteristic
405C4⋊C8C23×C4311yescharacteristic
406C4⋊C8C23×C4311yescharacteristic
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103D4×C4311yescharacteristic
414#103D4×C4311yescharacteristic
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—41no—
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×Q8C2×D4×C4311yescharacteristic
439C2×Q8C2×D4×C4311yescharacteristic
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4C2×D4×C4311yescharacteristic
446C2×D4C2×D4×C4311yescharacteristic
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452Q16—41no—
453Q16—82no—
454SD16—42no—
455SD16—81no—
456D8—41no—
457D8—42no—
458M16—42no—
459M16—81no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8C2×D4×C4311yescharacteristic
466C2×C8C2×D4×C4311yescharacteristic
467C2×C8C2×D4×C4311yescharacteristic
468C2×C8C2×D4×C4311yescharacteristic
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⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4C2×D4×C4311yescharacteristic
483C4⋊C4C2×D4×C4311yescharacteristic
484C4⋊C4C2×D4×C4311yescharacteristic
485C4⋊C4C2×D4×C4311yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C42—21no—
494C42—21no—
495C42—41no—
496C42C24×C4311yescharacteristic
497C23—21no—
498C23—21no—
499C23—41no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—21no—
504Q8—41no—
505Q8—41no—
506Q8—81no—
507Q8—81no—
508D4—21no—
509D4—21no—
510D4—21no—
511D4—21no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—81no—
517D4—82no—
518D4—161no—
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—82no—
533C2×C4—161no—
534C2×C4—161no—
535C2×C4C22×D4×C4311yescharacteristic
536C2×C4C22×D4×C4311yescharacteristic
537C2×C4H(5,𝔽2)×C4311yescharacteristic
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22D42×C4311yescharacteristic
557C4—21no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4C43×#57511yescharacteristic
568C4C43×#57511yescharacteristic
569C4C43×#57711yescharacteristic
570C4C43×#57811yescharacteristic
571C2—81no—
572C2—81no—
573C2—161no—
574C2C43×#326711yescharacteristic
575C2C43×#327711yescharacteristic
576C2C43×#328811yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3366C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#3360C2semidirect
3. C43×#3356C2semidirect
4. C43×#3333C2semidirect
5. C43×#1720C2semidirect
6. C43×#1704C2semidirect
7. C43×#1697C2semidirect
8. C43×#1691C2semidirect
9. C43×#1678C2semidirect
10. C43×#1642C2semidirect
11. C43×#1632C2semidirect
12. C43×#1632C2semidirect
13. C43×#1628C2semidirect
14. C43×#1594C2semidirect
15. C43×#1584C2semidirect
258. #20253C43direct (N × H)
284. #3360C2×C43semidirect
285. #3356C2×C43semidirect
286. #3333C2×C43semidirect
287. #1720C2×C43semidirect
288. #1704C2×C43semidirect
289. #1697C2×C43semidirect
290. #1691C2×C43semidirect
291. #1678C2×C43semidirect
292. #1642C2×C43semidirect
293. #1632C2×C43semidirect
294. #1632C2×C43semidirect
295. #1628C2×C43semidirect
296. #1594C2×C43semidirect
297. #1584C2×C43semidirect
355. C43#20253direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33662
C43×#33602
C43×#33562
C43×#33332
C43×#17202
C43×#17042
C43×#16972
C43×#16912
C43×#16782
C43×#16422
C43×#16322
C43×#16282
C43×#15942
C43×#15842
#2025343