Finite Group Databasebeta

← C43×#20230 #24940247

Subgroups — C43×#20230 #24940247

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×#3373C211yesmaximal, characteristic, complemented
2C43×#3361C211yesmaximal, characteristic, complemented
3C43×#3357C211yesmaximal, characteristic, complemented
4C43×#3329C211yesmaximal, characteristic, complemented
5C43×#1719C211yesmaximal, characteristic, complemented
6C43×#1701C211yesmaximal, characteristic, complemented
7C43×#1697C211yesmaximal, characteristic, complemented
8C43×#1696C211yesmaximal, characteristic, complemented
9C43×#1684C211yesmaximal, characteristic, complemented
10C43×#1643C211yesmaximal, characteristic, complemented
11C43×#1637C211yesmaximal, characteristic, complemented
12C43×#1630C211yesmaximal, characteristic, complemented
13C43×#1624C211yesmaximal, characteristic
14C43×#1592C211yesmaximal, characteristic, complemented
15C43×#1583C211yesmaximal, characteristic, complemented
16C43×#559C2211yescharacteristic
17C43×#555C2211yescharacteristic
18C43×#554C2211yescharacteristic
19D4×Q8×C43C2211yescharacteristic
20C43×#500C2211yescharacteristic
21C43×#492C2211yescharacteristic
22C43×#489—21no—
23C43×#488—21no—
24C43×#487C2211yescharacteristic
25C43×#487C2211yescharacteristic
26C43×#486C2211yescharacteristic
27C43×#486C2211yescharacteristic
28C43×#485—21no—
29C43×#485—21no—
30C43×#480—21no—
31C43×#478—21no—
32C43×#477C2211yescharacteristic
33C43×#477C2211yescharacteristic
34C43×#477C2211yescharacteristic
35C43×#476—21no—
36C43×#476C2211yescharacteristic
37C43×#475C2211yescharacteristic
38C43×#468—21no—
39C43×#468—21no—
40C43×#463—21no—
41C43×#463—21no—
42C43×#461C2211yescharacteristic
43C43×#459C2211yescharacteristic
44C43×#459C2211yescharacteristic
45C43×#448—21no—
46C43×#446C2211yescharacteristic
47C8×Q8×C43C2211yescharacteristic
48C43×#442—21no—
49C4×SD16×C43C2211yescharacteristic
50C4×SD16×C43C2211yescharacteristic
51C4×D8×C43—21no—
52C43×#436C2211yescharacteristic
53C43×#436C2211yescharacteristic
54C43×#428—21no—
55C43×#419—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
67C22×Q8×C43—21no—
68C2×SD16×C43—21no—
69C2×SD16×C43—41no—
70C2×SD16×C43D411yescharacteristic
71C2×SD16×C43D411yescharacteristic
72C2×D8×C43—21no—
73C2×D8×C43—21no—
74C2×M16×C43—21no—
75C2×M16×C43—21no—
76C4⋊Q8×C43—21no—
77C4⋊Q8×C43C2311yescharacteristic
78C4⋊Q8×C43C2311yescharacteristic
79C4⋊Q8×C43C2311yescharacteristic
80#127×C43C2311yescharacteristic
81#125×C43—21no—
82#124×C43—21no—
83#124×C43—21no—
84#124×C43—41no—
85#123×C43—41no—
86C22⋊Q8×C43—21no—
87C22⋊Q8×C43—21no—
88C22⋊Q8×C43—41no—
89C22⋊Q8×C43—41no—
90#121×C43—21no—
91#121×C43—21no—
92C4×Q8×C43C2311yescharacteristic
93C4×Q8×C43C2311yescharacteristic
94C4×D4×C43—21no—
95C4×D4×C43—21no—
96C4×D4×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43C2311yescharacteristic
99C4×D4×C43C2311yescharacteristic
100#117×C43—21no—
101#117×C43—21no—
102C2×C4⋊C4×C43—21no—
103#107×C43—21no—
104#107×C43—21no—
105#107×C43—21no—
106#107×C43—21no—
107#107×C43—21no—
108#106×C43—21no—
109#106×C43—21no—
110#106×C43D411yescharacteristic
111#106×C43D411yescharacteristic
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×C43—21no—
125#103×C43—41no—
126#103×C43D411yescharacteristic
127#103×C43D411yescharacteristic
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—21no—
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
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—41no—
148C2×Q8×C43—42no—
149C2×Q8×C43—81no—
150C2×Q8×C43C2×D411yescharacteristic
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
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—
163SD16×C43—41no—
164SD16×C43—41no—
165SD16×C43—81no—
166SD16×C43—82no—
167D8×C43—42no—
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×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—41no—
198C22⋊C4×C43—41no—
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—
219Q8×C43—82no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—81no—
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#20230C4311yesmaximal, 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#3373C2×C4311yescharacteristic, complemented
284#3361C2×C4311yescharacteristic, complemented
285#3357C2×C4311yescharacteristic, complemented
286#3329C2×C4311yescharacteristic, complemented
287#1719C2×C4311yescharacteristic, complemented
288#1701C2×C4311yescharacteristic, complemented
289#1697C2×C4311yescharacteristic, complemented
290#1696C2×C4311yescharacteristic, complemented
291#1684C2×C4311yescharacteristic, complemented
292#1643C2×C4311yescharacteristic, complemented
293#1637C2×C4311yescharacteristic, complemented
294#1630C2×C4311yescharacteristic, complemented
295#1624C2×C4311yescharacteristic
296#1592C2×C4311yescharacteristic, complemented
297#1583C2×C4311yescharacteristic, complemented
298C2×C43—81no—
299C2×C43—81no—
300C2×C43—161no—
301C2×C43#326911yescharacteristic
302C2×C43#327511yescharacteristic
303C2×C43#328811yescharacteristic
304#559C22×C4311yescharacteristic
305#555C22×C4311yescharacteristic
306#554C22×C4311yescharacteristic
307D4×Q8C22×C4311yescharacteristic
308#500C22×C4311yescharacteristic
309#492C22×C4311yescharacteristic
310#489—21no—
311#488—21no—
312#487C22×C4311yescharacteristic
313#487C22×C4311yescharacteristic
314#486C22×C4311yescharacteristic
315#486C22×C4311yescharacteristic
316#485—21no—
317#485—21no—
318#480—21no—
319#478—21no—
320#477C22×C4311yescharacteristic
321#477C22×C4311yescharacteristic
322#477C22×C4311yescharacteristic
323#476—21no—
324#476C22×C4311yescharacteristic
325#475C22×C4311yescharacteristic
326#468—21no—
327#468—21no—
328#463—21no—
329#463—21no—
330#461C22×C4311yescharacteristic
331#459C22×C4311yescharacteristic
332#459C22×C4311yescharacteristic
333#448—21no—
334#446C22×C4311yescharacteristic
335C8×Q8C22×C4311yescharacteristic
336#442—21no—
337C4×SD16C22×C4311yescharacteristic
338C4×SD16C22×C4311yescharacteristic
339C4×D8—21no—
340#436C22×C4311yescharacteristic
341#436C22×C4311yescharacteristic
342#428—21no—
343#419—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#2023011yescharacteristic, direct product factor, Sylow
356C22×Q8—21no—
357C2×SD16—21no—
358C2×SD16—41no—
359C2×SD16D4×C4311yescharacteristic
360C2×SD16D4×C4311yescharacteristic
361C2×D8—21no—
362C2×D8—21no—
363C2×M16—21no—
364C2×M16—21no—
365C4⋊Q8—21no—
366C4⋊Q8C23×C4311yescharacteristic
367C4⋊Q8C23×C4311yescharacteristic
368C4⋊Q8C23×C4311yescharacteristic
369#127C23×C4311yescharacteristic
370#125—21no—
371#124—21no—
372#124—21no—
373#124—41no—
374#123—41no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C22⋊Q8—41no—
378C22⋊Q8—41no—
379#121—21no—
380#121—21no—
381C4×Q8C23×C4311yescharacteristic
382C4×Q8C23×C4311yescharacteristic
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4C23×C4311yescharacteristic
388C4×D4C23×C4311yescharacteristic
389#117—21no—
390#117—21no—
391C2×C4⋊C4—21no—
392#107—21no—
393#107—21no—
394#107—21no—
395#107—21no—
396#107—21no—
397#106—21no—
398#106—21no—
399#106D4×C4311yescharacteristic
400#106D4×C4311yescharacteristic
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#103—21no—
414#103—41no—
415#103D4×C4311yescharacteristic
416#103D4×C4311yescharacteristic
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
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
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—41no—
437C2×Q8—42no—
438C2×Q8—81no—
439C2×Q8C2×D4×C4311yescharacteristic
440C2×Q8C2×D4×C4311yescharacteristic
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
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—
452SD16—41no—
453SD16—41no—
454SD16—81no—
455SD16—82no—
456D8—42no—
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⋊C4C2×D4×C4311yescharacteristic
481C4⋊C4C2×D4×C4311yescharacteristic
482C4⋊C4C2×D4×C4311yescharacteristic
483C4⋊C4C2×D4×C4311yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—41no—
487C22⋊C4—41no—
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—
508Q8—82no—
509D4—21no—
510D4—21no—
511D4—21no—
512D4—21no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—41no—
517D4—81no—
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×#326911yescharacteristic
575C2C43×#327511yescharacteristic
576C2C43×#328811yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#1624C2
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×#3373C2semidirect
2. C43×#3361C2semidirect
3. C43×#3357C2semidirect
4. C43×#3329C2semidirect
5. C43×#1719C2semidirect
6. C43×#1701C2semidirect
7. C43×#1697C2semidirect
8. C43×#1696C2semidirect
9. C43×#1684C2semidirect
10. C43×#1643C2semidirect
11. C43×#1637C2semidirect
12. C43×#1630C2semidirect
14. C43×#1592C2semidirect
15. C43×#1583C2semidirect
258. #20230C43direct (N × H)
283. #3373C2×C43semidirect
284. #3361C2×C43semidirect
285. #3357C2×C43semidirect
286. #3329C2×C43semidirect
287. #1719C2×C43semidirect
288. #1701C2×C43semidirect
289. #1697C2×C43semidirect
290. #1696C2×C43semidirect
291. #1684C2×C43semidirect
292. #1643C2×C43semidirect
293. #1637C2×C43semidirect
294. #1630C2×C43semidirect
296. #1592C2×C43semidirect
297. #1583C2×C43semidirect
355. C43#20230direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33732
C43×#33612
C43×#33572
C43×#33292
C43×#17192
C43×#17012
C43×#16972
C43×#16962
C43×#16842
C43×#16432
C43×#16372
C43×#16302
C43×#16242
C43×#15922
C43×#15832
#2023043