Finite Group Databasebeta

← C43×#20227 #24940244

Subgroups — C43×#20227 #24940244

Order 11008.

624 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3367C211yesmaximal, characteristic, complemented
2C43×#3354C211yesmaximal, characteristic
3C43×#3340C211yesmaximal, characteristic, complemented
4C43×#3276C211yesmaximal, characteristic, complemented
5C43×#1716C211yesmaximal, characteristic, complemented
6C43×#1699C211yesmaximal, characteristic, complemented
7C43×#1692C211yesmaximal, characteristic, complemented
8C43×#1691C211yesmaximal, characteristic, complemented
9C43×#1669C211yesmaximal, characteristic, complemented
10C43×#1654C211yesmaximal, characteristic, complemented
11C43×#1652C211yesmaximal, characteristic, complemented
12C43×#1646C211yesmaximal, characteristic, complemented
13C43×#1637C211yesmaximal, characteristic, complemented
14C43×#1592C211yesmaximal, characteristic, complemented
15C43×#1581C211yesmaximal, characteristic, complemented
16C2×#137×C43—21no—
17C43×#556C2211yescharacteristic
18C43×#555C2211yescharacteristic
19D4×Q8×C43C2211yescharacteristic
20C43×#547C2211yescharacteristic
21C43×#498C2211yescharacteristic
22C43×#498C2211yescharacteristic
23C43×#498C2211yescharacteristic
24C43×#494C2211yescharacteristic
25C43×#489—21no—
26C43×#487C2211yescharacteristic
27C43×#487C2211yescharacteristic
28C43×#485—21no—
29C43×#482—21no—
30C43×#482—21no—
31C43×#481—21no—
32C43×#477—21no—
33C43×#477C2211yescharacteristic
34C43×#476C2211yescharacteristic
35C43×#474C2211yescharacteristic
36C43×#474C2211yescharacteristic
37C43×#474C2211yescharacteristic
38C43×#470—21no—
39C43×#469—21no—
40C43×#465—21no—
41C43×#463—21no—
42C43×#462C2211yescharacteristic
43C43×#461C2211yescharacteristic
44C43×#461C2211yescharacteristic
45C43×#452—21no—
46C43×#451—21no—
47C43×#446C2211yescharacteristic
48C43×#440—21no—
49C4×SD16×C43C2211yescharacteristic
50C4×D8×C43C2211yescharacteristic
51C43×#436C2211yescharacteristic
52C43×#436C2211yescharacteristic
53C8×D4×C43C2211yescharacteristic
54C43×#428—21no—
55C43×#427—21no—
56C43×#335C2211yescharacteristic
57C43×#335C2211yescharacteristic
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—
68C22×Q8×C43—21no—
69#137×C43—44no—
70C2×Q16×C43—21no—
71C2×Q16×C43—21no—
72C2×Q16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—21no—
75C2×SD16×C43D411yescharacteristic
76C2×D8×C43D411yescharacteristic
77C2×M16×C43—21no—
78C2×M16×C43—21no—
79C22×C8×C43—21no—
80C4⋊Q8×C43—21no—
81C4⋊Q8×C43C2311yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83C4⋊Q8×C43C2311yescharacteristic
84C4⋊Q8×C43C2311yescharacteristic
85#126×C43—41no—
86#124×C43—21no—
87#124×C43—41no—
88#123×C43—41no—
89C22⋊Q8×C43—21no—
90C22⋊Q8×C43—21no—
91C22⋊Q8×C43—21no—
92C22⋊Q8×C43—41no—
93#121×C43—21no—
94#121×C43—21no—
95#121×C43—21no—
96C4×Q8×C43—21no—
97C4×Q8×C43C2311yescharacteristic
98C4×D4×C43—21no—
99C4×D4×C43C2311yescharacteristic
100C4×D4×C43C2311yescharacteristic
101C4×D4×C43C2311yescharacteristic
102#117×C43—21no—
103#117×C43—21no—
104#117×C43—21no—
105C2×C4⋊C4×C43—21no—
106#107×C43—21no—
107#107×C43—21no—
108#107×C43—21no—
109#107×C43—21no—
110#107×C43D411yescharacteristic
111#106×C43—21no—
112#106×C43—21no—
113#106×C43—21no—
114#106×C43—21no—
115#106×C43—21no—
116#106×C43—41no—
117#106×C43D411yescharacteristic
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—41no—
130#103×C43D411yescharacteristic
131#102×C43—21no—
132#102×C43—21no—
133#102×C43—21no—
134#102×C43—21no—
135#102×C43D411yescharacteristic
136#102×C43D411yescharacteristic
137#102×C43D411yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
141#97×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—42no—
153C2×Q8×C43—81no—
154C2×Q8×C43C2×D411yescharacteristic
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43C2×D411yescharacteristic
158C2×D4×C43C2×D411yescharacteristic
159C2×D4×C43C2×D411yescharacteristic
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—41no—
164C22×C4×C43—41no—
165Q16×C43—42no—
166Q16×C43—42no—
167Q16×C43—81no—
168SD16×C43—22no—
169SD16×C43—42no—
170SD16×C43—42no—
171D8×C43—41no—
172M16×C43—42no—
173M16×C43—42no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—42no—
180C2×C8×C43C2×D411yescharacteristic
181C2×C8×C43C2×D411yescharacteristic
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
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—21no—
193C4⋊C4×C43—41no—
194C4⋊C4×C43—41no—
195C4⋊C4×C43—41no—
196C4⋊C4×C43C2×D411yescharacteristic
197C4⋊C4×C43C2×D411yescharacteristic
198C4⋊C4×C43C2×D411yescharacteristic
199C4⋊C4×C43C2×D411yescharacteristic
200C22⋊C4×C43—21no—
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—
208C22⋊C4×C43—41no—
209C42×C43—21no—
210C42×C43—41no—
211C42×C43—41no—
212C42×C43C2411yescharacteristic
213C23×C43—21no—
214C23×C43—21no—
215C23×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—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—21no—
232D4×C43—82no—
233D4×C43—161no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
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—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—82no—
250C2×C4×C43—82no—
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—41no—
258C8×C43—41no—
259C8×C43—41no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43AGL(1,ℤ/8)12yes—
263#20227C4311yesmaximal, characteristic, direct product factor, Sylow
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43D4211yescharacteristic
274C4×C43—21no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
285C4×C43#57511yescharacteristic
286C4×C43#57711yescharacteristic
287C4×C43#57811yescharacteristic
288#3367C2×C4311yescharacteristic, complemented
289#3354C2×C4311yescharacteristic
290#3340C2×C4311yescharacteristic, complemented
291#3276C2×C4311yescharacteristic, complemented
292#1716C2×C4311yescharacteristic, complemented
293#1699C2×C4311yescharacteristic, complemented
294#1692C2×C4311yescharacteristic, complemented
295#1691C2×C4311yescharacteristic, complemented
296#1669C2×C4311yescharacteristic, complemented
297#1654C2×C4311yescharacteristic, complemented
298#1652C2×C4311yescharacteristic, complemented
299#1646C2×C4311yescharacteristic, complemented
300#1637C2×C4311yescharacteristic, complemented
301#1592C2×C4311yescharacteristic, complemented
302#1581C2×C4311yescharacteristic, complemented
303C2×C43—81no—
304C2×C43—81no—
305C2×C43—81no—
306C2×C43#326911yescharacteristic
307C2×C43#327211yescharacteristic
308C2×C43#328911yescharacteristic
309C2×#137—21no—
310#556C22×C4311yescharacteristic
311#555C22×C4311yescharacteristic
312D4×Q8C22×C4311yescharacteristic
313#547C22×C4311yescharacteristic
314#498C22×C4311yescharacteristic
315#498C22×C4311yescharacteristic
316#498C22×C4311yescharacteristic
317#494C22×C4311yescharacteristic
318#489—21no—
319#487C22×C4311yescharacteristic
320#487C22×C4311yescharacteristic
321#485—21no—
322#482—21no—
323#482—21no—
324#481—21no—
325#477—21no—
326#477C22×C4311yescharacteristic
327#476C22×C4311yescharacteristic
328#474C22×C4311yescharacteristic
329#474C22×C4311yescharacteristic
330#474C22×C4311yescharacteristic
331#470—21no—
332#469—21no—
333#465—21no—
334#463—21no—
335#462C22×C4311yescharacteristic
336#461C22×C4311yescharacteristic
337#461C22×C4311yescharacteristic
338#452—21no—
339#451—21no—
340#446C22×C4311yescharacteristic
341#440—21no—
342C4×SD16C22×C4311yescharacteristic
343C4×D8C22×C4311yescharacteristic
344#436C22×C4311yescharacteristic
345#436C22×C4311yescharacteristic
346C8×D4C22×C4311yescharacteristic
347#428—21no—
348#427—21no—
349#335C22×C4311yescharacteristic
350#335C22×C4311yescharacteristic
351#333C22×C4311yescharacteristic
352#332C22×C4311yescharacteristic
353#332C22×C4311yescharacteristic
354#332C22×C4311yescharacteristic
355Q8⋊C8C22×C4311yescharacteristic
356D4⋊C8C22×C4311yescharacteristic
357D4⋊C8C22×C4311yescharacteristic
358D4⋊C8C22×C4311yescharacteristic
359#322C22×C4311yescharacteristic
360C43#2022711yescharacteristic, direct product factor, Sylow
361C2×#41—21no—
362C22×Q8—21no—
363#137—44no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×Q16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16D4×C4311yescharacteristic
370C2×D8D4×C4311yescharacteristic
371C2×M16—21no—
372C2×M16—21no—
373C22×C8—21no—
374C4⋊Q8—21no—
375C4⋊Q8C23×C4311yescharacteristic
376C4⋊Q8C23×C4311yescharacteristic
377C4⋊Q8C23×C4311yescharacteristic
378C4⋊Q8C23×C4311yescharacteristic
379#126—41no—
380#124—21no—
381#124—41no—
382#123—41no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—41no—
387#121—21no—
388#121—21no—
389#121—21no—
390C4×Q8—21no—
391C4×Q8C23×C4311yescharacteristic
392C4×D4—21no—
393C4×D4C23×C4311yescharacteristic
394C4×D4C23×C4311yescharacteristic
395C4×D4C23×C4311yescharacteristic
396#117—21no—
397#117—21no—
398#117—21no—
399C2×C4⋊C4—21no—
400#107—21no—
401#107—21no—
402#107—21no—
403#107—21no—
404#107D4×C4311yescharacteristic
405#106—21no—
406#106—21no—
407#106—21no—
408#106—21no—
409#106—21no—
410#106—41no—
411#106D4×C4311yescharacteristic
412C4⋊C8—21no—
413C4⋊C8C23×C4311yescharacteristic
414C4⋊C8C23×C4311yescharacteristic
415C4⋊C8C23×C4311yescharacteristic
416C4⋊C8C23×C4311yescharacteristic
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103—41no—
424#103D4×C4311yescharacteristic
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102D4×C4311yescharacteristic
430#102D4×C4311yescharacteristic
431#102D4×C4311yescharacteristic
432C22⋊C8—21no—
433C22⋊C8—21no—
434C22⋊C8—21no—
435#97—21no—
436C4×C8C23×C4311yescharacteristic
437C4×C8C23×C4311yescharacteristic
438C4×C8C23×C4311yescharacteristic
439#41—42no—
440#41—81no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—41no—
446C2×Q8—42no—
447C2×Q8—81no—
448C2×Q8C2×D4×C4311yescharacteristic
449C2×D4—41no—
450C2×D4—41no—
451C2×D4C2×D4×C4311yescharacteristic
452C2×D4C2×D4×C4311yescharacteristic
453C2×D4C2×D4×C4311yescharacteristic
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—41no—
458C22×C4—41no—
459Q16—42no—
460Q16—42no—
461Q16—81no—
462SD16—22no—
463SD16—42no—
464SD16—42no—
465D8—41no—
466M16—42no—
467M16—42no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—42no—
474C2×C8C2×D4×C4311yescharacteristic
475C2×C8C2×D4×C4311yescharacteristic
476C2×C8C2×D4×C4311yescharacteristic
477C2×C8C2×D4×C4311yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4C2×D4×C4311yescharacteristic
491C4⋊C4C2×D4×C4311yescharacteristic
492C4⋊C4C2×D4×C4311yescharacteristic
493C4⋊C4C2×D4×C4311yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C42—21no—
504C42—41no—
505C42—41no—
506C42C24×C4311yescharacteristic
507C23—21no—
508C23—21no—
509C23—21no—
510Q8—21no—
511Q8—21no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8—81no—
519Q8—82no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—82no—
527D4—161no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—82no—
544C2×C4—82no—
545C2×C4C22×D4×C4311yescharacteristic
546C2×C4C22×D4×C4311yescharacteristic
547C2×C4H(5,𝔽2)×C4311yescharacteristic
548C8—21no—
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8AGL(1,ℤ/8)×C4312yes—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22D42×C4311yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
578C4C43×#57511yescharacteristic
579C4C43×#57711yescharacteristic
580C4C43×#57811yescharacteristic
581C2—81no—
582C2—81no—
583C2—81no—
584C2C43×#326911yescharacteristic
585C2C43×#327211yescharacteristic
586C2C43×#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×#3367C2semidirect
3. C43×#3340C2semidirect
4. C43×#3276C2semidirect
5. C43×#1716C2semidirect
6. C43×#1699C2semidirect
7. C43×#1692C2semidirect
8. C43×#1691C2semidirect
9. C43×#1669C2semidirect
10. C43×#1654C2semidirect
11. C43×#1652C2semidirect
12. C43×#1646C2semidirect
13. C43×#1637C2semidirect
14. C43×#1592C2semidirect
15. C43×#1581C2semidirect
263. #20227C43direct (N × H)
288. #3367C2×C43semidirect
290. #3340C2×C43semidirect
291. #3276C2×C43semidirect
292. #1716C2×C43semidirect
293. #1699C2×C43semidirect
294. #1692C2×C43semidirect
295. #1691C2×C43semidirect
296. #1669C2×C43semidirect
297. #1654C2×C43semidirect
298. #1652C2×C43semidirect
299. #1646C2×C43semidirect
300. #1637C2×C43semidirect
301. #1592C2×C43semidirect
302. #1581C2×C43semidirect
360. C43#20227direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33672
C43×#33542
C43×#33402
C43×#32762
C43×#17162
C43×#16992
C43×#16922
C43×#16912
C43×#16692
C43×#16542
C43×#16522
C43×#16462
C43×#16372
C43×#15922
C43×#15812
#2022743