Finite Group Databasebeta

← C43×#19493 #24939510

Subgroups — C43×#19493 #24939510

Order 11008.

608 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3210C211yesmaximal, characteristic, complemented
2C43×#3115C211yesmaximal, characteristic
3C43×#3076C211yesmaximal, characteristic, complemented
4C43×#2991C211yesmaximal, characteristic, complemented
5C43×#1703C211yesmaximal, characteristic, complemented
6C43×#1697C211yesmaximal, characteristic, complemented
7C43×#1689C211yesmaximal, characteristic, complemented
8C43×#1685C211yesmaximal, characteristic, complemented
9C43×#1684C211yesmaximal, characteristic, complemented
10C43×#1678C211yesmaximal, characteristic, complemented
11C43×#1670C211yesmaximal, characteristic, complemented
12C43×#1666C211yesmaximal, characteristic, complemented
13C43×#1573C211yesmaximal, characteristic, complemented
14C43×#1559C211yesmaximal, characteristic, complemented
15C43×#1547C211yesmaximal, characteristic, complemented
16C43×#533C2211yescharacteristic
17C43×#532C2211yescharacteristic
18C4×#41×C43C2211yescharacteristic
19C43×#494C2211yescharacteristic
20C43×#492C2211yescharacteristic
21C43×#487C2211yescharacteristic
22C43×#486C2211yescharacteristic
23C43×#482—21no—
24C43×#479—21no—
25C43×#478—21no—
26C43×#477C2211yescharacteristic
27C43×#476C2211yescharacteristic
28C43×#475C2211yescharacteristic
29C43×#475C2211yescharacteristic
30C43×#474C2211yescharacteristic
31C43×#474C2211yescharacteristic
32C43×#464—21no—
33C43×#464—21no—
34C43×#460C2211yescharacteristic
35C43×#459C2211yescharacteristic
36C43×#452—21no—
37C43×#452—21no—
38C43×#449—21no—
39C8×Q8×C43C2211yescharacteristic
40C8×Q8×C43C2211yescharacteristic
41C43×#442—21no—
42C43×#440—21no—
43C43×#436—21no—
44C43×#436—21no—
45C43×#436C2211yescharacteristic
46C43×#436C2211yescharacteristic
47C43×#432C2211yescharacteristic
48C43×#431—21no—
49C43×#431C2211yescharacteristic
50C43×#427—21no—
51C43×#423—21no—
52C43×#423C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C43×#416—21no—
55C43×#335C2211yescharacteristic
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#334C2211yescharacteristic
59C43×#333C2211yescharacteristic
60C43×#333C2211yescharacteristic
61C43×#332C2211yescharacteristic
62C43×#332C2211yescharacteristic
63C43×#332C2211yescharacteristic
64C43×#332C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#41×C43—21no—
68C2×#41×C43D411yescharacteristic
69C2×Q16×C43—21no—
70C2×Q16×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×D8×C43—21no—
75C2×M16×C43—21no—
76C2×M16×C43—21no—
77C2×M16×C43—21no—
78C22×C8×C43—21no—
79C4⋊Q8×C43C2311yescharacteristic
80C4⋊Q8×C43C2311yescharacteristic
81C4⋊Q8×C43C2311yescharacteristic
82#127×C43C2311yescharacteristic
83#125×C43—21no—
84#124×C43—21no—
85C22⋊Q8×C43—21no—
86C22⋊Q8×C43—21no—
87#121×C43—21no—
88#121×C43—21no—
89C4×Q8×C43—21no—
90C4×Q8×C43—21no—
91C4×Q8×C43D411yescharacteristic
92C4×Q8×C43C2311yescharacteristic
93C4×D4×C43—21no—
94C4×D4×C43—21no—
95C4×D4×C43—21no—
96C4×D4×C43—21no—
97C4×D4×C43D411yescharacteristic
98C4×D4×C43C2311yescharacteristic
99#117×C43—21no—
100#117×C43—21no—
101#117×C43D411yescharacteristic
102C2×C42×C43—21no—
103C2×C42×C43C2311yescharacteristic
104#107×C43—21no—
105#107×C43—21no—
106#107×C43—21no—
107#106×C43—21no—
108#106×C43—21no—
109#106×C43—21no—
110C4⋊C8×C43—21no—
111C4⋊C8×C43—21no—
112C4⋊C8×C43—21no—
113C4⋊C8×C43—21no—
114C4⋊C8×C43D411yescharacteristic
115C4⋊C8×C43D411yescharacteristic
116C4⋊C8×C43C2311yescharacteristic
117C4⋊C8×C43C2311yescharacteristic
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#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—
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43D411yescharacteristic
138C22⋊C8×C43D411yescharacteristic
139#97×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—22no—
145#41×C43—41no—
146#41×C43—81no—
147#41×C43—81no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—41no—
157C2×D4×C43C2×D411yescharacteristic
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—41no—
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43#4111yescharacteristic
165Q16×C43—81no—
166Q16×C43—81no—
167SD16×C43—42no—
168SD16×C43—81no—
169SD16×C43—81no—
170D8×C43—42no—
171M16×C43—81no—
172M16×C43—81no—
173M16×C43—81no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—42no—
181C2×C8×C43C2×D411yescharacteristic
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C2×C8×C43C2×D411yescharacteristic
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×C43C2×D411yescharacteristic
196C4⋊C4×C43C2×D411yescharacteristic
197C22⋊C4×C43—21no—
198C22⋊C4×C43—21no—
199C22⋊C4×C43—21no—
200C22⋊C4×C43—41no—
201C22⋊C4×C43—41no—
202C22⋊C4×C43—41no—
203C42×C43—21no—
204C42×C43—21no—
205C42×C43—21no—
206C42×C43—41no—
207C42×C43C2×D411yescharacteristic
208C42×C43C2×D411yescharacteristic
209C42×C43#4111yescharacteristic
210C42×C43C2411yescharacteristic
211C23×C43—21no—
212C23×C43—41no—
213C23×C43#12111yescharacteristic
214Q8×C43—21no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—81no—
220Q8×C43#13712yes—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—42no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—81no—
229D4×C43—82no—
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—21no—
237C2×C4×C43—41no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
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#12111yescharacteristic
247C2×C4×C43#12111yescharacteristic
248C2×C4×C43#12111yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—41no—
257C8×C43—41no—
258C8×C43—41no—
259C8×C43—41no—
260C8×C43—41no—
261C8×C43—41no—
262#19493C4311yesmaximal, characteristic, direct product factor, Sylow
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43C2×#12111yescharacteristic
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—22no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43C2×#13711yescharacteristic
284C4×C43#57511yescharacteristic
285C4×C43#57611yescharacteristic
286C4×C43#57711yescharacteristic
287#3210C2×C4311yescharacteristic, complemented
288#3115C2×C4311yescharacteristic
289#3076C2×C4311yescharacteristic, complemented
290#2991C2×C4311yescharacteristic, complemented
291#1703C2×C4311yescharacteristic, complemented
292#1697C2×C4311yescharacteristic, complemented
293#1689C2×C4311yescharacteristic, complemented
294#1685C2×C4311yescharacteristic, complemented
295#1684C2×C4311yescharacteristic, complemented
296#1678C2×C4311yescharacteristic, complemented
297#1670C2×C4311yescharacteristic, complemented
298#1666C2×C4311yescharacteristic, complemented
299#1573C2×C4311yescharacteristic, complemented
300#1559C2×C4311yescharacteristic, complemented
301#1547C2×C4311yescharacteristic, complemented
302C2×C43—41no—
303C2×C43—81no—
304C2×C43—161no—
305C2×C43#304511yescharacteristic
306C2×C43#305611yescharacteristic
307C2×C43#306711yescharacteristic
308#533C22×C4311yescharacteristic
309#532C22×C4311yescharacteristic
310C4×#41C22×C4311yescharacteristic
311#494C22×C4311yescharacteristic
312#492C22×C4311yescharacteristic
313#487C22×C4311yescharacteristic
314#486C22×C4311yescharacteristic
315#482—21no—
316#479—21no—
317#478—21no—
318#477C22×C4311yescharacteristic
319#476C22×C4311yescharacteristic
320#475C22×C4311yescharacteristic
321#475C22×C4311yescharacteristic
322#474C22×C4311yescharacteristic
323#474C22×C4311yescharacteristic
324#464—21no—
325#464—21no—
326#460C22×C4311yescharacteristic
327#459C22×C4311yescharacteristic
328#452—21no—
329#452—21no—
330#449—21no—
331C8×Q8C22×C4311yescharacteristic
332C8×Q8C22×C4311yescharacteristic
333#442—21no—
334#440—21no—
335#436—21no—
336#436—21no—
337#436C22×C4311yescharacteristic
338#436C22×C4311yescharacteristic
339#432C22×C4311yescharacteristic
340#431—21no—
341#431C22×C4311yescharacteristic
342#427—21no—
343#423—21no—
344#423C22×C4311yescharacteristic
345C2×C4⋊C8C22×C4311yescharacteristic
346#416—21no—
347#335C22×C4311yescharacteristic
348#335C22×C4311yescharacteristic
349#334C22×C4311yescharacteristic
350#334C22×C4311yescharacteristic
351#333C22×C4311yescharacteristic
352#333C22×C4311yescharacteristic
353#332C22×C4311yescharacteristic
354#332C22×C4311yescharacteristic
355#332C22×C4311yescharacteristic
356#332C22×C4311yescharacteristic
357#331C22×C4311yescharacteristic
358#331C22×C4311yescharacteristic
359C43#1949311yescharacteristic, direct product factor, Sylow
360C2×#41—21no—
361C2×#41D4×C4311yescharacteristic
362C2×Q16—21no—
363C2×Q16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×D8—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C22×C8—21no—
372C4⋊Q8C23×C4311yescharacteristic
373C4⋊Q8C23×C4311yescharacteristic
374C4⋊Q8C23×C4311yescharacteristic
375#127C23×C4311yescharacteristic
376#125—21no—
377#124—21no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380#121—21no—
381#121—21no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8D4×C4311yescharacteristic
385C4×Q8C23×C4311yescharacteristic
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4D4×C4311yescharacteristic
391C4×D4C23×C4311yescharacteristic
392#117—21no—
393#117—21no—
394#117D4×C4311yescharacteristic
395C2×C42—21no—
396C2×C42C23×C4311yescharacteristic
397#107—21no—
398#107—21no—
399#107—21no—
400#106—21no—
401#106—21no—
402#106—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8D4×C4311yescharacteristic
408C4⋊C8D4×C4311yescharacteristic
409C4⋊C8C23×C4311yescharacteristic
410C4⋊C8C23×C4311yescharacteristic
411C4⋊C8C23×C4311yescharacteristic
412C4⋊C8C23×C4311yescharacteristic
413C4⋊C8C23×C4311yescharacteristic
414C4⋊C8C23×C4311yescharacteristic
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8D4×C4311yescharacteristic
431C22⋊C8D4×C4311yescharacteristic
432#97—21no—
433C4×C8—21no—
434C4×C8—21no—
435C4×C8C23×C4311yescharacteristic
436C4×C8C23×C4311yescharacteristic
437#41—22no—
438#41—41no—
439#41—81no—
440#41—81no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8C2×D4×C4311yescharacteristic
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—41no—
450C2×D4C2×D4×C4311yescharacteristic
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—41no—
455C22×C4C2×D4×C4311yescharacteristic
456C22×C4C2×D4×C4311yescharacteristic
457C22×C4#41×C4311yescharacteristic
458Q16—81no—
459Q16—81no—
460SD16—42no—
461SD16—81no—
462SD16—81no—
463D8—42no—
464M16—81no—
465M16—81no—
466M16—81no—
467C2×C8—21no—
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—41no—
487C4⋊C4—41no—
488C4⋊C4C2×D4×C4311yescharacteristic
489C4⋊C4C2×D4×C4311yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—41no—
500C42C2×D4×C4311yescharacteristic
501C42C2×D4×C4311yescharacteristic
502C42#41×C4311yescharacteristic
503C42C24×C4311yescharacteristic
504C23—21no—
505C23—41no—
506C23#121×C4311yescharacteristic
507Q8—21no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—81no—
513Q8#137×C4312yes—
514D4—21no—
515D4—21no—
516D4—42no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—81no—
522D4—82no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4#121×C4311yescharacteristic
540C2×C4#121×C4311yescharacteristic
541C2×C4#121×C4311yescharacteristic
542C2×C4C22×D4×C4311yescharacteristic
543C2×C4C22×D4×C4311yescharacteristic
544C2×C4C2×#41×C4311yescharacteristic
545C8—21no—
546C8—21no—
547C8—21no—
548C8—21no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22C2×#121×C4311yescharacteristic
565C4—21no—
566C4—21no—
567C4—22no—
568C4—21no—
569C4—21no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C2×#137×C4311yescharacteristic
576C4C43×#57511yescharacteristic
577C4C43×#57611yescharacteristic
578C4C43×#57711yescharacteristic
579C2—41no—
580C2—81no—
581C2—161no—
582C2C43×#304511yescharacteristic
583C2C43×#305611yescharacteristic
584C2C43×#306711yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3115C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3210C2semidirect
3. C43×#3076C2semidirect
4. C43×#2991C2semidirect
5. C43×#1703C2semidirect
6. C43×#1697C2semidirect
7. C43×#1689C2semidirect
8. C43×#1685C2semidirect
9. C43×#1684C2semidirect
10. C43×#1678C2semidirect
11. C43×#1670C2semidirect
12. C43×#1666C2semidirect
13. C43×#1573C2semidirect
14. C43×#1559C2semidirect
15. C43×#1547C2semidirect
262. #19493C43direct (N × H)
287. #3210C2×C43semidirect
289. #3076C2×C43semidirect
290. #2991C2×C43semidirect
291. #1703C2×C43semidirect
292. #1697C2×C43semidirect
293. #1689C2×C43semidirect
294. #1685C2×C43semidirect
295. #1684C2×C43semidirect
296. #1678C2×C43semidirect
297. #1670C2×C43semidirect
298. #1666C2×C43semidirect
299. #1573C2×C43semidirect
300. #1559C2×C43semidirect
301. #1547C2×C43semidirect
359. C43#19493direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32102
C43×#31152
C43×#30762
C43×#29912
C43×#17032
C43×#16972
C43×#16892
C43×#16852
C43×#16842
C43×#16782
C43×#16702
C43×#16662
C43×#15732
C43×#15592
C43×#15472
#1949343