Finite Group Databasebeta

← C43×#19581 #24939598

Subgroups — C43×#19581 #24939598

Order 11008.

644 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3248C211yesmaximal, characteristic, complemented
2C43×#3217C211yesmaximal, characteristic
3C43×#3208C211yesmaximal, characteristic, complemented
4C43×#2994C211yesmaximal, characteristic, complemented
5C43×#1702C211yesmaximal, characteristic, complemented
6C43×#1701C211yesmaximal, characteristic, complemented
7C43×#1686C211yesmaximal, characteristic, complemented
8C43×#1685C211yesmaximal, characteristic, complemented
9C43×#1682C211yesmaximal, characteristic, complemented
10C43×#1681C211yesmaximal, characteristic, complemented
11C43×#1666C211yesmaximal, characteristic, complemented
12C43×#1665C211yesmaximal, characteristic, complemented
13C43×#1573C211yesmaximal, characteristic, complemented
14C43×#1552C211yesmaximal, characteristic, complemented
15C2×C43×#331C211yesmaximal, characteristic, complemented
16C43×#533C2211yescharacteristic
17C2×#127×C43C2211yescharacteristic
18C43×#529C2211yescharacteristic
19C43×#496—21no—
20C43×#492C2211yescharacteristic
21C43×#492C2211yescharacteristic
22C43×#490—21no—
23C43×#486C2211yescharacteristic
24C43×#486C2211yescharacteristic
25C43×#479—21no—
26C43×#475C2211yescharacteristic, complemented
27C43×#474C2211yescharacteristic, complemented
28C43×#467—21no—
29C43×#465—21no—
30C43×#464—21no—
31C43×#462C2211yescharacteristic, complemented
32C43×#461C2211yescharacteristic, complemented
33C43×#460—21no—
34C43×#460—21no—
35C43×#460C2211yescharacteristic
36C43×#460C2211yescharacteristic
37C43×#459C2211yescharacteristic
38C43×#459C2211yescharacteristic
39C43×#450—21no—
40C43×#450—21no—
41C43×#450—21no—
42C43×#447—21no—
43C43×#446C2211yescharacteristic, complemented
44C8×Q8×C43C2211yescharacteristic, complemented
45C43×#436C2211yescharacteristic, complemented
46C43×#435—21no—
47C8×D4×C43—21no—
48C8×D4×C43C2211yescharacteristic, complemented
49C43×#433—21no—
50C43×#432C2211yescharacteristic
51C43×#431C2211yescharacteristic
52C43×#424—21no—
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×C4⋊C8×C43C2211yescharacteristic
55C43×#335C2211yescharacteristic, complemented
56C43×#335C2211yescharacteristic, complemented
57C43×#334C2211yescharacteristic, complemented
58C43×#334C2211yescharacteristic, complemented
59C43×#332C2211yescharacteristic, complemented
60C43×#332C2211yescharacteristic, complemented
61C43×#332C2211yescharacteristic, complemented
62C43×#332C2211yescharacteristic, complemented
63C43×#331C2211yescharacteristic
64C43×#331C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C22×D4×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70C2×Q16×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—21no—
75C2×SD16×C43—21no—
76C2×SD16×C43—21no—
77C2×SD16×C43—21no—
78C2×D8×C43—21no—
79C2×D8×C43—21no—
80C2×M16×C43—21no—
81C22×C8×C43—21no—
82C22×C8×C43—21no—
83C22×C8×C43—21no—
84C4⋊Q8×C43C2311yescharacteristic
85C4⋊Q8×C43C2311yescharacteristic
86#127×C43—21no—
87#127×C43—21no—
88#127×C43—21no—
89#127×C43C2311yescharacteristic
90#127×C43C2311yescharacteristic
91#126×C43—21no—
92#125×C43—21no—
93#125×C43D411yescharacteristic
94#124×C43D411yescharacteristic
95#123×C43—21no—
96C22⋊Q8×C43—21no—
97C22⋊Q8×C43—21no—
98C22⋊Q8×C43D411yescharacteristic
99#121×C43D411yescharacteristic
100C4×Q8×C43—21no—
101C4×Q8×C43—21no—
102C4×Q8×C43C2311yescharacteristic
103C4×D4×C43—21no—
104C4×D4×C43C2311yescharacteristic
105#117×C43—21no—
106#117×C43—21no—
107C2×C42×C43C2311yescharacteristic
108#107×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#102×C43—21no—
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—
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43D411yescharacteristic
138C22⋊C8×C43D411yescharacteristic
139#97×C43—21no—
140#97×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C24×C43—41no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43—81no—
159C2×D4×C43—81no—
160C2×D4×C43—81no—
161C2×D4×C43—81no—
162C2×D4×C43—82no—
163C2×D4×C43C2×D411yescharacteristic
164C22×C4×C43—21no—
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43#4111yescharacteristic
168Q16×C43—81no—
169SD16×C43—81no—
170SD16×C43—81no—
171SD16×C43—81no—
172SD16×C43—81no—
173SD16×C43—81no—
174SD16×C43—81no—
175SD16×C43—81no—
176D8×C43—81no—
177D8×C43—81no—
178M16×C43—81no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—81no—
186C2×C8×C43—81no—
187C2×C8×C43—81no—
188C2×C8×C43C2×D411yescharacteristic
189C2×C8×C43C2×D411yescharacteristic
190C2×C8×C43C2×D411yescharacteristic
191C2×C8×C43C2×D411yescharacteristic
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—41no—
201C4⋊C4×C43—41no—
202C4⋊C4×C43C2×D411yescharacteristic
203C4⋊C4×C43C2×D411yescharacteristic
204C22⋊C4×C43—21no—
205C22⋊C4×C43—21no—
206C22⋊C4×C43—21no—
207C22⋊C4×C43—21no—
208C22⋊C4×C43—21no—
209C22⋊C4×C43—41no—
210C42×C43—21no—
211C42×C43—41no—
212C42×C43C2×D411yescharacteristic
213C42×C43C2×D411yescharacteristic
214C42×C43#4111yescharacteristic
215C42×C43C2411yescharacteristic
216C23×C43—21no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—82no—
220C23×C43—82no—
221C23×C43—82no—
222C23×C43#12111yescharacteristic
223Q8×C43—21no—
224Q8×C43—21no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×C43—41no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—42no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—81no—
241D4×C43—81no—
242D4×C43—82no—
243D4×C43—82no—
244D4×C43—82no—
245C2×C4×C43—22no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43#12111yescharacteristic
258C2×C4×C43#12111yescharacteristic
259C2×C4×C43#12111yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C8×C43—21no—
264C8×C43—21no—
265C8×C43—21no—
266C8×C43—21no—
267C8×C43—41no—
268C8×C43—41no—
269C8×C43—41no—
270C8×C43—41no—
271C8×C43—41no—
272C8×C43—41no—
273#19581C4311yesmaximal, characteristic, direct product factor, Sylow
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—164no—
286C22×C43#47112yes—
287C22×C43C2×#12111yescharacteristic
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—81no—
296C4×C43—81no—
297C4×C43#57611yescharacteristic
298C4×C43#57611yescharacteristic
299C4×C43#57711yescharacteristic
300C4×C43#57711yescharacteristic
301#3248C2×C4311yescharacteristic, complemented
302#3217C2×C4311yescharacteristic
303#3208C2×C4311yescharacteristic, complemented
304#2994C2×C4311yescharacteristic, complemented
305#1702C2×C4311yescharacteristic, complemented
306#1701C2×C4311yescharacteristic, complemented
307#1686C2×C4311yescharacteristic, complemented
308#1685C2×C4311yescharacteristic, complemented
309#1682C2×C4311yescharacteristic, complemented
310#1681C2×C4311yescharacteristic, complemented
311#1666C2×C4311yescharacteristic, complemented
312#1665C2×C4311yescharacteristic, complemented
313#1573C2×C4311yescharacteristic, complemented
314#1552C2×C4311yescharacteristic, complemented
315C2×#331C2×C4311yescharacteristic, complemented
316C2×C43—22no—
317C2×C43—81no—
318C2×C43—161no—
319C2×C43—161no—
320C2×C43#304511yescharacteristic
321C2×C43#306211yescharacteristic
322C2×C43C2×#47111yescharacteristic
323#533C22×C4311yescharacteristic
324C2×#127C22×C4311yescharacteristic
325#529C22×C4311yescharacteristic
326#496—21no—
327#492C22×C4311yescharacteristic
328#492C22×C4311yescharacteristic
329#490—21no—
330#486C22×C4311yescharacteristic
331#486C22×C4311yescharacteristic
332#479—21no—
333#475C22×C4311yescharacteristic, complemented
334#474C22×C4311yescharacteristic, complemented
335#467—21no—
336#465—21no—
337#464—21no—
338#462C22×C4311yescharacteristic, complemented
339#461C22×C4311yescharacteristic, complemented
340#460—21no—
341#460—21no—
342#460C22×C4311yescharacteristic
343#460C22×C4311yescharacteristic
344#459C22×C4311yescharacteristic
345#459C22×C4311yescharacteristic
346#450—21no—
347#450—21no—
348#450—21no—
349#447—21no—
350#446C22×C4311yescharacteristic, complemented
351C8×Q8C22×C4311yescharacteristic, complemented
352#436C22×C4311yescharacteristic, complemented
353#435—21no—
354C8×D4—21no—
355C8×D4C22×C4311yescharacteristic, complemented
356#433—21no—
357#432C22×C4311yescharacteristic
358#431C22×C4311yescharacteristic
359#424—21no—
360C2×C4⋊C8C22×C4311yescharacteristic
361C2×C4⋊C8C22×C4311yescharacteristic
362#335C22×C4311yescharacteristic, complemented
363#335C22×C4311yescharacteristic, complemented
364#334C22×C4311yescharacteristic, complemented
365#334C22×C4311yescharacteristic, complemented
366#332C22×C4311yescharacteristic, complemented
367#332C22×C4311yescharacteristic, complemented
368#332C22×C4311yescharacteristic, complemented
369#332C22×C4311yescharacteristic, complemented
370#331C22×C4311yescharacteristic
371#331C22×C4311yescharacteristic
372#331C22×C4311yescharacteristic
373#331C22×C4311yescharacteristic
374C43#1958111yescharacteristic, direct product factor, Sylow
375C22×D4—21no—
376C22×D4—21no—
377C22×D4—21no—
378C2×Q16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×D8—21no—
387C2×D8—21no—
388C2×M16—21no—
389C22×C8—21no—
390C22×C8—21no—
391C22×C8—21no—
392C4⋊Q8C23×C4311yescharacteristic
393C4⋊Q8C23×C4311yescharacteristic
394#127—21no—
395#127—21no—
396#127—21no—
397#127C23×C4311yescharacteristic
398#127C23×C4311yescharacteristic
399#126—21no—
400#125—21no—
401#125D4×C4311yescharacteristic
402#124D4×C4311yescharacteristic
403#123—21no—
404C22⋊Q8—21no—
405C22⋊Q8—21no—
406C22⋊Q8D4×C4311yescharacteristic
407#121D4×C4311yescharacteristic
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8C23×C4311yescharacteristic
411C4×D4—21no—
412C4×D4C23×C4311yescharacteristic
413#117—21no—
414#117—21no—
415C2×C42C23×C4311yescharacteristic
416#107—21no—
417#106—21no—
418C4⋊C8—21no—
419C4⋊C8—21no—
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8D4×C4311yescharacteristic
423C4⋊C8D4×C4311yescharacteristic
424C4⋊C8C23×C4311yescharacteristic
425C4⋊C8C23×C4311yescharacteristic
426C4⋊C8C23×C4311yescharacteristic
427C4⋊C8C23×C4311yescharacteristic
428C4⋊C8C23×C4311yescharacteristic
429C4⋊C8C23×C4311yescharacteristic
430#103—21no—
431#103—21no—
432#103—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442C22⋊C8—21no—
443C22⋊C8—21no—
444C22⋊C8—21no—
445C22⋊C8D4×C4311yescharacteristic
446C22⋊C8D4×C4311yescharacteristic
447#97—21no—
448#97—21no—
449C4×C8—21no—
450C4×C8C23×C4311yescharacteristic
451C4×C8C23×C4311yescharacteristic
452C24—41no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8C2×D4×C4311yescharacteristic
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—81no—
467C2×D4—81no—
468C2×D4—81no—
469C2×D4—81no—
470C2×D4—82no—
471C2×D4C2×D4×C4311yescharacteristic
472C22×C4—21no—
473C22×C4C2×D4×C4311yescharacteristic
474C22×C4C2×D4×C4311yescharacteristic
475C22×C4#41×C4311yescharacteristic
476Q16—81no—
477SD16—81no—
478SD16—81no—
479SD16—81no—
480SD16—81no—
481SD16—81no—
482SD16—81no—
483SD16—81no—
484D8—81no—
485D8—81no—
486M16—81no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—81no—
494C2×C8—81no—
495C2×C8—81no—
496C2×C8C2×D4×C4311yescharacteristic
497C2×C8C2×D4×C4311yescharacteristic
498C2×C8C2×D4×C4311yescharacteristic
499C2×C8C2×D4×C4311yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4C2×D4×C4311yescharacteristic
511C4⋊C4C2×D4×C4311yescharacteristic
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—41no—
518C42—21no—
519C42—41no—
520C42C2×D4×C4311yescharacteristic
521C42C2×D4×C4311yescharacteristic
522C42#41×C4311yescharacteristic
523C42C24×C4311yescharacteristic
524C23—21no—
525C23—41no—
526C23—41no—
527C23—82no—
528C23—82no—
529C23—82no—
530C23#121×C4311yescharacteristic
531Q8—21no—
532Q8—21no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537D4—21no—
538D4—21no—
539D4—42no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—81no—
549D4—81no—
550D4—82no—
551D4—82no—
552D4—82no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4#121×C4311yescharacteristic
566C2×C4#121×C4311yescharacteristic
567C2×C4#121×C4311yescharacteristic
568C2×C4C22×D4×C4311yescharacteristic
569C2×C4C22×D4×C4311yescharacteristic
570C2×C4C2×#41×C4311yescharacteristic
571C8—21no—
572C8—21no—
573C8—21no—
574C8—21no—
575C8—41no—
576C8—41no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—41no—
581C22—21no—
582C22—21no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22—164no—
593C22C43×#47112yes—
594C22C2×#121×C4311yescharacteristic
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—81no—
603C4—81no—
604C4C43×#57611yescharacteristic
605C4C43×#57611yescharacteristic
606C4C43×#57711yescharacteristic
607C4C43×#57711yescharacteristic
608C2—22no—
609C2—81no—
610C2—161no—
611C2—161no—
612C2C43×#304511yescharacteristic
613C2C43×#306211yescharacteristic
614C2C2×C43×#47111yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3217C2
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×#3248C2semidirect
3. C43×#3208C2semidirect
4. C43×#2994C2semidirect
5. C43×#1702C2semidirect
6. C43×#1701C2semidirect
7. C43×#1686C2semidirect
8. C43×#1685C2semidirect
9. C43×#1682C2semidirect
10. C43×#1681C2semidirect
11. C43×#1666C2semidirect
12. C43×#1665C2semidirect
13. C43×#1573C2semidirect
14. C43×#1552C2semidirect
15. C2×C43×#331C2semidirect
26. C43×#475C22semidirect
27. C43×#474C22semidirect
31. C43×#462C22semidirect
32. C43×#461C22semidirect
43. C43×#446C22semidirect
44. C8×Q8×C43C22semidirect
45. C43×#436C22semidirect
48. C8×D4×C43C22semidirect
55. C43×#335C22semidirect
56. C43×#335C22semidirect
57. C43×#334C22semidirect
58. C43×#334C22semidirect
59. C43×#332C22semidirect
60. C43×#332C22semidirect
61. C43×#332C22semidirect
62. C43×#332C22semidirect
273. #19581C43direct (N × H)
301. #3248C2×C43semidirect
303. #3208C2×C43semidirect
304. #2994C2×C43semidirect
305. #1702C2×C43semidirect
306. #1701C2×C43semidirect
307. #1686C2×C43semidirect
308. #1685C2×C43semidirect
309. #1682C2×C43semidirect
310. #1681C2×C43semidirect
311. #1666C2×C43semidirect
312. #1665C2×C43semidirect
313. #1573C2×C43semidirect
314. #1552C2×C43semidirect
315. C2×#331C2×C43semidirect
333. #475C22×C43semidirect
334. #474C22×C43semidirect
338. #462C22×C43semidirect
339. #461C22×C43semidirect
350. #446C22×C43semidirect
351. C8×Q8C22×C43semidirect
352. #436C22×C43semidirect
355. C8×D4C22×C43semidirect
362. #335C22×C43semidirect
363. #335C22×C43semidirect
364. #334C22×C43semidirect
365. #334C22×C43semidirect
366. #332C22×C43semidirect
367. #332C22×C43semidirect
368. #332C22×C43semidirect
369. #332C22×C43semidirect
374. C43#19581direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32482
C43×#32172
C43×#32082
C43×#29942
C43×#17022
C43×#17012
C43×#16862
C43×#16852
C43×#16822
C43×#16812
C43×#16662
C43×#16652
C43×#15732
C43×#15522
C2×C43×#3312
#1958143