Finite Group Databasebeta

← C43×#19580 #24939597

Subgroups — C43×#19580 #24939597

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3247C211yesmaximal, characteristic
2C43×#3239C211yesmaximal, characteristic, complemented
3C43×#3206C211yesmaximal, characteristic, complemented
4C43×#2994C211yesmaximal, characteristic, complemented
5C43×#1704C211yesmaximal, characteristic, complemented
6C43×#1703C211yesmaximal, characteristic, complemented
7C43×#1686C211yesmaximal, characteristic, complemented
8C43×#1685C211yesmaximal, characteristic, complemented
9C43×#1684C211yesmaximal, characteristic, complemented
10C43×#1683C211yesmaximal, characteristic, complemented
11C43×#1666C211yesmaximal, characteristic, complemented
12C43×#1665C211yesmaximal, characteristic, complemented
13C43×#1573C211yesmaximal, characteristic, complemented
14C43×#1551C211yesmaximal, characteristic, complemented
15C2×C43×#332C211yesmaximal, characteristic, complemented
16C43×#532C2211yescharacteristic
17C2×C4⋊Q8×C43C2211yescharacteristic
18C43×#529C2211yescharacteristic
19C43×#501—21no—
20C43×#492C2211yescharacteristic
21C43×#492C2211yescharacteristic
22C43×#489—21no—
23C43×#487C2211yescharacteristic
24C43×#487C2211yescharacteristic
25C43×#484—21no—
26C43×#481—21no—
27C43×#478—21no—
28C43×#477C2211yescharacteristic
29C43×#476C2211yescharacteristic
30C43×#475C2211yescharacteristic
31C43×#475C2211yescharacteristic
32C43×#474C2211yescharacteristic
33C43×#474C2211yescharacteristic
34C43×#466—21no—
35C43×#465—21no—
36C43×#463—21no—
37C43×#461—21no—
38C43×#461—21no—
39C43×#460C2211yescharacteristic
40C43×#459C2211yescharacteristic
41C43×#448—21no—
42C43×#448—21no—
43C43×#446C2211yescharacteristic
44C8×Q8×C43C2211yescharacteristic
45C43×#436C2211yescharacteristic
46C43×#435—21no—
47C8×D4×C43—21no—
48C8×D4×C43C2211yescharacteristic
49C43×#433—21no—
50C43×#432C2211yescharacteristic
51C43×#431C2211yescharacteristic
52C43×#424—21no—
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×C4⋊C8×C43C2211yescharacteristic
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—
68C22×Q8×C43—21no—
69C2×SD16×C43—21no—
70C2×SD16×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×D8×C43—21no—
75C2×M16×C43—21no—
76C22×C8×C43—21no—
77C22×C8×C43—21no—
78C22×C8×C43—21no—
79C4⋊Q8×C43—21no—
80C4⋊Q8×C43—21no—
81C4⋊Q8×C43—21no—
82C4⋊Q8×C43C2311yescharacteristic
83C4⋊Q8×C43C2311yescharacteristic
84C4⋊Q8×C43C2311yescharacteristic
85#127×C43C2311yescharacteristic
86#126×C43—21no—
87#125×C43D411yescharacteristic
88#124×C43—21no—
89#124×C43D411yescharacteristic
90#123×C43—21no—
91C22⋊Q8×C43D411yescharacteristic
92#121×C43—21no—
93#121×C43—21no—
94#121×C43D411yescharacteristic
95C4×Q8×C43C2311yescharacteristic
96C4×D4×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43C2311yescharacteristic
100#117×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×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#103×C43—21no—
128#103×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
144#41×C43—82no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—41no—
149C2×Q8×C43—81no—
150C2×Q8×C43—81no—
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—41no—
160C22×C4×C43—41no—
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43#4111yescharacteristic
164SD16×C43—81no—
165SD16×C43—81no—
166SD16×C43—81no—
167SD16×C43—81no—
168SD16×C43—81no—
169D8×C43—81no—
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×C43—21no—
177C2×C8×C43—81no—
178C2×C8×C43—81no—
179C2×C8×C43—81no—
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—21no—
194C4⋊C4×C43—41no—
195C4⋊C4×C43—41no—
196C4⋊C4×C43C2×D411yescharacteristic
197C4⋊C4×C43C2×D411yescharacteristic
198C22⋊C4×C43—21no—
199C22⋊C4×C43—21no—
200C22⋊C4×C43—21no—
201C22⋊C4×C43—21no—
202C22⋊C4×C43—21no—
203C22⋊C4×C43—41no—
204C22⋊C4×C43—41no—
205C42×C43—21no—
206C42×C43C2×D411yescharacteristic
207C42×C43C2×D411yescharacteristic
208C42×C43#4111yescharacteristic
209C42×C43C2411yescharacteristic
210C23×C43—21no—
211C23×C43—41no—
212C23×C43#12111yescharacteristic
213Q8×C43—21no—
214Q8×C43—21no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—81no—
220Q8×C43—82no—
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—22no—
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—21no—
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—82no—
245C2×C4×C43#12111yescharacteristic
246C2×C4×C43#12111yescharacteristic
247C2×C4×C43#12111yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43—41no—
258C8×C43—41no—
259C8×C43—41no—
260C8×C43—41no—
261#19580C4311yesmaximal, characteristic, direct product factor, Sylow
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43#47112yes—
271C22×C43C2×#12111yescharacteristic
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43#57611yescharacteristic
283C4×C43#57711yescharacteristic
284C4×C43#57711yescharacteristic
285C4×C43#57811yescharacteristic
286#3247C2×C4311yescharacteristic
287#3239C2×C4311yescharacteristic, complemented
288#3206C2×C4311yescharacteristic, complemented
289#2994C2×C4311yescharacteristic, complemented
290#1704C2×C4311yescharacteristic, complemented
291#1703C2×C4311yescharacteristic, complemented
292#1686C2×C4311yescharacteristic, complemented
293#1685C2×C4311yescharacteristic, complemented
294#1684C2×C4311yescharacteristic, complemented
295#1683C2×C4311yescharacteristic, complemented
296#1666C2×C4311yescharacteristic, complemented
297#1665C2×C4311yescharacteristic, complemented
298#1573C2×C4311yescharacteristic, complemented
299#1551C2×C4311yescharacteristic, complemented
300C2×#332C2×C4311yescharacteristic, complemented
301C2×C43—22no—
302C2×C43—81no—
303C2×C43—161no—
304C2×C43#304511yescharacteristic
305C2×C43#306311yescharacteristic
306C2×C43C2×#47111yescharacteristic
307#532C22×C4311yescharacteristic
308C2×C4⋊Q8C22×C4311yescharacteristic
309#529C22×C4311yescharacteristic
310#501—21no—
311#492C22×C4311yescharacteristic
312#492C22×C4311yescharacteristic
313#489—21no—
314#487C22×C4311yescharacteristic
315#487C22×C4311yescharacteristic
316#484—21no—
317#481—21no—
318#478—21no—
319#477C22×C4311yescharacteristic
320#476C22×C4311yescharacteristic
321#475C22×C4311yescharacteristic
322#475C22×C4311yescharacteristic
323#474C22×C4311yescharacteristic
324#474C22×C4311yescharacteristic
325#466—21no—
326#465—21no—
327#463—21no—
328#461—21no—
329#461—21no—
330#460C22×C4311yescharacteristic
331#459C22×C4311yescharacteristic
332#448—21no—
333#448—21no—
334#446C22×C4311yescharacteristic
335C8×Q8C22×C4311yescharacteristic
336#436C22×C4311yescharacteristic
337#435—21no—
338C8×D4—21no—
339C8×D4C22×C4311yescharacteristic
340#433—21no—
341#432C22×C4311yescharacteristic
342#431C22×C4311yescharacteristic
343#424—21no—
344C2×C4⋊C8C22×C4311yescharacteristic
345C2×C4⋊C8C22×C4311yescharacteristic
346#335C22×C4311yescharacteristic
347#335C22×C4311yescharacteristic
348#334C22×C4311yescharacteristic
349#334C22×C4311yescharacteristic
350#333C22×C4311yescharacteristic
351#333C22×C4311yescharacteristic
352#332C22×C4311yescharacteristic
353#332C22×C4311yescharacteristic
354#332C22×C4311yescharacteristic
355#332C22×C4311yescharacteristic
356#331C22×C4311yescharacteristic
357#331C22×C4311yescharacteristic
358C43#1958011yescharacteristic, direct product factor, Sylow
359C2×#41—21no—
360C22×Q8—21no—
361C2×SD16—21no—
362C2×SD16—21no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×D8—21no—
367C2×M16—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8C23×C4311yescharacteristic
375C4⋊Q8C23×C4311yescharacteristic
376C4⋊Q8C23×C4311yescharacteristic
377#127C23×C4311yescharacteristic
378#126—21no—
379#125D4×C4311yescharacteristic
380#124—21no—
381#124D4×C4311yescharacteristic
382#123—21no—
383C22⋊Q8D4×C4311yescharacteristic
384#121—21no—
385#121—21no—
386#121D4×C4311yescharacteristic
387C4×Q8C23×C4311yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4C23×C4311yescharacteristic
392#117—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C42C23×C4311yescharacteristic
396#107—21no—
397#107—21no—
398#107—21no—
399#106—21no—
400#106—21no—
401#106—21no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8D4×C4311yescharacteristic
407C4⋊C8D4×C4311yescharacteristic
408C4⋊C8C23×C4311yescharacteristic
409C4⋊C8C23×C4311yescharacteristic
410C4⋊C8C23×C4311yescharacteristic
411C4⋊C8C23×C4311yescharacteristic
412C4⋊C8C23×C4311yescharacteristic
413C4⋊C8C23×C4311yescharacteristic
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8D4×C4311yescharacteristic
430C22⋊C8D4×C4311yescharacteristic
431#97—21no—
432#97—21no—
433C4×C8—21no—
434C4×C8C23×C4311yescharacteristic
435C4×C8C23×C4311yescharacteristic
436#41—82no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—41no—
441C2×Q8—81no—
442C2×Q8—81no—
443C2×Q8C2×D4×C4311yescharacteristic
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—41no—
449C2×D4C2×D4×C4311yescharacteristic
450C22×C4—21no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4C2×D4×C4311yescharacteristic
454C22×C4C2×D4×C4311yescharacteristic
455C22×C4#41×C4311yescharacteristic
456SD16—81no—
457SD16—81no—
458SD16—81no—
459SD16—81no—
460SD16—81no—
461D8—81no—
462M16—81no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—81no—
470C2×C8—81no—
471C2×C8—81no—
472C2×C8C2×D4×C4311yescharacteristic
473C2×C8C2×D4×C4311yescharacteristic
474C2×C8C2×D4×C4311yescharacteristic
475C2×C8C2×D4×C4311yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
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—21no—
494C22⋊C4—21no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C42—21no—
498C42C2×D4×C4311yescharacteristic
499C42C2×D4×C4311yescharacteristic
500C42#41×C4311yescharacteristic
501C42C24×C4311yescharacteristic
502C23—21no—
503C23—41no—
504C23#121×C4311yescharacteristic
505Q8—21no—
506Q8—21no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—81no—
512Q8—82no—
513D4—21no—
514D4—21no—
515D4—42no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—81no—
521D4—82no—
522C2×C4—22no—
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—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—82no—
536C2×C4—82no—
537C2×C4#121×C4311yescharacteristic
538C2×C4#121×C4311yescharacteristic
539C2×C4#121×C4311yescharacteristic
540C2×C4C22×D4×C4311yescharacteristic
541C2×C4C22×D4×C4311yescharacteristic
542C2×C4C2×#41×C4311yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C22—21no—
554C22—21no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22C43×#47112yes—
562C22C2×#121×C4311yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—21no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4C43×#57611yescharacteristic
574C4C43×#57711yescharacteristic
575C4C43×#57711yescharacteristic
576C4C43×#57811yescharacteristic
577C2—22no—
578C2—81no—
579C2—161no—
580C2C43×#304511yescharacteristic
581C2C43×#306311yescharacteristic
582C2C2×C43×#47111yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3247C2
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
2. C43×#3239C2semidirect
3. C43×#3206C2semidirect
4. C43×#2994C2semidirect
5. C43×#1704C2semidirect
6. C43×#1703C2semidirect
7. C43×#1686C2semidirect
8. C43×#1685C2semidirect
9. C43×#1684C2semidirect
10. C43×#1683C2semidirect
11. C43×#1666C2semidirect
12. C43×#1665C2semidirect
13. C43×#1573C2semidirect
14. C43×#1551C2semidirect
15. C2×C43×#332C2semidirect
261. #19580C43direct (N × H)
287. #3239C2×C43semidirect
288. #3206C2×C43semidirect
289. #2994C2×C43semidirect
290. #1704C2×C43semidirect
291. #1703C2×C43semidirect
292. #1686C2×C43semidirect
293. #1685C2×C43semidirect
294. #1684C2×C43semidirect
295. #1683C2×C43semidirect
296. #1666C2×C43semidirect
297. #1665C2×C43semidirect
298. #1573C2×C43semidirect
299. #1551C2×C43semidirect
300. C2×#332C2×C43semidirect
358. C43#19580direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32472
C43×#32392
C43×#32062
C43×#29942
C43×#17042
C43×#17032
C43×#16862
C43×#16852
C43×#16842
C43×#16832
C43×#16662
C43×#16652
C43×#15732
C43×#15512
C2×C43×#3322
#1958043