Finite Group Databasebeta

← C43×#19619 #24939636

Subgroups — C43×#19619 #24939636

Order 11008.

820 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3169C211yesmaximal, characteristic, complemented
2C43×#3169C211yesmaximal, characteristic, complemented
3C43×#3167C211yesmaximal, characteristic, complemented
4C43×#3167C211yesmaximal, characteristic, complemented
5C43×#3147C211yesmaximal, characteristic, complemented
6C43×#3131C211yesmaximal, characteristic, complemented
7C43×#1723C211yesmaximal, characteristic, complemented
8C43×#1721C211yesmaximal, characteristic, complemented
9C43×#1720C211yesmaximal, characteristic, complemented
10C43×#1719C211yesmaximal, characteristic, complemented
11C43×#1717C211yesmaximal, characteristic, complemented
12C43×#1717C211yesmaximal, characteristic, complemented
13C43×#1715C211yesmaximal, characteristic, complemented
14C43×#1714C211yesmaximal, characteristic, complemented
15C2×C43×#322C211yesmaximal, characteristic, complemented
16C2×#135×C43—22no—
17C43×#533C2211yescharacteristic
18C43×#532C2211yescharacteristic
19C43×#532C2211yescharacteristic
20C43×#532C2211yescharacteristic
21C43×#500C2211yescharacteristic
22C43×#500C2211yescharacteristic
23C43×#498C2211yescharacteristic
24C43×#498C2211yescharacteristic
25C43×#495—22no—
26C43×#494C2211yescharacteristic
27C43×#493C2211yescharacteristic
28C43×#493C2211yescharacteristic
29C43×#493C2211yescharacteristic
30C43×#492C2211yescharacteristic
31C43×#492C2211yescharacteristic
32C43×#492C2211yescharacteristic
33C43×#492C2211yescharacteristic
34C43×#488—22no—
35C43×#487C2211yescharacteristic
36C43×#487C2211yescharacteristic
37C43×#487C2211yescharacteristic
38C43×#487C2211yescharacteristic
39C43×#486C2211yescharacteristic
40C43×#486C2211yescharacteristic
41C43×#486C2211yescharacteristic
42C43×#486C2211yescharacteristic
43C43×#486C2211yescharacteristic
44C43×#486C2211yescharacteristic
45C43×#486C2211yescharacteristic
46C43×#486C2211yescharacteristic
47C43×#466—22no—
48C43×#466—22no—
49C43×#465—22no—
50C43×#465—22no—
51C4×SD16×C43—22no—
52C4×SD16×C43—22no—
53C4×D8×C43—22no—
54C4×D8×C43—22no—
55C43×#416—22no—
56C2×C4×C8×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic
58C2×C4×C8×C43C2211yescharacteristic
59C43×#322C2211yescharacteristic
60C43×#322C2211yescharacteristic
61C43×#322C2211yescharacteristic
62C43×#322C2211yescharacteristic
63C2×#41×C43—21no—
64C2×#41×C43—21no—
65C2×#41×C43—21no—
66#135×C43—48no—
67C2×Q16×C43—22no—
68C2×SD16×C43—22no—
69C2×SD16×C43—22no—
70C2×SD16×C43—22no—
71C2×SD16×C43—22no—
72C2×D8×C43—22no—
73C2×D8×C43—22no—
74C2×D8×C43—22no—
75C22×C8×C43D412yes—
76C22×C8×C43D412yes—
77C22×C8×C43D412yes—
78C4⋊Q8×C43C2311yescharacteristic
79C4⋊Q8×C43C2311yescharacteristic
80C4⋊Q8×C43C2311yescharacteristic
81C4⋊Q8×C43C2311yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83#127×C43C2311yescharacteristic
84#127×C43C2311yescharacteristic
85#127×C43C2311yescharacteristic
86#125×C43—21no—
87#124×C43—21no—
88#124×C43—21no—
89#124×C43—21no—
90C22⋊Q8×C43—21no—
91C22⋊Q8×C43—21no—
92#121×C43—21no—
93#121×C43—21no—
94#121×C43—21no—
95#121×C43—21no—
96#121×C43—21no—
97#121×C43—21no—
98C4×Q8×C43—21no—
99C4×Q8×C43—21no—
100C4×D4×C43—21no—
101C4×D4×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43—21no—
106#117×C43—21no—
107C2×C42×C43C2311yescharacteristic
108#107×C43—22no—
109#107×C43—22no—
110#106×C43—22no—
111#106×C43—22no—
112#103×C43—22no—
113#103×C43—22no—
114#103×C43—22no—
115#103×C43—22no—
116#102×C43—22no—
117#102×C43—22no—
118#102×C43—22no—
119#102×C43—22no—
120#102×C43—22no—
121#102×C43—22no—
122#102×C43—22no—
123#102×C43—22no—
124C4×C8×C43D412yes—
125C4×C8×C43D412yes—
126C4×C8×C43D412yes—
127C4×C8×C43C2311yescharacteristic
128C4×C8×C43C2311yescharacteristic
129C4×C8×C43C2311yescharacteristic
130C4×C8×C43C2311yescharacteristic
131C4×C8×C43C2311yescharacteristic
132C4×C8×C43C2311yescharacteristic
133#41×C43—44no—
134#41×C43—44no—
135#41×C43—44no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—41no—
151C2×D4×C43—41no—
152C2×D4×C43—41no—
153C22×C4×C43—41no—
154C22×C4×C43—41no—
155C22×C4×C43—41no—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159Q16×C43—44no—
160SD16×C43—44no—
161SD16×C43—44no—
162SD16×C43—44no—
163SD16×C43—44no—
164D8×C43—44no—
165D8×C43—44no—
166D8×C43—44no—
167C2×C8×C43—24no—
168C2×C8×C43—24no—
169C2×C8×C43—42no—
170C2×C8×C43C2×D412yes—
171C2×C8×C43C2×D412yes—
172C2×C8×C43C2×D412yes—
173C2×C8×C43C2×D412yes—
174C2×C8×C43C2×D412yes—
175C2×C8×C43C2×D412yes—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
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—41no—
187C4⋊C4×C43—41no—
188C22⋊C4×C43—41no—
189C22⋊C4×C43—41no—
190C22⋊C4×C43—41no—
191C22⋊C4×C43—41no—
192C22⋊C4×C43—41no—
193C22⋊C4×C43—41no—
194C22⋊C4×C43—41no—
195C42×C43—41no—
196C42×C43C2×D411yescharacteristic
197C42×C43C2×D411yescharacteristic
198C42×C43C2×D411yescharacteristic
199C42×C43C2411yescharacteristic
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43#12711yescharacteristic
204Q8×C43—42no—
205Q8×C43—42no—
206Q8×C43—42no—
207Q8×C43—42no—
208Q8×C43—42no—
209D4×C43—42no—
210D4×C43—42no—
211D4×C43—42no—
212D4×C43—42no—
213D4×C43—42no—
214D4×C43—42no—
215D4×C43—42no—
216D4×C43—42no—
217D4×C43—42no—
218D4×C43—82no—
219D4×C43—82no—
220D4×C43—82no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—82no—
229C2×C4×C43—82no—
230C2×C4×C43—82no—
231C2×C4×C43#12711yescharacteristic
232C2×C4×C43#12711yescharacteristic
233C2×C4×C43#12711yescharacteristic
234C2×C4×C43AGL(1,ℤ/8)14yes—
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C8×C43—22no—
239C8×C43—22no—
240C8×C43—22no—
241C8×C43—22no—
242C8×C43—22no—
243C8×C43#13514yescomplemented
244#19619C4311yesmaximal, characteristic, direct product factor, Sylow
245C22×C43—21no—
246C22×C43—21no—
247C22×C43—81no—
248C22×C43—81no—
249C22×C43—81no—
250C22×C43—81no—
251C22×C43—81no—
252C22×C43—81no—
253C22×C43—81no—
254C22×C43—81no—
255C22×C43—81no—
256C22×C43#49612yes—
257C22×C43C2×#12711yescharacteristic
258C4×C43—21no—
259C4×C43—21no—
260C4×C43—81no—
261C4×C43—81no—
262C4×C43—81no—
263C4×C43—81no—
264C4×C43—81no—
265C4×C43#49612yes—
266C4×C43C2×#13512yes—
267C4×C43C2×AGL(1,ℤ/8)12yes—
268C4×C43#57512yes—
269#3169C2×C4311yescharacteristic, complemented
270#3169C2×C4311yescharacteristic, complemented
271#3167C2×C4311yescharacteristic, complemented
272#3167C2×C4311yescharacteristic, complemented
273#3147C2×C4311yescharacteristic, complemented
274#3131C2×C4311yescharacteristic, complemented
275#1723C2×C4311yescharacteristic, complemented
276#1721C2×C4311yescharacteristic, complemented
277#1720C2×C4311yescharacteristic, complemented
278#1719C2×C4311yescharacteristic, complemented
279#1717C2×C4311yescharacteristic, complemented
280#1717C2×C4311yescharacteristic, complemented
281#1715C2×C4311yescharacteristic, complemented
282#1714C2×C4311yescharacteristic, complemented
283C2×#322C2×C4311yescharacteristic, complemented
284C2×C43—22no—
285C2×C43—161no—
286C2×C43—161no—
287C2×C43—161no—
288C2×C43#314711yescharacteristic
289C2×C43C2×#49611yescharacteristic
290C2×C43#315011yescharacteristic
291C2×#135—22no—
292#533C22×C4311yescharacteristic
293#532C22×C4311yescharacteristic
294#532C22×C4311yescharacteristic
295#532C22×C4311yescharacteristic
296#500C22×C4311yescharacteristic
297#500C22×C4311yescharacteristic
298#498C22×C4311yescharacteristic
299#498C22×C4311yescharacteristic
300#495—22no—
301#494C22×C4311yescharacteristic
302#493C22×C4311yescharacteristic
303#493C22×C4311yescharacteristic
304#493C22×C4311yescharacteristic
305#492C22×C4311yescharacteristic
306#492C22×C4311yescharacteristic
307#492C22×C4311yescharacteristic
308#492C22×C4311yescharacteristic
309#488—22no—
310#487C22×C4311yescharacteristic
311#487C22×C4311yescharacteristic
312#487C22×C4311yescharacteristic
313#487C22×C4311yescharacteristic
314#486C22×C4311yescharacteristic
315#486C22×C4311yescharacteristic
316#486C22×C4311yescharacteristic
317#486C22×C4311yescharacteristic
318#486C22×C4311yescharacteristic
319#486C22×C4311yescharacteristic
320#486C22×C4311yescharacteristic
321#486C22×C4311yescharacteristic
322#466—22no—
323#466—22no—
324#465—22no—
325#465—22no—
326C4×SD16—22no—
327C4×SD16—22no—
328C4×D8—22no—
329C4×D8—22no—
330#416—22no—
331C2×C4×C8C22×C4311yescharacteristic
332C2×C4×C8C22×C4311yescharacteristic
333C2×C4×C8C22×C4311yescharacteristic
334#322C22×C4311yescharacteristic
335#322C22×C4311yescharacteristic
336#322C22×C4311yescharacteristic
337#322C22×C4311yescharacteristic
338C43#1961911yescharacteristic, direct product factor, Sylow
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342#135—48no—
343C2×Q16—22no—
344C2×SD16—22no—
345C2×SD16—22no—
346C2×SD16—22no—
347C2×SD16—22no—
348C2×D8—22no—
349C2×D8—22no—
350C2×D8—22no—
351C22×C8D4×C4312yes—
352C22×C8D4×C4312yes—
353C22×C8D4×C4312yes—
354C4⋊Q8C23×C4311yescharacteristic
355C4⋊Q8C23×C4311yescharacteristic
356C4⋊Q8C23×C4311yescharacteristic
357C4⋊Q8C23×C4311yescharacteristic
358C4⋊Q8C23×C4311yescharacteristic
359#127C23×C4311yescharacteristic
360#127C23×C4311yescharacteristic
361#127C23×C4311yescharacteristic
362#125—21no—
363#124—21no—
364#124—21no—
365#124—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368#121—21no—
369#121—21no—
370#121—21no—
371#121—21no—
372#121—21no—
373#121—21no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382#117—21no—
383C2×C42C23×C4311yescharacteristic
384#107—22no—
385#107—22no—
386#106—22no—
387#106—22no—
388#103—22no—
389#103—22no—
390#103—22no—
391#103—22no—
392#102—22no—
393#102—22no—
394#102—22no—
395#102—22no—
396#102—22no—
397#102—22no—
398#102—22no—
399#102—22no—
400C4×C8D4×C4312yes—
401C4×C8D4×C4312yes—
402C4×C8D4×C4312yes—
403C4×C8C23×C4311yescharacteristic
404C4×C8C23×C4311yescharacteristic
405C4×C8C23×C4311yescharacteristic
406C4×C8C23×C4311yescharacteristic
407C4×C8C23×C4311yescharacteristic
408C4×C8C23×C4311yescharacteristic
409#41—44no—
410#41—44no—
411#41—44no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4C2×D4×C4311yescharacteristic
433C22×C4C2×D4×C4311yescharacteristic
434C22×C4C2×D4×C4311yescharacteristic
435Q16—44no—
436SD16—44no—
437SD16—44no—
438SD16—44no—
439SD16—44no—
440D8—44no—
441D8—44no—
442D8—44no—
443C2×C8—24no—
444C2×C8—24no—
445C2×C8—42no—
446C2×C8C2×D4×C4312yes—
447C2×C8C2×D4×C4312yes—
448C2×C8C2×D4×C4312yes—
449C2×C8C2×D4×C4312yes—
450C2×C8C2×D4×C4312yes—
451C2×C8C2×D4×C4312yes—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C42—41no—
472C42C2×D4×C4311yescharacteristic
473C42C2×D4×C4311yescharacteristic
474C42C2×D4×C4311yescharacteristic
475C42C24×C4311yescharacteristic
476C23—41no—
477C23—41no—
478C23—41no—
479C23#127×C4311yescharacteristic
480Q8—42no—
481Q8—42no—
482Q8—42no—
483Q8—42no—
484Q8—42no—
485D4—42no—
486D4—42no—
487D4—42no—
488D4—42no—
489D4—42no—
490D4—42no—
491D4—42no—
492D4—42no—
493D4—42no—
494D4—82no—
495D4—82no—
496D4—82no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—82no—
505C2×C4—82no—
506C2×C4—82no—
507C2×C4#127×C4311yescharacteristic
508C2×C4#127×C4311yescharacteristic
509C2×C4#127×C4311yescharacteristic
510C2×C4AGL(1,ℤ/8)×C4314yes—
511C2×C4C22×D4×C4311yescharacteristic
512C2×C4C22×D4×C4311yescharacteristic
513C2×C4C22×D4×C4311yescharacteristic
514C8—22no—
515C8—22no—
516C8—22no—
517C8—22no—
518C8—22no—
519C8#135×C4314yescomplemented
520C22—21no—
521C22—21no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22—81no—
531C22C43×#49612yes—
532C22C2×#127×C4311yescharacteristic
533C4—21no—
534C4—21no—
535C4—81no—
536C4—81no—
537C4—81no—
538C4—81no—
539C4—81no—
540C4C43×#49612yes—
541C4C2×#135×C4312yes—
542C4C2×AGL(1,ℤ/8)×C4312yes—
543C4C43×#57512yes—
544C2—22no—
545C2—161no—
546C2—161no—
547C2—161no—
548C2C43×#314711yescharacteristic
549C2C2×C43×#49611yescharacteristic
550C2C43×#315011yescharacteristic
subgroupG/H
centerC2×C4×C43#127
commutator, Frattini, cosocleC42C24×C43
socleC22×C43C2×#127
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3169C2semidirect
2. C43×#3169C2semidirect
3. C43×#3167C2semidirect
4. C43×#3167C2semidirect
5. C43×#3147C2semidirect
6. C43×#3131C2semidirect
7. C43×#1723C2semidirect
8. C43×#1721C2semidirect
9. C43×#1720C2semidirect
10. C43×#1719C2semidirect
11. C43×#1717C2semidirect
12. C43×#1717C2semidirect
13. C43×#1715C2semidirect
14. C43×#1714C2semidirect
15. C2×C43×#322C2semidirect
243. C8×C43#135semidirect
244. #19619C43direct (N × H)
269. #3169C2×C43semidirect
270. #3169C2×C43semidirect
271. #3167C2×C43semidirect
272. #3167C2×C43semidirect
273. #3147C2×C43semidirect
274. #3131C2×C43semidirect
275. #1723C2×C43semidirect
276. #1721C2×C43semidirect
277. #1720C2×C43semidirect
278. #1719C2×C43semidirect
279. #1717C2×C43semidirect
280. #1717C2×C43semidirect
281. #1715C2×C43semidirect
282. #1714C2×C43semidirect
283. C2×#322C2×C43semidirect
338. C43#19619direct (N × H)
519. C8#135×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#31692
C43×#31672
C43×#31472
C43×#31312
C43×#17232
C43×#17212
C43×#17202
C43×#17192
C43×#17172
C43×#17152
C43×#17142
C2×C43×#3222
#1961943