Subgroups — C₄²×C₄₇⋊C₁₆ #26131097

Order 12032.

558 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₄₇⋊C₁₆	C₂	1	6	yes	maximal
2	C₄²×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄₇⋊C₁₆	C₂²	1	4	yes	—
4	C₄×C₄₇⋊C₁₆	C₄	1	24	yes	direct product factor
5	C₂×C₄×C₈×C₄₇	C₄	1	3	yes	—
6	C₂×C₄×C₈×C₄₇	C₂²	1	3	yes	—
7	C₄³×C₄₇	C₄	1	1	yes	characteristic
8	C₂×C₄₇⋊C₁₆	C₂×C₄	1	24	yes	—
9	C₂²×C₈×C₄₇	C₂×C₄	1	3	yes	—
10	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
11	C₂×C₄²×C₄₇	C₈	1	4	yes	—
12	C₂×C₄²×C₄₇	C₂×C₄	1	3	yes	—
13	C₄×C₈×C₄₇	C₈	1	12	yes	—
14	C₄×C₈×C₄₇	C₂×C₄	1	12	yes	—
15	C₂²×C₄×C₄₇	C₂×C₈	1	6	yes	—
16	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₈×C₄₇	C₄²	1	6	yes	—
18	C₂×C₈×C₄₇	C₂×C₈	1	12	yes	—
19	C₂×C₈×C₄₇	C₂²×C₄	1	6	yes	—
20	C₄²×C₄₇	C₁₆	1	16	yes	complemented
21	C₄²×C₄₇	C₄²	1	6	yes	—
22	C₄²×C₄₇	C₂×C₈	1	6	yes	—
23	C₄₇⋊C₁₆	C₄²	1	16	yes	direct product factor
24	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
25	C₂×C₄×C₄₇	C₄×C₈	1	12	yes	—
26	C₂×C₄×C₄₇	C₂×C₁₆	1	24	yes	—
27	C₂×C₄×C₄₇	C₂×C₄²	1	3	yes	—
28	C₂×C₄×C₄₇	C₂²×C₈	1	3	yes	—
29	C₈×C₄₇	C₄×C₈	1	12	yes	—
30	C₈×C₄₇	C₂×C₄²	1	4	yes	—
31	C₄²×C₁₆	—	47	1	no	maximal, Sylow
32	C₂²×C₄₇	C₂×C₄×C₈	1	3	yes	—
33	C₂²×C₄₇	C₂²×C₁₆	1	4	yes	—
34	C₄×C₄₇	C₄×C₁₆	1	24	yes	complemented
35	C₄×C₄₇	C₄³	1	1	yes	characteristic
36	C₄×C₄₇	C₂×C₄×C₈	1	3	yes	—
37	C₂×C₄×C₁₆	—	47	6	no	—
38	C₄²×C₈	D₄₇	1	1	yes	characteristic
39	C₂×C₄₇	C₄²×C₈	1	1	yes	characteristic
40	C₂×C₄₇	C₂×C₄×C₁₆	1	6	yes	—
41	C₂²×C₁₆	—	47	4	no	—
42	C₂×C₄×C₈	Dic₄₇	1	3	yes	—
43	C₂×C₄×C₈	C₂×D₄₇	1	3	yes	—
44	C₄³	Dic₄₇	1	1	yes	characteristic
45	C₄×C₁₆	—	47	24	no	—
46	C₄₇	C₄²×C₁₆	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₈	C₂×Dic₄₇	1	3	yes	—
48	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
49	C₂×C₄²	C₄₇⋊C₈	1	4	yes	—
50	C₂×C₄²	C₂×Dic₄₇	1	3	yes	—
51	C₂×C₁₆	—	47	24	no	—
52	C₄×C₈	C₄₇⋊C₈	1	12	yes	—
53	C₄×C₈	C₄×D₄₇	1	12	yes	—
54	C₂²×C₄	C₂×C₄₇⋊C₈	1	6	yes	—
55	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
56	C₂×C₈	C₂×C₄₇⋊C₈	1	12	yes	—
57	C₂×C₈	C₄×Dic₄₇	1	6	yes	—
58	C₂×C₈	C₂×C₄×D₄₇	1	6	yes	—
59	C₄²	C₄₇⋊C₁₆	1	16	yes	direct product factor
60	C₄²	C₂×C₄₇⋊C₈	1	6	yes	—
61	C₄²	C₄×Dic₄₇	1	6	yes	—
62	C₁₆	—	47	16	no	—
63	C₂³	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
64	C₂×C₄	C₄×C₄₇⋊C₈	1	12	yes	—
65	C₂×C₄	C₂×C₄₇⋊C₁₆	1	24	yes	—
66	C₂×C₄	C₂×C₄×Dic₄₇	1	3	yes	—
67	C₂×C₄	C₂²×C₄₇⋊C₈	1	3	yes	—
68	C₈	C₄×C₄₇⋊C₈	1	12	yes	—
69	C₈	C₄²×D₄₇	1	4	yes	—
70	C₂²	C₂×C₄×C₄₇⋊C₈	1	3	yes	—
71	C₂²	C₂²×C₄₇⋊C₁₆	1	4	yes	—
72	C₄	C₄×C₄₇⋊C₁₆	1	24	yes	direct product factor
73	C₄	C₄²×Dic₄₇	1	1	yes	characteristic
74	C₄	C₂×C₄×C₄₇⋊C₈	1	3	yes	—
75	C₂	C₄²×C₄₇⋊C₈	1	1	yes	characteristic
76	C₂	C₂×C₄×C₄₇⋊C₁₆	1	6	yes	—

	subgroup	G/H
center, hypercenter	C₄²×C₈	D₄₇
commutator, hypocenter	C₄₇	C₄²×C₁₆
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₄²×C₈×C₄₇	C₂
socle, prime radical	C₂³×C₄₇	C₂²×C₈
cosocle	C₂²×C₈×C₄₇	C₂³
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
4. C₄×C₄₇⋊C₁₆	C₄	direct (N × H)
20. C₄²×C₄₇	C₁₆	semidirect
23. C₄₇⋊C₁₆	C₄²	direct (N × H)
34. C₄×C₄₇	C₄×C₁₆	semidirect
46. C₄₇	C₄²×C₁₆	semidirect
59. C₄²	C₄₇⋊C₁₆	direct (N × H)
72. C₄	C₄×C₄₇⋊C₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₄₇⋊C₁₆	2
C₄²×C₈×C₄₇	2
C₄²×C₁₆	47

Subgroups — C42×C47⋊C16 #26131097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×C₄₇⋊C₁₆ #26131097