Subgroups — C₂×C₁₆×Dic₄₇ #20244974

Order 6016.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂²×C₁₆	D₄₇
commutator, hypocenter	C₄₇	C₂×C₄×C₁₆
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₂²×C₁₆×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₈
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
3. C₁₆×Dic₄₇	C₂	direct (N × H)
7. C₂×C₄₇⋊C₁₆	C₄	semidirect
12. C₂×C₁₆×C₄₇	C₄	semidirect
24. C₁₆×C₄₇	C₂×C₄	semidirect
25. C₄₇⋊C₁₆	C₂×C₄	semidirect
31. C₂×Dic₄₇	C₁₆	direct (N × H)
43. Dic₄₇	C₂×C₁₆	direct (N × H)
45. C₂×C₄₇	C₄×C₁₆	semidirect
52. C₄₇	C₂×C₄×C₁₆	semidirect
58. C₂×C₁₆	Dic₄₇	direct (N × H)
73. C₁₆	C₂×Dic₄₇	direct (N × H)
92. C₂	C₁₆×Dic₄₇	direct (N × H)

Subgroups — C2×C16×Dic47 #20244974

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₆×Dic₄₇ #20244974