Subgroups — C₂×C₄×Dic₈₆ #14583364

Order 2752.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₈₆	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₈₆	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₄₃⋊C₄	C₂	1	2	yes	maximal
5	C₂×C₄×Dic₄₃	C₂	1	2	yes	maximal
6	C₂×C₄²×C₄₃	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄×C₄₃	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₄₃	C₂²	1	1	yes	characteristic
9	C₂²×C₄×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²×Dic₄₃	C₂²	1	2	yes	—
11	C₂²×Dic₄₃	C₂²	1	2	yes	—
12	C₂×Dic₈₆	C₄	1	8	yes	direct product factor
13	C₂×Dic₈₆	C₂²	1	4	yes	—
14	C₄²×C₄₃	C₂²	1	4	yes	—
15	C₄⋊Dic₄₃	C₂²	1	4	yes	—
16	Dic₄₃⋊C₄	C₂²	1	8	yes	—
17	C₄×Dic₄₃	C₂²	1	8	yes	—
18	C₂³×C₄₃	C₂³	1	1	yes	characteristic
19	C₂×C₄×C₄₃	—	2	2	no	—
20	C₂×C₄×C₄₃	C₂×C₄	1	4	yes	—
21	C₂×C₄×C₄₃	Q₈	1	4	yes	complemented
22	C₂×C₄×C₄₃	C₂³	1	2	yes	—
23	C₂×C₄×C₄₃	C₂³	1	2	yes	—
24	C₂×C₄×C₄₃	C₂³	1	2	yes	—
25	C₂×Dic₄₃	—	2	4	no	—
26	C₂×Dic₄₃	C₂×C₄	1	8	yes	—
27	C₂×Dic₄₃	C₂³	1	4	yes	—
28	C₂×Dic₄₃	C₂³	1	4	yes	—
29	Dic₈₆	C₂×C₄	1	16	yes	direct product factor
30	C₂²×C₄₃	C₂²×C₄	1	2	yes	—
31	C₂²×C₄₃	C₂×Q₈	1	2	yes	—
32	C₂²×C₄₃	#41	1	2	yes	—
33	C₂²×C₄₃	C₂⁴	1	1	yes	characteristic
34	C₄×C₄₃	—	2	2	no	—
35	C₄×C₄₃	C₂²×C₄	1	4	yes	—
36	C₄×C₄₃	C₂×Q₈	1	4	yes	complemented
37	Dic₄₃	—	2	4	no	—
38	Dic₄₃	C₂²×C₄	1	8	yes	—
39	C₂×C₄₃	C₄×Q₈	1	4	yes	complemented
40	C₂×C₄₃	C₂³×C₄	1	1	yes	characteristic
41	C₂×C₄₃	C₂²×Q₈	1	1	yes	characteristic
42	C₂×C₄₃	C₂×#41	1	1	yes	characteristic
43	C₂×C₄×Q₈	—	43	1	no	maximal, Sylow
44	C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
45	C₂²×Q₈	—	43	1	no	—
46	C₄×Q₈	—	43	8	no	—
47	C₂×C₄⋊C₄	—	43	2	no	—
48	C₂×C₄⋊C₄	—	43	1	no	—
49	C₂×C₄²	—	43	2	no	—
50	C₂×C₄²	D₄₃	1	1	yes	characteristic
51	C₂×Q₈	—	43	4	no	—
52	C₂×Q₈	—	43	8	no	—
53	C₂²×C₄	—	43	2	no	—
54	C₂²×C₄	—	43	2	no	—
55	C₂²×C₄	C₂×D₄₃	1	1	yes	characteristic
56	C₂²×C₄	C₂×D₄₃	1	1	yes	characteristic
57	C₂²×C₄	C₂×D₄₃	1	1	yes	characteristic
58	C₄⋊C₄	—	43	8	no	—
59	C₄⋊C₄	—	43	4	no	—
60	C₄²	—	43	8	no	—
61	C₄²	C₂×D₄₃	1	4	yes	—
62	C₂³	C₂²×D₄₃	1	1	yes	characteristic
63	Q₈	—	43	16	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	43	8	no	—
66	C₂×C₄	—	43	4	no	—
67	C₂×C₄	—	43	4	no	—
68	C₂×C₄	—	86	4	no	—
69	C₂×C₄	Dic₈₆	1	4	yes	direct product factor
70	C₂×C₄	C₄×D₄₃	1	4	yes	—
71	C₂×C₄	C₂²×D₄₃	1	2	yes	—
72	C₂×C₄	C₂²×D₄₃	1	2	yes	—
73	C₂×C₄	C₂²×D₄₃	1	2	yes	—
74	C₂²	C₂×Dic₈₆	1	2	yes	—
75	C₂²	C₂×C₄×D₄₃	1	2	yes	—
76	C₂²	#10621898	1	2	yes	—
77	C₂²	C₂³×D₄₃	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	43	8	no	—
80	C₄	—	86	4	no	—
81	C₄	C₂×Dic₈₆	1	4	yes	direct product factor
82	C₄	C₂×C₄×D₄₃	1	4	yes	—
83	C₂	C₄×Dic₈₆	1	4	yes	direct product factor
84	C₂	C₂²×C₄×D₄₃	1	1	yes	characteristic
85	C₂	C₂²×Dic₈₆	1	1	yes	characteristic
86	C₂	C₂×#10621898	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₄₃
commutator	C₂×C₄₃	C₂³×C₄
Frattini	C₂²	C₂³×D₄₃
Fitting	C₂×C₄²×C₄₃	C₂
socle, prime radical	C₂³×C₄₃	C₂³
cosocle	C₂²×C₄₃	C₂⁴
hypercenter	C₂×C₄²	D₄₃
hypocenter	C₄₃	C₂×C₄×Q₈
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₄×Dic₈₆	C₂	direct (N × H)
12. C₂×Dic₈₆	C₄	direct (N × H)
21. C₂×C₄×C₄₃	Q₈	semidirect
29. Dic₈₆	C₂×C₄	direct (N × H)
36. C₄×C₄₃	C₂×Q₈	semidirect
39. C₂×C₄₃	C₄×Q₈	semidirect
44. C₄₃	C₂×C₄×Q₈	semidirect
69. C₂×C₄	Dic₈₆	direct (N × H)
81. C₄	C₂×Dic₈₆	direct (N × H)
83. C₂	C₄×Dic₈₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₈₆	2
C₄×Dic₈₆	2
C₂×C₄⋊Dic₄₃	2
C₂×Dic₄₃⋊C₄	2
C₂×C₄×Dic₄₃	2
C₂×C₄²×C₄₃	2
C₂×C₄×Q₈	43

Subgroups — C2×C4×Dic86 #14583364

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×Dic₈₆ #14583364