Subgroups — C₂×#13063372 #14583732

Order 2752.

794 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063372	C₂	1	16	yes	maximal, direct product factor
2	C₂×#10621898	C₂	1	3	yes	maximal, complemented
3	C₂×#10621900	C₂	1	6	yes	maximal, complemented
4	C₂²×Dic₈₆	C₂	1	3	yes	maximal, complemented
5	C₂×Q₈×D₄₃	C₂	1	2	yes	maximal, complemented
6	C₂×#41×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#41×C₄₃	C₂²	1	8	yes	complemented
8	C₂×Q₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×D₄×C₄₃	C₂²	1	3	yes	—
10	C₂²×C₄×C₄₃	C₂²	1	3	yes	—
11	C₂×C₂²⋊D₄₃	C₂²	1	6	yes	—
12	C₂²×Dic₄₃	C₂²	1	6	yes	—
13	Q₈×D₄₃	C₂²	1	16	yes	complemented
14	#10621900	C₂²	1	48	yes	complemented
15	#10621898	C₂²	1	24	yes	complemented
16	C₂×D₁₇₂	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄₃	C₂²	1	6	yes	—
18	C₂×Dic₈₆	C₂²	1	6	yes	—
19	C₂×Dic₈₆	C₂²	1	3	yes	—
20	C₂×Dic₈₆	C₂²	1	24	yes	complemented
21	C₂³×C₄₃	C₂³	1	3	yes	—
22	C₂²×D₄₃	C₂³	1	2	yes	—
23	Q₈×C₄₃	C₂³	1	4	yes	—
24	D₄×C₄₃	C₂³	1	12	yes	—
25	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
26	C₂×C₄×C₄₃	C₂³	1	3	yes	—
27	C₂×C₄×C₄₃	C₂³	1	12	yes	—
28	C₂²⋊D₄₃	C₂³	1	24	yes	—
29	C₂×Dic₄₃	C₂³	1	6	yes	—
30	C₂×Dic₄₃	C₂³	1	24	yes	—
31	D₁₇₂	C₂³	1	4	yes	—
32	C₄×D₄₃	C₂³	1	24	yes	—
33	Dic₈₆	C₂³	1	12	yes	—
34	Dic₈₆	C₂³	1	24	yes	—
35	C₂²×C₄₃	—	2	6	no	—
36	C₂²×C₄₃	C₂⁴	1	6	yes	—
37	C₂²×C₄₃	C₂⁴	1	1	yes	characteristic
38	C₂×D₄₃	—	2	4	no	—
39	C₂×D₄₃	C₂⁴	1	4	yes	—
40	C₄×C₄₃	C₂⁴	1	2	yes	—
41	C₄×C₄₃	C₂⁴	1	6	yes	—
42	Dic₄₃	C₂⁴	1	12	yes	—
43	C₂×C₄₃	—	2	6	no	—
44	C₂×C₄₃	2₋¹⁺⁴	1	2	yes	complemented
45	C₂×C₄₃	C₂⁵	1	1	yes	characteristic
46	D₄₃	—	2	4	no	—
47	C₂×2₋¹⁺⁴	—	43	1	no	maximal, Sylow
48	C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
49	2₋¹⁺⁴	—	43	16	no	—
50	C₂×#41	—	43	6	no	—
51	C₂×#41	—	43	3	no	—
52	C₂×#41	D₄₃	1	1	yes	characteristic, complemented
53	C₂²×Q₈	—	43	2	no	—
54	C₂²×Q₈	—	43	3	no	—
55	#41	—	43	48	no	—
56	#41	—	43	24	no	—
57	#41	C₂×D₄₃	1	8	yes	complemented
58	C₂×Q₈	—	43	16	no	—
59	C₂×Q₈	—	43	6	no	—
60	C₂×Q₈	—	43	3	no	—
61	C₂×Q₈	—	43	24	no	—
62	C₂×Q₈	C₂×D₄₃	1	1	yes	characteristic
63	C₂×D₄	—	43	6	no	—
64	C₂×D₄	—	43	1	no	—
65	C₂×D₄	C₂×D₄₃	1	3	yes	—
66	C₂²×C₄	—	43	6	no	—
67	C₂²×C₄	—	43	6	no	—
68	C₂²×C₄	C₂×D₄₃	1	3	yes	—
69	C₂³	—	43	2	no	—
70	C₂³	C₂²×D₄₃	1	3	yes	—
71	Q₈	—	43	24	no	—
72	Q₈	—	43	12	no	—
73	Q₈	C₂²×D₄₃	1	4	yes	—
74	D₄	—	43	24	no	—
75	D₄	—	43	4	no	—
76	D₄	C₂²×D₄₃	1	12	yes	—
77	C₂×C₄	—	43	24	no	—
78	C₂×C₄	—	43	6	no	—
79	C₂×C₄	—	43	24	no	—
80	C₂×C₄	C₂²×D₄₃	1	12	yes	—
81	C₂×C₄	C₂²×D₄₃	1	3	yes	—
82	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
83	C₂²	—	2	6	no	—
84	C₂²	—	43	4	no	—
85	C₂²	—	86	4	no	—
86	C₂²	C₂³×D₄₃	1	6	yes	—
87	C₂²	C₂³×D₄₃	1	1	yes	characteristic
88	C₄	—	43	12	no	—
89	C₄	C₂³×D₄₃	1	6	yes	—
90	C₄	C₂³×D₄₃	1	2	yes	—
91	C₂	—	2	6	no	—
92	C₂	—	86	4	no	—
93	C₂	#13063372	1	2	yes	direct product factor
94	C₂	C₂⁴×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₄₃
commutator, cosocle	C₂×C₄₃	C₂⁵
Frattini	C₂	C₂⁴×D₄₃
Fitting	C₂×#41×C₄₃	C₂
socle	C₂²×C₄₃	C₂⁴
hypercenter	C₂×#41	D₄₃
hypocenter	C₄₃	C₂×2₋¹⁺⁴
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. #13063372	C₂	direct (N × H)
2. C₂×#10621898	C₂	semidirect
3. C₂×#10621900	C₂	semidirect
4. C₂²×Dic₈₆	C₂	semidirect
5. C₂×Q₈×D₄₃	C₂	semidirect
6. C₂×#41×C₄₃	C₂	semidirect
7. #41×C₄₃	C₂²	semidirect
13. Q₈×D₄₃	C₂²	semidirect
14. #10621900	C₂²	semidirect
15. #10621898	C₂²	semidirect
20. C₂×Dic₈₆	C₂²	semidirect
44. C₂×C₄₃	2₋¹⁺⁴	semidirect
48. C₄₃	C₂×2₋¹⁺⁴	semidirect
52. C₂×#41	D₄₃	semidirect
57. #41	C₂×D₄₃	semidirect
93. C₂	#13063372	direct (N × H)

Maximal subgroups

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

subgroup	index
#13063372	2
C₂×#10621898	2
C₂×#10621900	2
C₂²×Dic₈₆	2
C₂×Q₈×D₄₃	2
C₂×#41×C₄₃	2
C₂×2₋¹⁺⁴	43

Subgroups — C2×#13063372 #14583732

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13063372 #14583732