Subgroups — C₂×#16811003 #20285131

Order 6784.

552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₂₁₂	C₂	1	4	yes	maximal
2	C₂×#13133217	C₂	1	2	yes	maximal
3	#16811003	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄×C₈×C₅₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₀₆	C₂²	1	4	yes	—
6	C₂×Dic₂₁₂	—	2	16	no	—
7	C₂×Dic₂₁₂	C₂²	1	16	yes	—
8	#13133217	—	2	4	no	—
9	#13133217	C₂²	1	8	yes	—
10	C₂×C₄⋊Dic₅₃	—	2	4	no	—
11	C₂²×C₈×C₅₃	C₂²	1	2	yes	—
12	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₅₃	C₂²	1	4	yes	—
14	C₂²×C₄×C₅₃	D₄	1	2	yes	—
15	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
16	C₂²×Dic₅₃	—	2	4	no	—
17	C₂×Dic₁₀₆	—	2	16	no	—
18	C₂×Dic₁₀₆	—	2	4	no	—
19	C₂×Dic₁₀₆	C₂³	1	8	yes	—
20	C₂×C₈×C₅₃	D₄	1	8	yes	—
21	C₂×C₈×C₅₃	C₂³	1	4	yes	—
22	C₄²×C₅₃	D₄	1	2	yes	—
23	C₄²×C₅₃	C₂³	1	2	yes	—
24	C₄⋊Dic₅₃	—	2	16	no	—
25	Dic₂₁₂	—	2	32	no	—
26	C₂³×C₅₃	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄×C₅₃	Q₁₆	1	8	yes	complemented
28	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₅₃	C₂×D₄	1	4	yes	—
30	C₂×C₄×C₅₃	C₂×D₄	1	4	yes	—
31	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
32	C₂×Dic₅₃	—	2	8	no	—
33	C₂×Dic₅₃	—	4	8	no	—
34	Dic₁₀₆	—	2	16	no	—
35	Dic₁₀₆	—	4	8	no	—
36	C₈×C₅₃	C₂×D₄	1	8	yes	—
37	C₂²×C₅₃	#127	1	2	yes	—
38	C₂²×C₅₃	C₂×Q₁₆	1	4	yes	—
39	C₂²×C₅₃	C₂²×D₄	1	1	yes	characteristic
40	C₄×C₅₃	#127	1	2	yes	—
41	C₄×C₅₃	C₂×Q₁₆	1	8	yes	complemented
42	C₄×C₅₃	C₂²×D₄	1	2	yes	—
43	Dic₅₃	—	4	8	no	—
44	C₂×#494	—	53	1	no	maximal, Sylow
45	C₂×C₅₃	#494	1	4	yes	complemented
46	C₂×C₅₃	C₂×#127	1	1	yes	characteristic
47	C₂×C₅₃	C₂²×Q₁₆	1	2	yes	—
48	C₂²×Q₁₆	—	53	4	no	—
49	C₂×C₄⋊Q₈	—	53	2	no	—
50	#494	—	53	8	no	—
51	C₂×C₄×C₈	D₅₃	1	1	yes	characteristic
52	C₅₃	C₂×#494	1	1	yes	characteristic, complemented, Sylow
53	C₂²×Q₈	—	53	4	no	—
54	C₂×Q₁₆	—	53	16	no	—
55	C₂×Q₁₆	—	106	16	no	—
56	C₂²×C₈	C₂×D₅₃	1	2	yes	—
57	C₄⋊Q₈	—	53	8	no	—
58	C₄⋊Q₈	—	106	4	no	—
59	C₂×C₄⋊C₄	—	106	4	no	—
60	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic
61	C₄×C₈	C₂×D₅₃	1	4	yes	—
62	C₂×Q₈	—	53	8	no	—
63	C₂×Q₈	—	106	4	no	—
64	C₂×Q₈	—	106	16	no	—
65	C₂²×C₄	—	106	4	no	—
66	C₂²×C₄	D₂₁₂	1	2	yes	—
67	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
68	Q₁₆	—	106	32	no	—
69	C₂×C₈	D₂₁₂	1	8	yes	—
70	C₂×C₈	C₂²×D₅₃	1	4	yes	—
71	C₄⋊C₄	—	106	16	no	—
72	C₄²	D₂₁₂	1	2	yes	—
73	C₄²	C₂²×D₅₃	1	2	yes	—
74	C₂³	C₂×D₂₁₂	1	1	yes	characteristic
75	Q₈	—	106	16	no	—
76	Q₈	—	212	8	no	—
77	C₂×C₄	—	106	8	no	—
78	C₂×C₄	—	212	8	no	—
79	C₂×C₄	Dic₂₁₂	1	8	yes	complemented
80	C₂×C₄	C₂×D₂₁₂	1	1	yes	characteristic
81	C₂×C₄	C₂×D₂₁₂	1	4	yes	—
82	C₂×C₄	C₂×D₂₁₂	1	4	yes	—
83	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
84	C₈	C₂×D₂₁₂	1	8	yes	—
85	C₂²	#13133214	1	2	yes	—
86	C₂²	C₂×Dic₂₁₂	1	4	yes	—
87	C₂²	C₂²×D₂₁₂	1	1	yes	characteristic
88	C₄	—	212	8	no	—
89	C₄	#13133214	1	2	yes	—
90	C₄	C₂×Dic₂₁₂	1	8	yes	complemented
91	C₄	C₂²×D₂₁₂	1	2	yes	—
92	C₂	#16811003	1	4	yes	direct product factor
93	C₂	C₂×#13133214	1	1	yes	characteristic
94	C₂	C₂²×Dic₂₁₂	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₂₁₂
commutator	C₂×C₄×C₅₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₃
Fitting	C₂×C₄×C₈×C₅₃	C₂
socle	C₂³×C₅₃	C₂×D₄
hypercenter	C₂×C₄×C₈	D₅₃
hypocenter	C₅₃	C₂×#494
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #16811003	C₂	direct (N × H)
27. C₂×C₄×C₅₃	Q₁₆	semidirect
41. C₄×C₅₃	C₂×Q₁₆	semidirect
45. C₂×C₅₃	#494	semidirect
52. C₅₃	C₂×#494	semidirect
79. C₂×C₄	Dic₂₁₂	semidirect
90. C₄	C₂×Dic₂₁₂	semidirect
92. C₂	#16811003	direct (N × H)

Subgroups — C2×#16811003 #20285131

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16811003 #20285131