Subgroups — C₂×#16810344 #20272990

Order 6784.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#88322	C₂	1	2	yes	maximal
2	#16810344	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×C₈×C₅₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×#88322	C₄	1	4	yes	—
5	C₄×#88322	C₄	1	4	yes	—
6	C₄×#88322	C₂²	1	4	yes	—
7	C₂²×C₈×C₅₃	C₄	1	2	yes	—
8	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₅₃	C₄	1	2	yes	—
10	C₄×C₈×C₅₃	C₂²	1	2	yes	—
11	C₂²×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄×C₅₃	C₂×C₄	1	2	yes	—
13	C₂×C₈×C₅₃	C₈	1	8	yes	complemented
14	C₂×C₈×C₅₃	C₂×C₄	1	4	yes	—
15	C₄²×C₅₃	C₂×C₄	1	2	yes	—
16	C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
17	C₄²×C₅₃	C₂³	1	1	yes	characteristic
18	C₂×#88322	—	2	8	no	—
19	C₂×#88322	C₂×C₄	1	8	yes	—
20	C₂³×C₅₃	C₄²	1	1	yes	characteristic
21	C₂×C₄×C₅₃	C₄²	1	1	yes	characteristic
22	C₂×C₄×C₅₃	C₄²	1	2	yes	—
23	C₂×C₄×C₅₃	C₂×C₈	1	4	yes	—
24	C₂×C₄×C₅₃	M₁₆	1	8	yes	—
25	C₂×C₄×C₅₃	C₂²×C₄	1	2	yes	—
26	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
27	C₈×C₅₃	C₂×C₈	1	8	yes	complemented
28	#88322	—	2	8	no	—
29	C₂²×C₅₃	C₄×C₈	1	2	yes	—
30	C₂²×C₅₃	#97	1	4	yes	—
31	C₂²×C₅₃	C₂×C₄²	1	1	yes	characteristic
32	C₄×C₅₃	C₄×C₈	1	2	yes	—
33	C₄×C₅₃	#97	1	4	yes	—
34	C₄×C₅₃	C₂²×C₈	1	2	yes	—
35	C₄×C₅₃	C₂×M₁₆	1	4	yes	—
36	C₂×#322	—	53	1	no	maximal, Sylow
37	C₂×C₅₃	#322	1	4	yes	complemented
38	C₂×C₅₃	C₂×C₄×C₈	1	1	yes	characteristic
39	C₂×C₅₃	C₂×#97	1	2	yes	—
40	C₂×C₄×C₈	—	53	2	no	—
41	C₂×C₄×C₈	D₅₃	1	1	yes	characteristic
42	#322	—	53	4	no	—
43	C₅₃	C₂×#322	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₈	—	53	4	no	—
45	C₂²×C₈	Dic₅₃	1	2	yes	—
46	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic
47	C₄×C₈	—	53	4	no	—
48	C₄×C₈	—	53	4	no	—
49	C₄×C₈	Dic₅₃	1	2	yes	—
50	C₄×C₈	C₂×D₅₃	1	2	yes	—
51	C₂²×C₄	C₄×D₅₃	1	2	yes	—
52	C₂²×C₄	C₂×Dic₅₃	1	1	yes	characteristic
53	C₂×C₈	—	53	8	no	—
54	C₂×C₈	—	106	8	no	—
55	C₂×C₈	#88322	1	8	yes	complemented
56	C₂×C₈	C₂×Dic₅₃	1	4	yes	—
57	C₄²	C₄×D₅₃	1	2	yes	—
58	C₄²	C₂×Dic₅₃	1	1	yes	characteristic
59	C₄²	C₂²×D₅₃	1	1	yes	characteristic
60	C₂³	C₄×Dic₅₃	1	1	yes	characteristic
61	C₂×C₄	#11719912	1	8	yes	—
62	C₂×C₄	C₂×#88322	1	4	yes	—
63	C₂×C₄	C₄×Dic₅₃	1	1	yes	characteristic
64	C₂×C₄	C₄×Dic₅₃	1	2	yes	—
65	C₂×C₄	C₂×C₄×D₅₃	1	2	yes	—
66	C₂×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
67	C₈	—	106	8	no	—
68	C₈	C₂×#88322	1	8	yes	complemented
69	C₂²	C₄×#88322	1	2	yes	—
70	C₂²	#13133127	1	4	yes	—
71	C₂²	C₂×C₄×Dic₅₃	1	1	yes	characteristic
72	C₄	C₄×#88322	1	2	yes	—
73	C₄	#13133127	1	4	yes	—
74	C₄	C₂²×#88322	1	2	yes	—
75	C₄	C₂×#11719912	1	4	yes	—
76	C₂	#16810344	1	4	yes	direct product factor
77	C₂	C₂×C₄×#88322	1	1	yes	characteristic
78	C₂	C₂×#13133127	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂×D₅₃
commutator	C₂×C₅₃	C₂×C₄×C₈
Frattini	C₄²	C₂²×D₅₃
Fitting	C₂×C₄×C₈×C₅₃	C₂
socle	C₂³×C₅₃	C₄²
hypercenter	C₂×C₄×C₈	D₅₃
hypocenter	C₅₃	C₂×#322
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #16810344	C₂	direct (N × H)
13. C₂×C₈×C₅₃	C₈	semidirect
27. C₈×C₅₃	C₂×C₈	semidirect
37. C₂×C₅₃	#322	semidirect
43. C₅₃	C₂×#322	semidirect
55. C₂×C₈	#88322	semidirect
68. C₈	C₂×#88322	semidirect
76. C₂	#16810344	direct (N × H)

Subgroups — C2×#16810344 #20272990

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16810344 #20272990