Subgroups — C₂×#13133150 #16810656

Order 3392.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88322	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₅₃	C₂	1	1	yes	maximal, characteristic
3	#13133150	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₅₃	—	2	1	no	—
6	C₂²×C₄×C₅₃	C₂²	1	1	yes	characteristic
7	C₂²×Dic₅₃	—	2	1	no	—
8	C₄⋊C₄×C₅₃	—	2	1	no	—
9	C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
10	C₄⋊Dic₅₃	—	2	1	no	—
11	C₄⋊Dic₅₃	C₂²	1	2	yes	—
12	C₂×#88322	C₄	1	4	yes	complemented
13	C₂×#88322	C₂²	1	2	yes	—
14	C₂³×C₅₃	D₄	1	1	yes	characteristic
15	C₂×C₄×C₅₃	—	2	2	no	—
16	C₂×C₄×C₅₃	—	4	2	no	—
17	C₂×C₄×C₅₃	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₅₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₅₃	Q₈	1	2	yes	—
20	C₂×C₄×C₅₃	C₂³	1	1	yes	characteristic
21	C₂×Dic₅₃	—	2	2	no	—
22	C₂×Dic₅₃	—	4	2	no	—
23	#88322	C₂×C₄	1	4	yes	complemented
24	C₂²×C₅₃	C₄⋊C₄	1	2	yes	—
25	C₂²×C₅₃	D₈	1	2	yes	—
26	C₂²×C₅₃	Q₁₆	1	2	yes	—
27	C₂²×C₅₃	C₂×D₄	1	1	yes	characteristic
28	C₄×C₅₃	—	4	2	no	—
29	C₄×C₅₃	C₄⋊C₄	1	2	yes	—
30	C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
32	Dic₅₃	—	4	2	no	—
33	C₂×C₅₃	#107	1	4	yes	complemented
34	C₂×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₅₃	C₂×D₈	1	1	yes	characteristic
36	C₂×C₅₃	C₂×Q₁₆	1	1	yes	characteristic
37	C₂×#107	—	53	1	no	maximal, Sylow
38	C₅₃	C₂×#107	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₈	—	53	1	no	—
40	C₂×C₄⋊C₄	—	53	1	no	—
41	C₂×C₄⋊C₄	D₅₃	1	1	yes	characteristic
42	#107	—	53	4	no	—
43	C₂²×C₄	—	2	1	no	—
44	C₂²×C₄	—	106	1	no	—
45	C₂²×C₄	C₂×D₅₃	1	1	yes	characteristic
46	C₂×C₈	—	53	4	no	—
47	C₂×C₈	—	53	2	no	—
48	C₄⋊C₄	—	2	1	no	—
49	C₄⋊C₄	—	53	2	no	—
50	C₄⋊C₄	—	106	1	no	—
51	C₄⋊C₄	C₂×D₅₃	1	2	yes	—
52	C₂³	C₂²⋊D₅₃	1	1	yes	characteristic
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	4	2	no	—
55	C₂×C₄	—	106	2	no	—
56	C₂×C₄	—	212	2	no	—
57	C₂×C₄	Dic₁₀₆	1	2	yes	—
58	C₂×C₄	C₄×D₅₃	1	2	yes	—
59	C₂×C₄	C₂²⋊D₅₃	1	1	yes	characteristic
60	C₂×C₄	C₂²×D₅₃	1	1	yes	characteristic
61	C₈	—	53	4	no	—
62	C₂²	#11719919	1	2	yes	—
63	C₂²	#11719922	1	2	yes	—
64	C₂²	#11719925	1	2	yes	—
65	C₂²	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
66	C₄	—	4	2	no	—
67	C₄	—	212	2	no	—
68	C₄	#11719919	1	2	yes	—
69	C₄	C₂×Dic₁₀₆	1	1	yes	characteristic
70	C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
71	C₂	#13133150	1	4	yes	direct product factor
72	C₂	C₂×#11719919	1	1	yes	characteristic
73	C₂	C₂×#11719922	1	1	yes	characteristic
74	C₂	C₂×#11719925	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₅₃
commutator	C₄×C₅₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₅₃
Fitting	C₂×C₄⋊C₄×C₅₃	C₂
socle, prime radical	C₂³×C₅₃	D₄
cosocle	C₂×C₄×C₅₃	C₂³
hypercenter	C₂×C₄⋊C₄	D₅₃
hypocenter	C₅₃	C₂×#107
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #13133150	C₂	direct (N × H)
12. C₂×#88322	C₄	semidirect
23. #88322	C₂×C₄	semidirect
33. C₂×C₅₃	#107	semidirect
38. C₅₃	C₂×#107	semidirect
71. C₂	#13133150	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×#88322	2
C₂×C₄⋊Dic₅₃	2
#13133150	2
C₂×C₄⋊C₄×C₅₃	2
C₂×#107	53

Subgroups — C2×#13133150 #16810656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13133150 #16810656