Subgroups — C₂×#16811552 #20291070

Order 6784.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13133288	C₂	1	2	yes	maximal
2	#16811552	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11719936	—	2	2	no	—
5	#13133288	—	2	2	no	—
6	#13133288	C₂²	1	4	yes	—
7	C₂×C₈×D₅₃	C₂²	1	1	yes	characteristic
8	C₂×#11719908	C₄	1	1	yes	characteristic
9	C₁₆×D₅₃	C₄	1	2	yes	—
10	C₁₆×D₅₃	C₂²	1	2	yes	—
11	C₂×C₁₆×C₅₃	C₄	1	1	yes	characteristic
12	C₂×C₄×D₅₃	D₄	1	1	yes	characteristic
13	C₂×#88324	—	4	2	no	—
14	#11719936	—	2	4	no	—
15	#11719936	—	4	2	no	—
16	C₂×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
17	C₂×#88322	Q₈	1	1	yes	characteristic
18	C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
19	C₈×D₅₃	D₄	1	1	yes	characteristic
20	C₈×D₅₃	Q₈	1	1	yes	characteristic
21	C₈×D₅₃	C₂³	1	1	yes	characteristic
22	C₁₆×C₅₃	C₂×C₄	1	2	yes	—
23	#11719908	C₂×C₄	1	2	yes	—
24	C₂²×D₅₃	Q₁₆	1	1	yes	characteristic
25	C₂×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
26	C₂×Dic₅₃	D₈	1	1	yes	characteristic
27	C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
28	C₄×D₅₃	D₈	1	1	yes	characteristic
29	C₄×D₅₃	Q₁₆	1	1	yes	characteristic
30	C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
31	#88324	—	4	4	no	—
32	C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
33	C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
34	#88322	C₄⋊C₄	1	1	yes	characteristic
35	#88322	C₂×Q₈	1	1	yes	characteristic
36	C₂²×C₅₃	#107	1	1	yes	characteristic
37	C₂×D₅₃	—	2	2	no	—
38	C₂×D₅₃	#107	1	1	yes	characteristic
39	C₂×D₅₃	C₂×Q₁₆	1	1	yes	characteristic
40	C₄×C₅₃	#107	1	1	yes	characteristic
41	C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
42	Dic₅₃	#107	1	1	yes	characteristic
43	Dic₅₃	C₂×D₈	1	1	yes	characteristic
44	C₂×#368	—	53	1	no	maximal, Sylow
45	C₂×C₅₃	#368	1	2	yes	complemented
46	C₂×C₅₃	C₂×#107	1	1	yes	characteristic
47	D₅₃	—	2	1	no	—
48	D₅₃	—	2	1	no	—
49	C₂²×C₁₆	—	53	1	no	—
50	C₂×#108	—	53	2	no	—
51	#368	—	53	4	no	—
52	C₅₃	C₂×#368	1	1	yes	characteristic, complemented, Sylow
53	C₂×M₁₆	—	106	2	no	—
54	C₂²×C₈	—	53	1	no	—
55	C₂×C₁₆	—	53	1	no	—
56	C₂×C₁₆	—	53	2	no	—
57	C₂×C₁₆	—	53	2	no	—
58	C₂×C₁₆	#6157	1	1	yes	characteristic
59	#108	—	53	4	no	—
60	#108	—	106	2	no	—
61	C₂²×C₄	—	53	1	no	—
62	M₁₆	—	106	4	no	—
63	M₁₆	—	212	2	no	—
64	C₂×C₈	—	53	1	no	—
65	C₂×C₈	—	53	1	no	—
66	C₂×C₈	—	53	1	no	—
67	C₂×C₈	—	53	1	no	—
68	C₂×C₈	—	53	1	no	—
69	C₂×C₈	—	212	2	no	—
70	C₂×C₈	C₂×#6157	1	1	yes	characteristic
71	C₁₆	—	53	2	no	—
72	C₁₆	C₂×#6157	1	2	yes	—
73	C₂³	—	53	1	no	—
74	C₂×C₄	—	53	1	no	—
75	C₂×C₄	—	53	1	no	—
76	C₂×C₄	—	53	1	no	—
77	C₂×C₄	—	53	1	no	—
78	C₂×C₄	—	53	1	no	—
79	C₂×C₄	C₄⋊#6157	1	1	yes	characteristic
80	C₈	—	53	1	no	—
81	C₈	—	53	1	no	—
82	C₈	—	212	4	no	—
83	C₈	C₄⋊#6157	1	1	yes	characteristic
84	C₈	C₂²×#6157	1	1	yes	characteristic
85	C₂²	—	53	1	no	—
86	C₂²	—	53	1	no	—
87	C₂²	—	106	2	no	—
88	C₂²	#13133286	1	1	yes	characteristic
89	C₄	—	53	1	no	—
90	C₄	—	53	1	no	—
91	C₄	#13133286	1	1	yes	characteristic
92	C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
93	C₂	—	106	1	no	—
94	C₂	—	106	1	no	—
95	C₂	#16811552	1	2	yes	direct product factor
96	C₂	C₂×#13133286	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13133286
commutator	C₈×C₅₃	C₂²×C₄
Frattini	C₈	C₂²×#6157
Fitting	C₂×C₁₆×C₅₃	C₄
socle	C₂²×C₅₃	#107
hypercenter	C₂×C₁₆	#6157
hypocenter	C₅₃	C₂×#368
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. #16811552	C₂	direct (N × H)
45. C₂×C₅₃	#368	semidirect
52. C₅₃	C₂×#368	semidirect
95. C₂	#16811552	direct (N × H)

Subgroups — C2×#16811552 #20291070

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16811552 #20291070