Subgroups — C₁₆₃⋊#1273 #35212363

Order 20864.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₆₃⋊C₈	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×C₁₆₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₆₃⋊C₈	C₄	1	4	yes	—
4	C₄×C₁₆₃⋊C₈	—	2	2	no	—
5	C₄×C₁₆₃⋊C₈	—	2	2	no	—
6	C₂²×C₈×C₁₆₃	C₄	1	2	yes	—
7	C₂×C₄²×C₁₆₃	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₁₆₃	—	2	2	no	—
9	C₂×C₁₆₃⋊C₈	—	2	4	no	—
10	C₂×C₁₆₃⋊C₈	—	2	4	no	—
11	C₂×C₁₆₃⋊C₈	C₈	1	8	yes	complemented
12	C₂²×C₄×C₁₆₃	C₂×C₄	1	2	yes	—
13	C₂²×C₄×C₁₆₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₁₆₃	—	2	2	no	—
15	C₂×C₈×C₁₆₃	—	2	2	no	—
16	C₂×C₈×C₁₆₃	C₈	1	4	yes	complemented
17	C₄²×C₁₆₃	D₄	1	2	yes	—
18	C₄²×C₁₆₃	D₄	1	1	yes	characteristic
19	C₄²×C₁₆₃	Q₈	1	1	yes	characteristic
20	C₁₆₃⋊C₈	—	2	8	no	—
21	C₂³×C₁₆₃	C₄²	1	1	yes	characteristic
22	C₂×C₄×C₁₆₃	C₂²⋊C₄	1	2	yes	—
23	C₂×C₄×C₁₆₃	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₁₆₃	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₁₆₃	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₆₃	C₂×C₈	1	4	yes	—
27	C₂×C₄×C₁₆₃	C₂×C₈	1	2	yes	—
28	C₂×C₄×C₁₆₃	M₁₆	1	4	yes	—
29	C₂×C₄×C₁₆₃	M₁₆	1	2	yes	—
30	C₈×C₁₆₃	—	2	4	no	—
31	C₂²×C₁₆₃	#95	1	1	yes	characteristic
32	C₂²×C₁₆₃	C₄×C₈	1	2	yes	—
33	C₂²×C₁₆₃	C₄×C₈	1	1	yes	characteristic
34	C₂²×C₁₆₃	#97	1	2	yes	—
35	C₂²×C₁₆₃	#97	1	1	yes	characteristic
36	C₄×C₁₆₃	C₂²⋊C₈	1	4	yes	—
37	C₄×C₁₆₃	C₂²⋊C₈	1	2	yes	—
38	C₄×C₁₆₃	C₄⋊C₈	1	4	yes	—
39	C₄×C₁₆₃	C₄⋊C₈	1	2	yes	—
40	C₂×C₁₆₃	C₈²	1	1	yes	characteristic
41	C₂×C₁₆₃	#322	1	1	yes	characteristic
42	C₂×C₁₆₃	#322	1	2	yes	—
43	C₂×C₁₆₃	#336	1	2	yes	—
44	C₂×C₁₆₃	#336	1	1	yes	characteristic
45	C₁₆₃	#1273	1	1	yes	characteristic, complemented, Sylow
46	#1273	—	163	1	no	maximal, Sylow
47	C₂×C₄×C₈	—	163	2	no	—
48	C₂×C₄×C₈	D₁₆₃	1	1	yes	characteristic
49	C₂²×C₈	—	163	4	no	—
50	C₂²×C₈	Dic₁₆₃	1	2	yes	—
51	C₂×C₄²	C₂×D₁₆₃	1	1	yes	characteristic
52	C₄×C₈	—	2	2	no	—
53	C₄×C₈	—	326	2	no	—
54	C₄×C₈	—	326	2	no	—
55	C₂²×C₄	C₄×D₁₆₃	1	2	yes	—
56	C₂²×C₄	C₂×Dic₁₆₃	1	1	yes	characteristic
57	C₂×C₈	—	2	2	no	—
58	C₂×C₈	—	2	2	no	—
59	C₂×C₈	—	326	4	no	—
60	C₂×C₈	—	326	4	no	—
61	C₂×C₈	—	163	8	no	—
62	C₂×C₈	C₁₆₃⋊C₈	1	4	yes	complemented
63	C₄²	C₂²⋊D₁₆₃	1	2	yes	—
64	C₄²	D₆₅₂	1	1	yes	characteristic
65	C₄²	Dic₃₂₆	1	1	yes	characteristic
66	C₂³	C₄×Dic₁₆₃	1	1	yes	characteristic
67	C₂×C₄	(C₂×D₁₆₃)⋊C₄	1	2	yes	—
68	C₂×C₄	C₂²⋊Dic₁₆₃	1	1	yes	characteristic
69	C₂×C₄	Dic₁₆₃⋊C₄	1	2	yes	—
70	C₂×C₄	C₄⋊Dic₁₆₃	1	1	yes	characteristic
71	C₂×C₄	C₈×D₁₆₃	1	4	yes	—
72	C₂×C₄	C₂×C₁₆₃⋊C₈	1	2	yes	—
73	C₂×C₄	#14579682	1	4	yes	—
74	C₂×C₄	#14579683	1	2	yes	—
75	C₈	—	2	4	no	—
76	C₈	—	326	8	no	—
77	C₂²	C₁₆₃⋊#95	1	1	yes	characteristic
78	C₂²	C₈×Dic₁₆₃	1	2	yes	—
79	C₂²	C₄×C₁₆₃⋊C₈	1	1	yes	characteristic
80	C₂²	#19104645	1	2	yes	—
81	C₂²	#19104646	1	1	yes	characteristic
82	C₄	(C₂×D₁₆₃)⋊C₈	1	4	yes	—
83	C₄	C₂²⋊(C₁₆₃⋊C₈)	1	2	yes	—
84	C₄	Dic₁₆₃⋊C₈	1	4	yes	—
85	C₄	C₄⋊(C₁₆₃⋊C₈)	1	2	yes	—
86	C₂	C₈×C₁₆₃⋊C₈	1	1	yes	characteristic
87	C₂	#23781386	1	1	yes	characteristic
88	C₂	#23781387	1	2	yes	—
89	C₂	#23781419	1	2	yes	—
90	C₂	#23781420	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂×D₁₆₃
commutator	C₂×C₁₆₃	C₈²
Fitting	C₂×C₄×C₈×C₁₆₃	C₂
socle, prime radical	C₂³×C₁₆₃	C₄²
cosocle	C₂×C₄²×C₁₆₃	C₂²
hypercenter	C₂×C₄×C₈	D₁₆₃
hypocenter	C₁₆₃	#1273
LCS	G ▷ C₂×C₁₆₃ ▷ C₁₆₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
11. C₂×C₁₆₃⋊C₈	C₈	semidirect
16. C₂×C₈×C₁₆₃	C₈	semidirect
45. C₁₆₃	#1273	semidirect
62. C₂×C₈	C₁₆₃⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₁₆₃⋊C₈	2
C₂×C₄×C₈×C₁₆₃	2
#1273	163

Subgroups — C163⋊#1273 #35212363

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₆₃⋊#1273 #35212363