Subgroups — C₂×Q₁₆×D₂₆₉ #31771380

Order 17216.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₂₆₉	C₂	1	2	yes	maximal
2	C₂×Dic₁₀₇₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16864392	C₂	1	2	yes	maximal, complemented
4	Q₁₆×D₂₆₉	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₈×D₂₆₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×Dic₅₃₈	—	2	2	no	—
8	C₂×Dic₅₃₈	C₂²	1	2	yes	—
9	Q₈×D₂₆₉	—	2	4	no	—
10	Q₈×D₂₆₉	C₂²	1	8	yes	—
11	C₂×C₄×D₂₆₉	—	2	2	no	—
12	C₂×C₄×D₂₆₉	C₂²	1	1	yes	characteristic
13	Dic₁₀₇₆	C₂²	1	4	yes	complemented
14	#16864392	C₂²	1	8	yes	complemented
15	C₂×#14524130	C₂²	1	1	yes	characteristic
16	C₈×D₂₆₉	C₂²	1	4	yes	—
17	C₂×Q₈×C₂₆₉	C₂²	1	2	yes	—
18	Q₁₆×C₂₆₉	C₂²	1	4	yes	complemented
19	C₂×C₈×C₂₆₉	C₂²	1	1	yes	characteristic
20	C₂²×D₂₆₉	D₄	1	1	yes	characteristic
21	Dic₅₃₈	—	2	2	no	—
22	Dic₅₃₈	—	2	8	no	—
23	Dic₅₃₈	C₂³	1	4	yes	—
24	C₂×Dic₂₆₉	—	2	2	no	—
25	C₂×Dic₂₆₉	D₄	1	1	yes	characteristic
26	C₄×D₂₆₉	—	2	8	no	—
27	C₄×D₂₆₉	D₄	1	2	yes	—
28	C₄×D₂₆₉	C₂³	1	2	yes	—
29	#14524130	C₂³	1	2	yes	—
30	Q₈×C₂₆₉	—	2	2	no	—
31	Q₈×C₂₆₉	C₂³	1	4	yes	—
32	C₂×C₄×C₂₆₉	—	2	2	no	—
33	C₂×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
34	C₈×C₂₆₉	C₂³	1	2	yes	—
35	C₂²×C₂₆₉	C₂×D₄	1	1	yes	characteristic
36	C₂×D₂₆₉	Q₁₆	1	4	yes	direct product factor
37	C₂×D₂₆₉	C₂×D₄	1	2	yes	—
38	C₄×C₂₆₉	—	2	4	no	—
39	C₄×C₂₆₉	C₂×D₄	1	1	yes	characteristic
40	C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
41	Dic₂₆₉	—	2	4	no	—
42	Dic₂₆₉	C₂×D₄	1	2	yes	—
43	C₂×C₂₆₉	C₂×Q₁₆	1	2	yes	complemented
44	C₂×C₂₆₉	C₂²×D₄	1	1	yes	characteristic
45	D₂₆₉	C₂×Q₁₆	1	4	yes	direct product factor
46	C₂₆₉	C₂²×Q₁₆	1	1	yes	characteristic, complemented, Sylow
47	C₂²×Q₁₆	—	269	1	no	maximal, Sylow
48	C₂²×Q₈	—	269	2	no	—
49	C₂×Q₁₆	—	269	2	no	—
50	C₂×Q₁₆	—	269	8	no	—
51	C₂×Q₁₆	—	269	1	no	—
52	C₂×Q₁₆	D₂₆₉	1	1	yes	characteristic, direct product factor
53	C₂²×C₈	—	269	1	no	—
54	C₂×Q₈	—	269	8	no	—
55	C₂×Q₈	—	269	2	no	—
56	C₂×Q₈	—	538	2	no	—
57	C₂×Q₈	—	538	4	no	—
58	C₂×Q₈	C₂×D₂₆₉	1	2	yes	—
59	C₂²×C₄	—	269	1	no	—
60	C₂²×C₄	—	538	2	no	—
61	Q₁₆	—	269	8	no	—
62	Q₁₆	—	269	4	no	—
63	Q₁₆	C₂×D₂₆₉	1	4	yes	direct product factor
64	C₂×C₈	—	269	1	no	—
65	C₂×C₈	—	269	4	no	—
66	C₂×C₈	C₂×D₂₆₉	1	1	yes	characteristic
67	C₂³	—	269	1	no	—
68	Q₈	—	2	2	no	—
69	Q₈	—	269	4	no	—
70	Q₈	—	538	8	no	—
71	Q₈	—	538	2	no	—
72	Q₈	C₂²×D₂₆₉	1	4	yes	—
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	269	1	no	—
75	C₂×C₄	—	269	2	no	—
76	C₂×C₄	—	269	2	no	—
77	C₂×C₄	—	538	8	no	—
78	C₂×C₄	—	538	2	no	—
79	C₂×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
80	C₈	—	269	2	no	—
81	C₈	C₂²×D₂₆₉	1	2	yes	—
82	C₂²	—	269	4	no	—
83	C₂²	—	269	2	no	—
84	C₂²	D₄×D₂₆₉	1	1	yes	characteristic
85	C₄	—	2	4	no	—
86	C₄	—	269	2	no	—
87	C₄	—	538	4	no	—
88	C₄	D₄×D₂₆₉	1	1	yes	characteristic
89	C₄	C₂³×D₂₆₉	1	1	yes	characteristic
90	C₂	—	269	4	no	—
91	C₂	Q₁₆×D₂₆₉	1	2	yes	direct product factor
92	C₂	C₂×D₄×D₂₆₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₆₉
commutator, cosocle	C₄×C₂₆₉	C₂⁴
Frattini	C₄	C₂³×D₂₆₉
Fitting	C₂×Q₁₆×C₂₆₉	C₂
socle	C₂²×C₂₆₉	C₂×D₄
prime radical	C₂²×D₂₆₉	D₄
hypercenter	C₂×Q₁₆	D₂₆₉
hypocenter	C₂₆₉	C₂²×Q₁₆
LCS	G ▷ C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₁₀₇₆	C₂	semidirect
3. C₂×#16864392	C₂	semidirect
4. Q₁₆×D₂₆₉	C₂	direct (N × H)
6. C₂×Q₁₆×C₂₆₉	C₂	semidirect
13. Dic₁₀₇₆	C₂²	semidirect
14. #16864392	C₂²	semidirect
18. Q₁₆×C₂₆₉	C₂²	semidirect
36. C₂×D₂₆₉	Q₁₆	direct (N × H)
43. C₂×C₂₆₉	C₂×Q₁₆	semidirect
45. D₂₆₉	C₂×Q₁₆	direct (N × H)
46. C₂₆₉	C₂²×Q₁₆	semidirect
52. C₂×Q₁₆	D₂₆₉	direct (N × H)
63. Q₁₆	C₂×D₂₆₉	direct (N × H)
91. C₂	Q₁₆×D₂₆₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₈×D₂₆₉	2
C₂×Dic₁₀₇₆	2
C₂×#16864392	2
Q₁₆×D₂₆₉	2
C₂×C₈×D₂₆₉	2
C₂×Q₁₆×C₂₆₉	2
C₂²×Q₁₆	269

Subgroups — C2×Q16×D269 #31771380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₁₆×D₂₆₉ #31771380