Subgroups — C₂×#11717826 #13109674

Order 1632.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×Dic₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊#3624	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3624	C₂	1	1	yes	maximal, characteristic, complemented
4	#11717826	C₂	1	4	yes	maximal, direct product factor
5	C₂×#63247	—	3	1	no	maximal, Hall
6	C₂²×D₃×C₁₇	C₄	1	1	yes	characteristic
7	C₂×Dic₅₁	C₄	1	1	yes	characteristic
8	C₂×C₃×Dic₁₇	C₂²	1	1	yes	characteristic
9	D₃×Dic₁₇	C₄	1	2	yes	—
10	D₃×Dic₁₇	C₂²	1	2	yes	—
11	C₃⋊#3624	C₂²	1	2	yes	complemented
12	C₃×#3624	C₂²	1	2	yes	complemented
13	C₂²×Dic₁₇	—	3	1	no	—
14	#63247	—	3	4	no	—
15	C₂×#3624	—	3	1	no	—
16	C₂×#3624	D₃	1	1	yes	characteristic, complemented
17	C₂²×C₃×C₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂×D₃×C₁₇	—	2	2	no	—
19	C₂×D₃×C₁₇	C₂×C₄	1	2	yes	—
20	Dic₅₁	C₂×C₄	1	2	yes	—
21	C₃×Dic₁₇	C₂×C₄	1	1	yes	characteristic
22	C₃×Dic₁₇	C₂³	1	1	yes	characteristic
23	C₂³×C₁₇	—	3	1	no	—
24	C₂×Dic₁₇	—	3	1	no	—
25	C₂×Dic₁₇	—	3	2	no	—
26	C₂×Dic₁₇	—	3	2	no	—
27	C₂×Dic₁₇	C₂×D₃	1	1	yes	characteristic
28	#3624	—	3	2	no	—
29	#3624	C₂×D₃	1	2	yes	complemented
30	C₂×C₃×C₁₇	M₁₆	1	2	yes	complemented
31	C₂×C₃×C₁₇	C₂²×C₄	1	1	yes	characteristic
32	D₃×C₁₇	—	2	2	no	—
33	C₂×ΓL(1,𝔽₂₅)	—	17	1	no	maximal, Hall
34	C₂²×C₁₇	—	3	2	no	—
35	C₂²×C₁₇	—	6	2	no	—
36	C₂²×C₁₇	C₄×D₃	1	1	yes	characteristic
37	Dic₁₇	—	3	2	no	—
38	Dic₁₇	C₄×D₃	1	1	yes	characteristic
39	Dic₁₇	C₂²×D₃	1	1	yes	characteristic
40	C₃×C₁₇	C₂×M₁₆	1	1	yes	characteristic, complemented, Hall
41	C₂×C₄×D₃	—	17	1	no	—
42	C₂×C₃×C₈	—	17	1	no	—
43	C₂×C₃⋊C₈	—	17	1	no	—
44	ΓL(1,𝔽₂₅)	—	17	4	no	—
45	C₂×C₁₇	—	6	2	no	—
46	C₂×C₁₇	ΓL(1,𝔽₂₅)	1	2	yes	complemented
47	C₂×C₁₇	C₂×C₄×D₃	1	1	yes	characteristic
48	C₂×M₁₆	—	51	1	no	Sylow
49	C₂²×D₃	#595	1	1	yes	characteristic
50	C₂×C₃×C₄	—	17	1	no	—
51	C₂×Dic₃	—	17	1	no	—
52	C₄×D₃	—	17	2	no	—
53	C₄×D₃	—	17	2	no	—
54	C₃×C₈	—	17	2	no	—
55	C₃⋊C₈	—	17	2	no	—
56	C₁₇	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₄	—	51	1	no	—
58	M₁₆	—	51	4	no	—
59	C₂×C₈	—	17	1	no	—
60	C₂×C₈	—	51	1	no	—
61	C₂²×C₃	C₂×#595	1	1	yes	characteristic
62	C₂×D₃	—	2	2	no	—
63	C₂×D₃	C₂×#595	1	2	yes	—
64	C₃×C₄	—	17	1	no	—
65	C₃×C₄	—	17	1	no	—
66	Dic₃	—	17	2	no	—
67	C₂³	—	3	1	no	—
68	C₂×C₄	—	17	1	no	—
69	C₂×C₄	—	51	2	no	—
70	C₂×C₄	—	51	2	no	—
71	C₂×C₄	—	51	1	no	—
72	C₈	—	17	2	no	—
73	C₈	—	51	2	no	—
74	C₂×C₃	#63247	1	2	yes	complemented
75	C₂×C₃	C₂²×#595	1	1	yes	characteristic
76	D₃	—	2	2	no	—
77	C₂²	—	3	2	no	—
78	C₂²	—	6	2	no	—
79	C₂²	D₃×#595	1	1	yes	characteristic
80	C₄	—	17	1	no	—
81	C₄	—	17	1	no	—
82	C₄	—	51	2	no	—
83	C₃	C₂×#63247	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	6	2	no	—
85	C₂	#11717826	1	2	yes	direct product factor
86	C₂	C₂×D₃×#595	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₃×#595
commutator	C₂×C₃×C₁₇	C₂²×C₄
Frattini	C₂	C₂×D₃×#595
Fitting, socle	C₂²×C₃×C₁₇	C₂×C₄
prime radical	C₂²×D₃×C₁₇	C₄
cosocle	C₃×Dic₁₇	C₂³
hypocenter	C₃×C₁₇	C₂×M₁₆
LCS	G ▷ C₂×C₃×C₁₇ ▷ C₃×C₁₇
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. C₂×C₃⋊#3624	C₂	semidirect
3. C₂×C₃×#3624	C₂	semidirect
4. #11717826	C₂	direct (N × H)
11. C₃⋊#3624	C₂²	semidirect
12. C₃×#3624	C₂²	semidirect
16. C₂×#3624	D₃	semidirect
29. #3624	C₂×D₃	semidirect
30. C₂×C₃×C₁₇	M₁₆	semidirect
40. C₃×C₁₇	C₂×M₁₆	semidirect
46. C₂×C₁₇	ΓL(1,𝔽₂₅)	semidirect
56. C₁₇	C₂×ΓL(1,𝔽₂₅)	semidirect
74. C₂×C₃	#63247	semidirect
83. C₃	C₂×#63247	semidirect
85. C₂	#11717826	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×D₃×Dic₁₇	2
C₂×C₃⋊#3624	2
C₂×C₃×#3624	2
#11717826	2
C₂×#63247	3
C₂×ΓL(1,𝔽₂₅)	17

Subgroups — C2×#11717826 #13109674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11717826 #13109674