Subgroups — C₂×C₁₇×#494 #14526151

Order 2176.

552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₁₆×C₁₇	C₂	1	4	yes	maximal
2	C₂×C₁₇×C₄⋊Q₈	C₂	1	2	yes	maximal
3	C₁₇×#494	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄×C₈×C₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×Q₈×C₁₇	C₂²	1	4	yes	—
6	C₂×Q₁₆×C₁₇	—	2	16	no	—
7	C₂×Q₁₆×C₁₇	C₂²	1	16	yes	—
8	C₂²×C₈×C₁₇	C₂²	1	2	yes	—
9	C₁₇×C₄⋊Q₈	—	2	4	no	—
10	C₁₇×C₄⋊Q₈	C₂²	1	8	yes	—
11	C₂×C₄⋊C₄×C₁₇	—	2	4	no	—
12	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₁₇	C₂²	1	4	yes	—
14	C₂×Q₈×C₁₇	—	2	4	no	—
15	C₂×Q₈×C₁₇	—	2	16	no	—
16	C₂×Q₈×C₁₇	C₂³	1	8	yes	—
17	C₂²×C₄×C₁₇	—	2	4	no	—
18	C₂²×C₄×C₁₇	D₄	1	2	yes	—
19	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
20	Q₁₆×C₁₇	—	2	32	no	—
21	C₂×C₈×C₁₇	D₄	1	8	yes	—
22	C₂×C₈×C₁₇	C₂³	1	4	yes	—
23	C₄⋊C₄×C₁₇	—	2	16	no	—
24	C₄²×C₁₇	D₄	1	2	yes	—
25	C₄²×C₁₇	C₂³	1	2	yes	—
26	C₂³×C₁₇	C₂×D₄	1	1	yes	characteristic
27	Q₈×C₁₇	—	2	16	no	—
28	Q₈×C₁₇	—	4	8	no	—
29	C₂×C₄×C₁₇	—	2	8	no	—
30	C₂×C₄×C₁₇	—	4	8	no	—
31	C₂×C₄×C₁₇	Q₁₆	1	8	yes	complemented
32	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₁₇	C₂×D₄	1	4	yes	—
34	C₂×C₄×C₁₇	C₂×D₄	1	4	yes	—
35	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
36	C₈×C₁₇	C₂×D₄	1	8	yes	—
37	C₂×#494	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂²×C₁₇	#127	1	2	yes	—
39	C₂²×C₁₇	C₂×Q₁₆	1	4	yes	—
40	C₂²×C₁₇	C₂²×D₄	1	1	yes	characteristic
41	C₄×C₁₇	—	4	8	no	—
42	C₄×C₁₇	#127	1	2	yes	—
43	C₄×C₁₇	C₂×Q₁₆	1	8	yes	complemented
44	C₄×C₁₇	C₂²×D₄	1	2	yes	—
45	C₂²×Q₁₆	C₂×C₁₇	1	4	yes	—
46	C₂×C₄⋊Q₈	C₂×C₁₇	1	2	yes	—
47	#494	C₂×C₁₇	1	8	yes	direct product factor
48	C₂×C₄×C₈	C₂×C₁₇	1	1	yes	characteristic
49	C₂×C₁₇	#494	1	4	yes	direct product factor
50	C₂×C₁₇	C₂×#127	1	1	yes	characteristic
51	C₂×C₁₇	C₂²×Q₁₆	1	2	yes	—
52	C₂²×Q₈	C₂²×C₁₇	1	4	yes	—
53	C₂×Q₁₆	—	2	16	no	—
54	C₂×Q₁₆	C₂²×C₁₇	1	16	yes	—
55	C₂²×C₈	C₂²×C₁₇	1	2	yes	—
56	C₄⋊Q₈	—	2	4	no	—
57	C₄⋊Q₈	C₂²×C₁₇	1	8	yes	—
58	C₂×C₄⋊C₄	—	2	4	no	—
59	C₂×C₄²	C₂²×C₁₇	1	1	yes	characteristic
60	C₄×C₈	C₂²×C₁₇	1	4	yes	—
61	C₁₇	C₂×#494	1	1	yes	characteristic, direct product factor, Sylow
62	C₂×Q₈	—	2	4	no	—
63	C₂×Q₈	—	2	16	no	—
64	C₂×Q₈	C₂³×C₁₇	1	8	yes	—
65	C₂²×C₄	—	2	4	no	—
66	C₂²×C₄	D₄×C₁₇	1	2	yes	—
67	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
68	Q₁₆	—	2	32	no	—
69	C₂×C₈	D₄×C₁₇	1	8	yes	—
70	C₂×C₈	C₂³×C₁₇	1	4	yes	—
71	C₄⋊C₄	—	2	16	no	—
72	C₄²	D₄×C₁₇	1	2	yes	—
73	C₄²	C₂³×C₁₇	1	2	yes	—
74	C₂³	C₂×D₄×C₁₇	1	1	yes	characteristic
75	Q₈	—	2	16	no	—
76	Q₈	—	4	8	no	—
77	C₂×C₄	—	2	8	no	—
78	C₂×C₄	—	4	8	no	—
79	C₂×C₄	Q₁₆×C₁₇	1	8	yes	complemented
80	C₂×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
81	C₂×C₄	C₂×D₄×C₁₇	1	4	yes	—
82	C₂×C₄	C₂×D₄×C₁₇	1	4	yes	—
83	C₂×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
84	C₈	C₂×D₄×C₁₇	1	8	yes	—
85	C₂²	C₁₇×#127	1	2	yes	—
86	C₂²	C₂×Q₁₆×C₁₇	1	4	yes	—
87	C₂²	C₂²×D₄×C₁₇	1	1	yes	characteristic
88	C₄	—	4	8	no	—
89	C₄	C₁₇×#127	1	2	yes	—
90	C₄	C₂×Q₁₆×C₁₇	1	8	yes	complemented
91	C₄	C₂²×D₄×C₁₇	1	2	yes	—
92	C₂	C₁₇×#494	1	4	yes	direct product factor
93	C₂	C₂×C₁₇×#127	1	1	yes	characteristic
94	C₂	C₂²×Q₁₆×C₁₇	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₇×#494	C₂	direct (N × H)
31. C₂×C₄×C₁₇	Q₁₆	semidirect
37. C₂×#494	C₁₇	direct (N × H)
43. C₄×C₁₇	C₂×Q₁₆	semidirect
47. #494	C₂×C₁₇	direct (N × H)
49. C₂×C₁₇	#494	direct (N × H)
61. C₁₇	C₂×#494	direct (N × H)
79. C₂×C₄	Q₁₆×C₁₇	semidirect
90. C₄	C₂×Q₁₆×C₁₇	semidirect
92. C₂	C₁₇×#494	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×Q₁₆×C₁₇	2
C₂×C₁₇×C₄⋊Q₈	2
C₁₇×#494	2
C₂×C₄×C₈×C₁₇	2
C₂×#494	17

Subgroups — C2×C17×#494 #14526151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×#494 #14526151