Subgroups — C₁₇×#1830 #14524836

Order 2176.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#519	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₇×#101	C₂	1	2	yes	maximal
3	C₁₇×#344	C₂	1	4	yes	maximal
4	C₂²×Q₈×C₁₇	C₂²	1	1	yes	characteristic
5	C₂×M₁₆×C₁₇	C₂²	1	4	yes	—
6	C₄×Q₈×C₁₇	—	2	4	no	—
7	C₁₇×#117	C₄	1	4	yes	—
8	C₁₇×#117	C₂²	1	2	yes	—
9	C₁₇×#101	—	2	4	no	—
10	C₂×Q₈×C₁₇	—	2	4	no	—
11	C₂×Q₈×C₁₇	D₄	1	4	yes	—
12	C₂²×C₄×C₁₇	C₂×C₄	1	2	yes	—
13	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
14	M₁₆×C₁₇	—	2	4	no	—
15	M₁₆×C₁₇	—	2	4	no	—
16	C₂×C₈×C₁₇	—	2	4	no	—
17	C₄⋊C₄×C₁₇	—	2	4	no	—
18	C₄⋊C₄×C₁₇	—	2	2	no	—
19	C₂²⋊C₄×C₁₇	C₂×C₄	1	4	yes	—
20	C₄²×C₁₇	—	2	4	no	—
21	C₄²×C₁₇	—	2	2	no	—
22	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
23	Q₈×C₁₇	—	2	8	no	—
24	C₂×C₄×C₁₇	—	2	4	no	—
25	C₂×C₄×C₁₇	—	2	4	no	—
26	C₂×C₄×C₁₇	C₂²⋊C₄	1	4	yes	—
27	C₂×C₄×C₁₇	C₂×D₄	1	2	yes	—
28	C₂×C₄×C₁₇	#41	1	4	yes	—
29	C₈×C₁₇	—	4	4	no	—
30	#1830	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂²×C₁₇	—	4	1	no	—
32	C₂²×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
33	C₂²×C₁₇	#117	1	2	yes	—
34	C₄×C₁₇	—	2	4	no	—
35	C₄×C₁₇	—	4	4	no	—
36	C₄×C₁₇	#123	1	4	yes	—
37	#519	C₂×C₁₇	1	1	yes	characteristic
38	C₂×#101	C₂×C₁₇	1	2	yes	—
39	#344	C₂×C₁₇	1	4	yes	—
40	C₂×C₁₇	—	2	1	no	—
41	C₂×C₁₇	—	2	2	no	—
42	C₂×C₁₇	#381	1	1	yes	characteristic
43	C₂²×Q₈	C₂²×C₁₇	1	1	yes	characteristic
44	C₂×M₁₆	C₂²×C₁₇	1	4	yes	—
45	C₄×Q₈	—	2	4	no	—
46	#117	C₄×C₁₇	1	4	yes	—
47	#117	C₂²×C₁₇	1	2	yes	—
48	#101	—	2	4	no	—
49	C₁₇	#1830	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×Q₈	—	2	4	no	—
51	C₂×Q₈	D₄×C₁₇	1	4	yes	—
52	C₂²×C₄	C₂×C₄×C₁₇	1	2	yes	—
53	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
54	M₁₆	—	2	4	no	—
55	M₁₆	—	2	4	no	—
56	C₂×C₈	—	2	4	no	—
57	C₄⋊C₄	—	2	4	no	—
58	C₄⋊C₄	—	2	2	no	—
59	C₂²⋊C₄	C₂×C₄×C₁₇	1	4	yes	—
60	C₄²	—	2	4	no	—
61	C₄²	—	2	2	no	—
62	C₂³	C₂²×C₄×C₁₇	1	1	yes	characteristic
63	Q₈	—	2	8	no	—
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	2	4	no	—
66	C₂×C₄	C₂²⋊C₄×C₁₇	1	4	yes	—
67	C₂×C₄	C₂×D₄×C₁₇	1	2	yes	—
68	C₂×C₄	#41×C₁₇	1	4	yes	—
69	C₈	—	4	4	no	—
70	C₂²	—	4	1	no	—
71	C₂²	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
72	C₂²	C₁₇×#117	1	2	yes	—
73	C₄	—	2	4	no	—
74	C₄	—	4	4	no	—
75	C₄	C₁₇×#123	1	4	yes	—
76	C₂	—	2	1	no	—
77	C₂	—	2	2	no	—
78	C₂	C₁₇×#381	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₇	#381
commutator	C₂³	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₂³×C₁₇	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
30. #1830	C₁₇	direct (N × H)
49. C₁₇	#1830	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×#519	2
C₂×C₁₇×#101	2
C₁₇×#344	2
#1830	17

Subgroups — C17×#1830 #14524836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#1830 #14524836