Subgroups — #14543690

Order 2176.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763830	C₂	1	2	yes	maximal
2	#11762832	C₂	1	1	yes	maximal, characteristic
3	C₂×M₁₆×C₁₇	C₄	1	1	yes	characteristic
4	C₂×C₄×Dic₁₇	C₂²	1	1	yes	characteristic
5	C₂×#63223	C₄	1	1	yes	characteristic
6	C₂²⋊#3624	C₄	1	4	yes	—
7	#10587542	—	2	2	no	—
8	C₄⋊#3624	—	2	2	no	—
9	#10587485	—	2	2	no	—
10	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
11	C₂²×Dic₁₇	C₂×C₄	1	2	yes	—
12	C₂×#3624	—	2	4	no	—
13	M₁₆×C₁₇	—	4	1	no	—
14	C₂×C₈×C₁₇	—	2	1	no	—
15	C₄×Dic₁₇	D₄	1	1	yes	characteristic
16	C₄×Dic₁₇	D₄	1	2	yes	—
17	C₄×Dic₁₇	Q₈	1	1	yes	characteristic
18	#63223	—	4	1	no	—
19	C₂×#3622	—	2	1	no	—
20	C₂³×C₁₇	C₄²	1	1	yes	characteristic
21	C₂×C₄×C₁₇	—	2	1	no	—
22	C₂×C₄×C₁₇	—	2	1	no	—
23	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
25	C₂×Dic₁₇	—	4	2	no	—
26	C₂×Dic₁₇	C₂²⋊C₄	1	2	yes	—
27	C₂×Dic₁₇	C₄⋊C₄	1	2	yes	—
28	#3624	—	4	4	no	—
29	C₈×C₁₇	—	4	1	no	—
30	#3622	—	4	1	no	—
31	#1307	—	17	1	no	maximal, Sylow
32	C₂²×C₁₇	—	2	1	no	—
33	C₂²×C₁₇	—	2	2	no	—
34	C₂²×C₁₇	#95	1	1	yes	characteristic
35	C₄×C₁₇	—	2	1	no	—
36	C₄×C₁₇	#100	1	1	yes	characteristic
37	C₄×C₁₇	#101	1	1	yes	characteristic
38	Dic₁₇	—	2	2	no	—
39	Dic₁₇	—	2	2	no	—
40	#432	—	17	2	no	—
41	#423	—	17	1	no	—
42	C₂×C₁₇	—	4	1	no	—
43	C₂×C₁₇	#343	1	1	yes	characteristic
44	C₂×C₁₇	#344	1	2	yes	—
45	C₂×M₁₆	—	17	1	no	—
46	C₂×M₁₆	#595	1	1	yes	characteristic
47	C₂×C₄²	—	17	1	no	—
48	C₄⋊C₈	—	34	2	no	—
49	C₄⋊C₈	—	34	2	no	—
50	C₂²⋊C₈	—	17	4	no	—
51	#97	—	34	2	no	—
52	C₁₇	#1307	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₄	—	17	2	no	—
54	C₂²×C₄	C₂×#595	1	1	yes	characteristic
55	M₁₆	—	4	1	no	—
56	M₁₆	—	68	1	no	—
57	C₂×C₈	—	2	1	no	—
58	C₂×C₈	—	34	4	no	—
59	C₂×C₈	—	34	1	no	—
60	C₄²	—	17	1	no	—
61	C₄²	—	17	1	no	—
62	C₄²	—	17	2	no	—
63	C₂³	C₄×#595	1	1	yes	characteristic
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	17	2	no	—
67	C₂×C₄	—	17	2	no	—
68	C₂×C₄	—	68	2	no	—
69	C₂×C₄	C₄⋊#595	1	1	yes	characteristic
70	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
71	C₈	—	4	1	no	—
72	C₈	—	68	4	no	—
73	C₈	—	68	1	no	—
74	C₂²	—	2	1	no	—
75	C₂²	—	2	2	no	—
76	C₂²	(C₂×#595)⋊C₄	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	34	2	no	—
79	C₄	—	34	2	no	—
80	C₄	#10587545	1	1	yes	characteristic
81	C₄	#10587553	1	1	yes	characteristic
82	C₂	—	4	1	no	—
83	C₂	#11763689	1	1	yes	characteristic
84	C₂	#11763692	1	2	yes	—

	subgroup	G/H
center	C₂²	(C₂×#595)⋊C₄
commutator, prime radical	C₂³×C₁₇	C₄²
Frattini	C₂²×C₄	C₂×#595
Fitting	C₂×M₁₆×C₁₇	C₄
socle	C₂²×C₁₇	#95
cosocle	C₂×C₄×Dic₁₇	C₂²
hypercenter	C₂×M₁₆	#595
hypocenter	C₁₇	#1307
LCS	G ▷ C₂³×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
52. C₁₇	#1307	semidirect

Maximal subgroups

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

subgroup	index
#11763830	2
#11762832	2
#1307	17