Subgroups — #14544709

Order 2176.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763814	C₂	1	2	yes	maximal
2	#11763685	C₂	1	4	yes	maximal
3	C₄×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#63243	C₂²	1	4	yes	—
5	C₂×C₈×D₁₇	C₂²	1	2	yes	—
6	C₄²×D₁₇	C₂²	1	1	yes	characteristic
7	#10587544	—	2	4	no	—
8	C₄×C₈×C₁₇	C₄	1	1	yes	characteristic
9	C₈×Dic₁₇	C₄	1	2	yes	—
10	C₄×#3622	C₄	1	1	yes	characteristic
11	C₂×C₄×D₁₇	Q₈	1	2	yes	—
12	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
13	C₂×#3624	—	2	4	no	—
14	#63243	—	2	8	no	—
15	C₂×C₈×C₁₇	C₂×C₄	1	2	yes	—
16	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₁₇	D₄	1	2	yes	—
19	C₂×#3622	C₂×C₄	1	2	yes	—
20	C₈×D₁₇	—	2	4	no	—
21	C₂²×D₁₇	C₂×Q₈	1	1	yes	characteristic
22	C₂×C₄×C₁₇	C₄⋊C₄	1	2	yes	—
23	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
24	C₂×Dic₁₇	C₄⋊C₄	1	2	yes	—
25	C₂×Dic₁₇	C₂×D₄	1	1	yes	characteristic
26	C₄×D₁₇	—	2	4	no	—
27	C₄×D₁₇	#41	1	4	yes	—
28	#3624	—	4	4	no	—
29	C₈×C₁₇	—	2	2	no	—
30	#3622	—	2	2	no	—
31	#1837	—	17	1	no	maximal, Sylow
32	C₂²×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
33	C₂×D₁₇	—	2	2	no	—
34	C₂×D₁₇	#125	1	2	yes	—
35	C₄×C₁₇	—	2	2	no	—
36	C₄×C₁₇	#117	1	2	yes	—
37	Dic₁₇	#108	1	4	yes	—
38	Dic₁₇	#124	1	2	yes	—
39	#423	—	17	2	no	—
40	C₂×C₄×C₈	—	17	1	no	—
41	#341	—	17	4	no	—
42	C₂×C₁₇	#382	1	1	yes	characteristic
43	C₂×C₁₇	C₂×#108	1	2	yes	—
44	D₁₇	—	2	2	no	—
45	C₂×M₁₆	—	17	4	no	—
46	C₂²×C₈	—	17	2	no	—
47	C₂×C₄²	—	17	1	no	—
48	C₄⋊C₈	—	34	4	no	—
49	C₄×C₈	—	17	2	no	—
50	C₄×C₈	—	17	1	no	—
51	C₄×C₈	#595	1	1	yes	characteristic
52	C₁₇	#1837	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₄	—	17	1	no	—
54	C₂²×C₄	—	17	2	no	—
55	M₁₆	—	34	8	no	—
56	C₂×C₈	—	17	2	no	—
57	C₂×C₈	—	34	4	no	—
58	C₂×C₈	—	34	4	no	—
59	C₂×C₈	C₂×#595	1	2	yes	—
60	C₄²	—	17	2	no	—
61	C₄²	—	17	1	no	—
62	C₄²	C₂×#595	1	1	yes	characteristic
63	C₂³	—	17	1	no	—
64	C₂×C₄	—	17	1	no	—
65	C₂×C₄	—	17	2	no	—
66	C₂×C₄	—	17	4	no	—
67	C₂×C₄	—	34	4	no	—
68	C₂×C₄	C₄⋊#595	1	2	yes	—
69	C₂×C₄	C₂²×#595	1	1	yes	characteristic
70	C₈	—	2	2	no	—
71	C₈	—	34	2	no	—
72	C₈	—	68	4	no	—
73	C₂²	—	17	2	no	—
74	C₂²	—	34	2	no	—
75	C₂²	C₂×C₄⋊#595	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	17	2	no	—
78	C₄	—	17	4	no	—
79	C₄	#10587677	1	2	yes	—
80	C₂	—	34	2	no	—
81	C₂	#11763753	1	1	yes	characteristic
82	C₂	D₁₇⋊#108	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#595
commutator	C₂×C₄×C₁₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×#595
Fitting	C₄×C₈×C₁₇	C₄
socle	C₂²×C₁₇	C₂×C₄⋊C₄
prime radical	C₂²×D₁₇	C₂×Q₈
cosocle	C₂×C₄×D₁₇	C₂³
hypercenter	C₄×C₈	#595
hypocenter	C₁₇	#1837
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
52. C₁₇	#1837	semidirect

Maximal subgroups

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

subgroup	index
#11763814	2
#11763685	2
C₄×C₈×D₁₇	2
#1837	17