Subgroups — #14543939

Order 2176.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763742	C₂	1	1	yes	maximal, characteristic, complemented
2	#11763738	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆×D₁₇	C₂	1	1	yes	maximal, characteristic
4	D₈×D₁₇	—	2	1	no	—
5	#10587536	—	2	1	no	—
6	C₁₇×D₁₆	C₄	1	1	yes	characteristic
7	#10587497	—	2	1	no	—
8	D₂₇₂	C₄	1	1	yes	characteristic
9	C₁₆×D₁₇	C₂²	1	1	yes	characteristic
10	#10587467	—	2	1	no	—
11	D₄×D₁₇	—	4	1	no	—
12	#63243	—	4	1	no	—
13	D₈×C₁₇	—	2	1	no	—
14	#63228	—	4	1	no	—
15	D₁₃₆	—	2	1	no	—
16	C₈×D₁₇	D₄	1	1	yes	characteristic
17	C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
18	#63214	D₄	1	1	yes	characteristic
19	C₂²×D₁₇	—	8	1	no	—
20	D₄×C₁₇	—	4	1	no	—
21	C₂²⋊D₁₇	—	8	1	no	—
22	D₆₈	—	4	1	no	—
23	C₄×D₁₇	D₈	1	1	yes	characteristic
24	#3624	—	8	1	no	—
25	C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
26	#3622	SD₁₆	1	1	yes	characteristic
27	#1419	—	17	1	no	maximal, Sylow
28	C₂²×C₁₇	—	8	1	no	—
29	C₂×D₁₇	—	8	1	no	—
30	C₂×D₁₇	—	16	2	no	—
31	C₂×D₁₇	SD₃₂	1	1	yes	characteristic
32	C₄×C₁₇	#102	1	1	yes	characteristic
33	Dic₁₇	D₁₆	1	1	yes	characteristic
34	C₂×D₁₆	—	17	1	no	—
35	M₆₄	—	17	1	no	—
36	#368	—	17	1	no	—
37	C₂×C₁₇	—	16	1	no	—
38	C₂×C₁₇	#357	1	1	yes	characteristic
39	D₁₇	—	2	1	no	—
40	D₁₇	—	16	1	no	—
41	C₂×D₈	—	34	1	no	—
42	D₁₆	—	17	1	no	—
43	D₁₆	—	34	1	no	—
44	D₁₆	#595	1	1	yes	characteristic
45	C₂×C₁₆	—	17	1	no	—
46	#108	—	34	1	no	—
47	C₃₂	—	34	1	no	—
48	C₁₇	#1419	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₄	—	68	1	no	—
50	D₈	—	2	1	no	—
51	D₈	—	34	1	no	—
52	D₈	—	68	1	no	—
53	M₁₆	—	68	1	no	—
54	C₂×C₈	—	17	1	no	—
55	C₁₆	—	17	1	no	—
56	C₁₆	C₂×#595	1	1	yes	characteristic
57	C₂³	—	136	1	no	—
58	D₄	—	4	1	no	—
59	D₄	—	68	1	no	—
60	D₄	—	136	1	no	—
61	C₂×C₄	—	17	1	no	—
62	C₈	—	17	1	no	—
63	C₈	—	136	1	no	—
64	C₈	C₂²⋊#595	1	1	yes	characteristic
65	C₂²	—	8	1	no	—
66	C₂²	—	272	2	no	—
67	C₂²	—	17	1	no	—
68	C₂²	—	136	1	no	—
69	C₄	—	17	1	no	—
70	C₄	#10587547	1	1	yes	characteristic
71	C₂	—	16	1	no	—
72	C₂	—	272	1	no	—
73	C₂	—	34	1	no	—
74	C₂	#11763721	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11763721
commutator	C₁₆×C₁₇	C₂×C₄
Frattini	C₁₆	C₂×#595
Fitting	C₁₇×D₁₆	C₄
socle	C₂×C₁₇	#357
prime radical	D₁₆×D₁₇	C₂
cosocle	C₁₆×D₁₇	C₂²
hypercenter	D₁₆	#595
hypocenter	C₁₇	#1419
LCS	G ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. #11763742	C₂	semidirect
2. #11763738	C₂	semidirect
48. C₁₇	#1419	semidirect

Maximal subgroups

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

subgroup	index
#11763742	2
#11763738	2
D₁₆×D₁₇	2
#1419	17