Subgroups — #14543695

Order 2176.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763695	C₂	1	1	yes	maximal, characteristic
2	C₈×#3624	C₂	1	1	yes	maximal, characteristic
3	C₁₆×Dic₁₇	C₂	1	1	yes	maximal, characteristic
4	C₄×#3624	C₄	1	2	yes	—
5	C₂×#63216	C₄	1	2	yes	—
6	C₂×C₁₆×C₁₇	C₄	1	1	yes	characteristic
7	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
8	C₂×#63214	C₄	1	1	yes	characteristic
9	C₂×#3624	C₈	1	4	yes	—
10	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
11	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
12	C₂×#3622	C₂×C₄	1	1	yes	characteristic
13	#63216	C₈	1	4	yes	complemented
14	C₁₆×C₁₇	C₈	1	2	yes	complemented
15	#63214	C₈	1	2	yes	complemented
16	C₂×C₄×C₁₇	C₄²	1	1	yes	characteristic
17	C₂×Dic₁₇	C₂×C₈	1	2	yes	—
18	#3624	—	2	4	no	—
19	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
20	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
21	#3622	C₂×C₈	1	2	yes	—
22	#1311	—	17	1	no	maximal, Sylow
23	C₂²×C₁₇	C₄×C₈	1	1	yes	characteristic
24	C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
25	C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
26	Dic₁₇	M₃₂	1	4	yes	—
27	C₄×C₁₆	—	17	1	no	—
28	C₄×C₁₆	—	17	1	no	—
29	C₈²	—	17	1	no	—
30	C₂×C₁₇	C₈²	1	1	yes	characteristic
31	C₂×C₁₇	#346	1	2	yes	—
32	C₂×C₁₆	—	17	2	no	—
33	C₂×C₁₆	—	17	1	no	—
34	C₂×C₁₆	#595	1	1	yes	characteristic
35	C₄×C₈	—	17	2	no	—
36	C₄×C₈	—	17	1	no	—
37	C₁₇	#1311	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₈	—	17	1	no	—
39	C₂×C₈	—	17	4	no	—
40	C₂×C₈	C₂×#595	1	1	yes	characteristic
41	C₄²	—	17	1	no	—
42	C₁₆	—	17	4	no	—
43	C₁₆	—	17	2	no	—
44	C₁₆	#3624	1	2	yes	complemented
45	C₂×C₄	—	17	2	no	—
46	C₂×C₄	C₄×#595	1	1	yes	characteristic
47	C₈	—	17	2	no	—
48	C₈	—	34	4	no	—
49	C₈	#63242	1	1	yes	characteristic
50	C₈	C₂×#3624	1	1	yes	characteristic
51	C₂²	C₈×#595	1	1	yes	characteristic
52	C₄	—	17	4	no	—
53	C₄	C₈×#595	1	1	yes	characteristic
54	C₄	C₄×#3624	1	1	yes	characteristic
55	C₂	C₈×#3624	1	1	yes	characteristic
56	C₂	#11763696	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#595
commutator	C₂×C₁₇	C₈²
Fitting	C₂×C₁₆×C₁₇	C₄
socle, prime radical	C₂²×C₁₇	C₄×C₈
cosocle	C₈×Dic₁₇	C₂²
hypercenter	C₂×C₁₆	#595
hypocenter	C₁₇	#1311
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
13. #63216	C₈	semidirect
14. C₁₆×C₁₇	C₈	semidirect
15. #63214	C₈	semidirect
37. C₁₇	#1311	semidirect
44. C₁₆	#3624	semidirect

Maximal subgroups

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

subgroup	index
#11763695	2
C₈×#3624	2
C₁₆×Dic₁₇	2
#1311	17