Subgroups — #14543702

Order 2176.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763697	C₂	1	1	yes	maximal, characteristic
2	#11763697	C₂	1	1	yes	maximal, characteristic
3	#11762531	C₂	1	1	yes	maximal, characteristic
4	C₂×#63216	C₄	1	2	yes	—
5	C₂×#63216	C₄	1	2	yes	—
6	C₄×C₈×C₁₇	C₄	1	1	yes	characteristic
7	C₄×#3622	C₄	1	1	yes	characteristic
8	C₄×#3622	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₁₇	—	2	1	no	—
10	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
11	C₂×#3622	—	2	1	no	—
12	C₂×#3622	C₂×C₄	1	1	yes	characteristic
13	C₂×#3622	C₂×C₄	1	1	yes	characteristic
14	#63216	—	2	2	no	—
15	#63216	C₈	1	4	yes	complemented
16	C₂×C₄×C₁₇	C₄²	1	1	yes	characteristic
17	C₂×C₄×C₁₇	M₁₆	1	1	yes	characteristic
18	C₂×C₄×C₁₇	M₁₆	1	1	yes	characteristic
19	C₈×C₁₇	—	4	1	no	—
20	#3622	—	4	1	no	—
21	#3622	C₂×C₈	1	2	yes	—
22	#3622	M₁₆	1	2	yes	—
23	#1313	—	17	1	no	maximal, Sylow
24	C₂²×C₁₇	#97	1	1	yes	characteristic
25	C₄×C₁₇	—	2	1	no	—
26	C₄×C₁₇	—	2	1	no	—
27	C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
28	C₄×C₁₇	#97	1	1	yes	characteristic
29	#346	—	17	1	no	—
30	#346	—	17	1	no	—
31	#322	—	17	1	no	—
32	C₂×C₁₇	#322	1	1	yes	characteristic
33	C₂×C₁₇	#347	1	1	yes	characteristic
34	C₂×C₁₇	#347	1	1	yes	characteristic
35	C₂×C₁₆	—	17	2	no	—
36	C₂×C₁₆	—	17	2	no	—
37	C₄×C₈	—	17	1	no	—
38	C₄×C₈	—	17	1	no	—
39	C₄×C₈	#595	1	1	yes	characteristic
40	C₁₇	#1313	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₈	—	2	1	no	—
42	C₂×C₈	—	17	1	no	—
43	C₂×C₈	—	17	1	no	—
44	C₂×C₈	—	34	1	no	—
45	C₄²	C₂×#595	1	1	yes	characteristic
46	C₁₆	—	17	4	no	—
47	C₁₆	—	34	2	no	—
48	C₂×C₄	#63243	1	1	yes	characteristic
49	C₂×C₄	C₄×#595	1	1	yes	characteristic
50	C₂×C₄	#63247	1	1	yes	characteristic
51	C₈	—	4	1	no	—
52	C₈	—	17	2	no	—
53	C₈	—	17	2	no	—
54	C₈	—	68	1	no	—
55	C₂²	#10587542	1	1	yes	characteristic
56	C₄	—	2	1	no	—
57	C₄	—	2	1	no	—
58	C₄	C₈×#595	1	1	yes	characteristic
59	C₄	#10587532	1	1	yes	characteristic
60	C₂	#11763651	1	1	yes	characteristic
61	C₂	#11763701	1	1	yes	characteristic
62	C₂	#11763702	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#595
commutator	C₄×C₁₇	C₄×C₈
Frattini	C₄²	C₂×#595
Fitting	C₄×C₈×C₁₇	C₄
socle, prime radical	C₂²×C₁₇	#97
cosocle	C₄×#3622	C₂²
hypercenter	C₄×C₈	#595
hypocenter	C₁₇	#1313
LCS	G ▷ C₄×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
15. #63216	C₈	semidirect
40. C₁₇	#1313	semidirect

Maximal subgroups

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

subgroup	index
#11763697	2
#11762531	2
#1313	17