Subgroups — #14544711

Order 2176.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763675	C₂	1	6	yes	maximal
2	C₄²×Dic₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×#3624	C₂²	1	4	yes	—
4	C₂×C₄²×C₁₇	C₄	1	1	yes	characteristic
5	C₂×C₄×Dic₁₇	C₄	1	3	yes	—
6	C₂×C₄×Dic₁₇	C₂²	1	3	yes	—
7	C₂²×C₄×C₁₇	C₂×C₄	1	3	yes	—
8	C₂²×Dic₁₇	C₂×C₄	1	3	yes	—
9	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
10	C₂×#3624	—	2	12	no	—
11	C₄²×C₁₇	C₈	1	4	yes	complemented
12	C₄×Dic₁₇	—	2	6	no	—
13	C₄×Dic₁₇	—	2	6	no	—
14	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₇	—	2	3	no	—
16	C₂×C₄×C₁₇	—	2	3	no	—
17	C₂×C₄×C₁₇	C₂×C₈	1	6	yes	—
18	C₂×Dic₁₇	—	2	3	no	—
19	C₂×Dic₁₇	—	2	3	no	—
20	C₂×Dic₁₇	M₁₆	1	6	yes	—
21	C₂×Dic₁₇	#41	1	6	yes	—
22	#3624	—	4	4	no	—
23	#1839	—	17	1	no	maximal, Sylow
24	C₂²×C₁₇	#117	1	3	yes	—
25	C₂²×C₁₇	C₂²×C₈	1	1	yes	characteristic
26	C₂²×C₁₇	C₂×M₁₆	1	3	yes	—
27	C₄×C₁₇	—	2	6	no	—
28	Dic₁₇	—	2	6	no	—
29	Dic₁₇	#126	1	4	yes	—
30	C₄³	—	17	1	no	—
31	#336	—	17	6	no	—
32	C₂×C₁₇	#383	1	1	yes	characteristic
33	C₂×C₁₇	#431	1	3	yes	—
34	C₂×C₁₇	#432	1	3	yes	—
35	C₂²×C₈	—	17	4	no	—
36	C₂×C₄²	—	17	3	no	—
37	C₂×C₄²	—	17	3	no	—
38	C₂×C₄²	#595	1	1	yes	characteristic
39	C₁₇	#1839	1	1	yes	characteristic, complemented, Sylow
40	C₂²×C₄	—	17	1	no	—
41	C₂²×C₄	—	17	3	no	—
42	C₂²×C₄	C₂×#595	1	3	yes	—
43	C₂×C₈	—	34	12	no	—
44	C₄²	—	34	6	no	—
45	C₄²	—	34	6	no	—
46	C₄²	#3624	1	4	yes	complemented
47	C₂³	C₂²×#595	1	1	yes	characteristic
48	C₂×C₄	—	2	3	no	—
49	C₂×C₄	—	2	3	no	—
50	C₂×C₄	—	17	6	no	—
51	C₂×C₄	—	17	6	no	—
52	C₂×C₄	—	34	3	no	—
53	C₂×C₄	—	34	3	no	—
54	C₂×C₄	C₂×#3624	1	6	yes	—
55	C₈	—	68	4	no	—
56	C₂²	D₁₇⋊M₁₆	1	3	yes	—
57	C₂²	#10587677	1	3	yes	—
58	C₂²	C₂²×#3624	1	1	yes	characteristic
59	C₄	—	2	6	no	—
60	C₄	—	17	4	no	—
61	C₄	—	34	6	no	—
62	C₂	#11763754	1	1	yes	characteristic
63	C₂	#11763825	1	3	yes	—
64	C₂	#11763832	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#595
commutator	C₂²×C₁₇	C₂²×C₈
Fitting	C₂×C₄²×C₁₇	C₄
socle, prime radical	C₂³×C₁₇	C₂²×C₄
cosocle	C₂²×Dic₁₇	C₂³
hypercenter	C₂×C₄²	#595
hypocenter	C₁₇	#1839
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
11. C₄²×C₁₇	C₈	semidirect
39. C₁₇	#1839	semidirect
46. C₄²	#3624	semidirect

Maximal subgroups

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

subgroup	index
#11763675	2
C₄²×Dic₁₇	2
#1839	17