Subgroups — #14543852

Order 2176.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763819	C₂	1	2	yes	maximal
2	C₂×#10587469	C₂	1	1	yes	maximal, characteristic
3	#10587677	—	2	2	no	—
4	C₂×C₈×D₁₇	C₂²	1	1	yes	characteristic
5	#10587534	—	2	2	no	—
6	#10587533	C₄	1	4	yes	complemented
7	C₂×C₁₆×C₁₇	C₄	1	1	yes	characteristic, complemented
8	C₂×#63214	C₄	1	1	yes	characteristic, complemented
9	#10587469	—	2	2	no	—
10	C₂×C₄×D₁₇	D₄	1	1	yes	characteristic
11	C₂²⋊#595	—	4	2	no	—
12	C₄⋊#595	—	2	4	no	—
13	C₄×#595	—	4	2	no	—
14	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂×#3622	Q₈	1	1	yes	characteristic
16	C₈×D₁₇	C₂×C₄	1	2	yes	—
17	C₈×D₁₇	D₄	1	2	yes	—
18	C₁₆×C₁₇	—	2	1	no	—
19	#63214	—	2	1	no	—
20	C₂²×D₁₇	D₈	1	1	yes	characteristic
21	C₂×#595	—	4	4	no	—
22	C₂×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
23	C₂×Dic₁₇	Q₁₆	1	1	yes	characteristic
24	C₄×D₁₇	C₂²⋊C₄	1	2	yes	—
25	C₄×D₁₇	SD₁₆	1	2	yes	—
26	C₈×C₁₇	C₄²	1	1	yes	characteristic
27	C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
28	#3622	C₄⋊C₄	1	2	yes	—
29	#1384	—	17	1	no	maximal, Sylow
30	C₂²×C₁₇	#107	1	1	yes	characteristic
31	C₂×D₁₇	—	4	1	no	—
32	C₂×D₁₇	#102	1	2	yes	—
33	#595	—	8	4	no	—
34	C₄×C₁₇	#95	1	1	yes	characteristic
35	C₄×C₁₇	#106	1	1	yes	characteristic
36	Dic₁₇	#103	1	2	yes	—
37	C₂×M₃₂	—	17	1	no	—
38	#427	—	17	2	no	—
39	C₂×C₁₇	—	2	1	no	—
40	C₂×C₁₇	#340	1	1	yes	characteristic
41	D₁₇	—	2	2	no	—
42	C₂²×C₈	—	17	1	no	—
43	#117	—	34	2	no	—
44	M₃₂	—	34	2	no	—
45	C₂×C₁₆	—	17	1	no	—
46	C₂×C₁₆	#595	1	1	yes	characteristic, complemented
47	#107	—	34	2	no	—
48	#106	—	17	4	no	—
49	C₁₇	#1384	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₄	—	17	1	no	—
51	C₂×C₈	—	17	1	no	—
52	C₂×C₈	—	17	2	no	—
53	C₂×C₈	—	17	2	no	—
54	C₂×C₈	C₂×#595	1	1	yes	characteristic
55	C₄⋊C₄	—	34	4	no	—
56	C₂²⋊C₄	—	68	2	no	—
57	C₄²	—	68	2	no	—
58	C₁₆	—	2	1	no	—
59	C₁₆	—	34	1	no	—
60	C₂³	—	17	1	no	—
61	C₂×C₄	—	17	1	no	—
62	C₂×C₄	—	17	2	no	—
63	C₂×C₄	—	17	2	no	—
64	C₂×C₄	—	68	4	no	—
65	C₂×C₄	C₄⋊#595	1	1	yes	characteristic
66	C₈	—	17	2	no	—
67	C₈	C₄×#595	1	1	yes	characteristic
68	C₈	C₂²⋊#595	1	1	yes	characteristic
69	C₂²	—	17	2	no	—
70	C₂²	—	68	1	no	—
71	C₂²	#10587534	1	1	yes	characteristic
72	C₄	—	17	2	no	—
73	C₄	—	136	4	no	—
74	C₄	#10587533	1	1	yes	characteristic
75	C₄	(C₂×#595)⋊C₄	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	34	2	no	—
78	C₂	#11763683	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10587533
commutator	C₈×C₁₇	C₄²
Frattini	C₂×C₈	C₂×#595
Fitting	C₂×C₁₆×C₁₇	C₄
socle	C₂×C₁₇	#340
prime radical	C₂²×D₁₇	D₈
cosocle	C₂×C₈×D₁₇	C₂²
hypercenter	C₂×C₁₆	#595
hypocenter	C₁₇	#1384
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
6. #10587533	C₄	semidirect
7. C₂×C₁₆×C₁₇	C₄	semidirect
8. C₂×#63214	C₄	semidirect
46. C₂×C₁₆	#595	semidirect
49. C₁₇	#1384	semidirect

Maximal subgroups

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

subgroup	index
#11763819	2
C₂×#10587469	2
#1384	17