Subgroups — #14543930

Order 2176.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763718	C₂	1	1	yes	maximal, characteristic
2	#11763716	C₂	1	1	yes	maximal, characteristic
3	#11763166	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#125	C₄	1	1	yes	characteristic, complemented
5	#10587561	C₂²	1	1	yes	characteristic
6	#10587545	—	2	1	no	—
7	#10587539	—	2	1	no	—
8	#10587481	—	2	1	no	—
9	#10587480	—	2	1	no	—
10	C₄×#3622	C₄	1	1	yes	characteristic, complemented
11	C₂×D₆₈	D₄	1	1	yes	characteristic
12	C₂×Dic₃₄	D₄	1	1	yes	characteristic
13	C₂²⋊#595	—	4	1	no	—
14	#63247	—	4	1	no	—
15	C₄⋊C₄×C₁₇	—	2	1	no	—
16	C₄⋊C₄×C₁₇	—	4	1	no	—
17	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
18	#63227	—	4	1	no	—
19	C₂×#3622	—	2	1	no	—
20	C₂²×D₁₇	—	2	1	no	—
21	C₂×#595	—	8	1	no	—
22	C₂×C₄×C₁₇	—	2	1	no	—
23	C₂×C₄×C₁₇	—	4	1	no	—
24	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×Dic₁₇	—	2	1	no	—
26	D₆₈	—	4	1	no	—
27	Dic₃₄	—	4	1	no	—
28	#3624	—	8	1	no	—
29	#3622	—	4	1	no	—
30	#1414	—	17	1	no	maximal, Sylow
31	C₂²×C₁₇	#99	1	1	yes	characteristic
32	C₂×D₁₇	—	4	1	no	—
33	C₂×D₁₇	—	8	1	no	—
34	#595	—	16	1	no	—
35	C₄×C₁₇	—	2	1	no	—
36	C₄×C₁₇	—	4	1	no	—
37	C₄×C₁₇	—	8	1	no	—
38	Dic₁₇	—	4	1	no	—
39	#488	—	17	1	no	—
40	#355	—	17	1	no	—
41	#354	—	17	1	no	—
42	C₂×C₁₇	—	2	1	no	—
43	C₂×C₁₇	#354	1	1	yes	characteristic
44	D₁₇	—	8	1	no	—
45	#125	#595	1	1	yes	characteristic, complemented
46	#124	—	17	1	no	—
47	#103	—	34	1	no	—
48	#102	—	34	1	no	—
49	#101	—	34	1	no	—
50	#99	—	34	1	no	—
51	C₄×C₈	—	17	1	no	—
52	C₁₇	#1414	1	1	yes	characteristic, complemented, Sylow
53	C₂×Q₈	—	17	1	no	—
54	C₂×D₄	—	17	1	no	—
55	M₁₆	—	68	1	no	—
56	C₂×C₈	—	34	1	no	—
57	C₄⋊C₄	—	2	1	no	—
58	C₄⋊C₄	—	4	1	no	—
59	C₂²⋊C₄	—	68	1	no	—
60	C₂²⋊C₄	—	68	1	no	—
61	C₄²	C₂×#595	1	1	yes	characteristic
62	C₂³	—	34	1	no	—
63	Q₈	—	68	1	no	—
64	D₄	—	68	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	4	1	no	—
67	C₂×C₄	—	34	1	no	—
68	C₂×C₄	—	136	1	no	—
69	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
70	C₈	—	68	1	no	—
71	C₈	—	136	1	no	—
72	C₂²	—	68	1	no	—
73	C₂²	—	136	1	no	—
74	C₂²	#10587551	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	8	1	no	—
78	C₄	—	272	1	no	—
79	C₄	—	68	1	no	—
80	C₂	—	2	1	no	—
81	C₂	—	136	1	no	—
82	C₂	#11763715	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11763715
commutator	C₄²×C₁₇	C₂×C₄
Frattini	C₄²	C₂×#595
Fitting	C₁₇×#125	C₄
socle	C₂×C₁₇	#354
prime radical	C₂×D₆₈	D₄
cosocle	#10587561	C₂²
hypercenter	#125	#595
hypocenter	C₁₇	#1414
LCS	G ▷ C₄²×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
4. C₁₇×#125	C₄	semidirect
10. C₄×#3622	C₄	semidirect
45. #125	#595	semidirect
52. C₁₇	#1414	semidirect

Maximal subgroups

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

subgroup	index
#11763718	2
#11763716	2
#11763166	2
#1414	17