Subgroups — #11763688

Order 1088.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#595	C₂	1	1	yes	maximal, characteristic
2	D₁₇⋊M₁₆	C₂	1	1	yes	maximal, characteristic
3	M₁₆×D₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×#595	C₄	1	2	yes	—
5	C₂×C₄×D₁₇	C₂²	1	1	yes	characteristic
6	#63247	C₄	1	2	yes	complemented
7	C₄⋊#595	—	2	1	no	—
8	C₄⋊#595	—	2	1	no	—
9	#63243	—	2	1	no	—
10	#63242	—	2	1	no	—
11	M₁₆×C₁₇	C₄	1	1	yes	characteristic, complemented
12	#63223	C₄	1	1	yes	characteristic, complemented
13	#63218	—	2	1	no	—
14	C₈×D₁₇	—	2	1	no	—
15	C₂²×D₁₇	C₂×C₄	1	1	yes	characteristic
16	C₂×#595	—	2	2	no	—
17	C₂×#595	—	4	2	no	—
18	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₁₇	C₂×C₄	1	1	yes	characteristic
20	C₄×D₁₇	D₄	1	1	yes	characteristic
21	C₄×D₁₇	D₄	1	1	yes	characteristic
22	C₄×D₁₇	D₄	1	1	yes	characteristic
23	C₄×D₁₇	Q₈	1	1	yes	characteristic
24	#3624	—	2	2	no	—
25	C₈×C₁₇	—	2	1	no	—
26	#3622	—	2	1	no	—
27	C₂²×C₁₇	C₄²	1	1	yes	characteristic
28	C₂×D₁₇	—	2	1	no	—
29	C₂×D₁₇	—	2	1	no	—
30	C₂×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×D₁₇	C₄⋊C₄	1	1	yes	characteristic
32	#595	—	4	2	no	—
33	C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
34	C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
35	Dic₁₇	C₂²⋊C₄	1	1	yes	characteristic
36	Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
37	#343	—	17	1	no	maximal, Sylow
38	C₂×C₁₇	—	2	1	no	—
39	C₂×C₁₇	#95	1	1	yes	characteristic
40	D₁₇	—	2	1	no	—
41	D₁₇	#100	1	1	yes	characteristic
42	D₁₇	#101	1	1	yes	characteristic
43	C₂×M₁₆	—	17	1	no	—
44	C₂×M₁₆	—	17	1	no	—
45	C₂×C₄⋊C₄	—	17	1	no	—
46	C₁₇	#343	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₄	—	17	1	no	—
48	C₂²×C₄	—	17	2	no	—
49	M₁₆	—	17	2	no	—
50	M₁₆	—	17	1	no	—
51	M₁₆	—	34	1	no	—
52	M₁₆	—	34	1	no	—
53	M₁₆	#595	1	1	yes	characteristic, complemented
54	C₂×C₈	—	34	1	no	—
55	C₂×C₈	—	34	1	no	—
56	C₄⋊C₄	—	34	1	no	—
57	C₄⋊C₄	—	34	1	no	—
58	C₂³	—	17	1	no	—
59	C₂×C₄	—	17	1	no	—
60	C₂×C₄	—	17	1	no	—
61	C₂×C₄	—	17	1	no	—
62	C₂×C₄	—	17	1	no	—
63	C₂×C₄	—	17	1	no	—
64	C₂×C₄	—	34	2	no	—
65	C₂×C₄	—	68	2	no	—
66	C₂×C₄	C₂×#595	1	1	yes	characteristic
67	C₈	—	2	1	no	—
68	C₈	—	34	2	no	—
69	C₈	—	34	1	no	—
70	C₂²	—	17	1	no	—
71	C₂²	—	17	1	no	—
72	C₂²	—	34	1	no	—
73	C₂²	—	34	1	no	—
74	C₂²	C₄×#595	1	1	yes	characteristic
75	C₄	—	17	1	no	—
76	C₄	—	17	1	no	—
77	C₄	—	68	2	no	—
78	C₄	C₄⋊#595	1	1	yes	characteristic
79	C₄	C₂²⋊#595	1	1	yes	characteristic
80	C₂	—	2	1	no	—
81	C₂	—	17	1	no	—
82	C₂	—	17	1	no	—
83	C₂	—	34	1	no	—
84	C₂	(C₂×#595)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂	(C₂×#595)⋊C₄
commutator	C₂²×C₁₇	C₄²
Frattini	C₂×C₄	C₂×#595
Fitting	M₁₆×C₁₇	C₄
socle	C₂×C₁₇	#95
prime radical	C₂²×D₁₇	C₂×C₄
cosocle	C₂×C₄×D₁₇	C₂²
hypercenter	M₁₆	#595
hypocenter	C₁₇	#343
LCS	G ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
6. #63247	C₄	semidirect
11. M₁₆×C₁₇	C₄	semidirect
12. #63223	C₄	semidirect
46. C₁₇	#343	semidirect
53. M₁₆	#595	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊#595	2
D₁₇⋊M₁₆	2
M₁₆×D₁₇	2
#343	17