Subgroups — #11763824

Order 1088.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₇⋊M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#63243	C₂	1	1	yes	maximal, characteristic
3	M₁₆×D₁₇	C₂	1	1	yes	maximal, characteristic
4	#10587536	C₂	1	2	yes	maximal, complemented
5	#10587535	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×D₁₇	C₂²	1	1	yes	characteristic
7	#63247	—	2	1	no	—
8	C₂×#3624	—	2	1	no	—
9	#63243	—	2	1	no	—
10	#63243	C₂²	1	2	yes	—
11	#63243	C₂²	1	1	yes	characteristic
12	#63243	C₂²	1	1	yes	characteristic
13	#63242	—	2	1	no	—
14	M₁₆×C₁₇	C₄	1	1	yes	characteristic
15	#63223	C₄	1	1	yes	characteristic
16	#63218	C₄	1	2	yes	—
17	C₈×D₁₇	C₂²	1	2	yes	—
18	C₂²×D₁₇	Q₈	1	1	yes	characteristic
19	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₁₇	D₄	1	1	yes	characteristic
21	C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
22	C₄×D₁₇	D₄	1	1	yes	characteristic
23	C₄×D₁₇	Q₈	1	1	yes	characteristic
24	C₄×D₁₇	C₂³	1	1	yes	characteristic
25	#3624	—	2	1	no	—
26	#3624	—	2	1	no	—
27	#3624	—	2	2	no	—
28	C₈×C₁₇	C₂×C₄	1	2	yes	—
29	#3622	C₂×C₄	1	2	yes	—
30	C₂²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
31	C₂×D₁₇	—	4	1	no	—
32	C₂×D₁₇	C₄⋊C₄	1	1	yes	characteristic
33	C₂×D₁₇	C₂×Q₈	1	1	yes	characteristic
34	C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
35	C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
36	Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
37	Dic₁₇	C₂×D₄	1	1	yes	characteristic
38	#430	—	17	1	no	maximal, Sylow
39	C₂×C₁₇	—	2	1	no	—
40	C₂×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
41	D₁₇	—	2	1	no	—
42	D₁₇	—	2	1	no	—
43	C₂×M₁₆	—	17	1	no	—
44	C₂×M₁₆	—	17	1	no	—
45	C₂×M₁₆	—	17	1	no	—
46	#108	—	17	2	no	—
47	#108	—	17	2	no	—
48	C₁₇	#430	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₄	—	17	1	no	—
50	M₁₆	—	17	1	no	—
51	M₁₆	—	17	2	no	—
52	M₁₆	—	17	2	no	—
53	M₁₆	—	17	1	no	—
54	M₁₆	—	17	1	no	—
55	M₁₆	—	34	1	no	—
56	M₁₆	—	34	1	no	—
57	M₁₆	#595	1	1	yes	characteristic
58	C₂×C₈	—	17	2	no	—
59	C₂×C₈	—	34	1	no	—
60	C₂×C₈	—	34	1	no	—
61	C₂³	—	17	1	no	—
62	C₂×C₄	—	17	1	no	—
63	C₂×C₄	—	17	1	no	—
64	C₂×C₄	—	17	1	no	—
65	C₂×C₄	—	17	1	no	—
66	C₂×C₄	—	17	1	no	—
67	C₂×C₄	C₂×#595	1	1	yes	characteristic
68	C₈	—	17	2	no	—
69	C₈	—	34	1	no	—
70	C₈	—	34	1	no	—
71	C₈	—	34	2	no	—
72	C₈	C₂×#595	1	2	yes	—
73	C₂²	—	17	1	no	—
74	C₂²	—	17	1	no	—
75	C₂²	—	68	1	no	—
76	C₂²	C₄⋊#595	1	1	yes	characteristic
77	C₄	—	17	1	no	—
78	C₄	—	17	1	no	—
79	C₄	C₄⋊#595	1	1	yes	characteristic
80	C₄	C₂²×#595	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	—	34	1	no	—
83	C₂	—	34	1	no	—
84	C₂	C₂×C₄⋊#595	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₄⋊#595
commutator	C₄×C₁₇	C₂²×C₄
Frattini	C₄	C₂²×#595
Fitting	M₁₆×C₁₇	C₄
socle	C₂×C₁₇	C₂×C₄⋊C₄
prime radical	C₂²×D₁₇	Q₈
cosocle	C₄×D₁₇	C₂³
hypercenter	M₁₆	#595
hypocenter	C₁₇	#430
LCS	G ▷ C₄×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
4. #10587536	C₂	semidirect
5. #10587535	C₂	semidirect
48. C₁₇	#430	semidirect

Maximal subgroups

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

subgroup	index
D₁₇⋊M₁₆	2
C₂×#63243	2
M₁₆×D₁₇	2
#10587536	2
#10587535	2
#430	17