Subgroups — #11763820

Order 1088.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587677	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊#595	C₂	1	1	yes	maximal, characteristic
3	M₁₆×D₁₇	C₂	1	1	yes	maximal, characteristic
4	#10587534	C₂	1	2	yes	maximal, complemented
5	#10587533	C₂	1	2	yes	maximal, complemented
6	C₂²×#595	—	2	1	no	—
7	C₂×C₄×D₁₇	C₂²	1	1	yes	characteristic
8	C₂²⋊#595	—	2	1	no	—
9	C₄⋊#595	—	2	1	no	—
10	C₄⋊#595	C₂²	1	2	yes	—
11	C₄⋊#595	C₂²	1	1	yes	characteristic
12	C₄⋊#595	C₂²	1	1	yes	characteristic
13	C₄×#595	—	2	1	no	—
14	M₁₆×C₁₇	C₄	1	1	yes	characteristic, complemented
15	#63223	C₄	1	1	yes	characteristic, complemented
16	#63218	C₄	1	2	yes	complemented
17	C₈×D₁₇	C₂²	1	2	yes	—
18	C₂²×D₁₇	D₄	1	1	yes	characteristic
19	C₂×#595	—	2	1	no	—
20	C₂×#595	—	2	1	no	—
21	C₂×#595	—	2	2	no	—
22	C₂×#595	—	4	2	no	—
23	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
24	C₂×Dic₁₇	Q₈	1	1	yes	characteristic
25	C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
26	C₄×D₁₇	D₄	1	1	yes	characteristic
27	C₄×D₁₇	Q₈	1	1	yes	characteristic
28	C₄×D₁₇	C₂³	1	1	yes	characteristic
29	C₈×C₁₇	C₂×C₄	1	2	yes	complemented
30	#3622	C₂×C₄	1	2	yes	complemented
31	C₂²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
32	C₂×D₁₇	—	2	1	no	—
33	C₂×D₁₇	—	2	1	no	—
34	C₂×D₁₇	C₄⋊C₄	1	1	yes	characteristic
35	C₂×D₁₇	C₂×D₄	1	1	yes	characteristic
36	#595	—	4	1	no	—
37	#595	—	4	2	no	—
38	#595	—	4	1	no	—
39	C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
40	C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
41	Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
42	Dic₁₇	C₂×Q₈	1	1	yes	characteristic
43	#428	—	17	1	no	maximal, Sylow
44	C₂×C₁₇	—	2	1	no	—
45	C₂×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
46	D₁₇	—	2	1	no	—
47	D₁₇	AGL(1,ℤ/8)	1	1	yes	characteristic
48	D₁₇	#137	1	1	yes	characteristic
49	C₂×M₁₆	—	17	1	no	—
50	#117	—	17	1	no	—
51	C₂×C₄⋊C₄	—	17	1	no	—
52	#107	—	17	2	no	—
53	#106	—	17	2	no	—
54	C₁₇	#428	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₄	—	17	1	no	—
56	C₂²×C₄	—	34	1	no	—
57	M₁₆	—	17	1	no	—
58	M₁₆	—	17	2	no	—
59	M₁₆	#595	1	1	yes	characteristic, complemented
60	C₂×C₈	—	17	2	no	—
61	C₄⋊C₄	—	17	1	no	—
62	C₄⋊C₄	—	17	2	no	—
63	C₄⋊C₄	—	17	1	no	—
64	C₄⋊C₄	—	34	1	no	—
65	C₂²⋊C₄	—	34	1	no	—
66	C₄²	—	34	1	no	—
67	C₂³	—	17	1	no	—
68	C₂×C₄	—	17	1	no	—
69	C₂×C₄	—	17	1	no	—
70	C₂×C₄	—	17	1	no	—
71	C₂×C₄	—	17	1	no	—
72	C₂×C₄	—	17	1	no	—
73	C₂×C₄	—	34	1	no	—
74	C₂×C₄	—	34	1	no	—
75	C₂×C₄	—	34	2	no	—
76	C₂×C₄	—	68	2	no	—
77	C₂×C₄	C₂×#595	1	1	yes	characteristic
78	C₈	—	17	2	no	—
79	C₈	C₂×#595	1	2	yes	complemented
80	C₂²	—	17	1	no	—
81	C₂²	—	17	1	no	—
82	C₂²	—	34	1	no	—
83	C₂²	—	34	1	no	—
84	C₂²	C₄⋊#595	1	1	yes	characteristic
85	C₄	—	17	1	no	—
86	C₄	—	17	1	no	—
87	C₄	—	68	2	no	—
88	C₄	—	68	1	no	—
89	C₄	—	68	1	no	—
90	C₄	C₄⋊#595	1	1	yes	characteristic
91	C₄	C₂²×#595	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	17	1	no	—
94	C₂	—	17	1	no	—
95	C₂	—	34	1	no	—
96	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	D₄
cosocle	C₄×D₁₇	C₂³
hypercenter	M₁₆	#595
hypocenter	C₁₇	#428
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. #10587534	C₂	semidirect
5. #10587533	C₂	semidirect
14. M₁₆×C₁₇	C₄	semidirect
15. #63223	C₄	semidirect
16. #63218	C₄	semidirect
29. C₈×C₁₇	C₂×C₄	semidirect
30. #3622	C₂×C₄	semidirect
54. C₁₇	#428	semidirect
59. M₁₆	#595	semidirect
79. C₈	C₂×#595	semidirect

Maximal subgroups

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

subgroup	index
#10587677	2
C₂×C₄⋊#595	2
M₁₆×D₁₇	2
#10587534	2
#10587533	2
#428	17