Subgroups — #11763726

Order 1088.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587605	C₂	1	1	yes	maximal, characteristic
2	#10587533	C₂	1	1	yes	maximal, characteristic, complemented
3	#10587530	C₂	1	1	yes	maximal, characteristic, complemented
4	#63256	—	2	1	no	—
5	C₄⋊#595	—	2	1	no	—
6	Q₁₆×C₁₇	C₄	1	1	yes	characteristic, complemented
7	#63230	—	2	1	no	—
8	D₁₃₆	C₄	1	1	yes	characteristic, complemented
9	C₈×D₁₇	C₂²	1	1	yes	characteristic
10	#63216	—	2	1	no	—
11	C₂×#595	—	4	1	no	—
12	Q₈×C₁₇	—	2	1	no	—
13	D₆₈	—	2	1	no	—
14	D₆₈	—	4	1	no	—
15	C₄×D₁₇	—	4	1	no	—
16	C₄×D₁₇	D₄	1	1	yes	characteristic
17	C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
18	#3622	D₄	1	1	yes	characteristic
19	C₂×D₁₇	—	4	1	no	—
20	C₂×D₁₇	D₈	1	1	yes	characteristic
21	#595	—	8	1	no	—
22	C₄×C₁₇	—	4	1	no	—
23	C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₁₇	SD₁₆	1	1	yes	characteristic
25	#360	—	17	1	no	maximal, Sylow
26	C₂×C₁₇	#102	1	1	yes	characteristic
27	D₁₇	—	2	1	no	—
28	D₁₇	—	8	1	no	—
29	#135	—	17	1	no	—
30	M₃₂	—	17	1	no	—
31	#106	—	17	1	no	—
32	C₁₇	#360	1	1	yes	characteristic, complemented, Sylow
33	#41	—	34	1	no	—
34	Q₁₆	#595	1	1	yes	characteristic, complemented
35	SD₁₆	—	34	1	no	—
36	D₈	—	17	1	no	—
37	C₂×C₈	—	17	1	no	—
38	C₄⋊C₄	—	34	1	no	—
39	C₁₆	—	34	1	no	—
40	Q₈	—	2	1	no	—
41	D₄	—	34	1	no	—
42	D₄	—	68	1	no	—
43	C₂×C₄	—	17	1	no	—
44	C₂×C₄	—	68	1	no	—
45	C₂×C₄	—	68	1	no	—
46	C₈	—	17	1	no	—
47	C₈	C₂×#595	1	1	yes	characteristic
48	C₂²	—	17	1	no	—
49	C₂²	—	68	1	no	—
50	C₄	—	4	1	no	—
51	C₄	—	17	1	no	—
52	C₄	—	136	1	no	—
53	C₄	C₂²⋊#595	1	1	yes	characteristic
54	C₂	—	34	1	no	—
55	C₂	—	136	1	no	—
56	C₂	#10587547	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10587547
commutator	C₈×C₁₇	C₂×C₄
Frattini	C₈	C₂×#595
Fitting	Q₁₆×C₁₇	C₄
socle	C₂×C₁₇	#102
prime radical	#10587605	C₂
cosocle	C₈×D₁₇	C₂²
hypercenter	Q₁₆	#595
hypocenter	C₁₇	#360
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
2. #10587533	C₂	semidirect
3. #10587530	C₂	semidirect
6. Q₁₆×C₁₇	C₄	semidirect
8. D₁₃₆	C₄	semidirect
32. C₁₇	#360	semidirect
34. Q₁₆	#595	semidirect

Maximal subgroups

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

subgroup	index
#10587605	2
#10587533	2
#10587530	2
#360	17