Subgroups — C₂×#10587534 #11763818

Order 1088.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#595	C₂	1	2	yes	maximal
2	C₂×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
3	#10587534	C₂	1	4	yes	maximal, direct product factor
4	C₂²×#595	—	2	2	no	—
5	C₂×C₄×D₁₇	C₂²	1	1	yes	characteristic
6	C₄⋊#595	—	2	2	no	—
7	C₄⋊#595	C₂²	1	4	yes	—
8	C₂×C₈×C₁₇	C₄	1	1	yes	characteristic, complemented
9	C₂×#3622	C₄	1	1	yes	characteristic, complemented
10	C₈×D₁₇	C₄	1	2	yes	complemented
11	C₈×D₁₇	C₂²	1	2	yes	—
12	C₂²×D₁₇	D₄	1	1	yes	characteristic
13	C₂×#595	—	2	4	no	—
14	C₂×#595	—	4	4	no	—
15	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
16	C₂×Dic₁₇	Q₈	1	1	yes	characteristic
17	C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
18	C₄×D₁₇	D₄	1	1	yes	characteristic
19	C₄×D₁₇	Q₈	1	1	yes	characteristic
20	C₄×D₁₇	C₂³	1	1	yes	characteristic
21	C₈×C₁₇	C₂×C₄	1	2	yes	complemented
22	#3622	C₂×C₄	1	2	yes	complemented
23	C₂²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
24	C₂×D₁₇	C₄⋊C₄	1	1	yes	characteristic
25	C₂×D₁₇	D₈	1	2	yes	—
26	C₂×D₁₇	Q₁₆	1	2	yes	—
27	C₂×D₁₇	C₂×D₄	1	1	yes	characteristic
28	#595	—	4	4	no	—
29	C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
30	C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
31	Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
32	Dic₁₇	C₂×Q₈	1	1	yes	characteristic
33	C₂×#107	—	17	1	no	maximal, Sylow
34	C₂×C₁₇	#107	1	2	yes	complemented
35	C₂×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
36	D₁₇	#107	1	2	yes	complemented
37	D₁₇	C₂×D₈	1	1	yes	characteristic
38	D₁₇	C₂×Q₁₆	1	1	yes	characteristic
39	C₂²×C₈	—	17	1	no	—
40	C₂×C₄⋊C₄	—	17	2	no	—
41	#107	—	17	4	no	—
42	C₁₇	C₂×#107	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₄	—	17	1	no	—
44	C₂²×C₄	—	34	2	no	—
45	C₂×C₈	—	17	1	no	—
46	C₂×C₈	—	17	2	no	—
47	C₂×C₈	—	17	2	no	—
48	C₂×C₈	#595	1	1	yes	characteristic, complemented
49	C₄⋊C₄	—	17	4	no	—
50	C₄⋊C₄	—	34	2	no	—
51	C₂³	—	17	1	no	—
52	C₂×C₄	—	17	1	no	—
53	C₂×C₄	—	17	1	no	—
54	C₂×C₄	—	17	1	no	—
55	C₂×C₄	—	17	1	no	—
56	C₂×C₄	—	17	1	no	—
57	C₂×C₄	—	34	4	no	—
58	C₂×C₄	—	68	4	no	—
59	C₂×C₄	C₂×#595	1	1	yes	characteristic
60	C₈	—	17	2	no	—
61	C₈	C₂×#595	1	2	yes	complemented
62	C₂²	—	17	1	no	—
63	C₂²	—	17	1	no	—
64	C₂²	—	17	2	no	—
65	C₂²	—	17	2	no	—
66	C₂²	C₄⋊#595	1	1	yes	characteristic
67	C₄	—	17	1	no	—
68	C₄	—	17	1	no	—
69	C₄	—	68	4	no	—
70	C₄	C₄⋊#595	1	1	yes	characteristic
71	C₄	C₂²×#595	1	1	yes	characteristic
72	C₂	—	17	1	no	—
73	C₂	—	17	2	no	—
74	C₂	—	17	1	no	—
75	C₂	#10587534	1	2	yes	direct product factor
76	C₂	C₂×C₄⋊#595	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#595
commutator	C₄×C₁₇	C₂²×C₄
Frattini	C₄	C₂²×#595
Fitting	C₂×C₈×C₁₇	C₄
socle	C₂²×C₁₇	C₄⋊C₄
prime radical	C₂²×D₁₇	D₄
cosocle	C₄×D₁₇	C₂³
hypercenter	C₂×C₈	#595
hypocenter	C₁₇	C₂×#107
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
3. #10587534	C₂	direct (N × H)
8. C₂×C₈×C₁₇	C₄	semidirect
9. C₂×#3622	C₄	semidirect
10. C₈×D₁₇	C₄	semidirect
21. C₈×C₁₇	C₂×C₄	semidirect
22. #3622	C₂×C₄	semidirect
34. C₂×C₁₇	#107	semidirect
36. D₁₇	#107	semidirect
42. C₁₇	C₂×#107	semidirect
48. C₂×C₈	#595	semidirect
61. C₈	C₂×#595	semidirect
75. C₂	#10587534	direct (N × H)

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
C₂×C₈×D₁₇	2
#10587534	2
C₂×#107	17

Subgroups — C2×#10587534 #11763818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10587534 #11763818