Subgroups — C₂×#10587530 #11763866

Order 1088.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#63216	C₂	1	2	yes	maximal, complemented
3	#10587530	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×D₁₇	C₄	1	1	yes	characteristic
5	C₂×C₈×C₁₇	C₄	1	1	yes	characteristic
6	C₂×#3622	C₂²	1	1	yes	characteristic
7	C₈×D₁₇	C₄	1	2	yes	—
8	C₈×D₁₇	C₂²	1	2	yes	—
9	#63216	C₂²	1	4	yes	complemented
10	C₂²×D₁₇	C₈	1	1	yes	characteristic
11	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
12	C₂×Dic₁₇	C₈	1	1	yes	characteristic
13	C₄×D₁₇	C₈	1	2	yes	—
14	C₄×D₁₇	C₂×C₄	1	2	yes	—
15	C₈×C₁₇	C₂×C₄	1	2	yes	—
16	#3622	C₂×C₄	1	1	yes	characteristic
17	#3622	C₂³	1	1	yes	characteristic
18	C₂²×C₁₇	C₂×C₈	1	1	yes	characteristic
19	C₂×D₁₇	—	2	2	no	—
20	C₂×D₁₇	C₂×C₈	1	2	yes	—
21	C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
22	C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
23	Dic₁₇	C₂×C₈	1	2	yes	—
24	C₂×M₃₂	—	17	1	no	maximal, Sylow
25	C₂×C₁₇	M₃₂	1	2	yes	complemented
26	C₂×C₁₇	C₂²×C₈	1	1	yes	characteristic
27	D₁₇	—	2	2	no	—
28	C₂²×C₈	—	17	1	no	—
29	M₃₂	—	17	4	no	—
30	C₂×C₁₆	—	17	2	no	—
31	C₁₇	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
32	C₂²×C₄	—	17	1	no	—
33	C₂×C₈	—	17	1	no	—
34	C₂×C₈	—	17	2	no	—
35	C₂×C₈	—	17	2	no	—
36	C₂×C₈	#595	1	1	yes	characteristic
37	C₁₆	—	17	4	no	—
38	C₂³	—	17	1	no	—
39	C₂×C₄	—	17	1	no	—
40	C₂×C₄	—	17	2	no	—
41	C₂×C₄	—	17	2	no	—
42	C₂×C₄	C₂×#595	1	1	yes	characteristic
43	C₈	—	17	1	no	—
44	C₈	—	17	1	no	—
45	C₈	C₂×#595	1	2	yes	—
46	C₂²	—	17	2	no	—
47	C₂²	—	34	2	no	—
48	C₂²	#63242	1	1	yes	characteristic
49	C₄	—	17	2	no	—
50	C₄	#63242	1	1	yes	characteristic
51	C₄	C₂²×#595	1	1	yes	characteristic
52	C₂	—	34	2	no	—
53	C₂	#10587530	1	2	yes	direct product factor
54	C₂	C₂×#63242	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#595
commutator	C₂×C₁₇	C₂²×C₈
Frattini	C₄	C₂²×#595
Fitting	C₂×C₈×C₁₇	C₄
socle	C₂²×C₁₇	C₂×C₈
prime radical	C₂²×D₁₇	C₈
cosocle	#3622	C₂³
hypercenter	C₂×C₈	#595
hypocenter	C₁₇	C₂×M₃₂
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#63216	C₂	semidirect
3. #10587530	C₂	direct (N × H)
9. #63216	C₂²	semidirect
25. C₂×C₁₇	M₃₂	semidirect
31. C₁₇	C₂×M₃₂	semidirect
53. C₂	#10587530	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×C₈×D₁₇	2
C₂×#63216	2
#10587530	2
C₂×M₃₂	17

Subgroups — C2×#10587530 #11763866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10587530 #11763866