Subgroups — C₂×#10587535 #11763821

Order 1088.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63243	C₂	1	2	yes	maximal
2	C₂×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
3	#10587535	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×D₁₇	C₂²	1	1	yes	characteristic
5	C₂×#3624	—	2	2	no	—
6	#63243	—	2	2	no	—
7	#63243	C₂²	1	4	yes	—
8	C₂×C₈×C₁₇	C₄	1	1	yes	characteristic
9	C₂×#3622	C₄	1	1	yes	characteristic
10	C₈×D₁₇	C₄	1	2	yes	—
11	C₈×D₁₇	C₂²	1	2	yes	—
12	C₂²×D₁₇	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₁₇	D₄	1	1	yes	characteristic
15	C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
16	C₄×D₁₇	D₄	1	1	yes	characteristic
17	C₄×D₁₇	Q₈	1	1	yes	characteristic
18	C₄×D₁₇	C₂³	1	1	yes	characteristic
19	#3624	—	2	4	no	—
20	C₈×C₁₇	C₂×C₄	1	2	yes	—
21	#3622	C₂×C₄	1	2	yes	—
22	C₂²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
23	C₂×D₁₇	—	2	2	no	—
24	C₂×D₁₇	C₄⋊C₄	1	1	yes	characteristic
25	C₂×D₁₇	C₂×Q₈	1	1	yes	characteristic
26	C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
27	C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
28	Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
29	Dic₁₇	C₂×D₄	1	1	yes	characteristic
30	C₂×#108	—	17	1	no	maximal, Sylow
31	C₂×C₁₇	#108	1	2	yes	complemented
32	C₂×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
33	D₁₇	—	2	1	no	—
34	D₁₇	—	2	1	no	—
35	C₂×M₁₆	—	17	2	no	—
36	C₂²×C₈	—	17	1	no	—
37	#108	—	17	4	no	—
38	C₁₇	C₂×#108	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₄	—	17	1	no	—
40	M₁₆	—	17	4	no	—
41	M₁₆	—	34	2	no	—
42	C₂×C₈	—	17	1	no	—
43	C₂×C₈	—	17	2	no	—
44	C₂×C₈	—	17	2	no	—
45	C₂×C₈	—	34	2	no	—
46	C₂×C₈	#595	1	1	yes	characteristic
47	C₂³	—	17	1	no	—
48	C₂×C₄	—	17	1	no	—
49	C₂×C₄	—	17	1	no	—
50	C₂×C₄	—	17	1	no	—
51	C₂×C₄	—	17	1	no	—
52	C₂×C₄	—	17	1	no	—
53	C₂×C₄	C₂×#595	1	1	yes	characteristic
54	C₈	—	17	2	no	—
55	C₈	—	34	4	no	—
56	C₈	C₂×#595	1	2	yes	—
57	C₂²	—	17	1	no	—
58	C₂²	—	17	1	no	—
59	C₂²	—	34	2	no	—
60	C₂²	C₄⋊#595	1	1	yes	characteristic
61	C₄	—	17	1	no	—
62	C₄	—	17	1	no	—
63	C₄	C₄⋊#595	1	1	yes	characteristic
64	C₄	C₂²×#595	1	1	yes	characteristic
65	C₂	—	34	1	no	—
66	C₂	—	34	1	no	—
67	C₂	#10587535	1	2	yes	direct product factor
68	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	Q₈
cosocle	C₄×D₁₇	C₂³
hypercenter	C₂×C₈	#595
hypocenter	C₁₇	C₂×#108
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. #10587535	C₂	direct (N × H)
31. C₂×C₁₇	#108	semidirect
38. C₁₇	C₂×#108	semidirect
67. C₂	#10587535	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×#63243	2
C₂×C₈×D₁₇	2
#10587535	2
C₂×#108	17

Subgroups — C2×#10587535 #11763821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10587535 #11763821