Subgroups — C₂×#10587558 #11763263

Order 1088.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#63227	C₂	1	2	yes	maximal
4	C₂×#63225	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×Dic₁₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#10587558	C₂	1	8	yes	maximal, direct product factor
7	C₂³×D₁₇	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₁₇	C₂²	1	2	yes	—
9	C₂²×C₄×C₁₇	C₂²	1	1	yes	characteristic
10	C₂²×Dic₁₇	C₂²	1	2	yes	—
11	C₂²×Dic₁₇	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₁₇	C₄	1	8	yes	complemented
13	C₂×C₄×D₁₇	C₂²	1	4	yes	—
14	C₄²×C₁₇	C₂²	1	4	yes	complemented
15	#63227	C₂²	1	8	yes	—
16	#63225	C₂²	1	8	yes	complemented
17	C₄×Dic₁₇	C₂²	1	4	yes	complemented
18	C₂³×C₁₇	C₂³	1	1	yes	characteristic
19	C₂²×D₁₇	—	2	4	no	—
20	C₂²×D₁₇	C₂×C₄	1	4	yes	—
21	C₂²×D₁₇	C₂³	1	2	yes	—
22	C₂×C₄×C₁₇	—	2	4	no	—
23	C₂×C₄×C₁₇	C₂×C₄	1	4	yes	—
24	C₂×C₄×C₁₇	C₂³	1	4	yes	—
25	C₂×C₄×C₁₇	C₂³	1	2	yes	—
26	C₂×Dic₁₇	—	2	4	no	—
27	C₂×Dic₁₇	C₂×C₄	1	4	yes	—
28	C₂×Dic₁₇	C₂³	1	4	yes	—
29	C₂×Dic₁₇	C₂³	1	2	yes	—
30	C₄×D₁₇	C₂×C₄	1	16	yes	complemented
31	C₂²×C₁₇	C₂²×C₄	1	2	yes	—
32	C₂²×C₁₇	#41	1	4	yes	—
33	C₂²×C₁₇	C₂⁴	1	1	yes	characteristic
34	C₂×D₁₇	—	2	8	no	—
35	C₂×D₁₇	—	2	4	no	—
36	C₂×D₁₇	C₂²×C₄	1	4	yes	—
37	C₄×C₁₇	—	2	4	no	—
38	C₄×C₁₇	C₂²×C₄	1	4	yes	—
39	Dic₁₇	—	2	4	no	—
40	Dic₁₇	C₂²×C₄	1	4	yes	—
41	C₂×#117	—	17	1	no	maximal, Sylow
42	C₂×C₁₇	#117	1	4	yes	complemented
43	C₂×C₁₇	C₂³×C₄	1	1	yes	characteristic
44	C₂×C₁₇	C₂×#41	1	2	yes	—
45	D₁₇	—	2	4	no	—
46	C₂³×C₄	—	17	1	no	—
47	#117	—	17	8	no	—
48	C₂×C₄⋊C₄	—	17	2	no	—
49	C₂×C₂²⋊C₄	—	17	2	no	—
50	C₂×C₄²	—	17	1	no	—
51	C₂×C₄²	D₁₇	1	1	yes	characteristic, complemented
52	C₁₇	C₂×#117	1	1	yes	characteristic, complemented, Sylow
53	C₂⁴	—	17	1	no	—
54	C₂²×C₄	—	17	1	no	—
55	C₂²×C₄	—	17	8	no	—
56	C₂²×C₄	—	17	4	no	—
57	C₂²×C₄	—	17	2	no	—
58	C₂²×C₄	C₂×D₁₇	1	2	yes	—
59	C₂²×C₄	C₂×D₁₇	1	1	yes	characteristic
60	C₄⋊C₄	—	17	8	no	—
61	C₂²⋊C₄	—	17	8	no	—
62	C₄²	—	17	4	no	—
63	C₄²	C₂×D₁₇	1	4	yes	complemented
64	C₂³	—	17	4	no	—
65	C₂³	—	17	2	no	—
66	C₂³	—	34	4	no	—
67	C₂³	C₂²×D₁₇	1	1	yes	characteristic
68	C₂×C₄	—	2	4	no	—
69	C₂×C₄	—	17	4	no	—
70	C₂×C₄	—	17	2	no	—
71	C₂×C₄	—	17	16	no	—
72	C₂×C₄	—	17	4	no	—
73	C₂×C₄	—	34	4	no	—
74	C₂×C₄	C₄×D₁₇	1	4	yes	—
75	C₂×C₄	C₂²×D₁₇	1	4	yes	—
76	C₂×C₄	C₂²×D₁₇	1	2	yes	—
77	C₂²	—	17	4	no	—
78	C₂²	—	34	4	no	—
79	C₂²	—	34	8	no	—
80	C₂²	C₂×C₄×D₁₇	1	2	yes	—
81	C₂²	#63252	1	4	yes	—
82	C₂²	C₂³×D₁₇	1	1	yes	characteristic
83	C₄	—	2	4	no	—
84	C₄	—	17	4	no	—
85	C₄	—	34	4	no	—
86	C₄	C₂×C₄×D₁₇	1	4	yes	—
87	C₂	—	34	4	no	—
88	C₂	#10587558	1	4	yes	direct product factor
89	C₂	C₂²×C₄×D₁₇	1	1	yes	characteristic
90	C₂	C₂×#63252	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₇
commutator	C₂×C₁₇	C₂³×C₄
Frattini	C₂²	C₂³×D₁₇
Fitting	C₂×C₄²×C₁₇	C₂
socle	C₂³×C₁₇	C₂³
prime radical	C₂³×D₁₇	C₂²
cosocle	C₂²×C₁₇	C₂⁴
hypercenter	C₂×C₄²	D₁₇
hypocenter	C₁₇	C₂×#117
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×C₄²×C₁₇	C₂	semidirect
4. C₂×#63225	C₂	semidirect
5. C₂×C₄×Dic₁₇	C₂	semidirect
6. #10587558	C₂	direct (N × H)
12. C₂×C₄×D₁₇	C₄	semidirect
14. C₄²×C₁₇	C₂²	semidirect
16. #63225	C₂²	semidirect
17. C₄×Dic₁₇	C₂²	semidirect
30. C₄×D₁₇	C₂×C₄	semidirect
42. C₂×C₁₇	#117	semidirect
51. C₂×C₄²	D₁₇	semidirect
52. C₁₇	C₂×#117	semidirect
63. C₄²	C₂×D₁₇	semidirect
88. C₂	#10587558	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₁₇	2
C₂×C₄²×C₁₇	2
C₂×#63227	2
C₂×#63225	2
C₂×C₄×Dic₁₇	2
#10587558	2
C₂×#117	17

Subgroups — C2×#10587558 #11763263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10587558 #11763263