Subgroups — C₂×#10587543 #11763778

Order 1088.

202 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	C₂²×#3624	C₂	1	2	yes	maximal, complemented
3	#10587543	C₂	1	4	yes	maximal, direct product factor
4	C₂³×D₁₇	C₄	1	1	yes	characteristic
5	C₂²×C₄×C₁₇	C₄	1	1	yes	characteristic
6	C₂²×Dic₁₇	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₁₇	—	2	4	no	—
8	C₂×C₄×D₁₇	C₄	1	2	yes	—
9	C₂×C₄×D₁₇	C₂²	1	2	yes	—
10	C₂×#3624	—	2	4	no	—
11	C₂×#3624	C₂²	1	4	yes	complemented
12	C₂³×C₁₇	C₂×C₄	1	1	yes	characteristic
13	C₂²×D₁₇	—	2	2	no	—
14	C₂²×D₁₇	—	2	2	no	—
15	C₂²×D₁₇	C₈	1	4	yes	complemented
16	C₂²×D₁₇	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₁₇	—	2	2	no	—
18	C₂×C₄×C₁₇	C₂×C₄	1	2	yes	—
19	C₂×Dic₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₁₇	D₄	1	4	yes	—
21	C₂×Dic₁₇	C₂³	1	1	yes	characteristic
22	C₄×D₁₇	—	2	4	no	—
23	C₄×D₁₇	—	2	4	no	—
24	#3624	—	2	4	no	—
25	C₂²×C₁₇	C₂²⋊C₄	1	2	yes	—
26	C₂²×C₁₇	C₂×C₈	1	2	yes	—
27	C₂²×C₁₇	M₁₆	1	2	yes	—
28	C₂²×C₁₇	C₂²×C₄	1	1	yes	characteristic
29	C₂×D₁₇	—	2	8	no	—
30	C₂×D₁₇	—	2	2	no	—
31	C₂×D₁₇	—	2	2	no	—
32	C₂×D₁₇	C₂×C₈	1	4	yes	complemented
33	C₄×C₁₇	—	2	2	no	—
34	Dic₁₇	C₂²⋊C₄	1	2	yes	—
35	Dic₁₇	C₂×D₄	1	2	yes	—
36	C₂×C₂²⋊C₈	—	17	1	no	maximal, Sylow
37	C₂×C₁₇	C₂²⋊C₈	1	4	yes	complemented
38	C₂×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
39	C₂×C₁₇	C₂²×C₈	1	1	yes	characteristic
40	C₂×C₁₇	C₂×M₁₆	1	1	yes	characteristic
41	D₁₇	—	2	4	no	—
42	C₂³×C₄	—	17	1	no	—
43	C₂²×C₈	—	17	2	no	—
44	C₂²⋊C₈	—	17	4	no	—
45	C₁₇	C₂×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
46	C₂⁴	—	17	1	no	—
47	C₂²×C₄	—	17	1	no	—
48	C₂²×C₄	—	17	2	no	—
49	C₂²×C₄	—	17	2	no	—
50	C₂²×C₄	—	34	4	no	—
51	C₂²×C₄	#595	1	1	yes	characteristic
52	C₂×C₈	—	17	4	no	—
53	C₂×C₈	—	34	4	no	—
54	C₂³	—	17	4	no	—
55	C₂³	—	17	2	no	—
56	C₂³	—	34	2	no	—
57	C₂³	—	34	2	no	—
58	C₂³	C₂×#595	1	1	yes	characteristic
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	17	4	no	—
61	C₂×C₄	—	17	1	no	—
62	C₂×C₄	—	17	1	no	—
63	C₂×C₄	—	34	4	no	—
64	C₂×C₄	—	34	4	no	—
65	C₂×C₄	C₂×#595	1	2	yes	—
66	C₈	—	34	4	no	—
67	C₂²	—	17	4	no	—
68	C₂²	—	34	2	no	—
69	C₂²	—	34	2	no	—
70	C₂²	—	34	8	no	—
71	C₂²	#63242	1	2	yes	—
72	C₂²	#63243	1	2	yes	—
73	C₂²	C₂²⋊#595	1	2	yes	—
74	C₂²	C₂²×#595	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	17	2	no	—
77	C₄	—	17	2	no	—
78	C₂	—	34	4	no	—
79	C₂	#10587543	1	4	yes	direct product factor
80	C₂	C₂×#63242	1	1	yes	characteristic
81	C₂	C₂×#63243	1	1	yes	characteristic
82	C₂	C₂×C₂²⋊#595	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#595
commutator	C₂×C₁₇	C₂²×C₈
Frattini	C₂²	C₂²×#595
Fitting	C₂²×C₄×C₁₇	C₄
socle	C₂³×C₁₇	C₂×C₄
prime radical	C₂³×D₁₇	C₄
cosocle	C₂×Dic₁₇	C₂³
hypercenter	C₂²×C₄	#595
hypocenter	C₁₇	C₂×C₂²⋊C₈
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×#3624	C₂	semidirect
3. #10587543	C₂	direct (N × H)
11. C₂×#3624	C₂²	semidirect
15. C₂²×D₁₇	C₈	semidirect
32. C₂×D₁₇	C₂×C₈	semidirect
37. C₂×C₁₇	C₂²⋊C₈	semidirect
45. C₁₇	C₂×C₂²⋊C₈	semidirect
79. C₂	#10587543	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
C₂²×#3624	2
#10587543	2
C₂×C₂²⋊C₈	17

Subgroups — C2×#10587543 #11763778

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10587543 #11763778