Subgroups — C₂×#14543952 #17962901

Order 4352.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543952	C₂	1	4	yes	maximal, direct product factor
2	C₂×#11763648	C₂	1	2	yes	maximal, complemented
3	C₂×C₃₂×D₁₇	C₂	1	1	yes	maximal, characteristic
4	#11763648	C₂²	1	4	yes	complemented
5	C₂×C₁₆×D₁₇	C₄	1	1	yes	characteristic
6	C₂×#10587465	C₂²	1	1	yes	characteristic
7	C₃₂×D₁₇	C₄	1	2	yes	—
8	C₃₂×D₁₇	C₂²	1	2	yes	—
9	C₂×C₁₇×C₃₂	C₄	1	1	yes	characteristic
10	C₂×C₈×D₁₇	C₈	1	1	yes	characteristic
11	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
12	C₂×#63214	C₈	1	1	yes	characteristic
13	C₁₆×D₁₇	C₈	1	2	yes	—
14	C₁₆×D₁₇	C₂×C₄	1	2	yes	—
15	C₁₇×C₃₂	C₂×C₄	1	2	yes	—
16	#10587465	C₂×C₄	1	1	yes	characteristic
17	#10587465	C₂³	1	1	yes	characteristic
18	C₂×C₄×D₁₇	C₁₆	1	1	yes	characteristic
19	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
20	C₂×#3622	C₁₆	1	1	yes	characteristic
21	C₈×D₁₇	C₁₆	1	2	yes	—
22	C₈×D₁₇	C₂×C₈	1	2	yes	—
23	C₁₆×C₁₇	C₂×C₈	1	1	yes	characteristic
24	C₁₆×C₁₇	C₂²×C₄	1	1	yes	characteristic
25	#63214	C₂×C₈	1	2	yes	—
26	C₂²×C₆₄	—	17	1	no	maximal, Sylow
27	C₂²×D₁₇	C₃₂	1	1	yes	characteristic
28	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
29	C₂×Dic₁₇	C₃₂	1	1	yes	characteristic
30	C₄×D₁₇	C₃₂	1	2	yes	—
31	C₄×D₁₇	C₂×C₁₆	1	2	yes	—
32	C₈×C₁₇	C₂×C₁₆	1	1	yes	characteristic
33	C₈×C₁₇	C₂²×C₈	1	1	yes	characteristic
34	#3622	C₂×C₁₆	1	2	yes	—
35	C₂²×C₃₂	—	17	1	no	—
36	C₂×C₆₄	—	17	2	no	—
37	C₂×C₆₄	—	17	4	no	—
38	C₂²×C₁₇	C₂×C₃₂	1	1	yes	characteristic
39	C₂×D₁₇	C₆₄	1	4	yes	complemented
40	C₂×D₁₇	C₂×C₃₂	1	2	yes	—
41	C₄×C₁₇	C₂×C₃₂	1	1	yes	characteristic
42	C₄×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
43	Dic₁₇	C₂×C₃₂	1	2	yes	—
44	C₂²×C₁₆	—	17	1	no	—
45	C₂×C₃₂	—	17	1	no	—
46	C₂×C₃₂	—	17	2	no	—
47	C₂×C₃₂	—	17	2	no	—
48	C₂×C₃₂	#595	1	1	yes	characteristic
49	C₆₄	—	17	4	no	—
50	C₂×C₁₇	C₂×C₆₄	1	2	yes	complemented
51	C₂×C₁₇	C₂²×C₃₂	1	1	yes	characteristic
52	D₁₇	C₂×C₆₄	1	4	yes	complemented
53	C₂²×C₈	—	17	1	no	—
54	C₂×C₁₆	—	17	1	no	—
55	C₂×C₁₆	—	17	2	no	—
56	C₂×C₁₆	—	17	2	no	—
57	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
58	C₃₂	—	17	1	no	—
59	C₃₂	—	17	1	no	—
60	C₃₂	C₂×#595	1	2	yes	—
61	C₁₇	C₂²×C₆₄	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₄	—	17	1	no	—
63	C₂×C₈	—	17	1	no	—
64	C₂×C₈	—	17	2	no	—
65	C₂×C₈	—	17	2	no	—
66	C₂×C₈	#63242	1	1	yes	characteristic
67	C₁₆	—	17	2	no	—
68	C₁₆	#63242	1	1	yes	characteristic
69	C₁₆	C₂²×#595	1	1	yes	characteristic
70	C₂³	—	17	1	no	—
71	C₂×C₄	—	17	1	no	—
72	C₂×C₄	—	17	2	no	—
73	C₂×C₄	—	17	2	no	—
74	C₂×C₄	#10587529	1	1	yes	characteristic
75	C₈	—	17	2	no	—
76	C₈	#10587529	1	1	yes	characteristic
77	C₈	C₂×#63242	1	1	yes	characteristic
78	C₂²	—	17	2	no	—
79	C₂²	—	17	4	no	—
80	C₂²	#11763740	1	1	yes	characteristic
81	C₄	—	17	2	no	—
82	C₄	#11763740	1	1	yes	characteristic
83	C₄	C₂×#10587529	1	1	yes	characteristic
84	C₂	—	17	4	no	—
85	C₂	#14543952	1	2	yes	direct product factor
86	C₂	C₂×#11763740	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃₂	#595
commutator, hypocenter	C₁₇	C₂²×C₆₄
Frattini	C₁₆	C₂²×#595
Fitting	C₂×C₁₇×C₃₂	C₄
socle	C₂²×C₁₇	C₂×C₃₂
prime radical	C₂²×D₁₇	C₃₂
cosocle	#10587465	C₂³
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. #14543952	C₂	direct (N × H)
2. C₂×#11763648	C₂	semidirect
4. #11763648	C₂²	semidirect
39. C₂×D₁₇	C₆₄	semidirect
50. C₂×C₁₇	C₂×C₆₄	semidirect
52. D₁₇	C₂×C₆₄	semidirect
61. C₁₇	C₂²×C₆₄	semidirect
85. C₂	#14543952	direct (N × H)

Maximal subgroups

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

subgroup	index
#14543952	2
C₂×#11763648	2
C₂×C₃₂×D₁₇	2
C₂²×C₆₄	17

Subgroups — C2×#14543952 #17962901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14543952 #17962901