Subgroups — C₂×#14543953 #17962902

Order 4352.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543953	C₂	1	4	yes	maximal, direct product factor
2	C₂×#11763648	C₂	1	2	yes	maximal, complemented
3	C₂²×#10587465	C₂	1	1	yes	maximal, characteristic
4	#11763648	C₂²	1	4	yes	complemented
5	C₂×#10587465	C₄	1	2	yes	—
6	C₂×#10587465	C₄	1	1	yes	characteristic
7	C₂×#10587465	C₂²	1	1	yes	characteristic
8	C₂×#10587465	C₂²	1	2	yes	—
9	C₂²×C₁₆×C₁₇	C₄	1	1	yes	characteristic
10	C₂²×C₈×C₁₇	C₈	1	1	yes	characteristic
11	C₂×C₁₆×C₁₇	C₈	1	2	yes	—
12	C₂×C₁₆×C₁₇	C₈	1	1	yes	characteristic
13	C₂×C₁₆×C₁₇	C₂×C₄	1	2	yes	—
14	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
15	#10587465	C₂×C₄	1	1	yes	characteristic
16	#10587465	C₂×C₄	1	2	yes	—
17	#10587465	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₁₇	C₁₆	1	1	yes	characteristic
19	C₂×C₈×C₁₇	C₁₆	1	2	yes	—
20	C₂×C₈×C₁₇	C₁₆	1	1	yes	characteristic
21	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
22	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
23	C₁₆×C₁₇	C₂×C₈	1	2	yes	—
24	C₁₆×C₁₇	C₂×C₈	1	1	yes	characteristic
25	C₁₆×C₁₇	C₂²×C₄	1	1	yes	characteristic
26	C₂×M₁₂₈	—	17	1	no	maximal, Sylow
27	C₂³×C₁₇	C₃₂	1	1	yes	characteristic
28	C₂×C₄×C₁₇	C₃₂	1	2	yes	—
29	C₂×C₄×C₁₇	C₃₂	1	1	yes	characteristic
30	C₂×C₄×C₁₇	C₂×C₁₆	1	2	yes	—
31	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
32	C₈×C₁₇	C₂×C₁₆	1	2	yes	—
33	C₈×C₁₇	C₂×C₁₆	1	1	yes	characteristic
34	C₈×C₁₇	C₂²×C₈	1	1	yes	characteristic
35	C₂²×C₃₂	—	17	1	no	—
36	M₁₂₈	—	17	4	no	—
37	C₂×C₆₄	—	17	2	no	—
38	C₂²×C₁₇	—	2	2	no	—
39	C₂²×C₁₇	C₂×C₃₂	1	2	yes	—
40	C₂²×C₁₇	C₂×C₃₂	1	1	yes	characteristic
41	C₄×C₁₇	C₂×C₃₂	1	1	yes	characteristic
42	C₄×C₁₇	C₂×C₃₂	1	2	yes	—
43	C₄×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
44	C₂²×C₁₆	#595	1	1	yes	characteristic
45	C₂×C₃₂	—	17	2	no	—
46	C₂×C₃₂	—	17	2	no	—
47	C₂×C₃₂	—	17	1	no	—
48	C₂×C₃₂	—	17	1	no	—
49	C₆₄	—	17	4	no	—
50	C₂×C₁₇	—	2	2	no	—
51	C₂×C₁₇	M₁₂₈	1	2	yes	complemented
52	C₂×C₁₇	C₂²×C₃₂	1	1	yes	characteristic
53	C₂²×C₈	#3624	1	1	yes	characteristic
54	C₂×C₁₆	#3624	1	1	yes	characteristic
55	C₂×C₁₆	#3624	1	2	yes	—
56	C₂×C₁₆	C₂×#595	1	2	yes	—
57	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
58	C₃₂	—	17	1	no	—
59	C₃₂	—	17	2	no	—
60	C₃₂	—	17	1	no	—
61	C₁₇	C₂×M₁₂₈	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₄	#63216	1	1	yes	characteristic
63	C₂×C₈	#63216	1	1	yes	characteristic
64	C₂×C₈	#63216	1	2	yes	—
65	C₂×C₈	C₂×#3624	1	2	yes	—
66	C₂×C₈	C₂×#3624	1	1	yes	characteristic
67	C₁₆	C₂×#3624	1	2	yes	—
68	C₁₆	C₂×#3624	1	1	yes	characteristic
69	C₁₆	C₂²×#595	1	1	yes	characteristic
70	C₂³	#10587467	1	1	yes	characteristic
71	C₂×C₄	#10587467	1	2	yes	—
72	C₂×C₄	#10587467	1	1	yes	characteristic
73	C₂×C₄	C₂×#63216	1	2	yes	—
74	C₂×C₄	C₂×#63216	1	1	yes	characteristic
75	C₈	C₂×#63216	1	2	yes	—
76	C₈	C₂×#63216	1	1	yes	characteristic
77	C₈	C₂²×#3624	1	1	yes	characteristic
78	C₂²	—	2	2	no	—
79	C₂²	C₂×#10587467	1	2	yes	—
80	C₂²	C₂×#10587467	1	1	yes	characteristic
81	C₄	C₂×#10587467	1	1	yes	characteristic
82	C₄	C₂×#10587467	1	2	yes	—
83	C₄	C₂²×#63216	1	1	yes	characteristic
84	C₂	—	2	2	no	—
85	C₂	#14543953	1	2	yes	direct product factor
86	C₂	C₂²×#10587467	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂×#595
commutator	C₂×C₁₇	C₂²×C₃₂
Frattini	C₁₆	C₂²×#595
Fitting	C₂²×C₁₆×C₁₇	C₄
socle	C₂²×C₁₇	C₂×C₃₂
prime radical	C₂³×C₁₇	C₃₂
cosocle	#10587465	C₂³
hypercenter	C₂²×C₁₆	#595
hypocenter	C₁₇	C₂×M₁₂₈
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
1. #14543953	C₂	direct (N × H)
2. C₂×#11763648	C₂	semidirect
4. #11763648	C₂²	semidirect
51. C₂×C₁₇	M₁₂₈	semidirect
61. C₁₇	C₂×M₁₂₈	semidirect
85. C₂	#14543953	direct (N × H)

Maximal subgroups

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

subgroup	index
#14543953	2
C₂×#11763648	2
C₂²×#10587465	2
C₂×M₁₂₈	17

Subgroups — C2×#14543953 #17962902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14543953 #17962902