Subgroups — C₂×#21444030 #29601050

Order 15616.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21444030	C₂	1	4	yes	maximal, direct product factor
2	C₂×#16839481	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃₂×C₆₁	C₂	1	1	yes	maximal, characteristic
4	#16839481	C₂²	1	4	yes	complemented
5	C₂²×C₁₆×C₆₁	C₄	1	1	yes	characteristic
6	C₂×C₃₂×C₆₁	C₄	1	1	yes	characteristic
7	C₂×C₃₂×C₆₁	C₄	1	2	yes	—
8	C₂×C₃₂×C₆₁	C₂²	1	2	yes	—
9	C₂×C₃₂×C₆₁	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₆₁	C₈	1	1	yes	characteristic
11	C₂×C₁₆×C₆₁	C₈	1	1	yes	characteristic
12	C₂×C₁₆×C₆₁	C₈	1	2	yes	—
13	C₂×C₁₆×C₆₁	C₂×C₄	1	2	yes	—
14	C₂×C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
15	C₃₂×C₆₁	C₂×C₄	1	2	yes	—
16	C₃₂×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₃₂×C₆₁	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₆₁	C₁₆	1	1	yes	characteristic
19	C₂×C₈×C₆₁	C₁₆	1	2	yes	—
20	C₂×C₈×C₆₁	C₁₆	1	1	yes	characteristic
21	C₂×C₈×C₆₁	C₂×C₈	1	2	yes	—
22	C₂×C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
23	C₁₆×C₆₁	C₂×C₈	1	2	yes	—
24	C₁₆×C₆₁	C₂×C₈	1	1	yes	characteristic
25	C₁₆×C₆₁	C₂²×C₄	1	1	yes	characteristic
26	C₂³×C₆₁	C₃₂	1	1	yes	characteristic
27	C₂×C₄×C₆₁	C₃₂	1	2	yes	—
28	C₂×C₄×C₆₁	C₃₂	1	1	yes	characteristic
29	C₂×C₄×C₆₁	C₂×C₁₆	1	2	yes	—
30	C₂×C₄×C₆₁	C₂×C₁₆	1	1	yes	characteristic
31	C₈×C₆₁	C₂×C₁₆	1	2	yes	—
32	C₈×C₆₁	C₂×C₁₆	1	1	yes	characteristic
33	C₈×C₆₁	C₂²×C₈	1	1	yes	characteristic
34	C₂×M₁₂₈	—	61	1	no	maximal, Sylow
35	C₂²×C₆₁	—	2	2	no	—
36	C₂²×C₆₁	C₂×C₃₂	1	2	yes	—
37	C₂²×C₆₁	C₂×C₃₂	1	1	yes	characteristic
38	C₄×C₆₁	C₂×C₃₂	1	1	yes	characteristic
39	C₄×C₆₁	C₂×C₃₂	1	2	yes	—
40	C₄×C₆₁	C₂²×C₁₆	1	1	yes	characteristic
41	C₂²×C₃₂	D₆₁	1	1	yes	characteristic
42	M₁₂₈	—	61	4	no	—
43	C₂×C₆₄	—	61	2	no	—
44	C₂×C₆₁	—	2	2	no	—
45	C₂×C₆₁	M₁₂₈	1	2	yes	complemented
46	C₂×C₆₁	C₂²×C₃₂	1	1	yes	characteristic
47	C₂²×C₁₆	Dic₆₁	1	1	yes	characteristic
48	C₂×C₃₂	Dic₆₁	1	1	yes	characteristic
49	C₂×C₃₂	Dic₆₁	1	2	yes	—
50	C₂×C₃₂	C₂×D₆₁	1	2	yes	—
51	C₂×C₃₂	C₂×D₆₁	1	1	yes	characteristic
52	C₆₄	—	61	4	no	—
53	C₆₁	C₂×M₁₂₈	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₈	#92418	1	1	yes	characteristic
55	C₂×C₁₆	#92418	1	1	yes	characteristic
56	C₂×C₁₆	#92418	1	2	yes	—
57	C₂×C₁₆	C₂×Dic₆₁	1	2	yes	—
58	C₂×C₁₆	C₂×Dic₆₁	1	1	yes	characteristic
59	C₃₂	C₂×Dic₆₁	1	2	yes	—
60	C₃₂	C₂×Dic₆₁	1	1	yes	characteristic
61	C₃₂	C₂²×D₆₁	1	1	yes	characteristic
62	C₂²×C₄	#11758185	1	1	yes	characteristic
63	C₂×C₈	#11758185	1	2	yes	—
64	C₂×C₈	#11758185	1	1	yes	characteristic
65	C₂×C₈	C₂×#92418	1	2	yes	—
66	C₂×C₈	C₂×#92418	1	1	yes	characteristic
67	C₁₆	C₂×#92418	1	2	yes	—
68	C₁₆	C₂×#92418	1	1	yes	characteristic
69	C₁₆	C₂²×Dic₆₁	1	1	yes	characteristic
70	C₂³	#14519683	1	1	yes	characteristic
71	C₂×C₄	#14519683	1	2	yes	—
72	C₂×C₄	#14519683	1	1	yes	characteristic
73	C₂×C₄	C₂×#11758185	1	2	yes	—
74	C₂×C₄	C₂×#11758185	1	1	yes	characteristic
75	C₈	C₂×#11758185	1	2	yes	—
76	C₈	C₂×#11758185	1	1	yes	characteristic
77	C₈	C₂²×#92418	1	1	yes	characteristic
78	C₂²	—	2	2	no	—
79	C₂²	C₂×#14519683	1	2	yes	—
80	C₂²	C₂×#14519683	1	1	yes	characteristic
81	C₄	C₂×#14519683	1	1	yes	characteristic
82	C₄	C₂×#14519683	1	2	yes	—
83	C₄	C₂²×#11758185	1	1	yes	characteristic
84	C₂	—	2	2	no	—
85	C₂	#21444030	1	2	yes	direct product factor
86	C₂	C₂²×#14519683	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃₂	C₂×D₆₁
commutator	C₂×C₆₁	C₂²×C₃₂
Frattini	C₃₂	C₂²×D₆₁
Fitting	C₂²×C₃₂×C₆₁	C₂
socle	C₂²×C₆₁	C₂×C₃₂
prime radical	C₂³×C₆₁	C₃₂
cosocle	C₃₂×C₆₁	C₂³
hypercenter	C₂²×C₃₂	D₆₁
hypocenter	C₆₁	C₂×M₁₂₈
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₃₂ ◁ C₂²×C₃₂

Complements

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

N	H ≅ G/N	type
1. #21444030	C₂	direct (N × H)
2. C₂×#16839481	C₂	semidirect
4. #16839481	C₂²	semidirect
45. C₂×C₆₁	M₁₂₈	semidirect
53. C₆₁	C₂×M₁₂₈	semidirect
85. C₂	#21444030	direct (N × H)

Maximal subgroups

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

subgroup	index
#21444030	2
C₂×#16839481	2
C₂²×C₃₂×C₆₁	2
C₂×M₁₂₈	61

Subgroups — C2×#21444030 #29601050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#21444030 #29601050