Subgroups — #30595242

Order 15616.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21460988	C₂	1	2	yes	maximal, complemented
2	C₂×#16839595	C₂	1	1	yes	maximal, characteristic
3	#16840601	—	2	2	no	—
4	C₂×C₁₆×D₆₁	C₄	1	1	yes	characteristic
5	#16839595	—	2	2	no	—
6	C₂×#14519683	C₂²	1	1	yes	characteristic
7	C₂×C₃₂×C₆₁	C₄	1	1	yes	characteristic
8	C₂×C₈×D₆₁	C₈	1	1	yes	characteristic
9	C₂×#11758185	C₈	1	1	yes	characteristic
10	C₁₆×D₆₁	—	2	1	no	—
11	C₁₆×D₆₁	—	2	1	no	—
12	#14519683	D₄	1	2	yes	—
13	C₂×C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
14	C₃₂×C₆₁	—	2	1	no	—
15	C₂×C₄×D₆₁	C₁₆	1	1	yes	characteristic
16	C₂×C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
17	C₂×#92418	C₁₆	1	1	yes	characteristic
18	C₈×D₆₁	—	2	1	no	—
19	C₈×D₆₁	—	2	1	no	—
20	C₁₆×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₁₆×C₆₁	M₁₆	1	1	yes	characteristic
22	#11758185	—	2	1	no	—
23	C₂²×D₆₁	C₃₂	1	1	yes	characteristic
24	C₂×C₄×C₆₁	C₂×C₁₆	1	1	yes	characteristic
25	C₂×Dic₆₁	C₃₂	1	1	yes	characteristic
26	C₄×D₆₁	—	2	1	no	—
27	C₄×D₆₁	—	2	1	no	—
28	C₈×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
29	C₈×C₆₁	M₃₂	1	1	yes	characteristic
30	#92418	—	2	1	no	—
31	#7513	—	61	1	no	maximal, Sylow
32	C₂²×C₆₁	C₂×C₃₂	1	1	yes	characteristic
33	C₂×D₆₁	—	2	1	no	—
34	C₂×D₆₁	—	4	1	no	—
35	C₄×C₆₁	C₂²⋊C₁₆	1	1	yes	characteristic
36	C₄×C₆₁	M₆₄	1	1	yes	characteristic
37	Dic₆₁	—	2	1	no	—
38	C₂×M₆₄	—	61	1	no	—
39	M₁₂₈	—	61	2	no	—
40	C₂×C₆₁	—	2	1	no	—
41	C₂×C₆₁	C₂²⋊C₃₂	1	1	yes	characteristic
42	D₆₁	—	4	1	no	—
43	C₂²×C₁₆	—	61	1	no	—
44	M₆₄	—	122	2	no	—
45	C₂×C₃₂	—	61	1	no	—
46	C₂×C₃₂	#6923	1	1	yes	characteristic
47	C₆₄	—	122	2	no	—
48	C₆₁	#7513	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₈	—	61	1	no	—
50	C₂×C₁₆	—	61	1	no	—
51	C₂×C₁₆	—	122	1	no	—
52	C₂×C₁₆	—	122	1	no	—
53	C₂×C₁₆	C₂×#6923	1	1	yes	characteristic
54	C₃₂	—	2	1	no	—
55	C₃₂	—	61	2	no	—
56	C₂²×C₄	—	61	1	no	—
57	C₂×C₈	—	61	1	no	—
58	C₂×C₈	—	122	1	no	—
59	C₂×C₈	—	122	1	no	—
60	C₂×C₈	D₆₁⋊C₈	1	1	yes	characteristic
61	C₁₆	—	122	1	no	—
62	C₁₆	#11758213	1	1	yes	characteristic
63	C₁₆	C₂²⋊#6923	1	1	yes	characteristic
64	C₂³	—	61	1	no	—
65	C₂×C₄	—	61	1	no	—
66	C₂×C₄	—	122	1	no	—
67	C₂×C₄	—	122	1	no	—
68	C₂×C₄	D₆₁⋊C₁₆	1	1	yes	characteristic
69	C₈	—	122	1	no	—
70	C₈	#14519834	1	1	yes	characteristic
71	C₈	#14519852	1	1	yes	characteristic
72	C₂²	—	122	1	no	—
73	C₂²	—	244	1	no	—
74	C₂²	D₆₁⋊C₃₂	1	1	yes	characteristic
75	C₄	—	122	1	no	—
76	C₄	#16840657	1	1	yes	characteristic
77	C₄	#16840695	1	1	yes	characteristic
78	C₂	—	2	1	no	—
79	C₂	—	244	1	no	—
80	C₂	#21460933	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂²⋊#6923
commutator	C₂²×C₆₁	C₂×C₃₂
Frattini	C₂×C₁₆	C₂×#6923
Fitting	C₂×C₃₂×C₆₁	C₄
socle	C₂×C₆₁	C₂²⋊C₃₂
prime radical	C₂²×D₆₁	C₃₂
cosocle	C₂×#14519683	C₂²
hypercenter	C₂×C₃₂	#6923
hypocenter	C₆₁	#7513
LCS	G ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. #21460988	C₂	semidirect
48. C₆₁	#7513	semidirect

Maximal subgroups

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

subgroup	index
#21460988	2
C₂×#16839595	2
#7513	61