Subgroups — #30595057

Order 15616.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14519827	C₂	1	2	yes	maximal
2	C₁₆×#92418	C₂	1	1	yes	maximal, characteristic
3	C₂×#14519827	—	2	2	no	—
4	C₄×#11758185	C₂²	1	1	yes	characteristic
5	C₈×#92418	C₄	1	1	yes	characteristic
6	C₄×C₁₆×C₆₁	C₄	1	1	yes	characteristic
7	#14519827	—	4	2	no	—
8	C₂×#11758185	D₄	1	1	yes	characteristic
9	C₂×#11758185	Q₈	1	1	yes	characteristic
10	C₄×#92418	C₈	1	1	yes	characteristic
11	C₄×#92418	C₈	1	1	yes	characteristic
12	C₂×C₁₆×C₆₁	—	2	1	no	—
13	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₈×C₆₁	M₁₆	1	1	yes	characteristic
16	C₄²×C₆₁	C₂×C₈	1	1	yes	characteristic
17	C₂×#92418	—	2	1	no	—
18	C₂×#92418	C₁₆	1	1	yes	characteristic
19	C₂×#92418	C₁₆	1	1	yes	characteristic
20	C₁₆×C₆₁	—	2	2	no	—
21	#11758185	—	2	1	no	—
22	#11758185	SD₁₆	1	2	yes	—
23	C₂×C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
24	C₂×C₄×C₆₁	C₂×C₁₆	1	1	yes	characteristic
25	C₂×C₄×C₆₁	M₃₂	1	1	yes	characteristic
26	C₈×C₆₁	—	2	1	no	—
27	C₈×C₆₁	#106	1	1	yes	characteristic
28	C₈×C₆₁	#108	1	1	yes	characteristic
29	#92418	—	2	2	no	—
30	#92418	—	2	1	no	—
31	#92418	C₃₂	1	2	yes	complemented
32	#7455	—	61	1	no	maximal, Sylow
33	C₂²×C₆₁	C₄⋊C₁₆	1	1	yes	characteristic
34	C₄×C₆₁	—	2	1	no	—
35	C₄×C₆₁	#334	1	1	yes	characteristic
36	C₄×C₆₁	#364	1	1	yes	characteristic
37	C₄×C₆₁	C₂×C₃₂	1	1	yes	characteristic
38	C₄×C₆₁	M₆₄	1	1	yes	characteristic
39	C₄⋊C₃₂	—	61	2	no	—
40	C₈×C₁₆	—	61	1	no	—
41	C₂×C₆₁	#1367	1	1	yes	characteristic
42	C₂×C₆₁	C₄⋊C₃₂	1	1	yes	characteristic
43	C₂×C₆₁	#1422	1	1	yes	characteristic
44	C₂×C₃₂	—	122	2	no	—
45	C₄×C₁₆	—	61	1	no	—
46	C₄×C₁₆	#6923	1	1	yes	characteristic
47	C₈²	—	61	1	no	—
48	C₆₁	#7455	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₁₆	—	2	1	no	—
50	C₂×C₁₆	—	61	1	no	—
51	C₂×C₁₆	—	61	1	no	—
52	C₄×C₈	—	61	1	no	—
53	C₄×C₈	—	61	1	no	—
54	C₄×C₈	C₂×#6923	1	1	yes	characteristic
55	C₃₂	—	244	2	no	—
56	C₂×C₈	—	61	1	no	—
57	C₂×C₈	—	61	1	no	—
58	C₂×C₈	—	122	1	no	—
59	C₂×C₈	C₄⋊#6923	1	1	yes	characteristic
60	C₂×C₈	#11758217	1	1	yes	characteristic
61	C₄²	D₆₁⋊C₈	1	1	yes	characteristic
62	C₁₆	—	2	2	no	—
63	C₁₆	—	61	2	no	—
64	C₁₆	—	122	1	no	—
65	C₂×C₄	#14519844	1	1	yes	characteristic
66	C₂×C₄	D₆₁⋊C₁₆	1	1	yes	characteristic
67	C₂×C₄	#14519852	1	1	yes	characteristic
68	C₈	—	2	1	no	—
69	C₈	—	61	2	no	—
70	C₈	—	122	2	no	—
71	C₈	—	122	1	no	—
72	C₈	#14519845	1	1	yes	characteristic
73	C₈	#14519848	1	1	yes	characteristic
74	C₂²	#16840683	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	#16840624	1	1	yes	characteristic
77	C₄	#16840685	1	1	yes	characteristic
78	C₄	D₆₁⋊C₃₂	1	1	yes	characteristic
79	C₄	#16840695	1	1	yes	characteristic
80	C₂	#21460842	1	1	yes	characteristic
81	C₂	#21460977	1	1	yes	characteristic
82	C₂	#21460979	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₄⋊#6923
commutator	C₄×C₆₁	C₂×C₃₂
Frattini	C₄×C₈	C₂×#6923
Fitting	C₄×C₁₆×C₆₁	C₄
socle, prime radical	C₂²×C₆₁	C₄⋊C₁₆
cosocle	C₄×#11758185	C₂²
hypercenter	C₄×C₁₆	#6923
hypocenter	C₆₁	#7455
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
31. #92418	C₃₂	semidirect
48. C₆₁	#7455	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#14519827	2
C₁₆×#92418	2
#7455	61