Subgroups — #16840055

Order 3904.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14519776	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₆₁	C₂	1	1	yes	maximal, characteristic
3	#14519711	C₂	1	1	yes	maximal, characteristic
4	#14519710	C₂	1	1	yes	maximal, characteristic
5	#14519706	C₂	1	1	yes	maximal, characteristic
6	#14519701	C₂	1	1	yes	maximal, characteristic
7	#103×C₆₁	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₆₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₂₂	—	2	1	no	—
10	C₂×C₈×C₆₁	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₆₁	—	2	1	no	—
13	C₄⋊Dic₆₁	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₆₁	C₂²	1	1	yes	characteristic
15	#11758196	—	2	1	no	—
16	C₄×Dic₆₁	—	2	1	no	—
17	C₄×Dic₆₁	C₂²	1	1	yes	characteristic
18	C₂×#92418	C₂²	1	1	yes	characteristic
19	Q₈×C₆₁	—	2	1	no	—
20	Q₈×C₆₁	Q₈	1	2	yes	complemented
21	C₂×C₄×C₆₁	—	2	1	no	—
22	C₂×C₄×C₆₁	—	2	1	no	—
23	C₂×C₄×C₆₁	C₂³	1	1	yes	characteristic
24	C₂×Dic₆₁	—	2	1	no	—
25	C₂×Dic₆₁	—	2	1	no	—
26	C₂×Dic₆₁	D₄	1	1	yes	characteristic
27	C₂×Dic₆₁	D₄	1	1	yes	characteristic
28	Dic₁₂₂	—	4	2	no	—
29	C₈×C₆₁	—	2	1	no	—
30	#92418	—	2	1	no	—
31	C₂²×C₆₁	C₂×D₄	1	1	yes	characteristic
32	C₄×C₆₁	—	2	2	no	—
33	C₄×C₆₁	—	4	1	no	—
34	C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
35	C₄×C₆₁	#41	1	1	yes	characteristic
36	Dic₆₁	—	2	1	no	—
37	Dic₆₁	—	4	1	no	—
38	Dic₆₁	—	4	1	no	—
39	Dic₆₁	Q₁₆	1	2	yes	—
40	C₂×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
41	C₂×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
42	C₂×C₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
43	#477	—	61	1	no	maximal, Sylow
44	C₆₁	#477	1	1	yes	characteristic, complemented, Sylow
45	C₄⋊Q₈	—	61	1	no	—
46	C₄×Q₈	—	61	1	no	—
47	#107	—	61	1	no	—
48	#107	—	61	1	no	—
49	C₄⋊C₈	—	61	1	no	—
50	#103	—	61	1	no	—
51	#103	D₆₁	1	1	yes	characteristic
52	C₂×Q₈	—	122	1	no	—
53	C₂×Q₈	C₂×D₆₁	1	1	yes	characteristic
54	C₂×C₈	—	61	1	no	—
55	C₂×C₈	C₂×D₆₁	1	1	yes	characteristic
56	C₄⋊C₄	—	61	1	no	—
57	C₄⋊C₄	—	61	1	no	—
58	C₄⋊C₄	—	122	1	no	—
59	C₄⋊C₄	—	122	1	no	—
60	C₄⋊C₄	C₂×D₆₁	1	1	yes	characteristic
61	C₄²	—	61	1	no	—
62	C₄²	—	122	1	no	—
63	Q₈	—	2	1	no	—
64	Q₈	—	244	2	no	—
65	Q₈	Dic₁₂₂	1	2	yes	complemented
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	61	1	no	—
69	C₂×C₄	—	61	1	no	—
70	C₂×C₄	—	122	1	no	—
71	C₂×C₄	—	122	1	no	—
72	C₂×C₄	C₂²×D₆₁	1	1	yes	characteristic
73	C₈	—	2	1	no	—
74	C₈	—	122	1	no	—
75	C₂²	D₄×D₆₁	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	4	1	no	—
78	C₄	—	61	2	no	—
79	C₄	—	122	1	no	—
80	C₄	—	244	1	no	—
81	C₄	—	244	1	no	—
82	C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
83	C₄	#11758224	1	1	yes	characteristic
84	C₂	#14519754	1	1	yes	characteristic
85	C₂	Q₁₆×D₆₁	1	1	yes	characteristic
86	C₂	#14519804	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₆₁
commutator, cosocle	C₂×C₄×C₆₁	C₂³
Frattini	C₂×C₄	C₂²×D₆₁
Fitting	#103×C₆₁	C₂
socle, prime radical	C₂²×C₆₁	C₂×D₄
hypercenter	#103	D₆₁
hypocenter	C₆₁	#477
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
20. Q₈×C₆₁	Q₈	semidirect
44. C₆₁	#477	semidirect
65. Q₈	Dic₁₂₂	semidirect

Maximal subgroups

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

subgroup	index
#14519776	2
Q₈×Dic₆₁	2
#14519711	2
#14519710	2
#14519706	2
#14519701	2
#103×C₆₁	2
#477	61