Subgroups — #16840029

Order 3904.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14519803	C₂	1	2	yes	maximal, complemented
2	#14519783	C₂	1	1	yes	maximal, characteristic, complemented
3	#14519713	C₂	1	1	yes	maximal, characteristic, complemented
4	#14519694	C₂	1	2	yes	maximal, complemented
5	C₂×D₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×C₆₁	C₂²	1	2	yes	—
7	#11758222	C₂²	1	1	yes	characteristic
8	D₈×C₆₁	—	2	1	no	—
9	D₈×C₆₁	—	2	1	no	—
10	C₂×C₈×C₆₁	C₂²	1	1	yes	characteristic
11	#11758200	—	2	2	no	—
12	#11758199	—	2	2	no	—
13	#11758194	C₂²	1	1	yes	characteristic
14	#11758194	C₂²	1	2	yes	—
15	#11758189	—	2	1	no	—
16	C₈×D₆₁	—	2	1	no	—
17	C₂³×C₆₁	—	2	2	no	—
18	D₄×C₆₁	—	2	2	no	—
19	D₄×C₆₁	—	2	2	no	—
20	C₂×C₄×C₆₁	C₂³	1	1	yes	characteristic
21	C₂²⋊D₆₁	—	2	1	no	—
22	D₂₄₄	D₄	1	1	yes	characteristic
23	C₄×D₆₁	—	2	1	no	—
24	Dic₁₂₂	D₄	1	1	yes	characteristic
25	C₈×C₆₁	D₄	1	1	yes	characteristic
26	C₈×C₆₁	D₄	1	1	yes	characteristic
27	#92418	—	2	1	no	—
28	#92418	—	2	2	no	—
29	C₂²×C₆₁	—	4	2	no	—
30	C₂²×C₆₁	—	8	2	no	—
31	C₂²×C₆₁	#41	1	1	yes	characteristic
32	C₂×D₆₁	—	2	1	no	—
33	C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
34	C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
35	Dic₆₁	—	2	1	no	—
36	C₂×C₆₁	—	2	1	no	—
37	C₂×C₆₁	—	8	2	no	—
38	C₂×C₆₁	#121	1	1	yes	characteristic
39	D₆₁	—	4	1	no	—
40	#472	—	61	1	no	maximal, Sylow
41	C₆₁	#472	1	1	yes	characteristic, complemented, Sylow
42	AGL(1,ℤ/8)	—	61	2	no	—
43	C₂×D₈	D₆₁	1	1	yes	characteristic, complemented
44	#131	—	61	1	no	—
45	#108	—	61	1	no	—
46	#100	—	61	2	no	—
47	#41	—	61	1	no	—
48	C₂×D₄	C₂×D₆₁	1	2	yes	—
49	SD₁₆	—	122	2	no	—
50	D₈	—	2	1	no	—
51	D₈	—	2	1	no	—
52	D₈	—	122	2	no	—
53	M₁₆	—	61	1	no	—
54	M₁₆	—	61	2	no	—
55	M₁₆	—	122	1	no	—
56	C₂×C₈	—	122	1	no	—
57	C₂×C₈	C₂×D₆₁	1	1	yes	characteristic
58	C₂³	—	2	2	no	—
59	Q₈	—	61	1	no	—
60	D₄	—	2	2	no	—
61	D₄	—	2	2	no	—
62	D₄	—	61	1	no	—
63	D₄	—	122	1	no	—
64	C₂×C₄	—	122	1	no	—
65	C₂×C₄	C₂²×D₆₁	1	1	yes	characteristic
66	C₈	—	122	2	no	—
67	C₈	—	122	1	no	—
68	C₈	C₂²⋊D₆₁	1	1	yes	characteristic
69	C₈	C₂²⋊D₆₁	1	1	yes	characteristic
70	C₂²	—	4	2	no	—
71	C₂²	—	8	2	no	—
72	C₂²	—	122	1	no	—
73	C₂²	#11758224	1	1	yes	characteristic
74	C₄	—	122	1	no	—
75	C₄	D₄×D₆₁	1	1	yes	characteristic
76	C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
77	C₂	—	2	1	no	—
78	C₂	—	8	2	no	—
79	C₂	—	244	1	no	—
80	C₂	#14519748	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14519748
commutator, cosocle	C₂×C₄×C₆₁	C₂³
Frattini	C₂×C₄	C₂²×D₆₁
Fitting	C₂×D₈×C₆₁	C₂
socle	C₂×C₆₁	#121
hypercenter	C₂×D₈	D₆₁
hypocenter	C₆₁	#472
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. #14519803	C₂	semidirect
2. #14519783	C₂	semidirect
3. #14519713	C₂	semidirect
4. #14519694	C₂	semidirect
5. C₂×D₈×C₆₁	C₂	semidirect
41. C₆₁	#472	semidirect
43. C₂×D₈	D₆₁	semidirect

Maximal subgroups

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

subgroup	index
#14519803	2
#14519783	2
#14519713	2
#14519694	2
C₂×D₈×C₆₁	2
#472	61