Subgroups — #21461741

Order 7808.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840706	C₂	1	2	yes	maximal
2	#16840636	C₂	1	4	yes	maximal
3	C₄×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊#6923	C₂²	1	4	yes	—
5	(C₂×#6923)⋊C₄	—	2	4	no	—
6	C₂×C₈×D₆₁	C₂²	1	2	yes	—
7	C₄²×D₆₁	C₂²	1	1	yes	characteristic
8	C₄×#92418	C₄	1	1	yes	characteristic, complemented
9	C₈×Dic₆₁	C₄	1	2	yes	complemented
10	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic, complemented
11	C₂²×#6923	—	2	4	no	—
12	C₂×C₄×D₆₁	D₄	1	2	yes	—
13	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
14	C₄⋊#6923	—	2	8	no	—
15	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
16	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₆₁	Q₈	1	2	yes	—
19	C₂×#92418	C₂×C₄	1	2	yes	—
20	C₈×D₆₁	—	2	4	no	—
21	C₂²×D₆₁	C₂×D₄	1	1	yes	characteristic
22	C₂×#6923	—	4	4	no	—
23	C₂×#6923	—	4	8	no	—
24	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
26	C₂×Dic₆₁	C₄⋊C₄	1	2	yes	—
27	C₂×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
28	C₄×D₆₁	—	2	4	no	—
29	C₄×D₆₁	#41	1	4	yes	—
30	C₈×C₆₁	—	2	2	no	—
31	#92418	—	2	2	no	—
32	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
33	C₂×D₆₁	#124	1	2	yes	—
34	C₂×D₆₁	#135	1	4	yes	—
35	#6923	—	8	4	no	—
36	C₄×C₆₁	—	2	2	no	—
37	C₄×C₆₁	#117	1	2	yes	—
38	Dic₆₁	—	2	2	no	—
39	Dic₆₁	#125	1	2	yes	—
40	#1835	—	61	1	no	maximal, Sylow
41	C₂×C₆₁	#382	1	1	yes	characteristic
42	C₂×C₆₁	#427	1	2	yes	—
43	D₆₁	#488	1	4	yes	—
44	C₂×C₄×C₈	—	61	1	no	—
45	#382	—	61	2	no	—
46	#340	—	61	4	no	—
47	C₆₁	#1835	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₈	—	61	2	no	—
49	C₂×C₄⋊C₄	—	61	4	no	—
50	C₂×C₄²	—	61	1	no	—
51	C₄×C₈	—	61	2	no	—
52	C₄×C₈	—	61	1	no	—
53	C₄×C₈	#6923	1	1	yes	characteristic, complemented
54	#95	—	122	4	no	—
55	C₂²×C₄	—	61	1	no	—
56	C₂²×C₄	—	61	2	no	—
57	C₂²×C₄	—	122	4	no	—
58	C₂×C₈	—	61	2	no	—
59	C₂×C₈	—	122	4	no	—
60	C₂×C₈	C₂×#6923	1	2	yes	—
61	C₄⋊C₄	—	122	8	no	—
62	C₄²	—	61	2	no	—
63	C₄²	—	61	1	no	—
64	C₄²	C₂×#6923	1	1	yes	characteristic
65	C₂³	—	61	1	no	—
66	C₂×C₄	—	61	1	no	—
67	C₂×C₄	—	61	4	no	—
68	C₂×C₄	—	61	2	no	—
69	C₂×C₄	—	122	4	no	—
70	C₂×C₄	—	244	4	no	—
71	C₂×C₄	—	244	8	no	—
72	C₂×C₄	C₄⋊#6923	1	2	yes	—
73	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
74	C₈	—	2	2	no	—
75	C₈	—	122	2	no	—
76	C₂²	—	61	2	no	—
77	C₂²	—	61	4	no	—
78	C₂²	C₂×C₄⋊#6923	1	1	yes	characteristic
79	C₄	—	2	2	no	—
80	C₄	—	61	2	no	—
81	C₄	—	122	2	no	—
82	C₄	—	488	4	no	—
83	C₄	#14519856	1	2	yes	—
84	C₂	—	61	4	no	—
85	C₂	#16840706	1	1	yes	characteristic
86	C₂	#16840772	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#6923
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₄×C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	C₄×C₈	#6923
hypocenter	C₆₁	#1835
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
8. C₄×#92418	C₄	semidirect
9. C₈×Dic₆₁	C₄	semidirect
10. C₄×C₈×C₆₁	C₄	semidirect
47. C₆₁	#1835	semidirect
53. C₄×C₈	#6923	semidirect