Subgroups — #21460725

Order 7808.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840783	C₂	1	2	yes	maximal
2	#16839785	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#92420	—	2	2	no	—
4	C₂²⋊#92420	C₄	1	4	yes	—
5	#14519832	—	2	2	no	—
6	C₂×#11758194	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
8	#14519706	—	2	2	no	—
9	C₂×M₁₆×C₆₁	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
11	C₂²×Dic₆₁	C₂×C₄	1	2	yes	—
12	C₂×#92420	—	2	4	no	—
13	M₁₆×C₆₁	—	4	1	no	—
14	C₂×C₈×C₆₁	—	2	1	no	—
15	C₄×Dic₆₁	D₄	1	1	yes	characteristic
16	C₄×Dic₆₁	D₄	1	2	yes	—
17	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
18	#11758194	—	4	1	no	—
19	C₂×#92418	—	2	1	no	—
20	C₂³×C₆₁	C₄²	1	1	yes	characteristic
21	C₂×C₄×C₆₁	—	2	1	no	—
22	C₂×C₄×C₆₁	—	2	1	no	—
23	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
25	C₂×Dic₆₁	—	4	2	no	—
26	C₂×Dic₆₁	C₂²⋊C₄	1	2	yes	—
27	C₂×Dic₆₁	C₄⋊C₄	1	2	yes	—
28	#92420	—	4	4	no	—
29	C₈×C₆₁	—	4	1	no	—
30	#92418	—	4	1	no	—
31	C₂²×C₆₁	—	2	1	no	—
32	C₂²×C₆₁	—	2	2	no	—
33	C₂²×C₆₁	#95	1	1	yes	characteristic
34	C₄×C₆₁	—	2	1	no	—
35	C₄×C₆₁	#100	1	1	yes	characteristic
36	C₄×C₆₁	#101	1	1	yes	characteristic
37	Dic₆₁	—	2	2	no	—
38	Dic₆₁	—	2	2	no	—
39	#1307	—	61	1	no	maximal, Sylow
40	C₂×C₆₁	—	4	1	no	—
41	C₂×C₆₁	#343	1	1	yes	characteristic
42	C₂×C₆₁	#344	1	2	yes	—
43	#432	—	61	2	no	—
44	#423	—	61	1	no	—
45	C₆₁	#1307	1	1	yes	characteristic, complemented, Sylow
46	C₂×M₁₆	—	61	1	no	—
47	C₂×M₁₆	#6923	1	1	yes	characteristic
48	C₂×C₄²	—	61	1	no	—
49	C₄⋊C₈	—	122	2	no	—
50	C₄⋊C₈	—	122	2	no	—
51	C₂²⋊C₈	—	61	4	no	—
52	#97	—	122	2	no	—
53	C₂²×C₄	—	61	2	no	—
54	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
55	M₁₆	—	4	1	no	—
56	M₁₆	—	244	1	no	—
57	C₂×C₈	—	2	1	no	—
58	C₂×C₈	—	122	4	no	—
59	C₂×C₈	—	122	1	no	—
60	C₄²	—	61	1	no	—
61	C₄²	—	61	1	no	—
62	C₄²	—	61	2	no	—
63	C₂³	C₄×#6923	1	1	yes	characteristic
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	61	2	no	—
67	C₂×C₄	—	61	2	no	—
68	C₂×C₄	—	244	2	no	—
69	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
70	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
71	C₈	—	4	1	no	—
72	C₈	—	244	4	no	—
73	C₈	—	244	1	no	—
74	C₂²	—	2	1	no	—
75	C₂²	—	2	2	no	—
76	C₂²	(C₂×#6923)⋊C₄	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	122	2	no	—
79	C₄	—	122	2	no	—
80	C₄	#14519837	1	1	yes	characteristic
81	C₄	#14519838	1	1	yes	characteristic
82	C₂	—	4	1	no	—
83	C₂	#16840642	1	1	yes	characteristic
84	C₂	#16840645	1	2	yes	—

	subgroup	G/H
center	C₂²	(C₂×#6923)⋊C₄
commutator	C₂³×C₆₁	C₄²
Frattini	C₂²×C₄	C₂×#6923
Fitting	C₂×M₁₆×C₆₁	C₄
socle	C₂²×C₆₁	#95
hypercenter	C₂×M₁₆	#6923
hypocenter	C₆₁	#1307
LCS	G ▷ C₂³×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
45. C₆₁	#1307	semidirect