Subgroups — #21443732

Order 7808.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839786	C₂	1	2	yes	maximal
2	C₆₁×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×#11758194	C₄	1	4	yes	—
4	C₄⋊#92418	—	2	2	no	—
5	C₄⋊#92418	—	2	2	no	—
6	C₂×M₁₆×C₆₁	C₄	1	2	yes	—
7	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
8	C₄⋊C₈×C₆₁	—	2	2	no	—
9	C₂²×C₄×C₆₁	C₂×C₄	1	2	yes	—
10	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
11	M₁₆×C₆₁	—	4	2	no	—
12	C₂×C₈×C₆₁	—	2	2	no	—
13	C₄²×C₆₁	D₄	1	1	yes	characteristic
14	C₄²×C₆₁	D₄	1	2	yes	—
15	C₄²×C₆₁	Q₈	1	1	yes	characteristic
16	#11758194	—	4	4	no	—
17	C₂×#92418	—	2	4	no	—
18	C₂³×C₆₁	C₄²	1	1	yes	characteristic
19	C₂×C₄×C₆₁	—	2	2	no	—
20	C₂×C₄×C₆₁	—	2	1	no	—
21	C₂×C₄×C₆₁	—	2	2	no	—
22	C₂×C₄×C₆₁	—	2	1	no	—
23	C₂×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
24	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
27	C₈×C₆₁	—	4	2	no	—
28	#92418	—	4	4	no	—
29	C₂²×C₆₁	—	2	2	no	—
30	C₂²×C₆₁	—	2	1	no	—
31	C₂²×C₆₁	#95	1	1	yes	characteristic
32	C₄×C₆₁	—	2	2	no	—
33	C₄×C₆₁	—	2	1	no	—
34	C₄×C₆₁	#100	1	2	yes	—
35	C₄×C₆₁	#100	1	1	yes	characteristic
36	C₄×C₆₁	#101	1	2	yes	—
37	C₄×C₆₁	#101	1	1	yes	characteristic
38	#1309	—	61	1	no	maximal, Sylow
39	C₂×C₆₁	—	4	1	no	—
40	C₂×C₆₁	#343	1	2	yes	—
41	C₂×C₆₁	#343	1	1	yes	characteristic
42	#423	—	61	2	no	—
43	#423	D₆₁	1	1	yes	characteristic
44	C₆₁	#1309	1	1	yes	characteristic, complemented, Sylow
45	C₂×M₁₆	—	61	4	no	—
46	C₂×M₁₆	Dic₆₁	1	2	yes	—
47	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
48	C₄⋊C₈	—	2	2	no	—
49	C₄⋊C₈	—	122	2	no	—
50	C₄⋊C₈	—	122	2	no	—
51	C₂²×C₄	C₄×D₆₁	1	2	yes	—
52	C₂²×C₄	C₂×Dic₆₁	1	1	yes	characteristic
53	M₁₆	—	4	2	no	—
54	M₁₆	—	244	4	no	—
55	C₂×C₈	—	2	2	no	—
56	C₂×C₈	—	122	4	no	—
57	C₄²	Dic₁₂₂	1	1	yes	characteristic
58	C₄²	D₂₄₄	1	1	yes	characteristic
59	C₄²	C₂²⋊D₆₁	1	2	yes	—
60	C₂³	C₄×Dic₆₁	1	1	yes	characteristic
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	2	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	#11758196	1	2	yes	—
66	C₂×C₄	C₄⋊Dic₆₁	1	1	yes	characteristic
67	C₂×C₄	#11758198	1	2	yes	—
68	C₂×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
69	C₈	—	4	2	no	—
70	C₈	—	244	4	no	—
71	C₂²	—	2	2	no	—
72	C₂²	—	2	1	no	—
73	C₂²	#14519684	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	2	1	no	—
76	C₄	#14519693	1	2	yes	—
77	C₄	#14519694	1	1	yes	characteristic
78	C₄	#14519695	1	2	yes	—
79	C₄	#14519696	1	1	yes	characteristic
80	C₂	—	4	1	no	—
81	C₂	#16839530	1	2	yes	—
82	C₂	#16839531	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14519684
commutator	C₂³×C₆₁	C₄²
Frattini	C₂×C₄²	C₂×D₆₁
Fitting	C₆₁×#423	C₂
socle	C₂²×C₆₁	#95
hypercenter	#423	D₆₁
hypocenter	C₆₁	#1309
LCS	G ▷ C₂³×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
44. C₆₁	#1309	semidirect