Subgroups — #21445960

Order 7808.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839786	C₂	1	2	yes	maximal
2	#16839527	C₂	1	4	yes	maximal
3	C₂×#97×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758194	C₂²	1	4	yes	—
5	C₄⋊#92418	—	2	4	no	—
6	C₂²×C₈×C₆₁	C₂²	1	2	yes	—
7	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
8	#97×C₆₁	C₄	1	4	yes	—
9	C₂²×C₄×C₆₁	Q₈	1	2	yes	—
10	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
11	C₂×C₈×C₆₁	—	2	4	no	—
12	C₂×C₈×C₆₁	C₂×C₄	1	4	yes	—
13	C₄²×C₆₁	C₂×C₄	1	2	yes	—
14	C₄²×C₆₁	D₄	1	2	yes	—
15	#11758194	—	2	8	no	—
16	C₂×#92418	—	2	4	no	—
17	C₂³×C₆₁	C₂×Q₈	1	1	yes	characteristic
18	C₂×C₄×C₆₁	—	4	2	no	—
19	C₂×C₄×C₆₁	C₄⋊C₄	1	4	yes	—
20	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
22	C₂×C₄×C₆₁	#41	1	4	yes	—
23	C₈×C₆₁	—	2	4	no	—
24	#92418	—	4	4	no	—
25	C₂²×C₆₁	—	2	2	no	—
26	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
27	C₂²×C₆₁	#125	1	2	yes	—
28	C₄×C₆₁	—	2	4	no	—
29	C₄×C₆₁	#117	1	2	yes	—
30	C₄×C₆₁	#124	1	2	yes	—
31	#1838	—	61	1	no	maximal, Sylow
32	C₂×C₆₁	—	2	2	no	—
33	C₂×C₆₁	#382	1	1	yes	characteristic
34	C₂×C₆₁	#430	1	2	yes	—
35	#423	—	61	2	no	—
36	C₂×#97	D₆₁	1	1	yes	characteristic
37	#341	—	61	4	no	—
38	C₆₁	#1838	1	1	yes	characteristic, complemented, Sylow
39	C₂×M₁₆	—	61	4	no	—
40	C₂²×C₈	C₂×D₆₁	1	2	yes	—
41	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
42	C₄⋊C₈	—	122	4	no	—
43	#97	Dic₆₁	1	4	yes	—
44	C₂²×C₄	Dic₁₂₂	1	2	yes	—
45	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
46	M₁₆	—	122	8	no	—
47	C₂×C₈	—	2	4	no	—
48	C₂×C₈	—	122	4	no	—
49	C₂×C₈	C₂×Dic₆₁	1	4	yes	—
50	C₄²	D₂₄₄	1	2	yes	—
51	C₄²	C₂×Dic₆₁	1	2	yes	—
52	C₂³	C₂×Dic₁₂₂	1	1	yes	characteristic
53	C₂×C₄	—	4	2	no	—
54	C₂×C₄	C₄⋊Dic₆₁	1	4	yes	—
55	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
56	C₂×C₄	#11758222	1	4	yes	—
57	C₂×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
58	C₈	—	2	4	no	—
59	C₈	—	244	4	no	—
60	C₂²	—	2	2	no	—
61	C₂²	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
62	C₂²	#14519769	1	2	yes	—
63	C₄	—	2	4	no	—
64	C₄	#14519736	1	2	yes	—
65	C₄	#14519765	1	2	yes	—
66	C₂	—	2	2	no	—
67	C₂	#16839628	1	1	yes	characteristic
68	C₂	#16839811	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₂₄₄
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₂×#97×C₆₁	C₂
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	C₂×#97	D₆₁
hypocenter	C₆₁	#1838
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
38. C₆₁	#1838	semidirect