Subgroups — #21460737

Order 7808.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840650	C₂	1	1	yes	maximal, characteristic
2	#16840650	C₂	1	1	yes	maximal, characteristic
3	#16839484	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758187	C₄	1	2	yes	—
5	C₂×#11758187	C₄	1	2	yes	—
6	C₄×#92418	C₄	1	1	yes	characteristic
7	C₄×#92418	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic
9	C₂×C₈×C₆₁	—	2	1	no	—
10	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
11	C₂×#92418	—	2	1	no	—
12	C₂×#92418	C₂×C₄	1	1	yes	characteristic
13	C₂×#92418	C₂×C₄	1	1	yes	characteristic
14	#11758187	—	2	2	no	—
15	#11758187	C₈	1	4	yes	complemented
16	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
17	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
18	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
19	C₈×C₆₁	—	4	1	no	—
20	#92418	—	4	1	no	—
21	#92418	C₂×C₈	1	2	yes	—
22	#92418	M₁₆	1	2	yes	—
23	C₂²×C₆₁	#97	1	1	yes	characteristic
24	C₄×C₆₁	—	2	1	no	—
25	C₄×C₆₁	—	2	1	no	—
26	C₄×C₆₁	C₄×C₈	1	1	yes	characteristic
27	C₄×C₆₁	#97	1	1	yes	characteristic
28	#1313	—	61	1	no	maximal, Sylow
29	C₂×C₆₁	#322	1	1	yes	characteristic
30	C₂×C₆₁	#347	1	1	yes	characteristic
31	C₂×C₆₁	#347	1	1	yes	characteristic
32	#346	—	61	1	no	—
33	#346	—	61	1	no	—
34	#322	—	61	1	no	—
35	C₆₁	#1313	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₁₆	—	61	2	no	—
37	C₂×C₁₆	—	61	2	no	—
38	C₄×C₈	—	61	1	no	—
39	C₄×C₈	—	61	1	no	—
40	C₄×C₈	#6923	1	1	yes	characteristic
41	C₂×C₈	—	2	1	no	—
42	C₂×C₈	—	61	1	no	—
43	C₂×C₈	—	61	1	no	—
44	C₂×C₈	—	122	1	no	—
45	C₄²	C₂×#6923	1	1	yes	characteristic
46	C₁₆	—	61	4	no	—
47	C₁₆	—	122	2	no	—
48	C₂×C₄	#11758213	1	1	yes	characteristic
49	C₂×C₄	C₄×#6923	1	1	yes	characteristic
50	C₂×C₄	#11758217	1	1	yes	characteristic
51	C₈	—	4	1	no	—
52	C₈	—	61	2	no	—
53	C₈	—	61	2	no	—
54	C₈	—	244	1	no	—
55	C₂²	#14519832	1	1	yes	characteristic
56	C₄	—	2	1	no	—
57	C₄	—	2	1	no	—
58	C₄	C₈×#6923	1	1	yes	characteristic
59	C₄	#14519831	1	1	yes	characteristic
60	C₂	#92420⋊C₈	1	1	yes	characteristic
61	C₂	#16840654	1	1	yes	characteristic
62	C₂	#16840655	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#6923
commutator	C₄×C₆₁	C₄×C₈
Frattini	C₄²	C₂×#6923
Fitting	C₄×C₈×C₆₁	C₄
socle	C₂²×C₆₁	#97
hypercenter	C₄×C₈	#6923
hypocenter	C₆₁	#1313
LCS	G ▷ C₄×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
15. #11758187	C₈	semidirect
35. C₆₁	#1313	semidirect