Subgroups — #21460841

Order 7808.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11758187	C₂	1	2	yes	maximal
2	C₈×#92418	C₂	1	1	yes	maximal, characteristic
3	C₂×#11758187	—	2	2	no	—
4	C₄×#92418	C₄	1	1	yes	characteristic
5	C₄×#92418	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic
7	C₂×C₈×C₆₁	C₈	1	1	yes	characteristic
8	C₂×C₈×C₆₁	C₈	1	1	yes	characteristic
9	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
10	C₂×#92418	—	2	1	no	—
11	C₂×#92418	D₄	1	1	yes	characteristic
12	C₂×#92418	Q₈	1	1	yes	characteristic
13	#11758187	—	4	2	no	—
14	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
16	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
17	C₈×C₆₁	—	2	1	no	—
18	C₈×C₆₁	C₁₆	1	2	yes	complemented
19	#92418	—	2	2	no	—
20	#92418	—	2	1	no	—
21	#92418	SD₁₆	1	2	yes	—
22	C₂²×C₆₁	C₄⋊C₈	1	1	yes	characteristic
23	C₄×C₆₁	—	2	1	no	—
24	C₄×C₆₁	#106	1	1	yes	characteristic
25	C₄×C₆₁	#108	1	1	yes	characteristic
26	C₄×C₆₁	C₂×C₁₆	1	1	yes	characteristic
27	C₄×C₆₁	M₃₂	1	1	yes	characteristic
28	#1367	—	61	1	no	maximal, Sylow
29	C₂×C₆₁	#334	1	1	yes	characteristic
30	C₂×C₆₁	C₄⋊C₁₆	1	1	yes	characteristic
31	C₂×C₆₁	#364	1	1	yes	characteristic
32	C₄⋊C₁₆	—	61	2	no	—
33	C₈²	—	61	1	no	—
34	C₆₁	#1367	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₁₆	—	122	2	no	—
36	C₄×C₈	—	61	1	no	—
37	C₄×C₈	—	61	1	no	—
38	C₄×C₈	#6923	1	1	yes	characteristic
39	C₂×C₈	—	61	1	no	—
40	C₂×C₈	—	61	1	no	—
41	C₂×C₈	—	122	1	no	—
42	C₂×C₈	#92420	1	1	yes	characteristic
43	C₂×C₈	#92420	1	1	yes	characteristic
44	C₄²	C₂×#6923	1	1	yes	characteristic
45	C₁₆	—	244	2	no	—
46	C₂×C₄	#11758213	1	1	yes	characteristic
47	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
48	C₂×C₄	C₂×#92420	1	1	yes	characteristic
49	C₈	—	2	1	no	—
50	C₈	—	61	2	no	—
51	C₈	—	122	2	no	—
52	C₈	—	122	1	no	—
53	C₈	#11758187	1	2	yes	complemented
54	C₂²	C₄⋊#92420	1	1	yes	characteristic
55	C₄	—	2	1	no	—
56	C₄	#14519845	1	1	yes	characteristic
57	C₄	#14519847	1	1	yes	characteristic
58	C₄	C₂×#11758187	1	1	yes	characteristic
59	C₄	#14519851	1	1	yes	characteristic
60	C₂	#16840623	1	1	yes	characteristic
61	C₂	C₄⋊#11758187	1	1	yes	characteristic
62	C₂	#16840684	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄⋊#6923
commutator	C₄×C₆₁	C₂×C₁₆
Frattini	C₄²	C₂×#6923
Fitting	C₄×C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₄⋊C₈
hypercenter	C₄×C₈	#6923
hypocenter	C₆₁	#1367
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
18. C₈×C₆₁	C₁₆	semidirect
34. C₆₁	#1367	semidirect
53. C₈	#11758187	semidirect