Subgroups — C₄×#14519827 #21460923

Order 7808.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519827	C₂	1	2	yes	maximal
2	C₄×#11758185	C₂	1	1	yes	maximal, characteristic
3	#14519827	C₄	1	4	yes	direct product factor
4	C₂×#11758185	C₄	1	1	yes	characteristic
5	C₂×#11758185	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	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₆₁	C₈	1	1	yes	characteristic
10	#11758185	C₈	1	2	yes	—
11	#11758185	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₆₁	C₁₆	1	2	yes	—
13	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
14	C₈×C₆₁	C₁₆	1	2	yes	—
15	C₈×C₆₁	C₄²	1	1	yes	characteristic
16	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
17	C₂²×C₆₁	C₂×C₁₆	1	1	yes	characteristic
18	C₄×C₆₁	C₃₂	1	4	yes	complemented
19	C₄×C₆₁	C₄×C₈	1	1	yes	characteristic
20	C₄×C₆₁	C₂×C₁₆	1	1	yes	characteristic
21	C₄×C₃₂	—	61	1	no	maximal, Sylow
22	C₂×C₆₁	C₄×C₁₆	1	1	yes	characteristic
23	C₂×C₆₁	C₂×C₃₂	1	2	yes	—
24	C₂×C₃₂	—	61	2	no	—
25	C₄×C₁₆	—	61	1	no	—
26	C₆₁	C₄×C₃₂	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₆	—	61	1	no	—
28	C₂×C₁₆	—	61	1	no	—
29	C₄×C₈	#6923	1	1	yes	characteristic
30	C₃₂	—	61	4	no	—
31	C₂×C₈	#92420	1	1	yes	characteristic
32	C₂×C₈	C₂×#6923	1	1	yes	characteristic
33	C₄²	#92420	1	1	yes	characteristic
34	C₁₆	—	61	2	no	—
35	C₁₆	—	61	2	no	—
36	C₂×C₄	#11758187	1	2	yes	—
37	C₂×C₄	C₂×#92420	1	1	yes	characteristic
38	C₈	#11758187	1	2	yes	—
39	C₈	D₆₁⋊C₈	1	1	yes	characteristic
40	C₈	C₄×#6923	1	1	yes	characteristic
41	C₂²	C₂×#11758187	1	1	yes	characteristic
42	C₄	#14519827	1	4	yes	direct product factor
43	C₄	C₄×#92420	1	1	yes	characteristic
44	C₄	C₂×#11758187	1	1	yes	characteristic
45	C₂	C₄×#11758187	1	1	yes	characteristic
46	C₂	C₂×#14519827	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₄×C₈	#6923
commutator, hypocenter	C₆₁	C₄×C₃₂
Frattini	C₂×C₈	C₂×#6923
Fitting	C₄×C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₁₆
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #14519827	C₄	direct (N × H)
18. C₄×C₆₁	C₃₂	semidirect
26. C₆₁	C₄×C₃₂	semidirect
42. C₄	#14519827	direct (N × H)

Subgroups — C4×#14519827 #21460923

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#14519827 #21460923