Subgroups — C₂×D₇₇₉₁ #44528348

Order 31164.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₇₉₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₄₉×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₅₉₇	—	3	1	no	maximal, Hall
4	C₃×C₄₉×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₂₅₉₇	—	3	2	no	—
6	C₂×C₄₉×C₅₃	D₃	1	1	yes	characteristic, complemented
7	C₂×D₁₁₁₃	—	7	1	no	maximal
8	C₄₉×C₅₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
9	D₁₁₁₃	—	7	2	no	—
10	C₂×C₃×C₇×C₅₃	D₇	1	1	yes	characteristic
11	C₂×D₃₇₁	—	21	1	no	—
12	C₃×C₇×C₅₃	C₂×D₇	1	1	yes	characteristic
13	C₂×C₇×C₅₃	D₂₁	1	1	yes	characteristic
14	D₃₇₁	—	21	2	no	—
15	C₂×D₁₅₉	—	49	1	no	Hall
16	C₂×D₁₄₇	—	53	1	no	maximal, Hall
17	C₇×C₅₃	C₂×D₂₁	1	1	yes	characteristic
18	C₂×C₃×C₅₃	D₄₉	1	1	yes	characteristic, complemented
19	D₁₅₉	—	49	2	no	—
20	C₂×C₃×C₄₉	D₅₃	1	1	yes	characteristic, complemented
21	D₁₄₇	—	53	2	no	—
22	C₂×D₅₃	—	147	1	no	Hall
23	C₂×D₄₉	—	159	1	no	Hall
24	C₃×C₅₃	C₂×D₄₉	1	1	yes	characteristic, complemented, Hall
25	C₃×C₄₉	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅₃	D₁₄₇	1	1	yes	characteristic, complemented
27	D₅₃	—	147	2	no	—
28	C₂×C₄₉	D₁₅₉	1	1	yes	characteristic, complemented
29	D₄₉	—	159	2	no	—
30	C₂×D₂₁	—	371	1	no	—
31	C₅₃	C₂×D₁₄₇	1	1	yes	characteristic, complemented, Sylow
32	C₄₉	C₂×D₁₅₉	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃×C₇	D₃₇₁	1	1	yes	characteristic
34	D₂₁	—	371	2	no	—
35	C₂×D₇	—	1113	1	no	—
36	C₃×C₇	C₂×D₃₇₁	1	1	yes	characteristic
37	C₂×C₇	D₁₁₁₃	1	1	yes	characteristic
38	D₇	—	1113	2	no	—
39	C₂×D₃	—	2597	1	no	Hall
40	C₇	C₂×D₁₁₁₃	1	1	yes	characteristic
41	C₂×C₃	D₂₅₉₇	1	1	yes	characteristic, complemented
42	D₃	—	2597	2	no	—
43	C₂²	—	7791	1	no	Sylow
44	C₃	C₂×D₂₅₉₇	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	7791	2	no	—
46	C₂	D₇₇₉₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₇₇₉₁
commutator, cosocle, hypocenter	C₃×C₄₉×C₅₃	C₂²
Frattini	C₇	C₂×D₁₁₁₃
Fitting	C₂×C₃×C₄₉×C₅₃	C₂
socle	C₂×C₃×C₇×C₅₃	D₇
LCS	G ▷ C₃×C₄₉×C₅₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₇₇₉₁	C₂	direct (N × H)
2. C₂×C₃×C₄₉×C₅₃	C₂	semidirect
4. C₃×C₄₉×C₅₃	C₂²	semidirect
6. C₂×C₄₉×C₅₃	D₃	semidirect
8. C₄₉×C₅₃	C₂×D₃	semidirect
18. C₂×C₃×C₅₃	D₄₉	semidirect
20. C₂×C₃×C₄₉	D₅₃	semidirect
24. C₃×C₅₃	C₂×D₄₉	semidirect
25. C₃×C₄₉	C₂×D₅₃	semidirect
26. C₂×C₅₃	D₁₄₇	semidirect
28. C₂×C₄₉	D₁₅₉	semidirect
31. C₅₃	C₂×D₁₄₇	semidirect
32. C₄₉	C₂×D₁₅₉	semidirect
41. C₂×C₃	D₂₅₉₇	semidirect
44. C₃	C₂×D₂₅₉₇	semidirect
46. C₂	D₇₇₉₁	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₇₇₉₁	2
C₂×C₃×C₄₉×C₅₃	2
C₂×D₂₅₉₇	3
C₂×D₁₁₁₃	7
C₂×D₁₄₇	53

Subgroups — C2×D7791 #44528348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₇₇₉₁ #44528348