Subgroups — C₂×(C₃₆₁⋊C₃)⋊D₇ #44476449

Order 30324.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₃₆₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₃₆₁⋊C₃)⋊D₇	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₂₅₂₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇×C₃₆₁⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₂₅₂₇	C₂×C₃	1	2	yes	complemented
6	C₂×C₇×C₃₆₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×D₃₆₁⋊C₃	—	7	1	no	maximal, Hall
8	C₇×C₃₆₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃₆₁⋊C₃	D₇	1	1	yes	characteristic, complemented
10	D₃₆₁⋊C₃	—	7	2	no	—
11	C₂×(C₁₉⋊C₃)⋊D₇	—	19	1	no	maximal
12	C₂×D₃₆₁	—	7	1	no	Hall
13	C₃₆₁⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇×C₁₉⋊C₃	—	38	1	no	—
15	(C₁₉⋊C₃)⋊D₇	—	19	2	no	—
16	C₂×C₃₆₁	C₃×D₇	1	1	yes	characteristic, complemented
17	D₃₆₁	—	7	2	no	—
18	C₂×D₁₃₃	—	19	1	no	—
19	C₇×C₁₉⋊C₃	—	38	1	no	—
20	C₃₆₁	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₇×C₁₉	D₁₉⋊C₃	1	1	yes	characteristic
22	D₁₃₃	—	19	2	no	—
23	C₂×D₁₉⋊C₃	—	133	1	no	—
24	C₇×C₁₉	C₂×D₁₉⋊C₃	1	1	yes	characteristic
25	C₂×C₁₉⋊C₃	—	38	1	no	—
26	D₁₉⋊C₃	—	133	2	no	—
27	C₂×C₃×D₇	—	361	1	no	Hall
28	C₂×D₁₉	—	133	1	no	—
29	C₁₉⋊C₃	—	38	1	no	—
30	C₂×C₃×C₇	—	722	1	no	—
31	C₃×D₇	—	361	2	no	—
32	C₂×C₁₉	(C₁₉⋊C₃)⋊D₇	1	1	yes	characteristic
33	D₁₉	—	133	2	no	—
34	C₂×D₇	—	361	1	no	Hall
35	C₃×C₇	—	722	1	no	Hall
36	C₁₉	C₂×(C₁₉⋊C₃)⋊D₇	1	1	yes	characteristic
37	C₂×C₇	D₃₆₁⋊C₃	1	1	yes	characteristic, complemented
38	D₇	—	361	2	no	—
39	C₂²×C₃	—	2527	1	no	Hall
40	C₇	C₂×D₃₆₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	—	722	1	no	—
42	C₂×C₃	—	2527	2	no	—
43	C₂²	—	2527	1	no	Sylow
44	C₃	—	722	1	no	Sylow
45	C₂	—	2527	2	no	—
46	C₂	(C₃₆₁⋊C₃)⋊D₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	(C₃₆₁⋊C₃)⋊D₇
commutator, cosocle, hypocenter	C₇×C₃₆₁	C₂²×C₃
Frattini	C₁₉	C₂×(C₁₉⋊C₃)⋊D₇
Fitting	C₂×C₇×C₃₆₁	C₂×C₃
socle	C₂×C₇×C₁₉	D₁₉⋊C₃
LCS	G ▷ C₇×C₃₆₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×C₃₆₁⋊C₃	C₂	semidirect
2. (C₃₆₁⋊C₃)⋊D₇	C₂	direct (N × H)
3. C₂×D₂₅₂₇	C₃	semidirect
4. C₇×C₃₆₁⋊C₃	C₂²	semidirect
5. D₂₅₂₇	C₂×C₃	semidirect
6. C₂×C₇×C₃₆₁	C₂×C₃	semidirect
8. C₇×C₃₆₁	C₂²×C₃	semidirect
9. C₂×C₃₆₁⋊C₃	D₇	semidirect
13. C₃₆₁⋊C₃	C₂×D₇	semidirect
16. C₂×C₃₆₁	C₃×D₇	semidirect
20. C₃₆₁	C₂×C₃×D₇	semidirect
37. C₂×C₇	D₃₆₁⋊C₃	semidirect
40. C₇	C₂×D₃₆₁⋊C₃	semidirect
46. C₂	(C₃₆₁⋊C₃)⋊D₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×C₃₆₁⋊C₃	2
(C₃₆₁⋊C₃)⋊D₇	2
C₂×D₂₅₂₇	3
C₂×D₃₆₁⋊C₃	7
C₂×(C₁₉⋊C₃)⋊D₇	19

Subgroups — C2×(C361⋊C3)⋊D7 #44476449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×(C₃₆₁⋊C₃)⋊D₇ #44476449