Subgroups — C₃×#1141 #66600

Order 336.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#1141	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×C₇	—	2	1	no	—
6	C₂×C₃×D₇	—	2	1	no	—
7	C₃×C₄×C₇	C₂²	1	1	yes	characteristic
8	C₇×D₄	C₂×C₃	1	1	yes	characteristic, complemented
9	D₂₈	C₂×C₃	1	1	yes	characteristic, complemented
10	C₇⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
11	C₃×D₈	—	7	1	no	maximal, Hall
12	C₂×C₃×C₇	—	4	1	no	—
13	C₂×C₃×C₇	D₄	1	1	yes	characteristic
14	C₃×D₇	—	4	1	no	—
15	C₂²×C₇	—	2	1	no	—
16	C₂×D₇	—	2	1	no	—
17	C₄×C₇	C₂²×C₃	1	1	yes	characteristic
18	C₃×D₄	—	7	1	no	—
19	C₃×D₄	D₇	1	1	yes	characteristic, complemented
20	C₃×C₈	—	7	1	no	—
21	C₃×C₇	D₈	1	1	yes	characteristic, complemented, Hall
22	D₈	—	7	1	no	Sylow
23	C₂×C₇	—	4	1	no	—
24	C₂×C₇	C₃×D₄	1	1	yes	characteristic
25	D₇	—	4	1	no	—
26	C₂²×C₃	—	2	1	no	—
27	C₂²×C₃	—	14	1	no	—
28	C₃×C₄	C₂×D₇	1	1	yes	characteristic
29	D₄	—	7	1	no	—
30	D₄	C₃×D₇	1	1	yes	characteristic, complemented
31	C₈	—	7	1	no	—
32	C₇	C₃×D₈	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃	—	4	1	no	—
34	C₂×C₃	—	28	1	no	—
35	C₂×C₃	C₂²⋊D₇	1	1	yes	characteristic
36	C₂²	—	2	1	no	—
37	C₂²	—	14	1	no	—
38	C₄	C₂×C₃×D₇	1	1	yes	characteristic
39	C₃	#1141	1	1	yes	characteristic, direct product factor, Sylow
40	C₂	—	4	1	no	—
41	C₂	—	28	1	no	—
42	C₂	C₃×C₂²⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²⋊D₇
commutator, cosocle	C₄×C₇	C₂²×C₃
Frattini	C₄	C₂×C₃×D₇
Fitting	C₃×C₇×D₄	C₂
socle	C₂×C₃×C₇	D₄
hypercenter	C₃×D₄	D₇
hypocenter	C₇	C₃×D₈
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×D₄	C₂	semidirect
2. C₃×D₂₈	C₂	semidirect
3. C₃×C₇⋊C₈	C₂	semidirect
4. #1141	C₃	direct (N × H)
8. C₇×D₄	C₂×C₃	semidirect
9. D₂₈	C₂×C₃	semidirect
10. C₇⋊C₈	C₂×C₃	semidirect
19. C₃×D₄	D₇	semidirect
21. C₃×C₇	D₈	semidirect
30. D₄	C₃×D₇	semidirect
32. C₇	C₃×D₈	semidirect
39. C₃	#1141	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇×D₄	2
C₃×D₂₈	2
C₃×C₇⋊C₈	2
#1141	3
C₃×D₈	7

Subgroups — C3×#1141 #66600

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1141 #66600