Subgroups — C₃×(C₂×D₇)⋊C₄ #66599

Order 336.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₂×D₇)⋊C₄	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×C₇	C₂²	1	1	yes	characteristic
6	C₂×C₃×D₇	—	2	1	no	—
7	C₂×C₃×D₇	—	2	1	no	—
8	C₂×C₃×D₇	C₄	1	2	yes	complemented
9	C₃×C₄×C₇	—	2	1	no	—
10	C₃×Dic₇	—	2	1	no	—
11	C₂²×D₇	C₂×C₃	1	1	yes	characteristic
12	C₂×C₄×C₇	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×Dic₇	C₂×C₃	1	1	yes	characteristic, complemented
14	C₃×C₂²⋊C₄	—	7	1	no	maximal, Hall
15	C₂×C₃×C₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₃×C₇	D₄	1	1	yes	characteristic
17	C₂×C₃×C₇	D₄	1	1	yes	characteristic
18	C₃×D₇	—	2	2	no	—
19	C₂²×C₇	C₂²×C₃	1	1	yes	characteristic
20	C₂×D₇	—	2	1	no	—
21	C₂×D₇	—	2	1	no	—
22	C₂×D₇	C₃×C₄	1	2	yes	complemented
23	C₄×C₇	—	2	1	no	—
24	Dic₇	—	2	1	no	—
25	C₂³×C₃	—	7	1	no	—
26	C₂×C₃×C₄	—	7	1	no	—
27	C₂×C₃×C₄	D₇	1	1	yes	characteristic, complemented
28	C₃×C₇	C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
29	C₂²⋊C₄	—	7	1	no	Sylow
30	C₂×C₇	C₂×C₃×C₄	1	1	yes	characteristic
31	C₂×C₇	C₃×D₄	1	1	yes	characteristic
32	C₂×C₇	C₃×D₄	1	1	yes	characteristic
33	D₇	—	2	2	no	—
34	C₂²×C₃	—	7	2	no	—
35	C₂²×C₃	—	14	1	no	—
36	C₂²×C₃	—	14	1	no	—
37	C₂²×C₃	C₂×D₇	1	1	yes	characteristic
38	C₃×C₄	—	2	1	no	—
39	C₃×C₄	—	14	1	no	—
40	C₂³	—	7	1	no	—
41	C₂×C₄	—	7	1	no	—
42	C₂×C₄	C₃×D₇	1	1	yes	characteristic, complemented
43	C₇	C₃×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₃	—	14	2	no	—
45	C₂×C₃	C₄×D₇	1	1	yes	characteristic
46	C₂×C₃	D₂₈	1	1	yes	characteristic
47	C₂×C₃	C₂²⋊D₇	1	1	yes	characteristic
48	C₂²	—	7	2	no	—
49	C₂²	—	14	1	no	—
50	C₂²	—	14	1	no	—
51	C₂²	C₂×C₃×D₇	1	1	yes	characteristic
52	C₄	—	2	1	no	—
53	C₄	—	14	1	no	—
54	C₃	(C₂×D₇)⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
55	C₂	—	14	2	no	—
56	C₂	C₃×C₄×D₇	1	1	yes	characteristic
57	C₂	C₃×D₂₈	1	1	yes	characteristic
58	C₂	C₃×C₂²⋊D₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄×C₇	C₂	semidirect
3. C₂×C₃×Dic₇	C₂	semidirect
4. (C₂×D₇)⋊C₄	C₃	direct (N × H)
8. C₂×C₃×D₇	C₄	semidirect
12. C₂×C₄×C₇	C₂×C₃	semidirect
13. C₂×Dic₇	C₂×C₃	semidirect
22. C₂×D₇	C₃×C₄	semidirect
27. C₂×C₃×C₄	D₇	semidirect
28. C₃×C₇	C₂²⋊C₄	semidirect
42. C₂×C₄	C₃×D₇	semidirect
43. C₇	C₃×C₂²⋊C₄	semidirect
54. C₃	(C₂×D₇)⋊C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₇	2
C₂×C₃×C₄×C₇	2
C₂×C₃×Dic₇	2
(C₂×D₇)⋊C₄	3
C₃×C₂²⋊C₄	7

Subgroups — C3×(C2×D7)⋊C4 #66599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×(C₂×D₇)⋊C₄ #66599