Subgroups — C₂×C₇×#127 #90551

Order 448.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×D₄	C₂	1	6	yes	maximal, complemented
2	C₇×#127	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄²×C₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁴×C₇	C₂²	1	4	yes	—
5	C₂×C₇×D₄	—	2	24	no	—
6	C₂×C₇×D₄	C₂²	1	24	yes	complemented
7	C₂²×C₄×C₇	C₂²	1	3	yes	—
8	C₄²×C₇	C₂²	1	4	yes	complemented
9	C₂×#127	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂³×C₇	—	2	24	no	—
11	C₂³×C₇	C₂³	1	8	yes	—
12	C₂³×C₇	C₂³	1	1	yes	characteristic
13	C₇×D₄	—	2	48	no	—
14	C₂×C₄×C₇	D₄	1	12	yes	complemented
15	C₂×C₄×C₇	C₂³	1	6	yes	—
16	C₂²×D₄	C₂×C₇	1	6	yes	complemented
17	#127	C₂×C₇	1	8	yes	direct product factor
18	C₂×C₄²	C₂×C₇	1	1	yes	characteristic, complemented
19	C₂²×C₇	—	2	24	no	—
20	C₂²×C₇	—	4	16	no	—
21	C₂²×C₇	C₂×D₄	1	6	yes	—
22	C₂²×C₇	C₂⁴	1	1	yes	characteristic
23	C₄×C₇	C₂×D₄	1	12	yes	complemented
24	C₂⁴	C₂²×C₇	1	4	yes	—
25	C₂×D₄	—	2	24	no	—
26	C₂×D₄	C₂²×C₇	1	24	yes	complemented
27	C₂²×C₄	C₂²×C₇	1	3	yes	—
28	C₄²	C₂²×C₇	1	4	yes	complemented
29	C₂×C₇	—	4	8	no	—
30	C₂×C₇	#127	1	4	yes	direct product factor
31	C₂×C₇	C₂²×D₄	1	3	yes	—
32	C₂³	—	2	24	no	—
33	C₂³	C₂³×C₇	1	8	yes	—
34	C₂³	C₂³×C₇	1	1	yes	characteristic
35	D₄	—	2	48	no	—
36	C₂×C₄	C₇×D₄	1	12	yes	complemented
37	C₂×C₄	C₂³×C₇	1	6	yes	—
38	C₇	C₂×#127	1	1	yes	characteristic, direct product factor, Sylow
39	C₂²	—	2	24	no	—
40	C₂²	—	4	16	no	—
41	C₂²	C₂×C₇×D₄	1	6	yes	—
42	C₂²	C₂⁴×C₇	1	1	yes	characteristic
43	C₄	C₂×C₇×D₄	1	12	yes	complemented
44	C₂	—	4	8	no	—
45	C₂	C₇×#127	1	4	yes	direct product factor
46	C₂	C₂²×C₇×D₄	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁴×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇×D₄	C₂	semidirect
2. C₇×#127	C₂	direct (N × H)
3. C₂×C₄²×C₇	C₂	semidirect
6. C₂×C₇×D₄	C₂²	semidirect
8. C₄²×C₇	C₂²	semidirect
9. C₂×#127	C₇	direct (N × H)
14. C₂×C₄×C₇	D₄	semidirect
16. C₂²×D₄	C₂×C₇	semidirect
17. #127	C₂×C₇	direct (N × H)
18. C₂×C₄²	C₂×C₇	semidirect
23. C₄×C₇	C₂×D₄	semidirect
26. C₂×D₄	C₂²×C₇	semidirect
28. C₄²	C₂²×C₇	semidirect
30. C₂×C₇	#127	direct (N × H)
36. C₂×C₄	C₇×D₄	semidirect
38. C₇	C₂×#127	direct (N × H)
43. C₄	C₂×C₇×D₄	semidirect
45. C₂	C₇×#127	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×C₇×D₄	2
C₇×#127	2
C₂×C₄²×C₇	2
C₂×#127	7

Subgroups — C2×C7×#127 #90551

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#127 #90551