Subgroups — C₂×C₇×#131 #90588

Order 448.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#41	C₂	1	1	yes	maximal, characteristic
2	C₇×#131	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₇×M₁₆	C₂	1	3	yes	maximal, complemented
4	C₂²×C₇×C₈	C₂	1	3	yes	maximal, complemented
5	C₇×#41	C₄	1	4	yes	—
6	C₇×#41	C₂²	1	4	yes	—
7	C₂×C₇×Q₈	C₄	1	1	yes	characteristic
8	C₂×C₇×D₄	C₄	1	3	yes	—
9	C₂²×C₄×C₇	C₂²	1	3	yes	—
10	C₇×M₁₆	C₂²	1	12	yes	complemented
11	C₂×C₇×C₈	C₂²	1	3	yes	—
12	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₇×C₈	C₂²	1	12	yes	complemented
14	C₂×#131	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂³×C₇	C₂×C₄	1	3	yes	—
16	C₇×Q₈	C₂×C₄	1	4	yes	—
17	C₇×D₄	C₂×C₄	1	12	yes	—
18	C₂×C₄×C₇	C₂×C₄	1	3	yes	—
19	C₂×C₄×C₇	C₂×C₄	1	6	yes	—
20	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
21	C₂×C₄×C₇	C₂³	1	6	yes	—
22	C₇×C₈	C₂³	1	6	yes	—
23	C₇×C₈	C₂³	1	2	yes	—
24	C₂×#41	C₂×C₇	1	1	yes	characteristic
25	#131	C₂×C₇	1	8	yes	direct product factor
26	C₂×M₁₆	C₂×C₇	1	3	yes	complemented
27	C₂²×C₈	C₂×C₇	1	3	yes	complemented
28	C₂²×C₇	—	2	6	no	—
29	C₂²×C₇	C₂²×C₄	1	6	yes	—
30	C₂²×C₇	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₇	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₇	C₂²×C₄	1	6	yes	—
33	C₄×C₇	C₂⁴	1	1	yes	characteristic
34	#41	C₄×C₇	1	4	yes	—
35	#41	C₂²×C₇	1	4	yes	—
36	C₂×Q₈	C₄×C₇	1	1	yes	characteristic
37	C₂×D₄	C₄×C₇	1	3	yes	—
38	C₂²×C₄	C₂²×C₇	1	3	yes	—
39	M₁₆	C₂²×C₇	1	12	yes	complemented
40	C₂×C₈	C₂²×C₇	1	3	yes	—
41	C₂×C₈	C₂²×C₇	1	1	yes	characteristic
42	C₂×C₈	C₂²×C₇	1	12	yes	complemented
43	C₂×C₇	—	2	6	no	—
44	C₂×C₇	#131	1	2	yes	direct product factor
45	C₂×C₇	C₂³×C₄	1	1	yes	characteristic
46	C₂³	C₂×C₄×C₇	1	3	yes	—
47	Q₈	C₂×C₄×C₇	1	4	yes	—
48	D₄	C₂×C₄×C₇	1	12	yes	—
49	C₂×C₄	C₂×C₄×C₇	1	3	yes	—
50	C₂×C₄	C₂×C₄×C₇	1	6	yes	—
51	C₂×C₄	C₂³×C₇	1	1	yes	characteristic
52	C₂×C₄	C₂³×C₇	1	6	yes	—
53	C₈	C₂³×C₇	1	2	yes	—
54	C₈	C₂³×C₇	1	6	yes	—
55	C₇	C₂×#131	1	1	yes	characteristic, direct product factor, Sylow
56	C₂²	—	2	6	no	—
57	C₂²	C₂²×C₄×C₇	1	6	yes	—
58	C₂²	C₂²×C₄×C₇	1	1	yes	characteristic
59	C₄	C₂²×C₄×C₇	1	1	yes	characteristic
60	C₄	C₂²×C₄×C₇	1	6	yes	—
61	C₄	C₂⁴×C₇	1	1	yes	characteristic
62	C₂	—	2	6	no	—
63	C₂	C₇×#131	1	2	yes	direct product factor
64	C₂	C₂³×C₄×C₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₇×C₈	C₂²
commutator	C₂	C₂³×C₄×C₇
Frattini, cosocle	C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂²×C₄
prime radical	C₂×C₇×#41	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#131	C₂	direct (N × H)
3. C₂×C₇×M₁₆	C₂	semidirect
4. C₂²×C₇×C₈	C₂	semidirect
10. C₇×M₁₆	C₂²	semidirect
13. C₂×C₇×C₈	C₂²	semidirect
14. C₂×#131	C₇	direct (N × H)
25. #131	C₂×C₇	direct (N × H)
26. C₂×M₁₆	C₂×C₇	semidirect
27. C₂²×C₈	C₂×C₇	semidirect
39. M₁₆	C₂²×C₇	semidirect
42. C₂×C₈	C₂²×C₇	semidirect
44. C₂×C₇	#131	direct (N × H)
55. C₇	C₂×#131	direct (N × H)
63. C₂	C₇×#131	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×#41	2
C₇×#131	2
C₂×C₇×M₁₆	2
C₂²×C₇×C₈	2
C₂×#131	7

Subgroups — C2×C7×#131 #90588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#131 #90588