Subgroups — C₄×C₇×M₁₆ #90050

Order 448.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₄²×C₇	C₂	1	1	yes	maximal, characteristic
3	C₇×#97	C₂	1	2	yes	maximal, complemented
4	C₄×C₇×C₈	C₂	1	2	yes	maximal, complemented
5	C₂²×C₄×C₇	C₄	1	2	yes	—
6	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
7	C₇×M₁₆	C₄	1	8	yes	direct product factor
8	C₂×C₇×C₈	C₂²	1	4	yes	—
9	C₄²×C₇	C₄	1	2	yes	—
10	C₄²×C₇	C₂²	1	1	yes	characteristic
11	C₄²×C₇	C₂²	1	1	yes	characteristic
12	C₄×M₁₆	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂³×C₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₇	—	2	4	no	—
15	C₂×C₄×C₇	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₇	C₂×C₄	1	4	yes	—
18	C₂×C₄×C₇	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
20	C₇×C₈	C₂×C₄	1	8	yes	complemented
21	C₂×M₁₆	C₂×C₇	1	2	yes	—
22	C₂×C₄²	C₂×C₇	1	1	yes	characteristic
23	#97	C₂×C₇	1	2	yes	complemented
24	C₄×C₈	C₂×C₇	1	2	yes	complemented
25	C₂²×C₇	—	2	2	no	—
26	C₂²×C₇	C₄²	1	2	yes	—
27	C₂²×C₇	C₂²×C₄	1	1	yes	characteristic
28	C₄×C₇	—	2	2	no	—
29	C₄×C₇	C₄²	1	2	yes	—
30	C₄×C₇	M₁₆	1	4	yes	direct product factor
31	C₄×C₇	C₂²×C₄	1	2	yes	—
32	C₂²×C₄	C₄×C₇	1	2	yes	—
33	C₂²×C₄	C₂²×C₇	1	1	yes	characteristic
34	M₁₆	C₄×C₇	1	8	yes	direct product factor
35	C₂×C₈	C₂²×C₇	1	4	yes	—
36	C₄²	C₄×C₇	1	2	yes	—
37	C₄²	C₂²×C₇	1	1	yes	characteristic
38	C₄²	C₂²×C₇	1	1	yes	characteristic
39	C₂×C₇	—	2	2	no	—
40	C₂×C₇	C₂×C₄²	1	1	yes	characteristic
41	C₂×C₇	C₂×M₁₆	1	2	yes	—
42	C₂³	C₂×C₄×C₇	1	1	yes	characteristic
43	C₂×C₄	—	2	4	no	—
44	C₂×C₄	C₂×C₄×C₇	1	2	yes	—
45	C₂×C₄	C₂×C₄×C₇	1	1	yes	characteristic
46	C₂×C₄	C₂×C₄×C₇	1	4	yes	—
47	C₂×C₄	C₂×C₄×C₇	1	2	yes	—
48	C₂×C₄	C₂³×C₇	1	1	yes	characteristic
49	C₈	C₂×C₄×C₇	1	8	yes	complemented
50	C₇	C₄×M₁₆	1	1	yes	characteristic, direct product factor, Sylow
51	C₂²	—	2	2	no	—
52	C₂²	C₄²×C₇	1	2	yes	—
53	C₂²	C₂²×C₄×C₇	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	C₄²×C₇	1	2	yes	—
56	C₄	C₇×M₁₆	1	4	yes	direct product factor
57	C₄	C₂²×C₄×C₇	1	2	yes	—
58	C₂	—	2	2	no	—
59	C₂	C₂×C₄²×C₇	1	1	yes	characteristic
60	C₂	C₂×C₇×M₁₆	1	2	yes	—

	subgroup	G/H
center	C₄²×C₇	C₂²
commutator	C₂	C₂×C₄²×C₇
Frattini, cosocle	C₂×C₄	C₂³×C₇
socle	C₂²×C₇	C₂²×C₄
prime radical	C₂³×C₇	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#97	C₂	semidirect
4. C₄×C₇×C₈	C₂	semidirect
7. C₇×M₁₆	C₄	direct (N × H)
12. C₄×M₁₆	C₇	direct (N × H)
20. C₇×C₈	C₂×C₄	semidirect
23. #97	C₂×C₇	semidirect
24. C₄×C₈	C₂×C₇	semidirect
30. C₄×C₇	M₁₆	direct (N × H)
34. M₁₆	C₄×C₇	direct (N × H)
49. C₈	C₂×C₄×C₇	semidirect
50. C₇	C₄×M₁₆	direct (N × H)
56. C₄	C₇×M₁₆	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×M₁₆	2
C₂×C₄²×C₇	2
C₇×#97	2
C₄×C₇×C₈	2
C₄×M₁₆	7

Subgroups — C4×C7×M16 #90050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×M₁₆ #90050