Subgroups — C₂×C₇×SD₁₆ #6536

Order 224.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×D₄	C₂	1	1	yes	maximal, characteristic
3	C₇×SD₁₆	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₇	—	2	1	no	—
6	C₇×Q₈	—	2	1	no	—
7	C₇×Q₈	C₂²	1	2	yes	complemented
8	C₇×D₄	—	2	1	no	—
9	C₇×D₄	C₂²	1	2	yes	—
10	C₂×C₄×C₇	—	2	1	no	—
11	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
12	C₇×C₈	C₂²	1	2	yes	complemented
13	C₂×SD₁₆	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂²×C₇	—	2	2	no	—
15	C₂²×C₇	—	4	2	no	—
16	C₂²×C₇	D₄	1	1	yes	characteristic
17	C₄×C₇	—	2	2	no	—
18	C₄×C₇	D₄	1	1	yes	characteristic
19	C₄×C₇	C₂³	1	1	yes	characteristic
20	C₂×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
21	C₂×D₄	C₂×C₇	1	1	yes	characteristic
22	SD₁₆	C₂×C₇	1	4	yes	direct product factor
23	C₂×C₈	C₂×C₇	1	1	yes	characteristic, complemented
24	C₂×C₇	—	4	2	no	—
25	C₂×C₇	SD₁₆	1	2	yes	direct product factor
26	C₂×C₇	C₂×D₄	1	1	yes	characteristic
27	C₂³	—	2	1	no	—
28	Q₈	—	2	1	no	—
29	Q₈	C₂²×C₇	1	2	yes	complemented
30	D₄	—	2	1	no	—
31	D₄	C₂²×C₇	1	2	yes	—
32	C₂×C₄	—	2	1	no	—
33	C₂×C₄	C₂²×C₇	1	1	yes	characteristic
34	C₈	C₂²×C₇	1	2	yes	complemented
35	C₇	C₂×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²	—	2	2	no	—
37	C₂²	—	4	2	no	—
38	C₂²	C₇×D₄	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	C₇×D₄	1	1	yes	characteristic
41	C₄	C₂³×C₇	1	1	yes	characteristic
42	C₂	—	4	2	no	—
43	C₂	C₇×SD₁₆	1	2	yes	direct product factor
44	C₂	C₂×C₇×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	D₄
commutator, Frattini, cosocle	C₄	C₂³×C₇
prime radical	C₂×C₇×D₄	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×Q₈	C₂	semidirect
3. C₇×SD₁₆	C₂	direct (N × H)
4. C₂×C₇×C₈	C₂	semidirect
7. C₇×Q₈	C₂²	semidirect
12. C₇×C₈	C₂²	semidirect
13. C₂×SD₁₆	C₇	direct (N × H)
20. C₂×Q₈	C₂×C₇	semidirect
22. SD₁₆	C₂×C₇	direct (N × H)
23. C₂×C₈	C₂×C₇	semidirect
25. C₂×C₇	SD₁₆	direct (N × H)
29. Q₈	C₂²×C₇	semidirect
34. C₈	C₂²×C₇	semidirect
35. C₇	C₂×SD₁₆	direct (N × H)
43. C₂	C₇×SD₁₆	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×Q₈	2
C₂×C₇×D₄	2
C₇×SD₁₆	2
C₂×C₇×C₈	2
C₂×SD₁₆	7

Subgroups — C2×C7×SD16 #6536

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×SD₁₆ #6536