Subgroups — C₂×C₇⋊C₁₆ #6385

Order 224.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₈	C₂	1	1	yes	maximal, characteristic
2	C₇⋊C₁₆	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₄×C₇	C₄	1	1	yes	characteristic
4	C₇×C₈	C₄	1	1	yes	characteristic
5	C₇×C₈	C₂²	1	1	yes	characteristic
6	C₂×C₁₆	—	7	1	no	maximal, Sylow
7	C₂²×C₇	C₈	1	1	yes	characteristic
8	C₄×C₇	C₈	1	1	yes	characteristic
9	C₄×C₇	C₂×C₄	1	1	yes	characteristic
10	C₂×C₈	D₇	1	1	yes	characteristic
11	C₁₆	—	7	2	no	—
12	C₂×C₇	C₁₆	1	2	yes	complemented
13	C₂×C₇	C₂×C₈	1	1	yes	characteristic
14	C₂×C₄	Dic₇	1	1	yes	characteristic
15	C₈	Dic₇	1	1	yes	characteristic
16	C₈	C₂×D₇	1	1	yes	characteristic
17	C₇	C₂×C₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₂²	C₇⋊C₈	1	1	yes	characteristic
19	C₄	C₇⋊C₈	1	1	yes	characteristic
20	C₄	C₂×Dic₇	1	1	yes	characteristic
21	C₂	C₇⋊C₁₆	1	2	yes	direct product factor
22	C₂	C₂×C₇⋊C₈	1	1	yes	characteristic

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

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