Subgroups — C₄²×D₇ #6434

Order 224.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₇	C₂	1	3	yes	maximal
2	C₄²×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×Dic₇	C₂	1	3	yes	maximal, complemented
4	C₂²×D₇	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₇	C₂²	1	3	yes	—
6	C₂×Dic₇	C₂²	1	3	yes	—
7	C₄×D₇	C₄	1	12	yes	direct product factor
8	C₂×C₄²	—	7	1	no	maximal, Sylow
9	C₂²×C₇	C₂³	1	1	yes	characteristic
10	C₂×D₇	C₂×C₄	1	6	yes	—
11	C₄×C₇	C₂×C₄	1	6	yes	complemented
12	Dic₇	C₂×C₄	1	6	yes	complemented
13	C₂²×C₄	—	7	3	no	—
14	C₄²	—	7	3	no	—
15	C₄²	D₇	1	1	yes	characteristic, direct product factor
16	C₂×C₇	C₂²×C₄	1	3	yes	—
17	D₇	C₄²	1	4	yes	direct product factor
18	C₂³	—	7	1	no	—
19	C₂×C₄	—	7	3	no	—
20	C₂×C₄	—	7	12	no	—
21	C₂×C₄	C₂×D₇	1	3	yes	—
22	C₇	C₂×C₄²	1	1	yes	characteristic, complemented, Sylow
23	C₂²	—	7	6	no	—
24	C₂²	C₂²×D₇	1	1	yes	characteristic
25	C₄	—	7	6	no	—
26	C₄	C₄×D₇	1	6	yes	direct product factor
27	C₂	—	7	4	no	—
28	C₂	C₂×C₄×D₇	1	3	yes	—

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.