Subgroups — C₂×Dic₂₈ #6468

Order 224.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₄	C₂	1	2	yes	maximal
2	C₂×C₇×C₈	C₂	1	1	yes	maximal, characteristic
3	Dic₂₈	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
5	C₂×Dic₇	—	2	2	no	—
6	Dic₁₄	—	2	2	no	—
7	Dic₁₄	C₂²	1	4	yes	—
8	C₇×C₈	C₂²	1	2	yes	—
9	C₂×Q₁₆	—	7	1	no	maximal, Sylow
10	C₂²×C₇	D₄	1	1	yes	characteristic
11	C₄×C₇	D₄	1	1	yes	characteristic
12	C₄×C₇	C₂³	1	1	yes	characteristic
13	Dic₇	—	2	4	no	—
14	C₂×Q₈	—	7	2	no	—
15	Q₁₆	—	7	4	no	—
16	C₂×C₈	D₇	1	1	yes	characteristic
17	C₂×C₇	Q₁₆	1	2	yes	complemented
18	C₂×C₇	C₂×D₄	1	1	yes	characteristic
19	Q₈	—	7	4	no	—
20	Q₈	—	14	2	no	—
21	C₂×C₄	—	14	2	no	—
22	C₂×C₄	C₂×D₇	1	1	yes	characteristic
23	C₈	C₂×D₇	1	2	yes	—
24	C₇	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
25	C₂²	D₂₈	1	1	yes	characteristic
26	C₄	—	14	4	no	—
27	C₄	D₂₈	1	1	yes	characteristic
28	C₄	C₂²×D₇	1	1	yes	characteristic
29	C₂	Dic₂₈	1	2	yes	direct product factor
30	C₂	C₂×D₂₈	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.