Subgroups — C₂²×D₂₈ #6544

Order 224.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₇	C₂	1	2	yes	maximal, complemented
2	C₂²×C₄×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₈	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₇	C₂²	1	1	yes	characteristic
5	C₂²×D₇	—	2	8	no	—
6	C₂²×D₇	C₂²	1	12	yes	complemented
7	C₂×C₄×C₇	C₂²	1	6	yes	complemented
8	D₂₈	C₂²	1	16	yes	direct product factor
9	C₂²×D₄	—	7	1	no	maximal, Sylow
10	C₂²×C₇	D₄	1	4	yes	complemented
11	C₂²×C₇	C₂³	1	3	yes	—
12	C₂×D₇	—	2	24	no	—
13	C₂×D₇	C₂³	1	8	yes	complemented
14	C₄×C₇	C₂³	1	4	yes	complemented
15	C₂⁴	—	7	2	no	—
16	C₂×D₄	—	7	12	no	—
17	C₂²×C₄	D₇	1	1	yes	characteristic, complemented
18	C₂×C₇	C₂×D₄	1	6	yes	complemented
19	C₂×C₇	C₂⁴	1	1	yes	characteristic
20	D₇	—	2	8	no	—
21	C₂³	—	7	12	no	—
22	C₂³	—	14	8	no	—
23	C₂³	C₂×D₇	1	1	yes	characteristic
24	D₄	—	7	16	no	—
25	C₂×C₄	C₂×D₇	1	6	yes	complemented
26	C₇	C₂²×D₄	1	1	yes	characteristic, complemented, Sylow
27	C₂²	—	7	8	no	—
28	C₂²	—	14	24	no	—
29	C₂²	D₂₈	1	4	yes	direct product factor
30	C₂²	C₂²×D₇	1	3	yes	—
31	C₄	C₂²×D₇	1	4	yes	complemented
32	C₂	—	14	8	no	—
33	C₂	C₂×D₂₈	1	6	yes	direct product factor
34	C₂	C₂³×D₇	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.