Subgroups — C₂²×C₄×D₇ #6543

Order 224.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₇	C₂	1	12	yes	maximal, direct product factor
5	C₂³×C₇	C₂²	1	1	yes	characteristic
6	C₂²×D₇	C₄	1	8	yes	direct product factor
7	C₂²×D₇	C₂²	1	6	yes	—
8	C₂×C₄×C₇	C₂²	1	6	yes	complemented
9	C₂×Dic₇	C₂²	1	6	yes	complemented
10	C₄×D₇	C₂²	1	16	yes	direct product factor
11	C₂³×C₄	—	7	1	no	maximal, Sylow
12	C₂²×C₇	C₂×C₄	1	4	yes	complemented
13	C₂²×C₇	C₂³	1	3	yes	—
14	C₂×D₇	C₂×C₄	1	24	yes	direct product factor
15	C₂×D₇	C₂³	1	4	yes	—
16	C₄×C₇	C₂³	1	4	yes	complemented
17	Dic₇	C₂³	1	4	yes	complemented
18	C₂⁴	—	7	1	no	—
19	C₂²×C₄	—	7	1	no	—
20	C₂²×C₄	—	7	12	no	—
21	C₂²×C₄	D₇	1	1	yes	characteristic, direct product factor
22	C₂×C₇	C₂²×C₄	1	6	yes	complemented
23	C₂×C₇	C₂⁴	1	1	yes	characteristic
24	D₇	C₂²×C₄	1	8	yes	direct product factor
25	C₂³	—	7	8	no	—
26	C₂³	—	7	6	no	—
27	C₂³	C₂×D₇	1	1	yes	characteristic
28	C₂×C₄	—	7	6	no	—
29	C₂×C₄	—	7	16	no	—
30	C₂×C₄	C₂×D₇	1	6	yes	direct product factor
31	C₇	C₂³×C₄	1	1	yes	characteristic, complemented, Sylow
32	C₂²	—	7	24	no	—
33	C₂²	—	7	4	no	—
34	C₂²	C₄×D₇	1	4	yes	direct product factor
35	C₂²	C₂²×D₇	1	3	yes	—
36	C₄	—	7	4	no	—
37	C₄	C₂²×D₇	1	4	yes	direct product factor
38	C₂	—	7	8	no	—
39	C₂	C₂×C₄×D₇	1	6	yes	direct product factor
40	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.