Subgroups — C₂×C₄×Dic₇ #6485

Order 224.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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