Subgroups — C₂×C₄⋊Dic₇ #6488

Order 224.

92 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	—	2	4	no	—
8	C₂×Dic₇	C₂²	1	4	yes	—
9	C₂×C₄⋊C₄	—	7	1	no	maximal, Sylow
10	C₂²×C₇	C₂×C₄	1	2	yes	—
11	C₂²×C₇	D₄	1	2	yes	—
12	C₂²×C₇	Q₈	1	2	yes	—
13	C₂²×C₇	C₂³	1	1	yes	characteristic
14	C₄×C₇	C₂×C₄	1	4	yes	complemented
15	Dic₇	—	2	4	no	—
16	C₂²×C₄	—	7	2	no	—
17	C₂²×C₄	D₇	1	1	yes	characteristic
18	C₄⋊C₄	—	7	4	no	—
19	C₂×C₇	C₄⋊C₄	1	4	yes	complemented
20	C₂×C₇	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₇	C₂×D₄	1	1	yes	characteristic
22	C₂×C₇	C₂×Q₈	1	1	yes	characteristic
23	C₂³	C₂×D₇	1	1	yes	characteristic
24	C₂×C₄	—	7	4	no	—
25	C₂×C₄	—	14	4	no	—
26	C₂×C₄	Dic₇	1	4	yes	complemented
27	C₂×C₄	C₂×D₇	1	2	yes	—
28	C₇	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
29	C₂²	Dic₁₄	1	2	yes	—
30	C₂²	D₂₈	1	2	yes	—
31	C₂²	C₂×Dic₇	1	2	yes	—
32	C₂²	C₂²×D₇	1	1	yes	characteristic
33	C₄	—	14	4	no	—
34	C₄	C₂×Dic₇	1	4	yes	complemented
35	C₂	C₄⋊Dic₇	1	4	yes	direct product factor
36	C₂	C₂×Dic₁₄	1	1	yes	characteristic
37	C₂	C₂×D₂₈	1	1	yes	characteristic
38	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.