Subgroups — C₂×Q₈×D₇ #6549

Order 224.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×D₇	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄×D₇	C₂	1	3	yes	maximal
4	C₂×Dic₁₄	C₂	1	3	yes	maximal, complemented
5	C₂²×D₇	C₂²	1	1	yes	characteristic
6	C₇×Q₈	C₂²	1	4	yes	complemented
7	C₂×C₄×C₇	C₂²	1	3	yes	—
8	C₂×Dic₇	C₂²	1	3	yes	—
9	C₄×D₇	C₂²	1	12	yes	—
10	Dic₁₄	C₂²	1	12	yes	complemented
11	C₂²×Q₈	—	7	1	no	maximal, Sylow
12	C₂²×C₇	C₂³	1	1	yes	characteristic
13	C₂×D₇	Q₈	1	4	yes	direct product factor
14	C₂×D₇	C₂³	1	2	yes	—
15	C₄×C₇	C₂³	1	6	yes	—
16	Dic₇	C₂³	1	6	yes	—
17	C₂×Q₈	—	7	8	no	—
18	C₂×Q₈	—	7	3	no	—
19	C₂×Q₈	D₇	1	1	yes	characteristic, direct product factor
20	C₂²×C₄	—	7	3	no	—
21	C₂×C₇	C₂×Q₈	1	2	yes	complemented
22	C₂×C₇	C₂⁴	1	1	yes	characteristic
23	D₇	C₂×Q₈	1	4	yes	direct product factor
24	C₂³	—	7	1	no	—
25	Q₈	—	7	12	no	—
26	Q₈	C₂×D₇	1	4	yes	direct product factor
27	C₂×C₄	—	7	3	no	—
28	C₂×C₄	—	7	12	no	—
29	C₂×C₄	C₂×D₇	1	3	yes	—
30	C₇	C₂²×Q₈	1	1	yes	characteristic, complemented, Sylow
31	C₂²	—	7	4	no	—
32	C₂²	—	7	2	no	—
33	C₂²	C₂²×D₇	1	1	yes	characteristic
34	C₄	—	7	6	no	—
35	C₄	C₂²×D₇	1	6	yes	—
36	C₂	—	7	4	no	—
37	C₂	Q₈×D₇	1	2	yes	direct product factor
38	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.