Subgroups — D₇×D₈ #6473

Order 224.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×D₇	C₂	1	2	yes	maximal, complemented
2	C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#1141	C₂	1	2	yes	maximal, complemented
4	D₅₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×D₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₇	—	2	2	no	—
7	C₇×D₄	C₂²	1	2	yes	complemented
8	C₂²⋊D₇	—	2	2	no	—
9	D₂₈	C₂²	1	2	yes	complemented
10	C₄×D₇	C₂²	1	1	yes	characteristic
11	C₇×C₈	C₂²	1	1	yes	characteristic, complemented
12	C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
13	C₂×D₈	—	7	1	no	maximal, Sylow
14	C₂²×C₇	—	2	2	no	—
15	C₂×D₇	—	2	2	no	—
16	C₂×D₇	—	4	4	no	—
17	C₂×D₇	D₄	1	1	yes	characteristic
18	C₄×C₇	C₂³	1	1	yes	characteristic
19	Dic₇	D₄	1	1	yes	characteristic
20	C₂×D₄	—	7	2	no	—
21	D₈	—	7	2	no	—
22	D₈	—	7	1	no	—
23	D₈	D₇	1	1	yes	characteristic, direct product factor
24	C₂×C₈	—	7	1	no	—
25	C₂×C₇	—	4	2	no	—
26	C₂×C₇	C₂×D₄	1	1	yes	characteristic
27	D₇	—	4	2	no	—
28	D₇	D₈	1	2	yes	direct product factor
29	C₂³	—	14	2	no	—
30	D₄	—	7	2	no	—
31	D₄	—	14	2	no	—
32	D₄	C₂×D₇	1	2	yes	complemented
33	C₂×C₄	—	7	1	no	—
34	C₈	—	7	1	no	—
35	C₈	C₂×D₇	1	1	yes	characteristic, complemented
36	C₇	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
37	C₂²	—	2	2	no	—
38	C₂²	—	7	1	no	—
39	C₂²	—	14	2	no	—
40	C₂²	—	28	4	no	—
41	C₄	—	7	1	no	—
42	C₄	C₂²×D₇	1	1	yes	characteristic
43	C₂	—	4	2	no	—
44	C₂	—	7	2	no	—
45	C₂	—	28	2	no	—
46	C₂	D₄×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.