Subgroups — D₇×Q₁₆ #6480

Order 224.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₇	C₂	1	2	yes	maximal
2	C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#1144	C₂	1	2	yes	maximal, complemented
4	Dic₂₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×D₇	C₂	1	1	yes	maximal, characteristic
6	C₇×Q₈	C₂²	1	2	yes	—
7	C₄×D₇	—	2	2	no	—
8	C₄×D₇	C₂²	1	1	yes	characteristic
9	Dic₁₄	—	2	2	no	—
10	Dic₁₄	C₂²	1	2	yes	—
11	C₇×C₈	C₂²	1	1	yes	characteristic
12	C₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×Q₁₆	—	7	1	no	maximal, Sylow
14	C₂×D₇	D₄	1	1	yes	characteristic
15	C₄×C₇	—	2	2	no	—
16	C₄×C₇	C₂³	1	1	yes	characteristic
17	Dic₇	—	2	2	no	—
18	Dic₇	D₄	1	1	yes	characteristic
19	C₂×Q₈	—	7	2	no	—
20	Q₁₆	—	7	2	no	—
21	Q₁₆	—	7	1	no	—
22	Q₁₆	D₇	1	1	yes	characteristic, direct product factor
23	C₂×C₈	—	7	1	no	—
24	C₂×C₇	C₂×D₄	1	1	yes	characteristic
25	D₇	Q₁₆	1	2	yes	direct product factor
26	Q₈	—	7	2	no	—
27	Q₈	—	14	2	no	—
28	Q₈	C₂×D₇	1	2	yes	—
29	C₂×C₄	—	7	1	no	—
30	C₂×C₄	—	14	2	no	—
31	C₈	—	7	1	no	—
32	C₈	C₂×D₇	1	1	yes	characteristic
33	C₇	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	7	1	no	—
35	C₄	—	2	2	no	—
36	C₄	—	7	1	no	—
37	C₄	—	14	2	no	—
38	C₄	C₂²×D₇	1	1	yes	characteristic
39	C₂	—	7	2	no	—
40	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.