Subgroups — C₂×Dic₄₂ #66725

Order 336.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₂₁	C₂	1	2	yes	maximal
3	Dic₄₂	C₂	1	4	yes	maximal, direct product factor
4	C₂×Dic₁₄	—	3	1	no	maximal, Hall
5	C₂²×C₃×C₇	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₇	C₂²	1	2	yes	—
7	Dic₂₁	C₂²	1	4	yes	—
8	C₂×C₄×C₇	D₃	1	1	yes	characteristic
9	C₂×Dic₇	—	3	2	no	—
10	Dic₁₄	—	3	4	no	—
11	C₂×Dic₆	—	7	1	no	maximal, Hall
12	C₂×C₃×C₇	Q₈	1	2	yes	complemented
13	C₂×C₃×C₇	C₂³	1	1	yes	characteristic
14	C₂²×C₇	C₂×D₃	1	1	yes	characteristic
15	C₄×C₇	C₂×D₃	1	2	yes	—
16	Dic₇	—	3	4	no	—
17	C₂×C₃×C₄	D₇	1	1	yes	characteristic
18	C₂×Dic₃	—	7	2	no	—
19	Dic₆	—	7	4	no	—
20	C₃×C₇	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
21	C₂×Q₈	—	21	1	no	Sylow
22	C₂×C₇	Dic₆	1	2	yes	complemented
23	C₂×C₇	C₂²×D₃	1	1	yes	characteristic
24	C₂²×C₃	C₂×D₇	1	1	yes	characteristic
25	C₃×C₄	C₂×D₇	1	2	yes	—
26	Dic₃	—	7	4	no	—
27	Q₈	—	21	4	no	—
28	C₂×C₄	—	21	2	no	—
29	C₂×C₄	D₂₁	1	1	yes	characteristic
30	C₇	C₂×Dic₆	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	Dic₁₄	1	2	yes	complemented
32	C₂×C₃	C₂²×D₇	1	1	yes	characteristic
33	C₂²	C₂×D₂₁	1	1	yes	characteristic
34	C₄	—	21	4	no	—
35	C₄	C₂×D₂₁	1	2	yes	—
36	C₃	C₂×Dic₁₄	1	1	yes	characteristic, complemented, Sylow
37	C₂	Dic₄₂	1	2	yes	direct product factor
38	C₂	C₂²×D₂₁	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.