Subgroups — C₂×Dic₅₆ #89677

Order 448.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₈	C₂	1	2	yes	maximal
2	C₂×C₇×C₁₆	C₂	1	1	yes	maximal, characteristic
3	Dic₅₆	C₂	1	4	yes	maximal, direct product factor
4	C₂×Dic₁₄	—	2	2	no	—
5	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
6	Dic₂₈	—	2	2	no	—
7	Dic₂₈	C₂²	1	4	yes	—
8	C₇×C₁₆	C₂²	1	2	yes	—
9	C₂×Q₃₂	—	7	1	no	maximal, Sylow
10	C₂×C₄×C₇	D₄	1	1	yes	characteristic
11	C₂×Dic₇	—	4	2	no	—
12	Dic₁₄	—	2	4	no	—
13	Dic₁₄	—	4	2	no	—
14	C₇×C₈	D₄	1	1	yes	characteristic
15	C₇×C₈	C₂³	1	1	yes	characteristic
16	C₂×Q₁₆	—	7	2	no	—
17	Q₃₂	—	7	4	no	—
18	C₂×C₁₆	D₇	1	1	yes	characteristic
19	C₂²×C₇	D₈	1	1	yes	characteristic
20	C₄×C₇	D₈	1	1	yes	characteristic
21	C₄×C₇	C₂×D₄	1	1	yes	characteristic
22	Dic₇	—	4	4	no	—
23	C₂×Q₈	—	14	2	no	—
24	Q₁₆	—	7	4	no	—
25	Q₁₆	—	14	2	no	—
26	C₂×C₈	C₂×D₇	1	1	yes	characteristic
27	C₁₆	C₂×D₇	1	2	yes	—
28	C₂×C₇	Q₃₂	1	2	yes	complemented
29	C₂×C₇	C₂×D₈	1	1	yes	characteristic
30	Q₈	—	14	4	no	—
31	Q₈	—	28	2	no	—
32	C₂×C₄	—	28	2	no	—
33	C₂×C₄	D₂₈	1	1	yes	characteristic
34	C₈	D₂₈	1	1	yes	characteristic
35	C₈	C₂²×D₇	1	1	yes	characteristic
36	C₇	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
37	C₂²	D₅₆	1	1	yes	characteristic
38	C₄	—	28	4	no	—
39	C₄	D₅₆	1	1	yes	characteristic
40	C₄	C₂×D₂₈	1	1	yes	characteristic
41	C₂	Dic₅₆	1	2	yes	direct product factor
42	C₂	C₂×D₅₆	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.