Subgroups — #89244

Order 448.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₅₆	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₁₂	C₂	1	1	yes	maximal, characteristic
3	C₇×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₂₈	—	2	1	no	—
5	D₅₆	—	2	1	no	—
6	C₇×C₁₆	C₂²	1	1	yes	characteristic
7	SD₆₄	—	7	1	no	maximal, Sylow
8	D₂₈	—	4	1	no	—
9	Dic₁₄	—	4	1	no	—
10	C₇×C₈	D₄	1	1	yes	characteristic
11	Q₃₂	—	7	1	no	—
12	D₁₆	—	7	1	no	—
13	C₃₂	D₇	1	1	yes	characteristic, complemented
14	C₂×D₇	—	8	1	no	—
15	C₄×C₇	D₈	1	1	yes	characteristic
16	Dic₇	—	8	1	no	—
17	Q₁₆	—	14	1	no	—
18	D₈	—	14	1	no	—
19	C₁₆	C₂×D₇	1	1	yes	characteristic
20	C₂×C₇	D₁₆	1	1	yes	characteristic
21	D₇	—	16	1	no	—
22	Q₈	—	28	1	no	—
23	D₄	—	28	1	no	—
24	C₈	D₂₈	1	1	yes	characteristic
25	C₇	SD₆₄	1	1	yes	characteristic, complemented, Sylow
26	C₂²	—	56	1	no	—
27	C₄	—	56	1	no	—
28	C₄	D₅₆	1	1	yes	characteristic
29	C₂	—	112	1	no	—
30	C₂	D₁₁₂	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.