Subgroups — D₁₁₂⋊C₃ #10620427

Order 672.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₆⋊C₃	C₂	1	2	yes	maximal, complemented
2	C₁₆×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₁₂	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₄⋊AGL(1,𝔽₇)	—	2	2	no	—
5	C₈×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
6	D₅₆	C₂×C₃	1	2	yes	complemented
7	C₇×C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×D₁₆	—	7	1	no	maximal, Hall
9	C₂×AGL(1,𝔽₇)	—	4	2	no	—
10	C₄×ΓL(1,𝔽₈)	D₄	1	1	yes	characteristic
11	D₂₈	—	2	2	no	—
12	C₇×C₈	C₂²×C₃	1	1	yes	characteristic
13	C₃×D₈	—	7	2	no	—
14	C₃×C₁₆	—	7	1	no	—
15	C₂×ΓL(1,𝔽₈)	D₈	1	1	yes	characteristic
16	AGL(1,𝔽₇)	—	8	2	no	—
17	D₁₆	—	7	1	no	Sylow
18	C₂×D₇	—	4	2	no	—
19	C₄×C₇	C₃×D₄	1	1	yes	characteristic
20	C₃×D₄	—	14	2	no	—
21	C₃×C₈	—	7	1	no	—
22	ΓL(1,𝔽₈)	D₁₆	1	1	yes	characteristic, complemented, Hall
23	D₈	—	7	2	no	—
24	C₁₆	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
25	C₂×C₇	C₃×D₈	1	1	yes	characteristic
26	D₇	—	8	2	no	—
27	C₂²×C₃	—	28	2	no	—
28	C₃×C₄	—	7	1	no	—
29	D₄	—	14	2	no	—
30	C₈	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
31	C₇	C₃×D₁₆	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃	—	7	1	no	—
33	C₂×C₃	—	56	2	no	—
34	C₂²	—	28	2	no	—
35	C₄	C₄⋊AGL(1,𝔽₇)	1	1	yes	characteristic
36	C₃	—	7	1	no	Sylow
37	C₂	—	56	2	no	—
38	C₂	D₅₆⋊C₃	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.