Subgroups — D₄×C₇⋊C₉ #92594

Order 504.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇⋊C₉	C₂	1	2	yes	maximal, complemented
2	C₄×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×D₄	C₃	1	1	yes	maximal, characteristic
4	C₂×C₇⋊C₉	—	2	2	no	—
5	C₂×C₇⋊C₉	C₂²	1	1	yes	characteristic
6	C₂²×C₃×C₇	C₂×C₃	1	2	yes	—
7	C₃×C₄×C₇	C₂×C₃	1	1	yes	characteristic
8	D₄×C₉	—	7	1	no	maximal, Hall
9	C₇⋊C₉	D₄	1	1	yes	characteristic, direct product factor, Hall
10	C₇×D₄	C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₇	—	2	2	no	—
12	C₂×C₃×C₇	C₂²×C₃	1	1	yes	characteristic
13	C₂²×C₉	—	7	2	no	—
14	C₄×C₉	—	7	1	no	—
15	C₂²×C₇	C₂×C₉	1	2	yes	complemented
16	C₄×C₇	C₂×C₉	1	1	yes	characteristic, complemented
17	C₃×D₄	ΓL(1,𝔽₈)	1	1	yes	characteristic
18	C₃×C₇	C₃×D₄	1	1	yes	characteristic
19	C₂×C₉	—	7	1	no	—
20	C₂×C₉	—	14	2	no	—
21	C₂×C₇	—	2	2	no	—
22	C₂×C₇	C₂²×C₉	1	1	yes	characteristic
23	C₂²×C₃	C₂×ΓL(1,𝔽₈)	1	2	yes	—
24	C₃×C₄	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
25	C₉	—	7	1	no	Sylow
26	D₄	C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	D₄×C₉	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	2	2	no	—
29	C₂×C₃	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
30	C₂²	C₂×C₇⋊C₉	1	2	yes	complemented
31	C₄	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
32	C₃	D₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
33	C₂	—	2	2	no	—
34	C₂	C₂²×C₇⋊C₉	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.