Subgroups — C₂×Dic₇⋊C₉ #92584

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	1	yes	maximal, characteristic
2	Dic₇⋊C₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×Dic₇	C₃	1	1	yes	maximal, characteristic
4	C₂×C₇⋊C₉	C₄	1	2	yes	complemented
5	C₂×C₇⋊C₉	C₂²	1	1	yes	characteristic
6	C₂²×C₃×C₇	C₂×C₃	1	1	yes	characteristic
7	C₃×Dic₇	C₂×C₃	1	2	yes	—
8	C₂×C₄×C₉	—	7	1	no	maximal, Hall
9	C₇⋊C₉	C₂×C₄	1	1	yes	characteristic, complemented, Hall
10	C₂×Dic₇	C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₇	C₃×C₄	1	2	yes	—
12	C₂×C₃×C₇	C₂²×C₃	1	1	yes	characteristic
13	C₂²×C₉	—	7	1	no	—
14	C₄×C₉	—	7	2	no	—
15	C₂²×C₇	C₂×C₉	1	1	yes	characteristic
16	Dic₇	C₂×C₉	1	2	yes	complemented
17	C₂×C₃×C₄	—	7	1	no	—
18	C₃×C₇	C₂×C₃×C₄	1	1	yes	characteristic
19	C₂×C₉	—	7	2	no	—
20	C₂×C₉	—	7	1	no	—
21	C₂×C₇	C₄×C₉	1	2	yes	complemented
22	C₂×C₇	C₂²×C₉	1	1	yes	characteristic
23	C₂²×C₃	AGL(1,𝔽₇)	1	1	yes	characteristic
24	C₃×C₄	—	7	2	no	—
25	C₉	—	7	1	no	Sylow
26	C₂×C₄	—	7	1	no	Sylow
27	C₇	C₂×C₄×C₉	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	ΓL(1,𝔽₈)⋊C₄	1	2	yes	—
29	C₂×C₃	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
30	C₂²	D₇⋊C₉	1	1	yes	characteristic
31	C₄	—	7	2	no	—
32	C₃	C₂×ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
33	C₂	Dic₇⋊C₉	1	2	yes	direct product factor
34	C₂	C₂×D₇⋊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.