Subgroups — C₂²×D₇⋊C₉ #92630

Order 504.

96 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, complemented
2	C₂×D₇⋊C₉	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₃×D₇	C₃	1	1	yes	maximal, characteristic
4	C₂×C₇⋊C₉	C₂²	1	3	yes	complemented
5	D₇⋊C₉	C₂²	1	4	yes	direct product factor
6	C₂²×C₃×C₇	C₂×C₃	1	1	yes	characteristic
7	C₂×C₃×D₇	C₂×C₃	1	6	yes	—
8	C₂³×C₉	—	7	1	no	maximal, Hall
9	C₇⋊C₉	C₂³	1	1	yes	characteristic, complemented, Hall
10	C₂²×D₇	C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₇	C₂²×C₃	1	3	yes	—
12	C₃×D₇	C₂²×C₃	1	4	yes	—
13	C₂²×C₉	—	7	6	no	—
14	C₂²×C₉	—	7	1	no	—
15	C₂²×C₇	C₂×C₉	1	1	yes	characteristic, complemented
16	C₂×D₇	C₂×C₉	1	6	yes	complemented
17	C₂³×C₃	—	7	1	no	—
18	C₃×C₇	C₂³×C₃	1	1	yes	characteristic
19	C₂×C₉	—	7	4	no	—
20	C₂×C₉	—	7	3	no	—
21	C₂×C₇	C₂²×C₉	1	3	yes	complemented
22	D₇	C₂²×C₉	1	4	yes	complemented
23	C₂²×C₃	—	7	6	no	—
24	C₂²×C₃	AGL(1,𝔽₇)	1	1	yes	characteristic
25	C₉	—	7	1	no	Sylow
26	C₂³	—	7	1	no	Sylow
27	C₇	C₂³×C₉	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	7	4	no	—
29	C₂×C₃	C₂×AGL(1,𝔽₇)	1	3	yes	—
30	C₂²	—	7	6	no	—
31	C₂²	D₇⋊C₉	1	1	yes	characteristic, direct product factor
32	C₃	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
33	C₂	—	7	4	no	—
34	C₂	C₂×D₇⋊C₉	1	3	yes	direct product factor

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.