Subgroups — C₄²×Dic₇ #89702

Order 448.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₇	C₂	1	6	yes	maximal
3	C₂²×C₄×C₇	C₂²	1	3	yes	—
4	C₂²×Dic₇	C₂²	1	4	yes	—
5	C₄²×C₇	C₄	1	4	yes	complemented
6	C₄×Dic₇	C₄	1	24	yes	direct product factor
7	C₄³	—	7	1	no	maximal, Sylow
8	C₂³×C₇	C₂³	1	1	yes	characteristic
9	C₂×C₄×C₇	C₂×C₄	1	12	yes	—
10	C₂×C₄×C₇	C₂×C₄	1	6	yes	—
11	C₂×Dic₇	C₂×C₄	1	24	yes	—
12	C₂×C₄²	—	7	6	no	—
13	C₂×C₄²	D₇	1	1	yes	characteristic
14	C₂²×C₇	C₂²×C₄	1	6	yes	—
15	C₂²×C₇	C₂²×C₄	1	1	yes	characteristic
16	C₄×C₇	C₄²	1	12	yes	complemented
17	Dic₇	C₄²	1	16	yes	direct product factor
18	C₂²×C₄	—	7	4	no	—
19	C₂²×C₄	C₂×D₇	1	3	yes	—
20	C₄²	—	7	24	no	—
21	C₄²	Dic₇	1	4	yes	direct product factor
22	C₂×C₇	C₂×C₄²	1	4	yes	—
23	C₂×C₇	C₂×C₄²	1	3	yes	—
24	C₂³	C₂²×D₇	1	1	yes	characteristic
25	C₂×C₄	—	7	24	no	—
26	C₂×C₄	C₄×D₇	1	12	yes	—
27	C₂×C₄	C₂×Dic₇	1	6	yes	—
28	C₇	C₄³	1	1	yes	characteristic, complemented, Sylow
29	C₂²	C₂×C₄×D₇	1	6	yes	—
30	C₂²	C₂²×Dic₇	1	1	yes	characteristic
31	C₄	—	7	16	no	—
32	C₄	C₄×Dic₇	1	12	yes	direct product factor
33	C₂	C₄²×D₇	1	4	yes	—
34	C₂	C₂×C₄×Dic₇	1	3	yes	—

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.