Subgroups — C₂×#6437 #90166

Order 448.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₂₈	C₂	1	6	yes	maximal, complemented
2	C₂×C₄²×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#6437	C₂	1	8	yes	maximal, direct product factor
4	C₂³×D₇	C₂²	1	4	yes	—
5	C₂²×C₄×C₇	C₂²	1	3	yes	—
6	C₂×D₂₈	—	2	24	no	—
7	C₂×D₂₈	C₂²	1	24	yes	complemented
8	C₄²×C₇	C₂²	1	4	yes	complemented
9	C₂×#127	—	7	1	no	maximal, Sylow
10	C₂³×C₇	C₂³	1	1	yes	characteristic
11	C₂²×D₇	—	2	24	no	—
12	C₂²×D₇	C₂³	1	8	yes	—
13	C₂×C₄×C₇	D₄	1	12	yes	complemented
14	C₂×C₄×C₇	C₂³	1	6	yes	—
15	D₂₈	—	2	48	no	—
16	C₂²×D₄	—	7	6	no	—
17	#127	—	7	8	no	—
18	C₂×C₄²	D₇	1	1	yes	characteristic, complemented
19	C₂²×C₇	C₂×D₄	1	6	yes	—
20	C₂²×C₇	C₂⁴	1	1	yes	characteristic
21	C₂×D₇	—	2	24	no	—
22	C₂×D₇	—	4	16	no	—
23	C₄×C₇	C₂×D₄	1	12	yes	complemented
24	C₂⁴	—	7	4	no	—
25	C₂×D₄	—	7	24	no	—
26	C₂×D₄	—	14	24	no	—
27	C₂²×C₄	C₂×D₇	1	3	yes	—
28	C₄²	C₂×D₇	1	4	yes	complemented
29	C₂×C₇	#127	1	4	yes	complemented
30	C₂×C₇	C₂²×D₄	1	3	yes	—
31	D₇	—	4	8	no	—
32	C₂³	—	7	8	no	—
33	C₂³	—	14	24	no	—
34	C₂³	C₂²×D₇	1	1	yes	characteristic
35	D₄	—	14	48	no	—
36	C₂×C₄	D₂₈	1	12	yes	complemented
37	C₂×C₄	C₂²×D₇	1	6	yes	—
38	C₇	C₂×#127	1	1	yes	characteristic, complemented, Sylow
39	C₂²	—	14	24	no	—
40	C₂²	—	28	16	no	—
41	C₂²	C₂×D₂₈	1	6	yes	—
42	C₂²	C₂³×D₇	1	1	yes	characteristic
43	C₄	C₂×D₂₈	1	12	yes	complemented
44	C₂	—	28	8	no	—
45	C₂	#6437	1	4	yes	direct product factor
46	C₂	C₂²×D₂₈	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.