Subgroups — #89467

Order 448.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₆	C₂	1	4	yes	maximal, complemented
2	#6437	C₂	1	2	yes	maximal, complemented
3	C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₈	—	2	4	no	—
5	C₂×D₂₈	C₂²	1	4	yes	—
6	C₂×C₇×C₈	C₂²	1	2	yes	—
7	C₄²×C₇	C₂²	1	1	yes	characteristic
8	D₅₆	—	2	8	no	—
9	#493	—	7	1	no	maximal, Sylow
10	C₂²×D₇	—	2	4	no	—
11	C₂×C₄×C₇	D₄	1	2	yes	—
12	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
13	D₂₈	—	2	8	no	—
14	D₂₈	—	4	8	no	—
15	C₇×C₈	D₄	1	4	yes	complemented
16	C₂×D₈	—	7	4	no	—
17	#127	—	7	2	no	—
18	C₄×C₈	D₇	1	1	yes	characteristic, complemented
19	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
20	C₂×D₇	—	4	4	no	—
21	C₂×D₇	—	4	8	no	—
22	C₄×C₇	D₈	1	4	yes	complemented
23	C₄×C₇	C₂×D₄	1	2	yes	—
24	C₂×D₄	—	7	4	no	—
25	C₂×D₄	—	14	4	no	—
26	D₈	—	14	8	no	—
27	C₂×C₈	C₂×D₇	1	2	yes	—
28	C₄²	C₂×D₇	1	1	yes	characteristic
29	C₂×C₇	#127	1	1	yes	characteristic
30	C₂×C₇	C₂×D₈	1	2	yes	—
31	D₇	—	8	4	no	—
32	C₂³	—	14	4	no	—
33	D₄	—	14	8	no	—
34	D₄	—	28	8	no	—
35	C₂×C₄	D₂₈	1	2	yes	—
36	C₂×C₄	C₂²×D₇	1	1	yes	characteristic
37	C₈	D₂₈	1	4	yes	complemented
38	C₇	#493	1	1	yes	characteristic, complemented, Sylow
39	C₂²	—	28	4	no	—
40	C₂²	—	28	8	no	—
41	C₂²	C₂×D₂₈	1	1	yes	characteristic
42	C₄	D₅₆	1	4	yes	complemented
43	C₄	C₂×D₂₈	1	2	yes	—
44	C₂	—	56	4	no	—
45	C₂	#6437	1	1	yes	characteristic
46	C₂	C₂×D₅₆	1	2	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.