Subgroups — #89471

Order 448.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₈	C₂	1	4	yes	maximal
2	#6432	C₂	1	2	yes	maximal
3	C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₄	C₂²	1	4	yes	—
5	C₂×C₇×C₈	C₂²	1	2	yes	—
6	C₄²×C₇	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₇	—	2	4	no	—
8	Dic₂₈	—	2	8	no	—
9	#494	—	7	1	no	maximal, Sylow
10	C₂×C₄×C₇	D₄	1	2	yes	—
11	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
12	C₂×Dic₇	—	2	4	no	—
13	Dic₁₄	—	2	8	no	—
14	C₇×C₈	D₄	1	4	yes	—
15	C₂×Q₁₆	—	7	4	no	—
16	C₄⋊Q₈	—	7	2	no	—
17	C₄×C₈	D₇	1	1	yes	characteristic
18	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
19	C₄×C₇	Q₁₆	1	4	yes	complemented
20	C₄×C₇	C₂×D₄	1	2	yes	—
21	Dic₇	—	4	4	no	—
22	C₂×Q₈	—	7	4	no	—
23	Q₁₆	—	14	8	no	—
24	C₂×C₈	C₂×D₇	1	2	yes	—
25	C₄⋊C₄	—	14	4	no	—
26	C₄²	C₂×D₇	1	1	yes	characteristic
27	C₂×C₇	#127	1	1	yes	characteristic
28	C₂×C₇	C₂×Q₁₆	1	2	yes	—
29	Q₈	—	14	8	no	—
30	C₂×C₄	—	14	4	no	—
31	C₂×C₄	D₂₈	1	2	yes	—
32	C₂×C₄	C₂²×D₇	1	1	yes	characteristic
33	C₈	D₂₈	1	4	yes	—
34	C₇	#494	1	1	yes	characteristic, complemented, Sylow
35	C₂²	C₂×D₂₈	1	1	yes	characteristic
36	C₄	—	28	4	no	—
37	C₄	Dic₂₈	1	4	yes	complemented
38	C₄	C₂×D₂₈	1	2	yes	—
39	C₂	#6437	1	1	yes	characteristic
40	C₂	C₂×Dic₂₈	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.