Subgroups — #10620482

Order 672.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₈₄	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₂₈	C₂	1	1	yes	maximal, characteristic
3	C₇×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	Dic₅₆	—	3	1	no	maximal, Hall
5	Dic₄₂	—	2	1	no	—
6	C₃×Dic₁₄	—	2	1	no	—
7	C₃×C₇×C₈	C₂²	1	1	yes	characteristic
8	Dic₂₈	—	3	1	no	—
9	Dic₂₈	D₃	1	1	yes	characteristic
10	C₇×C₁₆	—	3	1	no	—
11	#829	—	7	1	no	maximal, Hall
12	C₃×C₄×C₇	D₄	1	1	yes	characteristic
13	Dic₂₁	—	4	1	no	—
14	C₃×Dic₇	—	4	1	no	—
15	Dic₁₄	—	2	1	no	—
16	Dic₁₄	—	6	1	no	—
17	C₇×C₈	C₂×D₃	1	1	yes	characteristic
18	C₃×Q₁₆	—	7	1	no	—
19	Dic₁₂	—	7	1	no	—
20	C₃⋊C₁₆	D₇	1	1	yes	characteristic
21	C₂×C₃×C₇	D₈	1	1	yes	characteristic
22	Q₃₂	—	21	1	no	Sylow
23	C₄×C₇	#67	1	1	yes	characteristic
24	Dic₇	—	4	1	no	—
25	Dic₇	—	12	1	no	—
26	C₃×Q₈	—	14	1	no	—
27	Dic₆	—	14	1	no	—
28	C₃×C₈	C₂×D₇	1	1	yes	characteristic
29	C₃×C₇	Q₃₂	1	1	yes	characteristic, complemented, Hall
30	Q₁₆	—	7	1	no	—
31	Q₁₆	—	21	1	no	—
32	C₁₆	—	3	1	no	—
33	C₂×C₇	#213	1	1	yes	characteristic
34	C₃×C₄	—	28	1	no	—
35	C₃×C₄	D₂₈	1	1	yes	characteristic
36	Dic₃	—	28	1	no	—
37	Q₈	—	14	1	no	—
38	Q₈	—	42	1	no	—
39	C₈	D₃×D₇	1	1	yes	characteristic
40	C₇	#829	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₅₆	1	1	yes	characteristic
42	C₄	—	28	1	no	—
43	C₄	—	84	1	no	—
44	C₄	#4246	1	1	yes	characteristic
45	C₃	Dic₅₆	1	1	yes	characteristic, complemented, Sylow
46	C₂	#66561	1	1	yes	characteristic

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.