Subgroups — #43247557

Order 28352.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₃₅₄₄	C₂	1	1	yes	maximal, characteristic
2	C₄₄₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic
3	Q₃₂×C₄₄₃	C₂	1	1	yes	maximal, characteristic
4	Dic₁₇₇₂	—	2	1	no	—
5	Q₁₆×C₄₄₃	—	2	1	no	—
6	C₁₆×C₄₄₃	C₂²	1	1	yes	characteristic
7	Dic₈₈₆	—	4	1	no	—
8	Q₈×C₄₄₃	—	4	1	no	—
9	C₈×C₄₄₃	D₄	1	1	yes	characteristic
10	C₄×C₄₄₃	—	8	1	no	—
11	C₄×C₄₄₃	D₈	1	1	yes	characteristic
12	Dic₄₄₃	—	8	1	no	—
13	C₂×C₄₄₃	D₁₆	1	1	yes	characteristic
14	C₄₄₃	Q₆₄	1	1	yes	characteristic, complemented, Sylow
15	Q₆₄	—	443	1	no	maximal, Sylow
16	Q₃₂	—	443	1	no	—
17	Q₃₂	D₄₄₃	1	1	yes	characteristic
18	C₃₂	—	443	1	no	—
19	Q₁₆	—	2	1	no	—
20	Q₁₆	—	886	1	no	—
21	C₁₆	C₂×D₄₄₃	1	1	yes	characteristic
22	Q₈	—	4	1	no	—
23	Q₈	—	1772	1	no	—
24	C₈	C₂²⋊D₄₄₃	1	1	yes	characteristic
25	C₄	—	8	1	no	—
26	C₄	—	3544	1	no	—
27	C₄	#20296772	1	1	yes	characteristic
28	C₂	#28381827	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
14. C₄₄₃	Q₆₄	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.