Subgroups — #43253007

Order 28544.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₁₃₆	C₂	1	1	yes	maximal, characteristic
2	C₂₂₃⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₆₄×C₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₅₆₈	—	2	1	no	—
5	Q₃₂×C₂₂₃	—	2	1	no	—
6	C₃₂×C₂₂₃	C₂²	1	1	yes	characteristic
7	D₁₇₈₄	—	4	1	no	—
8	Q₁₆×C₂₂₃	—	4	1	no	—
9	C₁₆×C₂₂₃	D₄	1	1	yes	characteristic
10	D₈₉₂	—	8	1	no	—
11	Q₈×C₂₂₃	—	8	1	no	—
12	C₈×C₂₂₃	D₈	1	1	yes	characteristic
13	C₂×D₂₂₃	—	16	1	no	—
14	C₄×C₂₂₃	—	16	1	no	—
15	C₄×C₂₂₃	D₁₆	1	1	yes	characteristic
16	C₂×C₂₂₃	D₃₂	1	1	yes	characteristic
17	D₂₂₃	—	32	1	no	—
18	C₂₂₃	SD₁₂₈	1	1	yes	characteristic, complemented, Sylow
19	SD₁₂₈	—	223	1	no	maximal, Sylow
20	Q₆₄	D₂₂₃	1	1	yes	characteristic, complemented
21	D₃₂	—	223	1	no	—
22	C₆₄	—	223	1	no	—
23	Q₃₂	—	2	1	no	—
24	D₁₆	—	446	1	no	—
25	C₃₂	C₂×D₂₂₃	1	1	yes	characteristic
26	Q₁₆	—	4	1	no	—
27	D₈	—	892	1	no	—
28	C₁₆	C₂²⋊D₂₂₃	1	1	yes	characteristic
29	Q₈	—	8	1	no	—
30	D₄	—	1784	1	no	—
31	C₈	#16813155	1	1	yes	characteristic
32	C₂²	—	3568	1	no	—
33	C₄	—	16	1	no	—
34	C₄	#20297245	1	1	yes	characteristic
35	C₂	—	7136	1	no	—
36	C₂	#28383415	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.