Subgroups — #17985836

Order 4544.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₁₃₆	C₂	1	1	yes	maximal, characteristic
2	C₇₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₃₂×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅₆₈	—	2	1	no	—
5	Q₁₆×C₇₁	—	2	1	no	—
6	C₁₆×C₇₁	C₂²	1	1	yes	characteristic
7	Q₈×C₇₁	—	4	1	no	—
8	D₂₈₄	—	4	1	no	—
9	C₈×C₇₁	D₄	1	1	yes	characteristic
10	C₂×D₇₁	—	8	1	no	—
11	C₄×C₇₁	—	8	1	no	—
12	C₄×C₇₁	D₈	1	1	yes	characteristic
13	C₂×C₇₁	D₁₆	1	1	yes	characteristic
14	D₇₁	—	16	1	no	—
15	C₇₁	SD₆₄	1	1	yes	characteristic, complemented, Sylow
16	SD₆₄	—	71	1	no	maximal, Sylow
17	Q₃₂	D₇₁	1	1	yes	characteristic, complemented
18	D₁₆	—	71	1	no	—
19	C₃₂	—	71	1	no	—
20	Q₁₆	—	2	1	no	—
21	D₈	—	142	1	no	—
22	C₁₆	C₂×D₇₁	1	1	yes	characteristic
23	Q₈	—	4	1	no	—
24	D₄	—	284	1	no	—
25	C₈	C₂²⋊D₇₁	1	1	yes	characteristic
26	C₂²	—	568	1	no	—
27	C₄	—	8	1	no	—
28	C₄	#11765850	1	1	yes	characteristic
29	C₂	—	1136	1	no	—
30	C₂	#14556069	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.