Subgroups — C₆₄×D₁₇₃ #36351771

Order 22144.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₂×D₁₇₃	C₂	1	1	yes	maximal, characteristic
2	#26011210	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₄×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×D₁₇₃	C₄	1	1	yes	characteristic
5	#19149585	C₄	1	1	yes	characteristic
6	C₃₂×C₁₇₃	C₂²	1	1	yes	characteristic
7	C₈×D₁₇₃	C₈	1	1	yes	characteristic
8	#14583801	C₈	1	1	yes	characteristic
9	C₁₆×C₁₇₃	C₂×C₄	1	1	yes	characteristic
10	C₄×D₁₇₃	C₁₆	1	1	yes	characteristic
11	#13063436	C₁₆	1	1	yes	characteristic
12	C₈×C₁₇₃	C₂×C₈	1	1	yes	characteristic
13	C₂×D₁₇₃	C₃₂	1	1	yes	characteristic
14	C₄×C₁₇₃	C₂×C₁₆	1	1	yes	characteristic
15	Dic₁₇₃	C₃₂	1	1	yes	characteristic
16	C₂×C₁₇₃	C₂×C₃₂	1	1	yes	characteristic
17	D₁₇₃	C₆₄	1	2	yes	direct product factor
18	C₁₇₃	C₂×C₆₄	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₆₄	—	173	1	no	maximal, Sylow
20	C₂×C₃₂	—	173	1	no	—
21	C₆₄	—	173	1	no	—
22	C₆₄	D₁₇₃	1	1	yes	characteristic, direct product factor
23	C₂×C₁₆	—	173	1	no	—
24	C₃₂	—	173	1	no	—
25	C₃₂	C₂×D₁₇₃	1	1	yes	characteristic
26	C₂×C₈	—	173	1	no	—
27	C₁₆	—	173	1	no	—
28	C₁₆	C₄×D₁₇₃	1	1	yes	characteristic
29	C₂×C₄	—	173	1	no	—
30	C₈	—	173	1	no	—
31	C₈	C₈×D₁₇₃	1	1	yes	characteristic
32	C₂²	—	173	1	no	—
33	C₄	—	173	1	no	—
34	C₄	C₁₆×D₁₇₃	1	1	yes	characteristic
35	C₂	—	173	2	no	—
36	C₂	C₃₂×D₁₇₃	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.