Subgroups — #22625036

Order 9344.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14556641	C₂	1	2	yes	maximal
2	C₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic
3	#14556641	C₄	1	4	yes	complemented
4	C₂×#11924003	C₂²	1	1	yes	characteristic
5	C₈×Dic₇₃	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₇₃	C₄	1	1	yes	characteristic
7	C₂×#10596831	C₈	1	1	yes	characteristic
8	C₄×Dic₇₃	C₈	1	1	yes	characteristic
9	#11924003	C₂×C₄	1	2	yes	—
10	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
11	C₁₆×C₇₃	C₈	1	2	yes	—
12	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
13	C₂×Dic₇₃	C₁₆	1	2	yes	—
14	C₈×C₇₃	C₄²	1	1	yes	characteristic
15	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
16	#10596831	C₁₆	1	2	yes	—
17	C₂²×C₇₃	C₂×C₁₆	1	1	yes	characteristic
18	C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
19	C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
20	Dic₇₃	C₃₂	1	4	yes	complemented
21	C₂×C₇₃	C₄×C₁₆	1	1	yes	characteristic
22	C₂×C₇₃	C₂×C₃₂	1	2	yes	—
23	C₄×C₃₂	—	73	1	no	maximal, Sylow
24	C₇₃	C₄×C₃₂	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃₂	—	73	2	no	—
26	C₄×C₁₆	—	73	1	no	—
27	C₂×C₁₆	—	73	1	no	—
28	C₂×C₁₆	#64408	1	1	yes	characteristic
29	C₄×C₈	—	73	1	no	—
30	C₃₂	—	73	4	no	—
31	C₂×C₈	—	73	1	no	—
32	C₂×C₈	C₂×#64408	1	1	yes	characteristic
33	C₄²	—	73	1	no	—
34	C₁₆	—	73	2	no	—
35	C₁₆	#10596833	1	2	yes	—
36	C₂×C₄	—	73	2	no	—
37	C₂×C₄	#11924036	1	1	yes	characteristic
38	C₈	—	73	2	no	—
39	C₈	C₄×#64408	1	1	yes	characteristic
40	C₈	C₂×#10596833	1	1	yes	characteristic
41	C₂²	#14556664	1	1	yes	characteristic
42	C₄	—	73	4	no	—
43	C₄	C₄×#10596833	1	1	yes	characteristic
44	C₄	#14556664	1	1	yes	characteristic
45	C₂	#17989473	1	1	yes	characteristic
46	C₂	#17989518	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₁₆	#64408
commutator, hypocenter	C₇₃	C₄×C₃₂
Frattini	C₂×C₈	C₂×#64408
Fitting	C₂×C₁₆×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₁₆
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
3. #14556641	C₄	semidirect
20. Dic₇₃	C₃₂	semidirect
24. C₇₃	C₄×C₃₂	semidirect