Subgroups — #22625089

Order 9344.

62 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	—	2	2	no	—
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	D₄	1	1	yes	characteristic
10	#11924003	Q₈	1	1	yes	characteristic
11	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₇₃	—	2	1	no	—
13	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
14	C₂×Dic₇₃	C₁₆	1	1	yes	characteristic
15	C₂×Dic₇₃	C₁₆	1	1	yes	characteristic
16	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₇₃	M₁₆	1	1	yes	characteristic
18	#10596831	—	2	1	no	—
19	C₂²×C₇₃	C₂×C₁₆	1	1	yes	characteristic
20	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
21	C₄×C₇₃	M₃₂	1	1	yes	characteristic
22	Dic₇₃	—	2	1	no	—
23	Dic₇₃	C₃₂	1	2	yes	complemented
24	C₂×C₇₃	C₄⋊C₁₆	1	1	yes	characteristic
25	C₂×C₇₃	C₂×C₃₂	1	1	yes	characteristic
26	C₂×C₇₃	M₆₄	1	1	yes	characteristic
27	C₄⋊C₃₂	—	73	1	no	maximal, Sylow
28	C₇₃	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃₂	—	73	2	no	—
30	C₄×C₁₆	—	73	1	no	—
31	C₂×C₁₆	—	73	1	no	—
32	C₂×C₁₆	#64408	1	1	yes	characteristic
33	C₄×C₈	—	73	1	no	—
34	C₃₂	—	146	2	no	—
35	C₂×C₈	—	73	1	no	—
36	C₂×C₈	C₂×#64408	1	1	yes	characteristic
37	C₄²	—	73	1	no	—
38	C₁₆	—	2	1	no	—
39	C₁₆	—	73	1	no	—
40	C₁₆	—	73	1	no	—
41	C₂×C₄	—	73	1	no	—
42	C₂×C₄	—	73	1	no	—
43	C₂×C₄	#11924036	1	1	yes	characteristic
44	C₈	—	146	1	no	—
45	C₈	C₄⋊#64408	1	1	yes	characteristic
46	C₈	#11924037	1	1	yes	characteristic
47	C₂²	#14556664	1	1	yes	characteristic
48	C₄	—	73	2	no	—
49	C₄	—	146	1	no	—
50	C₄	#14556658	1	1	yes	characteristic
51	C₄	#14556666	1	1	yes	characteristic
52	C₂	#17989508	1	1	yes	characteristic
53	C₂	#17989518	1	1	yes	characteristic
54	C₂	#17989520	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
23. Dic₇₃	C₃₂	semidirect
28. C₇₃	C₄⋊C₃₂	semidirect