Subgroups — #22625040

Order 9344.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989520	C₂	1	1	yes	maximal, characteristic
2	#17989474	C₂	1	1	yes	maximal, characteristic
3	#17988420	C₂	1	1	yes	maximal, characteristic
4	#14556664	C₄	1	1	yes	characteristic
5	C₈×#64408	C₄	1	1	yes	characteristic
6	#14556641	C₄	1	2	yes	complemented
7	C₁₆×D₇₃	C₂²	1	1	yes	characteristic
8	#14556497	C₄	1	1	yes	characteristic, complemented
9	C₃₂×C₇₃	C₄	1	1	yes	characteristic, complemented
10	#11924036	C₈	1	1	yes	characteristic
11	C₄×#64408	C₈	1	1	yes	characteristic
12	#11924031	C₈	1	2	yes	—
13	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
14	#11924003	C₂×C₄	1	1	yes	characteristic
15	C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
16	C₂×#64408	—	2	1	no	—
17	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
18	#10596833	—	2	1	no	—
19	C₈×C₇₃	C₄²	1	1	yes	characteristic
20	#10596831	C₂×C₈	1	1	yes	characteristic
21	C₂×D₇₃	M₃₂	1	1	yes	characteristic
22	#64408	—	4	1	no	—
23	C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
24	Dic₇₃	M₃₂	1	1	yes	characteristic
25	C₂×C₇₃	#346	1	1	yes	characteristic
26	D₇₃	—	2	1	no	—
27	#1398	—	73	1	no	maximal, Sylow
28	C₇₃	#1398	1	1	yes	characteristic, complemented, Sylow
29	M₆₄	—	73	1	no	—
30	M₆₄	—	73	1	no	—
31	#346	—	73	1	no	—
32	C₂×C₁₆	—	73	1	no	—
33	C₂×C₁₆	—	73	1	no	—
34	C₄×C₈	—	73	1	no	—
35	C₃₂	—	73	2	no	—
36	C₃₂	—	73	1	no	—
37	C₃₂	#64408	1	1	yes	characteristic, complemented
38	C₂×C₈	—	73	1	no	—
39	C₂×C₈	—	73	1	no	—
40	C₄²	—	73	1	no	—
41	C₁₆	—	73	2	no	—
42	C₁₆	—	73	1	no	—
43	C₁₆	C₂×#64408	1	1	yes	characteristic
44	C₂×C₄	—	73	1	no	—
45	C₂×C₄	—	146	1	no	—
46	C₈	—	73	1	no	—
47	C₈	—	146	1	no	—
48	C₈	C₄×#64408	1	1	yes	characteristic
49	C₂²	—	73	1	no	—
50	C₄	—	292	1	no	—
51	C₄	—	73	1	no	—
52	C₄	C₈×#64408	1	1	yes	characteristic
53	C₂	—	146	1	no	—
54	C₂	#17989474	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄×#64408
commutator	C₄×C₇₃	C₄×C₈
Frattini	C₁₆	C₂×#64408
Fitting	C₃₂×C₇₃	C₄
socle	C₂×C₇₃	#346
hypercenter	C₃₂	#64408
hypocenter	C₇₃	#1398
LCS	G ▷ C₄×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
6. #14556641	C₄	semidirect
8. #14556497	C₄	semidirect
9. C₃₂×C₇₃	C₄	semidirect
28. C₇₃	#1398	semidirect
37. C₃₂	#64408	semidirect