Subgroups — #22626354

Order 9344.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989519	C₂	1	3	yes	maximal, complemented
2	C₂×#14556641	C₂	1	3	yes	maximal, complemented
3	#17989004	C₂	1	1	yes	maximal, characteristic
4	#14556641	C₂²	1	1	yes	characteristic
5	#14556641	C₂²	1	3	yes	—
6	#14556531	C₄	1	3	yes	—
7	C₂×#11924003	C₂²	1	3	yes	—
8	#131×C₇₃	C₄	1	1	yes	characteristic
9	#11924003	C₂×C₄	1	3	yes	—
10	#11924003	C₂³	1	1	yes	characteristic
11	#41×C₇₃	C₈	1	1	yes	characteristic
12	M₁₆×C₇₃	C₈	1	3	yes	—
13	C₂×C₈×C₇₃	C₂×C₄	1	3	yes	—
14	Q₈×C₇₃	C₁₆	1	1	yes	characteristic
15	D₄×C₇₃	C₁₆	1	3	yes	—
16	C₂×C₄×C₇₃	C₂×C₈	1	3	yes	—
17	C₈×C₇₃	C₂×C₈	1	3	yes	—
18	C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
19	C₂²×C₇₃	C₂×C₁₆	1	3	yes	—
20	C₄×C₇₃	C₂×C₁₆	1	3	yes	—
21	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₇₃	—	2	3	no	—
23	C₂×C₇₃	C₂²×C₁₆	1	1	yes	characteristic
24	#2258	—	73	1	no	maximal, Sylow
25	C₇₃	#2258	1	1	yes	characteristic, complemented, Sylow
26	#504	—	73	1	no	—
27	M₆₄	—	73	3	no	—
28	C₂×C₃₂	—	73	3	no	—
29	#131	#64408	1	1	yes	characteristic
30	M₃₂	—	73	3	no	—
31	C₂×C₁₆	—	73	3	no	—
32	C₃₂	—	73	1	no	—
33	C₃₂	—	73	3	no	—
34	#41	#10596833	1	1	yes	characteristic
35	M₁₆	#10596833	1	3	yes	—
36	C₂×C₈	C₂×#64408	1	3	yes	—
37	C₁₆	—	73	3	no	—
38	C₁₆	—	73	1	no	—
39	Q₈	#11924031	1	1	yes	characteristic
40	D₄	#11924031	1	3	yes	—
41	C₂×C₄	C₂×#10596833	1	3	yes	—
42	C₈	C₂×#10596833	1	3	yes	—
43	C₈	C₂²×#64408	1	1	yes	characteristic
44	C₂²	C₂×#11924031	1	3	yes	—
45	C₄	C₂×#11924031	1	3	yes	—
46	C₄	C₂²×#10596833	1	1	yes	characteristic
47	C₂	—	2	3	no	—
48	C₂	C₂²×#11924031	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×#64408
commutator, socle	C₂×C₇₃	C₂²×C₁₆
Fitting	#131×C₇₃	C₄
hypercenter	#131	#64408
hypocenter	C₇₃	#2258
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ #131

Complements

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

N	H ≅ G/N	type
1. #17989519	C₂	semidirect
2. C₂×#14556641	C₂	semidirect
25. C₇₃	#2258	semidirect