Subgroups — #22624962

Order 9344.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989450	C₂	1	2	yes	maximal
2	C₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#10596833	—	2	2	no	—
4	C₂×#11924003	C₄	1	1	yes	characteristic
5	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
6	C₂×C₁₆×C₇₃	C₄	1	1	yes	characteristic
7	C₂×#10596833	—	4	2	no	—
8	C₂×#10596831	Q₈	1	1	yes	characteristic
9	C₄×Dic₇₃	D₄	1	1	yes	characteristic
10	#11924003	—	2	1	no	—
11	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₇₃	C₈	1	2	yes	complemented
13	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
14	C₂×Dic₇₃	D₈	1	1	yes	characteristic
15	C₂×Dic₇₃	Q₁₆	1	1	yes	characteristic
16	#10596833	—	8	2	no	—
17	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
18	C₈×C₇₃	M₁₆	1	1	yes	characteristic
19	#10596831	—	2	1	no	—
20	C₂²×C₇₃	#107	1	1	yes	characteristic
21	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₇₃	#108	1	1	yes	characteristic
23	Dic₇₃	—	2	1	no	—
24	Dic₇₃	D₁₆	1	1	yes	characteristic
25	Dic₇₃	Q₃₂	1	1	yes	characteristic
26	C₂×C₇₃	#335	1	1	yes	characteristic
27	C₂×C₇₃	#366	1	1	yes	characteristic
28	C₂×C₇₃	#368	1	1	yes	characteristic
29	#1371	—	73	1	no	maximal, Sylow
30	C₇₃	#1371	1	1	yes	characteristic, complemented, Sylow
31	C₄×C₁₆	—	73	1	no	—
32	#335	—	73	2	no	—
33	C₂×C₁₆	—	73	1	no	—
34	C₂×C₁₆	#64408	1	1	yes	characteristic
35	C₄⋊C₈	—	146	2	no	—
36	C₄×C₈	—	73	1	no	—
37	C₂×C₈	—	292	2	no	—
38	C₂×C₈	—	73	1	no	—
39	C₂×C₈	C₂×#64408	1	1	yes	characteristic
40	C₄²	—	73	1	no	—
41	C₁₆	—	146	1	no	—
42	C₁₆	#10596833	1	2	yes	complemented
43	C₂×C₄	—	73	1	no	—
44	C₂×C₄	—	73	1	no	—
45	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
46	C₈	—	584	2	no	—
47	C₈	—	146	1	no	—
48	C₈	C₂×#10596833	1	1	yes	characteristic
49	C₈	#11924038	1	1	yes	characteristic
50	C₂²	#14556660	1	1	yes	characteristic
51	C₄	—	73	1	no	—
52	C₄	—	73	1	no	—
53	C₄	—	146	1	no	—
54	C₄	C₄⋊#10596833	1	1	yes	characteristic
55	C₄	#14556662	1	1	yes	characteristic
56	C₂	#17989450	1	1	yes	characteristic
57	C₂	#17989513	1	1	yes	characteristic
58	C₂	#17989515	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14556660
commutator	C₈×C₇₃	C₂×C₈
Frattini	C₂×C₈	C₂×#64408
Fitting	C₂×C₁₆×C₇₃	C₄
socle	C₂²×C₇₃	#107
hypercenter	C₂×C₁₆	#64408
hypocenter	C₇₃	#1371
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
12. C₁₆×C₇₃	C₈	semidirect
30. C₇₃	#1371	semidirect
42. C₁₆	#10596833	semidirect