Subgroups — #22625081

Order 9344.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989518	C₂	1	1	yes	maximal, characteristic
2	#17989513	C₂	1	1	yes	maximal, characteristic
3	Q₃₂×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#14556660	—	2	1	no	—
5	#14556641	—	2	1	no	—
6	Q₁₆×D₇₃	—	2	1	no	—
7	Dic₅₈₄	C₄	1	1	yes	characteristic, complemented
8	#14556537	—	2	1	no	—
9	C₁₆×D₇₃	C₂²	1	1	yes	characteristic
10	Q₃₂×C₇₃	C₄	1	1	yes	characteristic, complemented
11	C₄⋊#64408	—	4	1	no	—
12	Q₈×D₇₃	—	4	1	no	—
13	Dic₂₉₂	—	2	1	no	—
14	#11924018	—	4	1	no	—
15	C₈×D₇₃	D₄	1	1	yes	characteristic
16	#11924003	D₄	1	1	yes	characteristic
17	Q₁₆×C₇₃	—	2	1	no	—
18	C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
19	C₂×#64408	—	8	1	no	—
20	Q₈×C₇₃	—	4	1	no	—
21	C₄×D₇₃	—	8	1	no	—
22	C₄×D₇₃	D₈	1	1	yes	characteristic
23	Dic₁₄₆	—	4	1	no	—
24	Dic₁₄₆	—	8	1	no	—
25	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
26	#10596831	SD₁₆	1	1	yes	characteristic
27	C₂×D₇₃	D₁₆	1	1	yes	characteristic
28	#64408	—	16	1	no	—
29	C₄×C₇₃	—	8	1	no	—
30	C₄×C₇₃	#102	1	1	yes	characteristic
31	Dic₇₃	—	8	1	no	—
32	Dic₇₃	SD₃₂	1	1	yes	characteristic
33	C₂×C₇₃	#357	1	1	yes	characteristic
34	D₇₃	SD₆₄	1	1	yes	characteristic
35	D₇₃	Q₆₄	1	1	yes	characteristic
36	#1416	—	73	1	no	maximal, Sylow
37	C₇₃	#1416	1	1	yes	characteristic, complemented, Sylow
38	C₂×Q₃₂	—	73	1	no	—
39	C₂×C₃₂	—	73	1	no	—
40	#366	—	73	1	no	—
41	C₂×Q₁₆	—	146	1	no	—
42	Q₃₂	—	73	1	no	—
43	Q₃₂	—	146	1	no	—
44	Q₃₂	#64408	1	1	yes	characteristic, complemented
45	C₂×C₁₆	—	73	1	no	—
46	#107	—	146	1	no	—
47	C₃₂	—	146	1	no	—
48	C₂×Q₈	—	292	1	no	—
49	Q₁₆	—	2	1	no	—
50	Q₁₆	—	292	1	no	—
51	Q₁₆	—	146	1	no	—
52	C₂×C₈	—	73	1	no	—
53	C₄⋊C₄	—	292	1	no	—
54	C₁₆	—	73	1	no	—
55	C₁₆	C₂×#64408	1	1	yes	characteristic
56	Q₈	—	4	1	no	—
57	Q₈	—	292	1	no	—
58	Q₈	—	584	1	no	—
59	C₂×C₄	—	584	1	no	—
60	C₂×C₄	—	584	1	no	—
61	C₂×C₄	—	73	1	no	—
62	C₈	—	73	1	no	—
63	C₈	C₂²⋊#64408	1	1	yes	characteristic
64	C₂²	—	73	1	no	—
65	C₄	—	8	1	no	—
66	C₄	—	584	1	no	—
67	C₄	—	73	1	no	—
68	C₄	—	1168	1	no	—
69	C₄	#14556653	1	1	yes	characteristic
70	C₂	—	73	1	no	—
71	C₂	—	73	1	no	—
72	C₂	#17989499	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17989499
commutator	C₁₆×C₇₃	C₂×C₄
Frattini	C₁₆	C₂×#64408
Fitting	Q₃₂×C₇₃	C₄
socle	C₂×C₇₃	#357
hypercenter	Q₃₂	#64408
hypocenter	C₇₃	#1416
LCS	G ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
7. Dic₅₈₄	C₄	semidirect
10. Q₃₂×C₇₃	C₄	semidirect
37. C₇₃	#1416	semidirect
44. Q₃₂	#64408	semidirect