Subgroups — #32973885

Order 18688.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988306	C₂	1	1	yes	maximal, characteristic
2	#22608131	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#1423	C₂	1	1	yes	maximal, characteristic
4	#17988413	—	2	1	no	—
5	#17988306	C₄	1	2	yes	complemented
6	C₂×C₃₂×C₇₃	C₂²	1	1	yes	characteristic
7	#366×C₇₃	—	2	1	no	—
8	#14556525	—	4	1	no	—
9	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
10	#107×C₇₃	—	4	1	no	—
11	C₃₂×C₇₃	C₂×C₄	1	1	yes	characteristic
12	C₃₂×C₇₃	Q₈	1	1	yes	characteristic
13	C₄⋊Dic₇₃	—	8	1	no	—
14	C₂×C₈×C₇₃	D₈	1	1	yes	characteristic
15	C₄⋊C₄×C₇₃	—	8	1	no	—
16	C₁₆×C₇₃	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₇₃	Q₁₆	1	1	yes	characteristic
18	C₂×C₄×C₇₃	—	16	1	no	—
19	C₂×C₄×C₇₃	D₁₆	1	1	yes	characteristic
20	C₂×Dic₇₃	—	16	1	no	—
21	C₈×C₇₃	#107	1	1	yes	characteristic
22	C₈×C₇₃	Q₃₂	1	1	yes	characteristic
23	C₂²×C₇₃	D₃₂	1	1	yes	characteristic
24	C₄×C₇₃	—	32	1	no	—
25	C₄×C₇₃	#366	1	1	yes	characteristic
26	C₄×C₇₃	Q₆₄	1	1	yes	characteristic
27	Dic₇₃	—	32	1	no	—
28	#7546	—	73	1	no	maximal, Sylow
29	C₂×C₇₃	#1423	1	1	yes	characteristic
30	C₂×C₇₃	SD₁₂₈	1	1	yes	characteristic
31	C₂×C₇₃	SD₁₂₈	1	1	yes	characteristic
32	C₂×C₆₄	—	73	1	no	—
33	#1423	—	73	1	no	—
34	#1423	D₇₃	1	1	yes	characteristic
35	C₇₃	#7546	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃₂	C₂×D₇₃	1	1	yes	characteristic
37	#366	—	2	1	no	—
38	#366	—	146	1	no	—
39	C₆₄	—	73	2	no	—
40	C₂×C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
41	#107	—	4	1	no	—
42	#107	—	292	1	no	—
43	C₃₂	Dic₁₄₆	1	1	yes	characteristic
44	C₃₂	C₄×D₇₃	1	1	yes	characteristic
45	C₂×C₈	#11924013	1	1	yes	characteristic
46	C₄⋊C₄	—	8	1	no	—
47	C₄⋊C₄	—	584	1	no	—
48	C₁₆	#11924007	1	1	yes	characteristic
49	C₁₆	#11924018	1	1	yes	characteristic
50	C₂×C₄	—	16	1	no	—
51	C₂×C₄	—	1168	1	no	—
52	C₂×C₄	#14556532	1	1	yes	characteristic
53	C₈	#14556524	1	1	yes	characteristic
54	C₈	#14556537	1	1	yes	characteristic
55	C₂²	#17988422	1	1	yes	characteristic
56	C₄	—	32	1	no	—
57	C₄	—	2336	1	no	—
58	C₄	#17988412	1	1	yes	characteristic
59	C₄	#17988427	1	1	yes	characteristic
60	C₂	#22608130	1	1	yes	characteristic
61	C₂	#22608145	1	1	yes	characteristic
62	C₂	#22608146	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#17988422
commutator	C₃₂×C₇₃	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₇₃
Fitting	C₇₃×#1423	C₂
socle, prime radical	C₂²×C₇₃	D₃₂
cosocle	C₂×C₃₂×C₇₃	C₂²
hypercenter	#1423	D₇₃
hypocenter	C₇₃	#7546
LCS	G ▷ C₃₂×C₇₃ ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #1423

Complements

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

N	H ≅ G/N	type
5. #17988306	C₄	semidirect
35. C₇₃	#7546	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#17988306	2
#22608131	2
C₇₃×#1423	2
#7546	73