Subgroups — #32973890

Order 18688.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22608135	C₂	1	1	yes	maximal, characteristic
2	#22608133	C₂	1	1	yes	maximal, characteristic
3	C₇₃×M₁₂₈	C₂	1	1	yes	maximal, characteristic
4	#17988417	—	2	1	no	—
5	#17988413	—	2	1	no	—
6	C₂×C₃₂×C₇₃	C₂²	1	1	yes	characteristic
7	C₆₄×C₇₃	C₄	1	2	yes	complemented
8	#14556527	—	4	1	no	—
9	#14556525	—	4	1	no	—
10	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
11	C₃₂×C₇₃	C₂×C₄	1	1	yes	characteristic
12	C₃₂×C₇₃	Q₈	1	1	yes	characteristic
13	#11924012	—	8	1	no	—
14	C₄⋊Dic₇₃	—	8	1	no	—
15	C₂×C₈×C₇₃	D₈	1	1	yes	characteristic
16	C₁₆×C₇₃	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₇₃	Q₁₆	1	1	yes	characteristic
18	C₂×C₄×C₇₃	D₁₆	1	1	yes	characteristic
19	C₂×Dic₇₃	—	16	1	no	—
20	C₈×C₇₃	#107	1	1	yes	characteristic
21	C₈×C₇₃	Q₃₂	1	1	yes	characteristic
22	#10596831	—	16	1	no	—
23	C₂²×C₇₃	SD₆₄	1	1	yes	characteristic
24	C₄×C₇₃	#366	1	1	yes	characteristic
25	C₄×C₇₃	SD₆₄	1	1	yes	characteristic
26	Dic₇₃	—	32	1	no	—
27	#7548	—	73	1	no	maximal, Sylow
28	C₂×C₇₃	—	2	1	no	—
29	C₂×C₇₃	#1424	1	1	yes	characteristic
30	M₁₂₈	D₇₃	1	1	yes	characteristic
31	#1425	—	73	1	no	—
32	#1424	—	73	1	no	—
33	C₇₃	#7548	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃₂	C₂×D₇₃	1	1	yes	characteristic
35	#368	—	146	1	no	—
36	#366	—	146	1	no	—
37	C₆₄	Dic₇₃	1	2	yes	complemented
38	C₂×C₁₆	D₂₉₂	1	1	yes	characteristic
39	#108	—	292	1	no	—
40	#107	—	292	1	no	—
41	C₃₂	Dic₁₄₆	1	1	yes	characteristic
42	C₃₂	C₂×Dic₇₃	1	1	yes	characteristic
43	M₁₆	—	584	1	no	—
44	C₂×C₈	D₅₈₄	1	1	yes	characteristic
45	C₄⋊C₄	—	584	1	no	—
46	C₁₆	C₄⋊Dic₇₃	1	1	yes	characteristic
47	C₁₆	Dic₂₉₂	1	1	yes	characteristic
48	C₂×C₄	—	1168	1	no	—
49	C₂×C₄	D₁₁₆₈	1	1	yes	characteristic
50	C₈	—	1168	1	no	—
51	C₈	#14556525	1	1	yes	characteristic
52	C₈	Dic₅₈₄	1	1	yes	characteristic
53	C₂²	#17988426	1	1	yes	characteristic
54	C₄	—	2336	1	no	—
55	C₄	#17988413	1	1	yes	characteristic
56	C₄	#17988426	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	#22608133	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#22608133
commutator	C₃₂×C₇₃	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₇₃
Fitting	C₇₃×M₁₂₈	C₂
socle	C₂×C₇₃	#1424
prime radical	C₂²×C₇₃	SD₆₄
cosocle	C₂×C₃₂×C₇₃	C₂²
hypercenter	M₁₂₈	D₇₃
hypocenter	C₇₃	#7548
LCS	G ▷ C₃₂×C₇₃ ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ M₁₂₈

Complements

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

N	H ≅ G/N	type
7. C₆₄×C₇₃	C₄	semidirect
33. C₇₃	#7548	semidirect
37. C₆₄	Dic₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22608135	2
#22608133	2
C₇₃×M₁₂₈	2
#7548	73