Subgroups — #32973888

Order 18688.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22608135	C₂	1	2	yes	maximal
2	C₂×C₆₄×C₇₃	C₂	1	1	yes	maximal, characteristic
3	#17988417	—	2	2	no	—
4	C₂×C₃₂×C₇₃	C₂²	1	1	yes	characteristic
5	C₆₄×C₇₃	C₄	1	2	yes	—
6	#14556527	—	4	2	no	—
7	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
8	C₃₂×C₇₃	C₂×C₄	1	1	yes	characteristic
9	C₃₂×C₇₃	Q₈	1	1	yes	characteristic
10	#11924012	—	8	2	no	—
11	C₂×C₈×C₇₃	D₈	1	1	yes	characteristic
12	C₁₆×C₇₃	C₄⋊C₄	1	1	yes	characteristic
13	C₁₆×C₇₃	Q₁₆	1	1	yes	characteristic
14	C₂×C₄×C₇₃	D₁₆	1	1	yes	characteristic
15	C₈×C₇₃	#107	1	1	yes	characteristic
16	C₈×C₇₃	Q₃₂	1	1	yes	characteristic
17	#10596831	—	16	2	no	—
18	C₂²×C₇₃	Q₆₄	1	1	yes	characteristic
19	C₄×C₇₃	#366	1	1	yes	characteristic
20	C₄×C₇₃	D₃₂	1	1	yes	characteristic
21	#7547	—	73	1	no	maximal, Sylow
22	C₂×C₇₃	—	2	1	no	—
23	C₂×C₇₃	#1423	1	1	yes	characteristic
24	C₂×C₆₄	D₇₃	1	1	yes	characteristic
25	#1425	—	73	2	no	—
26	C₇₃	#7547	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃₂	C₂×D₇₃	1	1	yes	characteristic
28	#368	—	146	2	no	—
29	C₆₄	Dic₇₃	1	2	yes	—
30	C₂×C₁₆	D₂₉₂	1	1	yes	characteristic
31	#108	—	292	2	no	—
32	C₃₂	Dic₁₄₆	1	1	yes	characteristic
33	C₃₂	C₂×Dic₇₃	1	1	yes	characteristic
34	M₁₆	—	584	2	no	—
35	C₂×C₈	D₅₈₄	1	1	yes	characteristic
36	C₁₆	C₄⋊Dic₇₃	1	1	yes	characteristic
37	C₁₆	Dic₂₉₂	1	1	yes	characteristic
38	C₂×C₄	D₁₁₆₈	1	1	yes	characteristic
39	C₈	—	1168	2	no	—
40	C₈	#14556525	1	1	yes	characteristic
41	C₈	Dic₅₈₄	1	1	yes	characteristic
42	C₂²	Dic₁₁₆₈	1	1	yes	characteristic
43	C₄	#17988413	1	1	yes	characteristic
44	C₄	D₂₃₃₆	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#22608131	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₂₃₃₆
commutator	C₃₂×C₇₃	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₇₃
Fitting	C₂×C₆₄×C₇₃	C₂
socle	C₂×C₇₃	#1423
prime radical	C₂²×C₇₃	Q₆₄
cosocle	C₂×C₃₂×C₇₃	C₂²
hypercenter	C₂×C₆₄	D₇₃
hypocenter	C₇₃	#7547
LCS	G ▷ C₃₂×C₇₃ ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
26. C₇₃	#7547	semidirect

Maximal subgroups

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

subgroup	index
#22608135	2
C₂×C₆₄×C₇₃	2
#7547	73