Subgroups — #34033162

Order 18688.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989669	C₂	1	2	yes	maximal
2	#22625036	C₂	1	1	yes	maximal, characteristic
3	#17989669	—	2	2	no	—
4	C₂×#14556641	C₄	1	1	yes	characteristic
5	C₂×#14556641	C₂²	1	1	yes	characteristic
6	C₁₆×Dic₇₃	C₄	1	1	yes	characteristic
7	#14556641	—	2	1	no	—
8	#14556641	D₄	1	1	yes	characteristic
9	#14556641	Q₈	1	1	yes	characteristic
10	C₂×#11924003	C₂×C₄	1	1	yes	characteristic
11	C₈×Dic₇₃	C₈	1	1	yes	characteristic
12	C₂×C₁₆×C₇₃	C₈	1	1	yes	characteristic
13	C₂×#10596831	C₁₆	1	1	yes	characteristic
14	C₄×Dic₇₃	C₁₆	1	1	yes	characteristic
15	#11924003	C₄⋊C₄	1	1	yes	characteristic
16	#11924003	M₁₆	1	1	yes	characteristic
17	C₂×C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
18	C₁₆×C₇₃	—	2	1	no	—
19	C₂×C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
20	C₂×Dic₇₃	C₃₂	1	1	yes	characteristic
21	C₂×Dic₇₃	C₃₂	1	1	yes	characteristic
22	C₈×C₇₃	C₄⋊C₈	1	1	yes	characteristic
23	C₈×C₇₃	M₃₂	1	1	yes	characteristic
24	#10596831	—	2	1	no	—
25	C₂²×C₇₃	C₂×C₃₂	1	1	yes	characteristic
26	C₄×C₇₃	C₄⋊C₁₆	1	1	yes	characteristic
27	C₄×C₇₃	M₆₄	1	1	yes	characteristic
28	Dic₇₃	—	2	1	no	—
29	Dic₇₃	C₆₄	1	2	yes	complemented
30	C₄⋊C₆₄	—	73	1	no	maximal, Sylow
31	C₂×C₇₃	C₄⋊C₃₂	1	1	yes	characteristic
32	C₂×C₇₃	C₂×C₆₄	1	1	yes	characteristic
33	C₂×C₇₃	M₁₂₈	1	1	yes	characteristic
34	C₂×C₆₄	—	73	2	no	—
35	C₄×C₃₂	—	73	1	no	—
36	C₇₃	C₄⋊C₆₄	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃₂	—	73	1	no	—
38	C₂×C₃₂	—	73	1	no	—
39	C₄×C₁₆	—	73	1	no	—
40	C₆₄	—	146	2	no	—
41	C₂×C₁₆	—	73	1	no	—
42	C₂×C₁₆	#10596842	1	1	yes	characteristic
43	C₄×C₈	—	73	1	no	—
44	C₃₂	—	73	1	no	—
45	C₃₂	—	73	1	no	—
46	C₃₂	—	146	1	no	—
47	C₂×C₈	—	73	1	no	—
48	C₂×C₈	C₂×#10596842	1	1	yes	characteristic
49	C₄²	—	73	1	no	—
50	C₁₆	—	2	1	no	—
51	C₁₆	—	73	1	no	—
52	C₁₆	—	73	1	no	—
53	C₂×C₄	—	73	1	no	—
54	C₂×C₄	—	73	1	no	—
55	C₂×C₄	#14556686	1	1	yes	characteristic
56	C₈	—	146	1	no	—
57	C₈	C₄⋊#10596842	1	1	yes	characteristic
58	C₈	#14556687	1	1	yes	characteristic
59	C₂²	#17989694	1	1	yes	characteristic
60	C₄	—	73	2	no	—
61	C₄	—	146	1	no	—
62	C₄	#17989690	1	1	yes	characteristic
63	C₄	#17989696	1	1	yes	characteristic
64	C₂	#22627030	1	1	yes	characteristic
65	C₂	#22627034	1	1	yes	characteristic
66	C₂	#22627036	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#10596842
commutator	C₂×C₇₃	C₂×C₆₄
Fitting	C₂×C₁₆×C₇₃	C₈
socle, prime radical	C₂²×C₇₃	C₂×C₃₂
cosocle	C₂×#14556641	C₂²
hypercenter	C₂×C₁₆	#10596842
hypocenter	C₇₃	C₄⋊C₆₄
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
29. Dic₇₃	C₆₄	semidirect
36. C₇₃	C₄⋊C₆₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17989669	2
#22625036	2
C₄⋊C₆₄	73