Subgroups — #34033110

Order 18688.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22627031	C₂	1	2	yes	maximal
2	#22624842	C₂	1	1	yes	maximal, characteristic
3	#17989695	—	2	2	no	—
4	#17989473	C₂²	1	1	yes	characteristic
5	C₈×#10596833	C₄	1	1	yes	characteristic
6	C₁₆×Dic₇₃	C₄	1	1	yes	characteristic
7	#14556681	—	4	2	no	—
8	C₂×#11924031	D₄	1	1	yes	characteristic
9	C₂×#11924031	Q₈	1	1	yes	characteristic
10	C₄×#10596833	—	2	1	no	—
11	C₂×#11924003	C₈	1	1	yes	characteristic
12	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₆×C₇₃	C₈	1	1	yes	characteristic
14	C₂×#10596833	—	2	2	no	—
15	#11924031	—	2	1	no	—
16	#11924031	SD₁₆	1	2	yes	—
17	C₂×#10596831	C₄⋊C₄	1	1	yes	characteristic
18	C₄×Dic₇₃	M₁₆	1	1	yes	characteristic
19	#11924003	C₁₆	1	2	yes	—
20	C₂×C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
21	C₁₆×C₇₃	—	2	1	no	—
22	C₂×C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
23	C₂×Dic₇₃	—	2	1	no	—
24	#10596833	—	4	2	no	—
25	C₈×C₇₃	C₂×C₁₆	1	1	yes	characteristic
26	C₈×C₇₃	M₃₂	1	1	yes	characteristic
27	#10596831	#106	1	1	yes	characteristic
28	#10596831	#108	1	1	yes	characteristic
29	C₂²×C₇₃	#364	1	1	yes	characteristic
30	C₄×C₇₃	#334	1	1	yes	characteristic
31	C₄×C₇₃	C₄⋊C₁₆	1	1	yes	characteristic
32	Dic₇₃	—	2	2	no	—
33	#7456	—	73	1	no	maximal, Sylow
34	C₂×C₇₃	—	2	1	no	—
35	C₂×C₇₃	#1367	1	1	yes	characteristic
36	#1422	—	73	2	no	—
37	#1311	—	73	1	no	—
38	C₇₃	#7456	1	1	yes	characteristic, complemented, Sylow
39	M₆₄	—	146	2	no	—
40	C₄×C₁₆	—	73	1	no	—
41	C₄×C₁₆	—	73	1	no	—
42	C₈²	—	73	1	no	—
43	C₂×C₁₆	—	73	1	no	—
44	C₂×C₁₆	—	73	1	no	—
45	C₂×C₁₆	—	73	1	no	—
46	C₂×C₁₆	#10596842	1	1	yes	characteristic
47	C₄×C₈	—	73	1	no	—
48	C₄×C₈	—	146	1	no	—
49	C₃₂	—	292	2	no	—
50	C₂×C₈	—	73	1	no	—
51	C₂×C₈	—	146	2	no	—
52	C₂×C₈	C₂×#10596842	1	1	yes	characteristic
53	C₄²	—	73	1	no	—
54	C₁₆	—	2	1	no	—
55	C₁₆	—	73	2	no	—
56	C₁₆	—	73	2	no	—
57	C₁₆	—	146	1	no	—
58	C₂×C₄	—	146	1	no	—
59	C₂×C₄	C₄⋊#10596842	1	1	yes	characteristic
60	C₈	—	292	2	no	—
61	C₈	—	73	1	no	—
62	C₈	—	73	1	no	—
63	C₈	#14556686	1	1	yes	characteristic
64	C₈	#14556687	1	1	yes	characteristic
65	C₂²	#17989692	1	1	yes	characteristic
66	C₄	—	146	2	no	—
67	C₄	#17989676	1	1	yes	characteristic
68	C₄	#17989690	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	#22626990	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#17989676
commutator	C₈×C₇₃	C₂×C₁₆
Frattini	C₂×C₈	C₂×#10596842
Fitting	C₂×C₁₆×C₇₃	C₈
socle	C₂×C₇₃	#1367
prime radical	C₂²×C₇₃	#364
cosocle	#17989473	C₂²
hypercenter	C₂×C₁₆	#10596842
hypocenter	C₇₃	#7456
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
38. C₇₃	#7456	semidirect

Maximal subgroups

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

subgroup	index
#22627031	2
#22624842	2
#7456	73