Subgroups — #17989462

Order 4672.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₃⋊M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#11924036	C₂	1	1	yes	maximal, characteristic
3	M₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#11924038	C₄	1	2	yes	—
5	#11924037	—	2	1	no	—
6	#11924036	—	2	1	no	—
7	#11924036	—	2	1	no	—
8	#11924036	C₄	1	2	yes	—
9	C₂×#10596833	—	2	1	no	—
10	C₂×C₄×D₇₃	C₂²	1	1	yes	characteristic
11	#11924012	C₄	1	1	yes	characteristic
12	#11924011	—	2	1	no	—
13	C₈×D₇₃	—	2	1	no	—
14	M₁₆×C₇₃	C₄	1	1	yes	characteristic
15	C₂²×D₇₃	Q₈	1	1	yes	characteristic
16	C₂×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₇₃	D₄	1	1	yes	characteristic
18	C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
19	C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
20	C₄×D₇₃	D₄	1	1	yes	characteristic
21	C₄×D₇₃	D₄	1	1	yes	characteristic
22	#10596833	—	2	2	no	—
23	#10596833	—	2	2	no	—
24	C₈×C₇₃	—	2	1	no	—
25	#10596831	—	2	1	no	—
26	C₂²×C₇₃	C₄⋊C₄	1	1	yes	characteristic
27	C₂×D₇₃	—	2	2	no	—
28	C₂×D₇₃	C₄⋊C₄	1	1	yes	characteristic
29	C₂×D₇₃	C₄⋊C₄	1	1	yes	characteristic
30	C₄×C₇₃	C₄²	1	1	yes	characteristic
31	C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
32	Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
33	Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₇₃	—	2	1	no	—
35	C₂×C₇₃	#95	1	1	yes	characteristic
36	D₇₃	—	2	1	no	—
37	D₇₃	#108	1	2	yes	—
38	C₇₃	#341	1	1	yes	characteristic, complemented, Sylow
39	#341	—	73	1	no	maximal, Sylow
40	C₂×M₁₆	—	73	1	no	—
41	C₂×M₁₆	—	73	1	no	—
42	C₂²×C₈	—	73	1	no	—
43	C₂²×C₄	—	73	1	no	—
44	M₁₆	—	73	2	no	—
45	M₁₆	—	73	1	no	—
46	M₁₆	—	146	1	no	—
47	M₁₆	—	146	1	no	—
48	M₁₆	#64408	1	1	yes	characteristic
49	C₂×C₈	—	73	2	no	—
50	C₂×C₈	—	146	1	no	—
51	C₂×C₈	—	146	1	no	—
52	C₂×C₈	—	146	1	no	—
53	C₂×C₈	—	146	1	no	—
54	C₂³	—	73	1	no	—
55	C₂×C₄	—	73	1	no	—
56	C₂×C₄	—	73	1	no	—
57	C₂×C₄	—	73	1	no	—
58	C₂×C₄	—	73	1	no	—
59	C₂×C₄	—	73	1	no	—
60	C₂×C₄	C₂×#64408	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	146	2	no	—
63	C₈	—	146	2	no	—
64	C₈	—	146	1	no	—
65	C₂²	—	73	1	no	—
66	C₂²	—	73	1	no	—
67	C₂²	—	146	2	no	—
68	C₂²	C₄⋊#64408	1	1	yes	characteristic
69	C₄	—	73	1	no	—
70	C₄	—	73	1	no	—
71	C₄	C₄×#64408	1	1	yes	characteristic
72	C₄	C₂²⋊#64408	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	—	73	2	no	—
75	C₂	—	146	1	no	—
76	C₂	(C₂×#64408)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#64408
commutator	C₄×C₇₃	C₄²
Frattini	C₂×C₄	C₂×#64408
Fitting	M₁₆×C₇₃	C₄
socle	C₂×C₇₃	#95
prime radical	C₂²×D₇₃	Q₈
cosocle	C₂×C₄×D₇₃	C₂²
hypercenter	M₁₆	#64408
hypocenter	C₇₃	#341
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
38. C₇₃	#341	semidirect

Maximal subgroups

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

subgroup	index
D₇₃⋊M₁₆	2
C₂×#11924036	2
M₁₆×D₇₃	2
#341	73