Subgroups — #32973879

Order 18688.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988306	C₂	1	1	yes	maximal, characteristic
2	C₃₂×Dic₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₄×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#14556497	C₄	1	1	yes	characteristic
5	C₁₆×Dic₇₃	C₄	1	1	yes	characteristic
6	#17988306	—	2	1	no	—
7	C₂×C₃₂×C₇₃	C₂²	1	1	yes	characteristic
8	C₆₄×C₇₃	—	2	1	no	—
9	C₂×#11924003	C₈	1	1	yes	characteristic
10	C₈×Dic₇₃	C₈	1	1	yes	characteristic
11	#14556497	—	2	1	no	—
12	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
13	C₃₂×C₇₃	D₄	1	1	yes	characteristic
14	C₃₂×C₇₃	Q₈	1	1	yes	characteristic
15	C₂×#10596831	C₁₆	1	1	yes	characteristic
16	C₄×Dic₇₃	C₁₆	1	1	yes	characteristic
17	#11924003	—	2	1	no	—
18	C₂×C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
19	C₁₆×C₇₃	C₄⋊C₄	1	1	yes	characteristic
20	C₁₆×C₇₃	M₁₆	1	1	yes	characteristic
21	C₂×C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
22	C₂×Dic₇₃	C₃₂	1	1	yes	characteristic
23	C₂×Dic₇₃	C₃₂	1	1	yes	characteristic
24	C₈×C₇₃	C₄⋊C₈	1	1	yes	characteristic
25	C₈×C₇₃	M₃₂	1	1	yes	characteristic
26	#10596831	—	2	1	no	—
27	C₂²×C₇₃	C₂×C₃₂	1	1	yes	characteristic
28	C₄×C₇₃	C₄⋊C₁₆	1	1	yes	characteristic
29	C₄×C₇₃	M₆₄	1	1	yes	characteristic
30	Dic₇₃	—	2	1	no	—
31	Dic₇₃	C₆₄	1	2	yes	complemented
32	C₄⋊C₆₄	—	73	1	no	maximal, Sylow
33	C₂×C₇₃	C₄⋊C₃₂	1	1	yes	characteristic
34	C₂×C₇₃	C₂×C₆₄	1	1	yes	characteristic
35	C₂×C₇₃	M₁₂₈	1	1	yes	characteristic
36	C₂×C₆₄	—	73	1	no	—
37	C₂×C₆₄	D₇₃	1	1	yes	characteristic
38	C₄×C₃₂	—	73	1	no	—
39	C₇₃	C₄⋊C₆₄	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃₂	—	73	1	no	—
41	C₂×C₃₂	C₂×D₇₃	1	1	yes	characteristic
42	C₄×C₁₆	—	73	1	no	—
43	C₆₄	—	2	1	no	—
44	C₆₄	—	146	1	no	—
45	C₂×C₁₆	—	73	1	no	—
46	C₂×C₁₆	C₄×D₇₃	1	1	yes	characteristic
47	C₄×C₈	—	73	1	no	—
48	C₃₂	—	146	1	no	—
49	C₃₂	Dic₁₄₆	1	1	yes	characteristic
50	C₃₂	C₂²⋊D₇₃	1	1	yes	characteristic
51	C₂×C₈	—	73	1	no	—
52	C₂×C₈	C₈×D₇₃	1	1	yes	characteristic
53	C₄²	—	73	1	no	—
54	C₁₆	—	146	1	no	—
55	C₁₆	#11924007	1	1	yes	characteristic
56	C₁₆	#11924011	1	1	yes	characteristic
57	C₂×C₄	—	73	1	no	—
58	C₂×C₄	—	73	1	no	—
59	C₂×C₄	C₁₆×D₇₃	1	1	yes	characteristic
60	C₈	—	146	1	no	—
61	C₈	#14556520	1	1	yes	characteristic
62	C₈	#14556530	1	1	yes	characteristic
63	C₂²	C₃₂×D₇₃	1	1	yes	characteristic
64	C₄	—	73	2	no	—
65	C₄	—	146	1	no	—
66	C₄	#17988405	1	1	yes	characteristic
67	C₄	#17988420	1	1	yes	characteristic
68	C₂	#22608126	1	1	yes	characteristic
69	C₂	C₆₄×D₇₃	1	1	yes	characteristic
70	C₂	#22608141	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₃₂	C₂×D₇₃
commutator	C₂×C₇₃	C₂×C₆₄
Fitting	C₂×C₆₄×C₇₃	C₂
socle, prime radical	C₂²×C₇₃	C₂×C₃₂
cosocle	C₂×C₃₂×C₇₃	C₂²
hypercenter	C₂×C₆₄	D₇₃
hypocenter	C₇₃	C₄⋊C₆₄
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
31. Dic₇₃	C₆₄	semidirect
39. 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×#17988306	2
C₃₂×Dic₇₃	2
C₂×C₆₄×C₇₃	2
C₄⋊C₆₄	73