Subgroups — #34015603

Order 18688.

2286 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989533	C₂	1	14	yes	maximal
2	C₄³×D₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄⋊#64408	C₂²	1	28	yes	—
4	#17989533	—	2	56	no	—
5	C₂×C₄²×D₇₃	C₂²	1	7	yes	—
6	C₄²×Dic₇₃	C₄	1	7	yes	complemented
7	C₄³×C₇₃	C₄	1	1	yes	characteristic, complemented
8	C₂³×#64408	C₂³	1	8	yes	—
9	C₂×C₄⋊#64408	—	2	168	no	—
10	C₂²×C₄×D₇₃	C₂³	1	7	yes	—
11	C₂×C₄×Dic₇₃	C₂×C₄	1	21	yes	—
12	C₄²×D₇₃	D₄	1	28	yes	—
13	C₄²×D₇₃	Q₈	1	28	yes	—
14	C₂×C₄²×C₇₃	C₂×C₄	1	7	yes	—
15	C₂²×#64408	—	2	56	no	—
16	C₄⋊#64408	—	4	112	no	—
17	C₂³×D₇₃	C₂⁴	1	1	yes	characteristic
18	C₂²×Dic₇₃	C₂²×C₄	1	7	yes	—
19	C₂×C₄×D₇₃	C₂×D₄	1	42	yes	—
20	C₂×C₄×D₇₃	C₂×Q₈	1	42	yes	—
21	C₄×Dic₇₃	C₄⋊C₄	1	84	yes	complemented
22	C₂²×C₄×C₇₃	C₂²×C₄	1	7	yes	—
23	C₄²×C₇₃	C₄⋊C₄	1	28	yes	complemented
24	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
25	C₂²×D₇₃	C₂²×D₄	1	7	yes	—
26	C₂²×D₇₃	C₂²×Q₈	1	7	yes	—
27	C₂×#64408	—	4	56	no	—
28	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	42	yes	—
29	C₂×Dic₇₃	C₂×C₄⋊C₄	1	42	yes	—
30	C₄×D₇₃	#127	1	28	yes	—
31	C₄×D₇₃	C₄⋊Q₈	1	84	yes	—
32	C₂²×C₇₃	C₂²×C₄⋊C₄	1	7	yes	—
33	C₂×D₇₃	C₂×#127	1	7	yes	—
34	C₂×D₇₃	C₂×C₄⋊Q₈	1	21	yes	—
35	#64408	—	8	8	no	—
36	C₄×C₇₃	#384	1	28	yes	complemented
37	Dic₇₃	#384	1	28	yes	complemented
38	#14692	—	73	1	no	maximal, Sylow
39	C₂×C₇₃	C₂×#384	1	7	yes	—
40	D₇₃	#2867	1	1	yes	characteristic
41	D₇₃	#2868	1	7	yes	—
42	C₂×#384	—	73	14	no	—
43	C₂×C₄³	—	73	1	no	—
44	C₇₃	#14692	1	1	yes	characteristic, complemented, Sylow
45	C₂²×C₄⋊C₄	—	73	28	no	—
46	C₂²×C₄²	—	73	7	no	—
47	#384	—	146	56	no	—
48	C₄³	—	73	7	no	—
49	C₄³	#64408	1	1	yes	characteristic, complemented
50	C₂³×C₄	—	73	7	no	—
51	C₂³×C₄	—	73	8	no	—
52	C₂×C₄⋊C₄	—	146	168	no	—
53	C₂×C₄²	—	73	21	no	—
54	C₂×C₄²	—	73	28	no	—
55	C₂×C₄²	—	73	28	no	—
56	C₂×C₄²	C₂×#64408	1	7	yes	—
57	C₂⁴	—	73	1	no	—
58	C₂²×C₄	—	73	7	no	—
59	C₂²×C₄	—	73	42	no	—
60	C₂²×C₄	—	73	42	no	—
61	C₂²×C₄	—	146	56	no	—
62	C₂²×C₄	C₂²×#64408	1	7	yes	—
63	C₄⋊C₄	—	292	112	no	—
64	C₄²	—	73	84	no	—
65	C₄²	C₄⋊#64408	1	28	yes	complemented
66	C₂³	—	73	7	no	—
67	C₂³	—	73	7	no	—
68	C₂³	C₂³×#64408	1	1	yes	characteristic
69	C₂×C₄	—	292	56	no	—
70	C₂×C₄	—	73	42	no	—
71	C₂×C₄	—	73	28	no	—
72	C₂×C₄	—	73	84	no	—
73	C₂×C₄	C₂×C₄⋊#64408	1	42	yes	—
74	C₂²	—	73	7	no	—
75	C₂²	—	73	21	no	—
76	C₂²	C₂²×C₄⋊#64408	1	7	yes	—
77	C₄	—	584	8	no	—
78	C₄	—	73	28	no	—
79	C₄	#17989533	1	28	yes	complemented
80	C₂	—	73	1	no	—
81	C₂	—	73	7	no	—
82	C₂	C₂×#17989533	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×#64408
commutator, socle	C₂³×C₇₃	C₂³×C₄
Fitting	C₄³×C₇₃	C₄
prime radical, cosocle	C₂³×D₇₃	C₂⁴
hypercenter	C₄³	#64408
hypocenter	C₇₃	#14692
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

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

N	H ≅ G/N	type
6. C₄²×Dic₇₃	C₄	semidirect
7. C₄³×C₇₃	C₄	semidirect
21. C₄×Dic₇₃	C₄⋊C₄	semidirect
23. C₄²×C₇₃	C₄⋊C₄	semidirect
36. C₄×C₇₃	#384	semidirect
37. Dic₇₃	#384	semidirect
44. C₇₃	#14692	semidirect
49. C₄³	#64408	semidirect
65. C₄²	C₄⋊#64408	semidirect
79. C₄	#17989533	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17989533	2
C₄³×D₇₃	2
#14692	73