Subgroups — C₄³×#64408 #34014567

Order 18688.

3966 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×#64408	C₂	1	14	yes	maximal
2	C₄³×D₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×#64408	C₂²	1	28	yes	—
4	C₄²×#64408	C₄	1	112	yes	direct product factor
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	C₂×C₄	1	336	yes	—
10	C₂²×C₄×D₇₃	C₂³	1	7	yes	—
11	C₂×C₄×Dic₇₃	C₂×C₄	1	21	yes	—
12	C₄²×D₇₃	C₂×C₄	1	56	yes	—
13	C₂×C₄²×C₇₃	C₂×C₄	1	7	yes	—
14	C₂²×#64408	C₂²×C₄	1	112	yes	—
15	C₄×#64408	C₄²	1	448	yes	direct product factor
16	C₂³×D₇₃	C₂⁴	1	1	yes	characteristic
17	C₂²×Dic₇₃	C₂²×C₄	1	7	yes	—
18	C₂×C₄×D₇₃	C₂²×C₄	1	84	yes	—
19	C₄×Dic₇₃	C₄²	1	84	yes	complemented
20	C₂²×C₄×C₇₃	C₂²×C₄	1	7	yes	—
21	C₄²×C₇₃	C₄²	1	28	yes	complemented
22	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
23	C₂²×D₇₃	C₂³×C₄	1	14	yes	—
24	C₂×#64408	C₂×C₄²	1	224	yes	—
25	C₂×C₄×C₇₃	C₂×C₄²	1	42	yes	—
26	C₂×Dic₇₃	C₂×C₄²	1	42	yes	—
27	C₄×D₇₃	C₂×C₄²	1	112	yes	—
28	C₂²×C₇₃	C₂²×C₄²	1	7	yes	—
29	C₂×D₇₃	C₂²×C₄²	1	28	yes	—
30	#64408	C₄³	1	64	yes	direct product factor
31	C₄×C₇₃	C₄³	1	28	yes	complemented
32	Dic₇₃	C₄³	1	28	yes	complemented
33	C₄⁴	—	73	1	no	maximal, Sylow
34	C₂×C₇₃	C₂×C₄³	1	7	yes	—
35	D₇₃	C₂×C₄³	1	8	yes	—
36	C₂×C₄³	—	73	14	no	—
37	C₂×C₄³	—	73	1	no	—
38	C₇₃	C₄⁴	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₄²	—	73	28	no	—
40	C₂²×C₄²	—	73	7	no	—
41	C₄³	—	73	112	no	—
42	C₄³	—	73	7	no	—
43	C₄³	#64408	1	1	yes	characteristic, direct product factor
44	C₂³×C₄	—	73	8	no	—
45	C₂³×C₄	—	73	7	no	—
46	C₂×C₄²	—	73	336	no	—
47	C₂×C₄²	—	73	21	no	—
48	C₂×C₄²	—	73	56	no	—
49	C₂×C₄²	C₂×#64408	1	7	yes	—
50	C₂⁴	—	73	1	no	—
51	C₂²×C₄	—	73	112	no	—
52	C₂²×C₄	—	73	7	no	—
53	C₂²×C₄	—	73	84	no	—
54	C₂²×C₄	C₂²×#64408	1	7	yes	—
55	C₄²	—	73	448	no	—
56	C₄²	—	73	84	no	—
57	C₄²	C₄×#64408	1	28	yes	direct product factor
58	C₂³	—	73	14	no	—
59	C₂³	C₂³×#64408	1	1	yes	characteristic
60	C₂×C₄	—	73	224	no	—
61	C₂×C₄	—	73	42	no	—
62	C₂×C₄	—	73	112	no	—
63	C₂×C₄	C₂×C₄×#64408	1	42	yes	—
64	C₂²	—	73	28	no	—
65	C₂²	C₂²×C₄×#64408	1	7	yes	—
66	C₄	—	73	64	no	—
67	C₄	—	73	28	no	—
68	C₄	C₄²×#64408	1	28	yes	direct product factor
69	C₂	—	73	8	no	—
70	C₂	C₂×C₄²×#64408	1	7	yes	—

	subgroup	G/H
center, hypercenter	C₄³	#64408
commutator, hypocenter	C₇₃	C₄⁴
Frattini	C₂³	C₂³×#64408
Fitting	C₄³×C₇₃	C₄
socle	C₂³×C₇₃	C₂³×C₄
prime radical, cosocle	C₂³×D₇₃	C₂⁴
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₄³

Complements

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

N	H ≅ G/N	type
4. C₄²×#64408	C₄	direct (N × H)
6. C₄²×Dic₇₃	C₄	semidirect
7. C₄³×C₇₃	C₄	semidirect
15. C₄×#64408	C₄²	direct (N × H)
19. C₄×Dic₇₃	C₄²	semidirect
21. C₄²×C₇₃	C₄²	semidirect
30. #64408	C₄³	direct (N × H)
31. C₄×C₇₃	C₄³	semidirect
32. Dic₇₃	C₄³	semidirect
38. C₇₃	C₄⁴	semidirect
43. C₄³	#64408	direct (N × H)
57. C₄²	C₄×#64408	direct (N × H)
68. C₄	C₄²×#64408	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄²×#64408	2
C₄³×D₇₃	2
C₄⁴	73

Subgroups — C43×#64408 #34014567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄³×#64408 #34014567