Subgroups — C₂³×#64528 #14578357

Order 2432.

1464 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Dic₃₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×#64528	C₂	1	28	yes	maximal, direct product factor
3	C₂³×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂³×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×Q₈×C₁₉	—	2	7	no	—
6	C₂²×Q₈×C₁₉	C₂²	1	14	yes	—
7	C₂³×C₄×C₁₉	—	2	1	no	—
8	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂³×Dic₁₉	—	2	1	no	—
10	C₂²×Dic₃₈	—	2	7	no	—
11	C₂²×Dic₃₈	C₂²	1	14	yes	—
12	C₂×#64528	C₂²	1	112	yes	direct product factor
13	C₂²×C₁₉⋊C₈	C₂²	1	14	yes	—
14	C₂⁴×C₁₉	D₄	1	1	yes	characteristic
15	C₂×Q₈×C₁₉	—	2	42	no	—
16	C₂×Q₈×C₁₉	C₂³	1	28	yes	—
17	C₂²×C₄×C₁₉	—	2	14	no	—
18	C₂²×C₄×C₁₉	D₄	1	7	yes	—
19	C₂²×C₄×C₁₉	C₂³	1	7	yes	—
20	C₂²×Dic₁₉	—	2	14	no	—
21	C₂×Dic₃₈	—	2	42	no	—
22	C₂×Dic₃₈	C₂³	1	28	yes	—
23	#64528	C₂³	1	64	yes	direct product factor
24	C₂×C₁₉⋊C₈	C₂³	1	28	yes	—
25	C₂³×C₁₉	Q₁₆	1	8	yes	complemented
26	C₂³×C₁₉	C₂×D₄	1	7	yes	—
27	Q₈×C₁₉	—	2	28	no	—
28	Q₈×C₁₉	C₂⁴	1	8	yes	—
29	C₂×C₄×C₁₉	—	2	28	no	—
30	C₂×C₄×C₁₉	C₂×D₄	1	21	yes	—
31	C₂×C₄×C₁₉	C₂⁴	1	7	yes	—
32	C₂×Dic₁₉	—	2	28	no	—
33	Dic₃₈	—	2	28	no	—
34	Dic₃₈	C₂⁴	1	8	yes	—
35	C₁₉⋊C₈	C₂⁴	1	8	yes	—
36	C₂³×Q₁₆	—	19	1	no	maximal, Sylow
37	C₂²×C₁₉	C₂×Q₁₆	1	28	yes	complemented
38	C₂²×C₁₉	C₂²×D₄	1	7	yes	—
39	C₄×C₁₉	—	2	8	no	—
40	C₄×C₁₉	C₂²×D₄	1	7	yes	—
41	C₄×C₁₉	C₂⁵	1	1	yes	characteristic
42	Dic₁₉	—	2	8	no	—
43	C₂³×Q₈	—	19	1	no	—
44	C₂³×Q₈	D₁₉	1	1	yes	characteristic
45	C₂²×Q₁₆	—	19	28	no	—
46	C₂³×C₈	—	19	1	no	—
47	C₂×C₁₉	C₂²×Q₁₆	1	14	yes	complemented
48	C₂×C₁₉	C₂³×D₄	1	1	yes	characteristic
49	C₂²×Q₈	—	2	7	no	—
50	C₂²×Q₈	—	19	14	no	—
51	C₂²×Q₈	—	38	7	no	—
52	C₂²×Q₈	C₂×D₁₉	1	14	yes	—
53	C₂³×C₄	—	2	1	no	—
54	C₂³×C₄	—	38	1	no	—
55	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
56	C₂×Q₁₆	—	19	112	no	—
57	C₂²×C₈	—	19	14	no	—
58	C₁₉	C₂³×Q₁₆	1	1	yes	characteristic, complemented, Sylow
59	C₂⁴	C₂²⋊D₁₉	1	1	yes	characteristic
60	C₂×Q₈	—	2	42	no	—
61	C₂×Q₈	—	19	28	no	—
62	C₂×Q₈	—	38	42	no	—
63	C₂×Q₈	C₂²×D₁₉	1	28	yes	—
64	C₂²×C₄	—	2	14	no	—
65	C₂²×C₄	—	38	14	no	—
66	C₂²×C₄	C₂²⋊D₁₉	1	7	yes	—
67	C₂²×C₄	C₂²×D₁₉	1	7	yes	—
68	Q₁₆	—	19	64	no	—
69	C₂×C₈	—	19	28	no	—
70	C₂³	#64528	1	8	yes	direct product factor
71	C₂³	C₂×C₂²⋊D₁₉	1	7	yes	—
72	Q₈	—	2	28	no	—
73	Q₈	—	19	8	no	—
74	Q₈	—	38	28	no	—
75	Q₈	C₂³×D₁₉	1	8	yes	—
76	C₂×C₄	—	2	28	no	—
77	C₂×C₄	—	38	28	no	—
78	C₂×C₄	C₂×C₂²⋊D₁₉	1	21	yes	—
79	C₂×C₄	C₂³×D₁₉	1	7	yes	—
80	C₈	—	19	8	no	—
81	C₂²	C₂×#64528	1	28	yes	direct product factor
82	C₂²	C₂²×C₂²⋊D₁₉	1	7	yes	—
83	C₄	—	2	8	no	—
84	C₄	—	38	8	no	—
85	C₄	C₂²×C₂²⋊D₁₉	1	7	yes	—
86	C₄	C₂⁴×D₁₉	1	1	yes	characteristic
87	C₂	C₂²×#64528	1	14	yes	direct product factor
88	C₂	C₂³×C₂²⋊D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂²⋊D₁₉
commutator, cosocle	C₄×C₁₉	C₂⁵
Frattini	C₄	C₂⁴×D₁₉
Fitting	C₂³×Q₈×C₁₉	C₂
socle, prime radical	C₂⁴×C₁₉	D₄
hypercenter	C₂³×Q₈	D₁₉
hypocenter	C₁₉	C₂³×Q₁₆
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×Q₈

Complements

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

N	H ≅ G/N	type
2. C₂²×#64528	C₂	direct (N × H)
12. C₂×#64528	C₂²	direct (N × H)
23. #64528	C₂³	direct (N × H)
25. C₂³×C₁₉	Q₁₆	semidirect
37. C₂²×C₁₉	C₂×Q₁₆	semidirect
47. C₂×C₁₉	C₂²×Q₁₆	semidirect
58. C₁₉	C₂³×Q₁₆	semidirect
70. C₂³	#64528	direct (N × H)
81. C₂²	C₂×#64528	direct (N × H)
87. C₂	C₂²×#64528	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×Dic₃₈	2
C₂²×#64528	2
C₂³×C₁₉⋊C₈	2
C₂³×Q₈×C₁₉	2
C₂³×Q₁₆	19

Subgroups — C23×#64528 #14578357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#64528 #14578357