Subgroups — C₂×#11926372 #14565415

Order 2432.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597275	C₂	1	2	yes	maximal
2	#11926372	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
5	C₂×C₄⋊Dic₁₉	—	2	2	no	—
6	C₂×C₁₆×C₁₉	C₄	1	4	yes	complemented
7	C₂×C₁₆×C₁₉	C₂²	1	2	yes	—
8	#10597275	—	2	2	no	—
9	#10597275	C₂²	1	4	yes	—
10	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
11	C₂²×Dic₁₉	—	4	2	no	—
12	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
13	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
14	C₂×C₈×C₁₉	Q₈	1	2	yes	—
15	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
16	C₄⋊Dic₁₉	—	2	4	no	—
17	C₄⋊Dic₁₉	—	4	2	no	—
18	C₁₆×C₁₉	C₂×C₄	1	4	yes	complemented
19	C₂³×C₁₉	D₈	1	1	yes	characteristic
20	C₂×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
21	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
22	C₂×C₄×C₁₉	Q₁₆	1	2	yes	—
23	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
24	C₂×Dic₁₉	—	4	4	no	—
25	C₂×Dic₁₉	—	8	4	no	—
26	C₈×C₁₉	C₄⋊C₄	1	2	yes	—
27	C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
28	C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
29	C₂×#367	—	19	1	no	maximal, Sylow
30	C₂²×C₁₉	#107	1	2	yes	—
31	C₂²×C₁₉	SD₃₂	1	4	yes	—
32	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
33	C₄×C₁₉	#107	1	2	yes	—
34	C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
36	Dic₁₉	—	8	4	no	—
37	C₂²×C₁₆	D₁₉	1	1	yes	characteristic
38	C₂×#107	—	19	2	no	—
39	#367	—	19	4	no	—
40	C₂×C₁₉	#367	1	4	yes	complemented
41	C₂×C₁₉	C₂×#107	1	1	yes	characteristic
42	C₂×C₁₉	C₂×SD₃₂	1	2	yes	—
43	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
44	C₂×C₄⋊C₄	—	38	2	no	—
45	C₂×C₁₆	Dic₁₉	1	4	yes	complemented
46	C₂×C₁₆	C₂×D₁₉	1	2	yes	—
47	#107	—	19	4	no	—
48	#107	—	38	2	no	—
49	C₁₉	C₂×#367	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₄	—	76	2	no	—
51	C₂²×C₄	D₇₆	1	1	yes	characteristic
52	C₂×C₈	Dic₃₈	1	2	yes	—
53	C₂×C₈	D₇₆	1	1	yes	characteristic
54	C₂×C₈	C₂×Dic₁₉	1	2	yes	—
55	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
56	C₄⋊C₄	—	38	4	no	—
57	C₄⋊C₄	—	76	2	no	—
58	C₁₆	C₂×Dic₁₉	1	4	yes	complemented
59	C₂³	D₁₅₂	1	1	yes	characteristic
60	C₂×C₄	—	76	4	no	—
61	C₂×C₄	—	152	4	no	—
62	C₂×C₄	D₁₅₂	1	1	yes	characteristic
63	C₂×C₄	Dic₇₆	1	2	yes	—
64	C₂×C₄	C₄⋊Dic₁₉	1	2	yes	—
65	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
66	C₈	C₄⋊Dic₁₉	1	2	yes	—
67	C₈	C₂×Dic₃₈	1	1	yes	characteristic
68	C₈	C₂²×Dic₁₉	1	1	yes	characteristic
69	C₂²	#10597257	1	4	yes	—
70	C₂²	#10597275	1	2	yes	—
71	C₂²	C₂×D₁₅₂	1	1	yes	characteristic
72	C₄	—	152	4	no	—
73	C₄	#10597275	1	2	yes	—
74	C₄	C₂×Dic₇₆	1	1	yes	characteristic
75	C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
76	C₂	#11926372	1	4	yes	direct product factor
77	C₂	C₂×#10597275	1	1	yes	characteristic
78	C₂	C₂×#10597257	1	2	yes	—

	subgroup	G/H
center	C₂³	D₁₅₂
commutator	C₈×C₁₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₂²×C₁₆×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	D₈
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	C₂²×C₁₆	D₁₉
hypocenter	C₁₉	C₂×#367
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #11926372	C₂	direct (N × H)
6. C₂×C₁₆×C₁₉	C₄	semidirect
18. C₁₆×C₁₉	C₂×C₄	semidirect
40. C₂×C₁₉	#367	semidirect
45. C₂×C₁₆	Dic₁₉	semidirect
49. C₁₉	C₂×#367	semidirect
58. C₁₆	C₂×Dic₁₉	semidirect
76. C₂	#11926372	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×#10597275	2
#11926372	2
C₂²×C₁₆×C₁₉	2
C₂×#367	19

Subgroups — C2×#11926372 #14565415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11926372 #14565415