Subgroups — #14565885

Order 2432.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₀₄	C₂	1	4	yes	maximal, complemented
2	#11926921	C₂	1	2	yes	maximal, complemented
3	C₄×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₅₂	—	2	2	no	—
5	C₂×D₁₅₂	C₂²	1	4	yes	—
6	#10597320	—	2	2	no	—
7	C₂×C₁₆×C₁₉	C₂²	1	2	yes	—
8	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	D₃₀₄	—	2	8	no	—
10	C₂×D₇₆	—	2	4	no	—
11	C₂×D₇₆	—	4	4	no	—
12	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
13	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
14	C₄²×C₁₉	D₄	1	1	yes	characteristic
15	D₁₅₂	—	2	8	no	—
16	D₁₅₂	—	4	4	no	—
17	C₁₆×C₁₉	D₄	1	4	yes	complemented
18	C₂²×D₁₉	—	4	4	no	—
19	C₂×C₄×C₁₉	D₈	1	2	yes	—
20	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
21	D₇₆	—	4	4	no	—
22	D₇₆	—	4	4	no	—
23	D₇₆	—	8	8	no	—
24	C₈×C₁₉	D₈	1	2	yes	—
25	C₈×C₁₉	C₂×D₄	1	2	yes	—
26	#2246	—	19	1	no	maximal, Sylow
27	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
28	C₂×D₁₉	—	8	4	no	—
29	C₂×D₁₉	—	8	8	no	—
30	C₄×C₁₉	D₁₆	1	4	yes	complemented
31	C₄×C₁₉	#127	1	1	yes	characteristic
32	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
33	C₂×D₁₆	—	19	4	no	—
34	#493	—	19	2	no	—
35	C₄×C₁₆	D₁₉	1	1	yes	characteristic, complemented
36	C₂×C₁₉	#493	1	1	yes	characteristic
37	C₂×C₁₉	C₂×D₁₆	1	2	yes	—
38	D₁₉	—	16	4	no	—
39	C₂×D₈	—	19	4	no	—
40	C₂×D₈	—	38	2	no	—
41	#127	—	38	2	no	—
42	D₁₆	—	38	8	no	—
43	C₂×C₁₆	C₂×D₁₉	1	2	yes	—
44	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
45	C₁₉	#2246	1	1	yes	characteristic, complemented, Sylow
46	C₂×D₄	—	38	4	no	—
47	C₂×D₄	—	76	4	no	—
48	D₈	—	38	8	no	—
49	D₈	—	76	4	no	—
50	C₂×C₈	D₇₆	1	1	yes	characteristic
51	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
52	C₄²	D₇₆	1	1	yes	characteristic
53	C₁₆	D₇₆	1	4	yes	complemented
54	C₂³	—	76	4	no	—
55	D₄	—	76	4	no	—
56	D₄	—	76	4	no	—
57	D₄	—	152	8	no	—
58	C₂×C₄	D₁₅₂	1	2	yes	—
59	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
60	C₈	D₁₅₂	1	2	yes	—
61	C₈	C₂×D₇₆	1	2	yes	—
62	C₂²	—	152	4	no	—
63	C₂²	—	152	8	no	—
64	C₂²	C₂×D₁₅₂	1	1	yes	characteristic
65	C₄	D₃₀₄	1	4	yes	complemented
66	C₄	#10597320	1	1	yes	characteristic
67	C₄	C₂×D₁₅₂	1	1	yes	characteristic
68	C₂	—	304	4	no	—
69	C₂	#11926921	1	1	yes	characteristic
70	C₂	C₂×D₃₀₄	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₅₂
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₄×C₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂×D₈
hypercenter	C₄×C₁₆	D₁₉
hypocenter	C₁₉	#2246
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×D₃₀₄	C₂	semidirect
2. #11926921	C₂	semidirect
3. C₄×C₁₆×C₁₉	C₂	semidirect
17. C₁₆×C₁₉	D₄	semidirect
30. C₄×C₁₉	D₁₆	semidirect
35. C₄×C₁₆	D₁₉	semidirect
45. C₁₉	#2246	semidirect
53. C₁₆	D₇₆	semidirect
65. C₄	D₃₀₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃₀₄	2
#11926921	2
C₄×C₁₆×C₁₉	2
#2246	19