Subgroups — #14565955

Order 2432.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926976	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₅₂	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₃₀₄	C₂	1	2	yes	maximal, complemented
4	#11926383	C₂	1	2	yes	maximal, complemented
5	C₁₉×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₇₆	—	2	1	no	—
7	#10597350	—	2	1	no	—
8	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	Dic₁₅₂	—	2	1	no	—
10	Dic₁₅₂	C₂²	1	2	yes	—
11	Dic₁₅₂	C₂²	1	1	yes	characteristic
12	#10597257	—	2	1	no	—
13	D₃₀₄	C₂²	1	1	yes	characteristic
14	C₁₉×C₃₂	C₂²	1	2	yes	—
15	#64541	—	4	1	no	—
16	C₂×Dic₃₈	—	4	1	no	—
17	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
18	Dic₇₆	—	2	1	no	—
19	Dic₇₆	—	2	2	no	—
20	Dic₇₆	—	4	1	no	—
21	D₁₅₂	—	2	1	no	—
22	#64516	—	4	1	no	—
23	C₁₆×C₁₉	D₄	1	1	yes	characteristic
24	C₁₆×C₁₉	C₂³	1	1	yes	characteristic
25	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
26	C₂²⋊D₁₉	—	8	1	no	—
27	C₂×Dic₁₉	—	8	1	no	—
28	D₇₆	—	4	1	no	—
29	C₄×D₁₉	—	8	1	no	—
30	Dic₃₈	—	4	1	no	—
31	Dic₃₈	—	4	2	no	—
32	Dic₃₈	—	8	1	no	—
33	C₈×C₁₉	D₈	1	1	yes	characteristic
34	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
35	#2264	—	19	1	no	maximal, Sylow
36	C₂²×C₁₉	D₁₆	1	1	yes	characteristic
37	C₂×D₁₉	—	8	1	no	—
38	C₄×C₁₉	D₁₆	1	1	yes	characteristic
39	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
40	Dic₁₉	—	8	2	no	—
41	Dic₁₉	—	8	1	no	—
42	#508	—	19	1	no	—
43	C₂×Q₃₂	—	19	1	no	—
44	Q₆₄	—	19	2	no	—
45	SD₆₄	—	19	2	no	—
46	M₆₄	D₁₉	1	1	yes	characteristic, complemented
47	C₂×C₁₉	—	2	1	no	—
48	C₂×C₁₉	C₂×D₁₆	1	1	yes	characteristic
49	D₁₉	—	16	1	no	—
50	#135	—	38	1	no	—
51	C₂×Q₁₆	—	38	1	no	—
52	Q₃₂	—	19	2	no	—
53	Q₃₂	—	19	1	no	—
54	Q₃₂	—	38	1	no	—
55	SD₃₂	—	38	1	no	—
56	D₁₆	—	19	1	no	—
57	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
58	C₃₂	C₂×D₁₉	1	2	yes	—
59	C₁₉	#2264	1	1	yes	characteristic, complemented, Sylow
60	#41	—	76	1	no	—
61	C₂×Q₈	—	76	1	no	—
62	Q₁₆	—	38	1	no	—
63	Q₁₆	—	38	2	no	—
64	Q₁₆	—	76	1	no	—
65	SD₁₆	—	76	1	no	—
66	D₈	—	38	1	no	—
67	C₂×C₈	D₇₆	1	1	yes	characteristic
68	C₁₆	D₇₆	1	1	yes	characteristic
69	C₁₆	C₂²×D₁₉	1	1	yes	characteristic
70	Q₈	—	76	1	no	—
71	Q₈	—	76	2	no	—
72	Q₈	—	152	1	no	—
73	D₄	—	76	1	no	—
74	D₄	—	152	1	no	—
75	C₂×C₄	—	152	1	no	—
76	C₂×C₄	—	152	1	no	—
77	C₂×C₄	D₁₅₂	1	1	yes	characteristic
78	C₈	D₁₅₂	1	1	yes	characteristic
79	C₈	C₂×D₇₆	1	1	yes	characteristic
80	C₂²	—	152	1	no	—
81	C₂²	D₃₀₄	1	1	yes	characteristic
82	C₄	—	152	1	no	—
83	C₄	—	152	2	no	—
84	C₄	D₃₀₄	1	1	yes	characteristic
85	C₄	C₂×D₁₅₂	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	304	1	no	—
88	C₂	C₂×D₃₀₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₃₀₄
commutator, cosocle	C₁₆×C₁₉	C₂³
Frattini	C₁₆	C₂²×D₁₉
Fitting	C₁₉×M₆₄	C₂
socle	C₂×C₁₉	C₂×D₁₆
prime radical	#11926976	C₂
hypercenter	M₆₄	D₁₉
hypocenter	C₁₉	#2264
LCS	G ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₁₅₂	C₂	semidirect
3. Dic₃₀₄	C₂	semidirect
4. #11926383	C₂	semidirect
5. C₁₉×M₆₄	C₂	semidirect
46. M₆₄	D₁₉	semidirect
59. C₁₉	#2264	semidirect

Maximal subgroups

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

subgroup	index
#11926976	2
C₂×Dic₁₅₂	2
Dic₃₀₄	2
#11926383	2
C₁₉×M₆₄	2
#2264	19