Subgroups — #14561826

Order 2432.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₀₄	C₂	1	1	yes	maximal, characteristic
2	#11926374	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₅₂	—	2	1	no	—
5	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
6	#10597276	—	2	1	no	—
7	D₃₀₄	—	2	1	no	—
8	D₃₀₄	C₄	1	2	yes	—
9	C₁₉×C₃₂	—	2	1	no	—
10	C₂×D₇₆	—	4	1	no	—
11	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
12	#64520	—	4	1	no	—
13	D₁₅₂	—	2	2	no	—
14	D₁₅₂	—	4	1	no	—
15	C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₁₉	D₄	1	1	yes	characteristic
17	C₂²×D₁₉	—	8	1	no	—
18	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
19	D₇₆	—	4	2	no	—
20	D₇₆	—	8	1	no	—
21	C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₁₉	SD₁₆	1	1	yes	characteristic
23	C₁₉⋊C₈	—	8	1	no	—
24	#1419	—	19	1	no	maximal, Sylow
25	C₂²×C₁₉	SD₃₂	1	1	yes	characteristic
26	C₂×D₁₉	—	8	2	no	—
27	C₂×D₁₉	—	16	2	no	—
28	C₄×C₁₉	#102	1	1	yes	characteristic
29	C₄×C₁₉	D₁₆	1	1	yes	characteristic
30	C₂×D₁₆	—	19	1	no	—
31	M₆₄	D₁₉	1	1	yes	characteristic, complemented
32	#368	—	19	1	no	—
33	C₂×C₁₉	—	2	1	no	—
34	C₂×C₁₉	#357	1	1	yes	characteristic
35	D₁₉	—	16	2	no	—
36	C₂×D₈	—	38	1	no	—
37	D₁₆	—	19	2	no	—
38	D₁₆	—	38	1	no	—
39	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
40	#108	—	38	1	no	—
41	C₃₂	—	2	1	no	—
42	C₁₉	#1419	1	1	yes	characteristic, complemented, Sylow
43	C₂×D₄	—	76	1	no	—
44	D₈	—	38	2	no	—
45	D₈	—	76	1	no	—
46	M₁₆	—	76	1	no	—
47	C₂×C₈	D₇₆	1	1	yes	characteristic
48	C₁₆	C₄×D₁₉	1	1	yes	characteristic
49	C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
50	C₂³	—	152	1	no	—
51	D₄	—	76	2	no	—
52	D₄	—	152	1	no	—
53	C₂×C₄	D₁₅₂	1	1	yes	characteristic
54	C₈	—	152	1	no	—
55	C₈	#64516	1	1	yes	characteristic
56	C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
57	C₂²	—	304	2	no	—
58	C₂²	—	152	2	no	—
59	C₂²	#10597257	1	1	yes	characteristic
60	C₄	D₃₀₄	1	1	yes	characteristic
61	C₄	#10597278	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	304	2	no	—
64	C₂	#11926346	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11926346
commutator	C₁₆×C₁₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₉
Fitting	C₁₉×M₆₄	C₂
socle	C₂×C₁₉	#357
prime radical	C₂×D₃₀₄	C₂
cosocle	C₂×C₁₆×C₁₉	C₂²
hypercenter	M₆₄	D₁₉
hypocenter	C₁₉	#1419
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. #11926374	C₂	semidirect
3. C₁₉×M₆₄	C₂	semidirect
31. M₆₄	D₁₉	semidirect
42. C₁₉	#1419	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
#11926374	2
C₁₉×M₆₄	2
#1419	19