Subgroups — #18070419

Order 4864.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃₀₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉⋊C₆₄	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1423	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₅₂	—	2	1	no	—
5	Dic₃₀₄	—	2	1	no	—
6	Dic₃₀₄	C₄	1	2	yes	complemented
7	C₁₉⋊C₆₄	—	2	1	no	—
8	C₂×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
9	C₁₉×#366	—	2	1	no	—
10	C₂×Dic₇₆	—	4	1	no	—
11	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
12	C₁₉×#107	—	4	1	no	—
13	Dic₁₅₂	—	2	2	no	—
14	Dic₁₅₂	—	4	1	no	—
15	C₁₉×C₃₂	C₂×C₄	1	1	yes	characteristic
16	C₁₉×C₃₂	D₄	1	1	yes	characteristic
17	C₂×Dic₃₈	—	8	1	no	—
18	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
19	C₄⋊C₄×C₁₉	—	8	1	no	—
20	Dic₇₆	—	4	2	no	—
21	Dic₇₆	—	8	1	no	—
22	C₁₆×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
24	#7538	—	19	1	no	maximal, Sylow
25	C₂×C₄×C₁₉	—	16	1	no	—
26	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
27	C₂×Dic₁₉	—	16	1	no	—
28	Dic₃₈	—	8	2	no	—
29	Dic₃₈	—	16	1	no	—
30	C₈×C₁₉	#102	1	1	yes	characteristic
31	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
32	C₂×Q₆₄	—	19	1	no	—
33	C₂×C₆₄	—	19	1	no	—
34	#1423	D₁₉	1	1	yes	characteristic
35	C₂²×C₁₉	D₃₂	1	1	yes	characteristic
36	C₄×C₁₉	—	32	1	no	—
37	C₄×C₁₉	#357	1	1	yes	characteristic
38	C₄×C₁₉	SD₆₄	1	1	yes	characteristic
39	Dic₁₉	—	16	2	no	—
40	C₂×Q₃₂	—	38	1	no	—
41	Q₆₄	—	19	2	no	—
42	Q₆₄	—	38	1	no	—
43	C₂×C₃₂	C₂×D₁₉	1	1	yes	characteristic
44	#366	—	2	1	no	—
45	C₆₄	—	38	1	no	—
46	C₂×C₁₉	#1415	1	1	yes	characteristic
47	C₂×C₁₉	SD₁₂₈	1	1	yes	characteristic
48	C₂×C₁₉	Q₁₂₈	1	1	yes	characteristic
49	C₂×Q₁₆	—	76	1	no	—
50	Q₃₂	—	38	2	no	—
51	Q₃₂	—	76	1	no	—
52	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
53	#107	—	4	1	no	—
54	C₃₂	C₄×D₁₉	1	1	yes	characteristic
55	C₃₂	D₇₆	1	1	yes	characteristic
56	C₁₉	#7538	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₈	—	152	1	no	—
58	Q₁₆	—	76	2	no	—
59	Q₁₆	—	152	1	no	—
60	C₂×C₈	#64525	1	1	yes	characteristic
61	C₄⋊C₄	—	8	1	no	—
62	C₁₆	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
63	C₁₆	#64527	1	1	yes	characteristic
64	Q₈	—	304	1	no	—
65	Q₈	—	152	2	no	—
66	C₂×C₄	—	16	1	no	—
67	C₂×C₄	—	304	1	no	—
68	C₂×C₄	#10597283	1	1	yes	characteristic
69	C₈	#10597266	1	1	yes	characteristic
70	C₈	#10597285	1	1	yes	characteristic
71	C₂²	#11926379	1	1	yes	characteristic
72	C₄	—	32	1	no	—
73	C₄	—	304	2	no	—
74	C₄	#11926344	1	1	yes	characteristic
75	C₄	#11926381	1	1	yes	characteristic
76	C₂	#14561812	1	1	yes	characteristic
77	C₂	#14561850	1	1	yes	characteristic
78	C₂	#14561852	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926379
commutator	C₁₉×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₉
Fitting	C₁₉×#1423	C₂
socle, prime radical	C₂²×C₁₉	D₃₂
cosocle	C₂×C₁₉×C₃₂	C₂²
hypercenter	#1423	D₁₉
hypocenter	C₁₉	#7538
LCS	G ▷ C₁₉×C₃₂ ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #1423

Complements

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

N	H ≅ G/N	type
6. Dic₃₀₄	C₄	semidirect
56. C₁₉	#7538	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₃₀₄	2
C₂×C₁₉⋊C₆₄	2
C₁₉×#1423	2
#7538	19