Subgroups — #18071904

Order 4864.

526 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563381	C₂	1	2	yes	maximal
2	C₂×#11926266	C₂	1	4	yes	maximal
3	C₄²×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₁₉⋊C₈	C₂²	1	4	yes	—
5	#11926299	C₄	1	8	yes	—
6	#11926266	C₄	1	16	yes	complemented
7	C₂×C₄×C₈×C₁₉	C₄	1	4	yes	—
8	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
9	C₄³×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
11	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
12	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
13	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
14	C₂²×C₁₉⋊C₈	C₂×C₄	1	8	yes	—
15	C₄×C₈×C₁₉	—	2	8	no	—
16	C₄×C₈×C₁₉	C₂×C₄	1	8	yes	—
17	C₄×C₁₉⋊C₈	C₂×C₄	1	16	yes	—
18	C₂²×C₄×C₁₉	C₄²	1	4	yes	—
19	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
20	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	—	2	8	no	—
22	C₂×C₈×C₁₉	C₄²	1	8	yes	—
23	C₄²×C₁₉	—	2	8	no	—
24	C₄²×C₁₉	M₁₆	1	8	yes	—
25	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
26	C₂×C₁₉⋊C₈	—	2	16	no	—
27	C₂×C₁₉⋊C₈	C₄²	1	16	yes	—
28	#7843	—	19	1	no	maximal, Sylow
29	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
30	C₂×C₄×C₁₉	—	2	8	no	—
31	C₂×C₄×C₁₉	#97	1	8	yes	—
32	C₂×C₄×C₁₉	C₂×C₄²	1	4	yes	—
33	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
34	C₂×C₄×C₁₉	C₂×M₁₆	1	4	yes	—
35	C₂×C₄×C₁₉	#131	1	8	yes	—
36	C₈×C₁₉	—	2	8	no	—
37	C₁₉⋊C₈	—	2	16	no	—
38	#1744	—	19	2	no	—
39	C₄²×C₈	D₁₉	1	1	yes	characteristic
40	C₂×#322	—	19	4	no	—
41	C₂²×C₁₉	C₄³	1	1	yes	characteristic
42	C₂²×C₁₉	C₂×#97	1	2	yes	—
43	C₂²×C₁₉	#405	1	4	yes	—
44	C₄×C₁₉	—	2	8	no	—
45	C₄×C₁₉	C₄×M₁₆	1	4	yes	—
46	C₄×C₁₉	#405	1	8	yes	—
47	C₂×C₄×C₈	—	19	4	no	—
48	C₂×C₄×C₈	Dic₁₉	1	4	yes	—
49	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
50	C₄³	C₂×D₁₉	1	1	yes	characteristic
51	#336	—	19	8	no	—
52	#322	—	19	16	no	—
53	C₂×C₁₉	#1452	1	4	yes	—
54	C₂×C₁₉	C₄×#97	1	1	yes	characteristic
55	C₂×C₁₉	#1726	1	2	yes	—
56	C₂²×C₈	—	19	8	no	—
57	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
58	C₂×C₄²	C₄×D₁₉	1	4	yes	—
59	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
60	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
61	C₄×C₈	—	2	8	no	—
62	C₄×C₈	—	19	16	no	—
63	C₄×C₈	C₄×D₁₉	1	8	yes	—
64	C₁₉	#7843	1	1	yes	characteristic, complemented, Sylow
65	C₂²×C₄	C₄×Dic₁₉	1	4	yes	—
66	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
67	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
68	C₂×C₈	—	2	8	no	—
69	C₂×C₈	—	19	16	no	—
70	C₂×C₈	—	38	16	no	—
71	C₂×C₈	C₄×Dic₁₉	1	8	yes	—
72	C₄²	—	2	8	no	—
73	C₄²	#64520	1	8	yes	—
74	C₄²	C₂×C₄×D₁₉	1	4	yes	—
75	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
76	C₂×C₄	—	2	8	no	—
77	C₂×C₄	#10597260	1	8	yes	—
78	C₂×C₄	C₄²×D₁₉	1	4	yes	—
79	C₂×C₄	#10597347	1	8	yes	—
80	C₂×C₄	C₂×#64520	1	4	yes	—
81	C₂×C₄	C₂×C₄×Dic₁₉	1	2	yes	—
82	C₈	—	2	8	no	—
83	C₈	—	38	16	no	—
84	C₂²	C₄²×Dic₁₉	1	1	yes	characteristic
85	C₂²	C₂×#10597260	1	2	yes	—
86	C₂²	#11926499	1	4	yes	—
87	C₄	—	2	8	no	—
88	C₄	C₄×#64520	1	4	yes	—
89	C₄	#11926498	1	8	yes	—
90	C₂	#14561927	1	4	yes	—
91	C₂	C₄×#10597260	1	1	yes	characteristic
92	C₂	#14563321	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₉
commutator	C₂²×C₁₉	C₄³
Fitting	C₄²×C₈×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄²×C₈	D₁₉
hypocenter	C₁₉	#7843
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄² ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
6. #11926266	C₄	semidirect
64. C₁₉	#7843	semidirect

Maximal subgroups

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

subgroup	index
#14563381	2
C₂×#11926266	2
C₄²×C₈×C₁₉	2
#7843	19