Subgroups — #14561717

Order 2432.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597269	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₁₉	C₄	1	1	yes	characteristic
4	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
5	C₂×C₄²×C₁₉	C₄	1	1	yes	characteristic
6	C₄×C₈×C₁₉	—	2	2	no	—
7	#10597269	—	2	2	no	—
8	#10597269	C₄	1	4	yes	complemented
9	C₂×C₁₉⋊C₁₆	—	2	2	no	—
10	C₂²×C₄×C₁₉	—	2	1	no	—
11	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₁₉	—	2	1	no	—
13	C₂×C₈×C₁₉	—	2	1	no	—
14	C₂×C₈×C₁₉	C₈	1	2	yes	—
15	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
16	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
17	C₂×C₈×C₁₉	D₄	1	2	yes	—
18	C₂×C₈×C₁₉	Q₈	1	1	yes	characteristic
19	C₄²×C₁₉	—	2	1	no	—
20	C₄²×C₁₉	C₈	1	2	yes	—
21	C₁₉⋊C₁₆	—	2	4	no	—
22	C₂³×C₁₉	M₁₆	1	1	yes	characteristic
23	C₂×C₄×C₁₉	—	2	4	no	—
24	C₂×C₄×C₁₉	—	2	2	no	—
25	C₂×C₄×C₁₉	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₁₉	M₁₆	1	1	yes	characteristic
31	C₈×C₁₉	—	2	2	no	—
32	C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
33	C₈×C₁₉	C₄⋊C₄	1	2	yes	—
34	#1376	—	19	1	no	maximal, Sylow
35	C₂²×C₁₉	—	2	2	no	—
36	C₂²×C₁₉	#97	1	1	yes	characteristic
37	C₂²×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
38	C₂²×C₁₉	C₄⋊C₈	1	1	yes	characteristic
39	C₄×C₁₉	—	2	4	no	—
40	C₄×C₁₉	#95	1	1	yes	characteristic
41	C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
42	C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
43	C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
44	C₂×M₃₂	—	19	2	no	—
45	C₂×C₄×C₈	D₁₉	1	1	yes	characteristic
46	C₂×C₁₉	—	2	1	no	—
47	C₂×C₁₉	—	2	1	no	—
48	C₂×C₁₉	#336	1	1	yes	characteristic
49	C₂×C₁₉	#364	1	2	yes	—
50	C₂²×C₈	Dic₁₉	1	1	yes	characteristic
51	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
52	C₂×C₄²	Dic₁₉	1	1	yes	characteristic
53	M₃₂	—	19	4	no	—
54	M₃₂	—	38	2	no	—
55	C₂×C₁₆	—	38	2	no	—
56	C₄×C₈	—	2	2	no	—
57	C₁₉	#1376	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	—	2	1	no	—
59	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
60	C₂×C₈	—	2	1	no	—
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	C₁₉⋊C₈	1	2	yes	—
63	C₂×C₈	Dic₃₈	1	1	yes	characteristic
64	C₂×C₈	C₄×D₁₉	1	2	yes	—
65	C₂×C₈	D₇₆	1	1	yes	characteristic
66	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
67	C₄²	—	2	1	no	—
68	C₄²	C₁₉⋊C₈	1	2	yes	—
69	C₁₆	—	38	4	no	—
70	C₂³	#64520	1	1	yes	characteristic
71	C₂×C₄	—	2	4	no	—
72	C₂×C₄	—	2	2	no	—
73	C₂×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
74	C₂×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
75	C₂×C₄	#64520	1	1	yes	characteristic
76	C₂×C₄	C₄×Dic₁₉	1	1	yes	characteristic
77	C₂×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
78	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	Dic₁₉⋊C₄	1	2	yes	—
81	C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
82	C₂²	—	2	2	no	—
83	C₂²	#10597260	1	1	yes	characteristic
84	C₂²	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
85	C₂²	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	C₄×C₁₉⋊C₈	1	1	yes	characteristic
88	C₄	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
89	C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
90	C₄	C₁₉⋊#95	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	2	1	no	—
93	C₂	#11926299	1	1	yes	characteristic
94	C₂	#11926365	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₇₆
commutator	C₄×C₁₉	C₄×C₈
Frattini	C₂²×C₈	C₂×D₁₉
Fitting	C₂×C₄×C₈×C₁₉	C₂
socle	C₂²×C₁₉	C₄⋊C₈
prime radical	C₂³×C₁₉	M₁₆
cosocle	C₂²×C₈×C₁₉	C₂²
hypercenter	C₂×C₄×C₈	D₁₉
hypocenter	C₁₉	#1376
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
8. #10597269	C₄	semidirect
57. C₁₉	#1376	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597269	2
C₂×C₄×C₈×C₁₉	2
#1376	19