Subgroups — #14565890

Order 2432.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597284	C₂	1	4	yes	maximal, complemented
2	#11926924	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#493	C₂	1	1	yes	maximal, characteristic
5	C₂×D₈×C₁₉	—	2	1	no	—
6	C₂×D₈×C₁₉	C₂²	1	2	yes	—
7	C₁₉×#127	—	2	1	no	—
8	C₂×Dic₇₆	—	2	1	no	—
9	C₂×Dic₇₆	C₂²	1	2	yes	—
10	#10597315	—	2	1	no	—
11	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	#10597284	—	2	8	no	—
13	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
14	C₂×D₄×C₁₉	—	2	2	no	—
15	C₂×D₄×C₁₉	—	4	2	no	—
16	C₂×Dic₃₈	—	2	2	no	—
17	D₈×C₁₉	—	2	4	no	—
18	D₈×C₁₉	—	4	2	no	—
19	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
21	C₄²×C₁₉	D₄	1	1	yes	characteristic
22	C₄⋊Dic₁₉	—	4	2	no	—
23	Dic₇₆	—	2	4	no	—
24	Dic₇₆	—	4	2	no	—
25	C₁₉⋊C₁₆	D₄	1	4	yes	complemented
26	C₂³×C₁₉	—	4	2	no	—
27	D₄×C₁₉	—	4	2	no	—
28	D₄×C₁₉	—	4	2	no	—
29	D₄×C₁₉	—	8	4	no	—
30	C₂×C₄×C₁₉	D₈	1	2	yes	—
31	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
32	C₂×Dic₁₉	—	4	2	no	—
33	Dic₃₈	—	4	2	no	—
34	Dic₃₈	—	4	2	no	—
35	C₈×C₁₉	D₈	1	2	yes	—
36	C₈×C₁₉	C₂×D₄	1	2	yes	—
37	#2248	—	19	1	no	maximal, Sylow
38	C₂²×C₁₉	—	8	2	no	—
39	C₂²×C₁₉	—	8	4	no	—
40	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
41	C₄×C₁₉	SD₃₂	1	4	yes	complemented
42	C₄×C₁₉	#127	1	1	yes	characteristic
43	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
44	Dic₁₉	—	8	2	no	—
45	C₂×SD₃₂	—	19	4	no	—
46	#494	—	19	1	no	—
47	#493	D₁₉	1	1	yes	characteristic
48	C₄×C₁₆	—	19	1	no	—
49	C₂×C₁₉	—	16	2	no	—
50	C₂×C₁₉	#493	1	1	yes	characteristic
51	C₂×C₁₉	C₂×SD₃₂	1	2	yes	—
52	C₂×Q₁₆	—	19	2	no	—
53	C₂×Q₁₆	—	38	1	no	—
54	C₂×D₈	—	2	1	no	—
55	C₂×D₈	C₂×D₁₉	1	2	yes	—
56	C₄⋊Q₈	—	38	1	no	—
57	#127	—	2	1	no	—
58	SD₃₂	—	38	8	no	—
59	C₂×C₁₆	—	19	2	no	—
60	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
61	C₁₉	#2248	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₈	—	38	2	no	—
63	C₂×D₄	—	2	2	no	—
64	C₂×D₄	—	4	2	no	—
65	Q₁₆	—	38	4	no	—
66	Q₁₆	—	76	2	no	—
67	D₈	—	2	4	no	—
68	D₈	—	4	2	no	—
69	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
70	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
71	C₄⋊C₄	—	76	2	no	—
72	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
73	C₁₆	—	19	4	no	—
74	C₂³	—	4	2	no	—
75	Q₈	—	76	2	no	—
76	Q₈	—	76	2	no	—
77	D₄	—	4	2	no	—
78	D₄	—	4	2	no	—
79	D₄	—	8	4	no	—
80	C₂×C₄	—	76	2	no	—
81	C₂×C₄	#64525	1	2	yes	—
82	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
83	C₈	#64525	1	2	yes	—
84	C₈	D₄×D₁₉	1	2	yes	—
85	C₂²	—	8	2	no	—
86	C₂²	—	8	4	no	—
87	C₂²	C₂×#64525	1	1	yes	characteristic
88	C₄	—	152	2	no	—
89	C₄	#10597284	1	4	yes	complemented
90	C₄	C₂×#64525	1	1	yes	characteristic
91	C₄	#10597386	1	1	yes	characteristic
92	C₂	—	16	2	no	—
93	C₂	#11926920	1	1	yes	characteristic
94	C₂	C₂×#10597284	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#64525
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting, prime radical	C₁₉×#493	C₂
socle	C₂²×C₁₉	C₂×D₈
hypercenter	#493	D₁₉
hypocenter	C₁₉	#2248
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

Complements

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

N	H ≅ G/N	type
1. C₂×#10597284	C₂	semidirect
2. #11926924	C₂	semidirect
3. C₄×C₁₉⋊C₁₆	C₂	semidirect
25. C₁₉⋊C₁₆	D₄	semidirect
41. C₄×C₁₉	SD₃₂	semidirect
61. C₁₉	#2248	semidirect
89. C₄	#10597284	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597284	2
#11926924	2
C₄×C₁₉⋊C₁₆	2
C₁₉×#493	2
#2248	19