Subgroups — #14565034

Order 2432.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926592	C₂	1	3	yes	maximal, complemented
2	C₂×#10597280	C₂	1	3	yes	maximal
3	C₁₉×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₇₆	C₂²	1	1	yes	characteristic
5	C₂×M₁₆×C₁₉	C₂²	1	3	yes	—
6	C₂×#64520	C₂²	1	3	yes	—
7	#10597280	—	2	6	no	—
8	#10597279	—	2	6	no	—
9	C₂³×D₁₉	Q₈	1	2	yes	—
10	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
11	C₂×D₇₆	—	2	3	no	—
12	C₂×D₇₆	—	2	3	no	—
13	M₁₆×C₁₉	—	2	3	no	—
14	M₁₆×C₁₉	—	2	3	no	—
15	C₂×C₈×C₁₉	—	2	3	no	—
16	#64520	—	2	3	no	—
17	#64520	D₄	1	6	yes	—
18	C₂×C₁₉⋊C₈	—	2	3	no	—
19	C₂³×C₁₉	C₂×Q₈	1	1	yes	characteristic
20	C₂²×D₁₉	—	2	6	no	—
21	C₂²×D₁₉	—	8	2	no	—
22	C₂×C₄×C₁₉	C₂×D₄	1	3	yes	—
23	C₂×C₄×C₁₉	#41	1	3	yes	—
24	D₇₆	—	4	3	no	—
25	D₇₆	—	4	1	no	—
26	C₈×C₁₉	—	4	3	no	—
27	C₁₉⋊C₈	—	2	6	no	—
28	#2069	—	19	1	no	maximal, Sylow
29	C₂²×C₁₉	—	4	1	no	—
30	C₂²×C₁₉	C₂²⋊Q₈	1	3	yes	—
31	C₂×D₁₉	—	4	2	no	—
32	C₂×D₁₉	—	8	6	no	—
33	C₄×C₁₉	#121	1	3	yes	—
34	C₄×C₁₉	#126	1	1	yes	characteristic
35	#430	—	19	3	no	—
36	C₂×#100	—	19	3	no	—
37	#338	D₁₉	1	1	yes	characteristic, complemented
38	C₂×C₁₉	—	2	3	no	—
39	C₂×C₁₉	#396	1	1	yes	characteristic
40	D₁₉	—	8	2	no	—
41	C₂²×D₄	—	19	1	no	—
42	C₂×M₁₆	—	19	3	no	—
43	C₂×M₁₆	C₂×D₁₉	1	3	yes	—
44	#108	—	38	6	no	—
45	#100	—	38	6	no	—
46	C₁₉	#2069	1	1	yes	characteristic, complemented, Sylow
47	C₂⁴	—	19	2	no	—
48	C₂×D₄	—	38	3	no	—
49	C₂×D₄	—	38	3	no	—
50	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
51	M₁₆	—	2	3	no	—
52	M₁₆	—	2	3	no	—
53	M₁₆	—	19	6	no	—
54	M₁₆	—	38	3	no	—
55	C₂×C₈	—	2	3	no	—
56	C₂×C₈	—	38	3	no	—
57	C₂³	—	38	6	no	—
58	C₂³	—	152	2	no	—
59	C₂³	Q₈×D₁₉	1	1	yes	characteristic
60	D₄	—	76	1	no	—
61	D₄	—	76	3	no	—
62	C₂×C₄	#64541	1	3	yes	—
63	C₂×C₄	D₄×D₁₉	1	3	yes	—
64	C₈	—	4	3	no	—
65	C₈	—	38	6	no	—
66	C₂²	—	4	1	no	—
67	C₂²	—	76	2	no	—
68	C₂²	—	152	6	no	—
69	C₂²	#10597342	1	3	yes	—
70	C₄	#10597322	1	1	yes	characteristic
71	C₄	#10597330	1	3	yes	—
72	C₂	—	2	3	no	—
73	C₂	—	152	2	no	—
74	C₂	#11926468	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11926468
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#338	C₂
socle	C₂×C₁₉	#396
prime radical	C₂²×D₇₆	C₂²
hypercenter	#338	D₁₉
hypocenter	C₁₉	#2069
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
1. #11926592	C₂	semidirect
3. C₁₉×#338	C₂	semidirect
37. #338	D₁₉	semidirect
46. C₁₉	#2069	semidirect

Maximal subgroups

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

subgroup	index
#11926592	2
C₂×#10597280	2
C₁₉×#338	2
#2069	19