Subgroups — C₂×#11744827 #14269286

Order 1824.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×Dic₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Dic₃₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	#11744827	C₂	1	4	yes	maximal, direct product factor
5	C₂×#64528	—	3	1	no	maximal, Hall
6	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×Dic₃×C₁₉	—	2	1	no	—
8	C₁₉×Dic₆	—	2	1	no	—
9	C₁₉×Dic₆	C₂²	1	2	yes	—
10	C₂×C₃×Dic₁₉	—	2	1	no	—
11	C₃×Dic₃₈	—	2	1	no	—
12	C₃×Dic₃₈	C₂²	1	2	yes	—
13	C₃⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
14	C₂×Q₈×C₁₉	—	3	1	no	—
15	C₂×Dic₃₈	D₃	1	1	yes	characteristic
16	#64528	—	3	4	no	—
17	C₂×C₁₉⋊C₈	—	3	1	no	—
18	C₂²×C₃×C₁₉	D₄	1	1	yes	characteristic
19	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
20	C₃×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₃×Dic₁₉	—	2	2	no	—
22	Dic₃×C₁₉	—	2	2	no	—
23	Q₈×C₁₉	—	3	2	no	—
24	Q₈×C₁₉	—	6	1	no	—
25	C₂×C₄×C₁₉	—	6	1	no	—
26	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
27	C₂×Dic₁₉	—	2	1	no	—
28	Dic₃₈	—	2	1	no	—
29	Dic₃₈	C₂×D₃	1	2	yes	—
30	C₁₉⋊C₈	—	3	2	no	—
31	C₂×C₃×C₁₉	Q₁₆	1	2	yes	complemented
32	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
33	C₂×#216	—	19	1	no	maximal, Hall
34	C₂²×C₁₉	#67	1	1	yes	characteristic
35	C₄×C₁₉	—	6	2	no	—
36	C₄×C₁₉	#67	1	1	yes	characteristic
37	C₄×C₁₉	C₂²×D₃	1	1	yes	characteristic
38	Dic₁₉	—	2	2	no	—
39	C₃×C₁₉	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
40	C₂×C₃×Q₈	—	19	1	no	—
41	C₂×Dic₆	D₁₉	1	1	yes	characteristic
42	#216	—	19	4	no	—
43	C₂×C₃⋊C₈	—	19	1	no	—
44	C₂×C₁₉	#216	1	2	yes	complemented
45	C₂×C₁₉	C₂×#67	1	1	yes	characteristic
46	C₂×Q₁₆	—	57	1	no	Sylow
47	C₃×Q₈	—	19	2	no	—
48	C₃×Q₈	—	38	1	no	—
49	C₂×C₃×C₄	—	38	1	no	—
50	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
51	C₂×Dic₃	—	2	1	no	—
52	Dic₆	—	2	1	no	—
53	Dic₆	C₂×D₁₉	1	2	yes	—
54	C₃⋊C₈	—	19	2	no	—
55	C₁₉	C₂×#216	1	1	yes	characteristic, complemented, Sylow
56	C₂×Q₈	—	3	1	no	—
57	C₂×Q₈	—	19	1	no	—
58	Q₁₆	—	57	4	no	—
59	C₂×C₈	—	57	1	no	—
60	C₂²×C₃	C₂²⋊D₁₉	1	1	yes	characteristic
61	C₃×C₄	—	38	2	no	—
62	C₃×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
63	C₃×C₄	C₂²×D₁₉	1	1	yes	characteristic
64	Dic₃	—	2	2	no	—
65	Q₈	—	3	2	no	—
66	Q₈	—	6	1	no	—
67	Q₈	—	19	2	no	—
68	Q₈	—	38	1	no	—
69	C₂×C₄	—	6	1	no	—
70	C₂×C₄	—	38	1	no	—
71	C₂×C₄	D₃×D₁₉	1	1	yes	characteristic
72	C₈	—	57	2	no	—
73	C₂×C₃	#64528	1	2	yes	complemented
74	C₂×C₃	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
75	C₂²	#90695	1	1	yes	characteristic
76	C₄	—	6	2	no	—
77	C₄	—	38	2	no	—
78	C₄	#90695	1	1	yes	characteristic
79	C₄	C₂×D₃×D₁₉	1	1	yes	characteristic
80	C₃	C₂×#64528	1	1	yes	characteristic, complemented, Sylow
81	C₂	#11744827	1	2	yes	direct product factor
82	C₂	C₂×#90695	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#90695
commutator, cosocle	C₃×C₄×C₁₉	C₂³
Frattini	C₄	C₂×D₃×D₁₉
Fitting	C₂×C₃×C₄×C₁₉	C₂²
socle, prime radical	C₂²×C₃×C₁₉	D₄
hypercenter	C₂×C₄	D₃×D₁₉
hypocenter	C₃×C₁₉	C₂×Q₁₆
LCS	G ▷ C₃×C₄×C₁₉ ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
4. #11744827	C₂	direct (N × H)
31. C₂×C₃×C₁₉	Q₁₆	semidirect
39. C₃×C₁₉	C₂×Q₁₆	semidirect
44. C₂×C₁₉	#216	semidirect
55. C₁₉	C₂×#216	semidirect
73. C₂×C₃	#64528	semidirect
80. C₃	C₂×#64528	semidirect
81. C₂	#11744827	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×Dic₆	2
C₂×C₃×Dic₃₈	2
C₂×C₃⋊(C₁₉⋊C₈)	2
#11744827	2
C₂×#64528	3
C₂×#216	19

Subgroups — C2×#11744827 #14269286

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11744827 #14269286