Subgroups — C₂×#11744822 #14269276

Order 1824.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	#11744822	C₂	1	4	yes	maximal, direct product factor
5	C₂×#64526	—	3	1	no	maximal, Hall
6	C₂²×D₃×C₁₉	—	2	1	no	—
7	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×D₁₂	—	2	1	no	—
9	C₁₉×D₁₂	C₂²	1	2	yes	—
10	C₂×C₃×Dic₁₉	—	2	1	no	—
11	C₃×Dic₃₈	—	2	1	no	—
12	C₃×Dic₃₈	C₂²	1	2	yes	complemented
13	C₃⋊(C₁₉⋊C₈)	C₂²	1	2	yes	complemented
14	C₂×D₄×C₁₉	—	3	1	no	—
15	C₂×Dic₃₈	D₃	1	1	yes	characteristic, complemented
16	#64526	—	3	4	no	—
17	C₂×C₁₉⋊C₈	—	3	1	no	—
18	C₂²×C₃×C₁₉	D₄	1	1	yes	characteristic
19	C₂×D₃×C₁₉	—	2	2	no	—
20	C₂×D₃×C₁₉	—	4	2	no	—
21	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₃×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	C₃×Dic₁₉	—	2	2	no	—
24	C₂³×C₁₉	—	6	1	no	—
25	D₄×C₁₉	—	3	2	no	—
26	D₄×C₁₉	—	6	1	no	—
27	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
28	C₂×Dic₁₉	—	2	1	no	—
29	Dic₃₈	—	2	1	no	—
30	Dic₃₈	C₂×D₃	1	2	yes	complemented
31	C₁₉⋊C₈	—	3	2	no	—
32	C₂×C₃×C₁₉	SD₁₆	1	2	yes	complemented
33	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
34	D₃×C₁₉	—	4	2	no	—
35	C₂×#215	—	19	1	no	maximal, Hall
36	C₂²×C₁₉	—	6	2	no	—
37	C₂²×C₁₉	—	12	2	no	—
38	C₂²×C₁₉	#67	1	1	yes	characteristic
39	C₄×C₁₉	#67	1	1	yes	characteristic
40	C₄×C₁₉	C₂²×D₃	1	1	yes	characteristic
41	Dic₁₉	—	2	2	no	—
42	C₃×C₁₉	C₂×SD₁₆	1	1	yes	characteristic, complemented, Hall
43	C₂×C₃×Q₈	—	19	1	no	—
44	C₂×D₁₂	D₁₉	1	1	yes	characteristic
45	#215	—	19	4	no	—
46	C₂×C₃⋊C₈	—	19	1	no	—
47	C₂×C₁₉	—	12	2	no	—
48	C₂×C₁₉	#215	1	2	yes	complemented
49	C₂×C₁₉	C₂×#67	1	1	yes	characteristic
50	C₂×SD₁₆	—	57	1	no	Sylow
51	C₂²×D₃	—	2	1	no	—
52	C₃×Q₈	—	19	2	no	—
53	C₃×Q₈	—	38	1	no	—
54	C₂×C₃×C₄	—	38	1	no	—
55	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
56	D₁₂	—	2	1	no	—
57	D₁₂	C₂×D₁₉	1	2	yes	—
58	C₃⋊C₈	—	19	2	no	—
59	C₁₉	C₂×#215	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₈	—	19	1	no	—
61	C₂×D₄	—	3	1	no	—
62	SD₁₆	—	57	4	no	—
63	C₂×C₈	—	57	1	no	—
64	C₂²×C₃	C₂²⋊D₁₉	1	1	yes	characteristic
65	C₂×D₃	—	2	2	no	—
66	C₂×D₃	—	4	2	no	—
67	C₃×C₄	—	38	2	no	—
68	C₃×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
69	C₃×C₄	C₂²×D₁₉	1	1	yes	characteristic
70	C₂³	—	6	1	no	—
71	Q₈	—	19	2	no	—
72	Q₈	—	38	1	no	—
73	D₄	—	3	2	no	—
74	D₄	—	6	1	no	—
75	C₂×C₄	—	38	1	no	—
76	C₂×C₄	D₃×D₁₉	1	1	yes	characteristic
77	C₈	—	57	2	no	—
78	C₂×C₃	#64526	1	2	yes	complemented
79	C₂×C₃	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
80	D₃	—	4	2	no	—
81	C₂²	—	6	2	no	—
82	C₂²	—	12	2	no	—
83	C₂²	#90695	1	1	yes	characteristic
84	C₄	—	38	2	no	—
85	C₄	#90695	1	1	yes	characteristic
86	C₄	C₂×D₃×D₁₉	1	1	yes	characteristic
87	C₃	C₂×#64526	1	1	yes	characteristic, complemented, Sylow
88	C₂	—	12	2	no	—
89	C₂	#11744822	1	2	yes	direct product factor
90	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	C₂²×C₃×C₁₉	D₄
prime radical	C₂×C₁₉×D₁₂	C₂
hypercenter	C₂×C₄	D₃×D₁₉
hypocenter	C₃×C₁₉	C₂×SD₁₆
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
2. C₂×C₃×Dic₃₈	C₂	semidirect
3. C₂×C₃⋊(C₁₉⋊C₈)	C₂	semidirect
4. #11744822	C₂	direct (N × H)
12. C₃×Dic₃₈	C₂²	semidirect
13. C₃⋊(C₁₉⋊C₈)	C₂²	semidirect
15. C₂×Dic₃₈	D₃	semidirect
30. Dic₃₈	C₂×D₃	semidirect
32. C₂×C₃×C₁₉	SD₁₆	semidirect
42. C₃×C₁₉	C₂×SD₁₆	semidirect
48. C₂×C₁₉	#215	semidirect
59. C₁₉	C₂×#215	semidirect
78. C₂×C₃	#64526	semidirect
87. C₃	C₂×#64526	semidirect
89. C₂	#11744822	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×D₁₂	2
C₂×C₃×Dic₃₈	2
C₂×C₃⋊(C₁₉⋊C₈)	2
#11744822	2
C₂×#64526	3
C₂×#215	19

Subgroups — C2×#11744822 #14269276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11744822 #14269276