Subgroups — #14269004

Order 1824.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₁₄	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	#10597267	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₁₉	—	2	1	no	—
6	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×Dic₅₇	—	2	1	no	—
8	Dic₁₁₄	—	2	1	no	—
9	Dic₁₁₄	C₄	1	2	yes	complemented
10	C₃⋊(C₁₉⋊C₈)	—	2	1	no	—
11	C₂×Dic₃₈	—	3	1	no	—
12	C₄⋊C₄×C₁₉	D₃	1	1	yes	characteristic
13	C₂×C₁₉⋊C₈	—	3	1	no	—
14	C₂²×C₃×C₁₉	D₄	1	1	yes	characteristic
15	C₃×C₄×C₁₉	—	4	1	no	—
16	C₃×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
18	Dic₅₇	—	2	2	no	—
19	C₂×C₄×C₁₉	—	2	1	no	—
20	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
21	C₂×Dic₁₉	—	6	1	no	—
22	Dic₃₈	—	3	2	no	—
23	Dic₃₈	—	6	1	no	—
24	C₁₉⋊C₈	—	6	1	no	—
25	C₂×C₃×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₃×C₁₉	SD₁₆	1	1	yes	characteristic
27	C₂×C₃×C₁₉	Q₁₆	1	1	yes	characteristic
28	#810	—	19	1	no	maximal, Hall
29	C₂²×C₁₉	#67	1	1	yes	characteristic
30	C₄×C₁₉	—	4	1	no	—
31	C₄×C₁₉	C₄×D₃	1	1	yes	characteristic
32	C₄×C₁₉	D₁₂	1	1	yes	characteristic
33	Dic₁₉	—	6	2	no	—
34	C₃×C₁₉	#103	1	1	yes	characteristic, complemented, Hall
35	C₂×Dic₆	—	19	1	no	—
36	C₃×C₄⋊C₄	D₁₉	1	1	yes	characteristic
37	C₂×C₃⋊C₈	—	19	1	no	—
38	C₂×C₁₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
39	C₂×C₁₉	#214	1	1	yes	characteristic
40	C₂×C₁₉	#216	1	1	yes	characteristic
41	#103	—	57	1	no	Sylow
42	C₂×C₃×C₄	—	2	1	no	—
43	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
44	C₂×Dic₃	—	38	1	no	—
45	Dic₆	—	19	2	no	—
46	Dic₆	—	38	1	no	—
47	C₃⋊C₈	—	38	1	no	—
48	C₁₉	#810	1	1	yes	characteristic, complemented, Sylow
49	C₂×Q₈	—	57	1	no	—
50	C₂×C₈	—	57	1	no	—
51	C₄⋊C₄	D₅₇	1	1	yes	characteristic
52	C₂²×C₃	C₂²⋊D₁₉	1	1	yes	characteristic
53	C₃×C₄	—	4	1	no	—
54	C₃×C₄	C₄×D₁₉	1	1	yes	characteristic
55	C₃×C₄	D₇₆	1	1	yes	characteristic
56	Dic₃	—	38	2	no	—
57	Q₈	—	57	2	no	—
58	Q₈	—	114	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	114	1	no	—
61	C₂×C₄	C₂×D₅₇	1	1	yes	characteristic
62	C₈	—	114	1	no	—
63	C₂×C₃	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
64	C₂×C₃	#64526	1	1	yes	characteristic
65	C₂×C₃	#64528	1	1	yes	characteristic
66	C₂²	#90718	1	1	yes	characteristic
67	C₄	—	4	1	no	—
68	C₄	—	114	2	no	—
69	C₄	C₄×D₅₇	1	1	yes	characteristic
70	C₄	D₂₂₈	1	1	yes	characteristic
71	C₃	#10597267	1	1	yes	characteristic, complemented, Sylow
72	C₂	#11744889	1	1	yes	characteristic
73	C₂	#11744891	1	1	yes	characteristic
74	C₂	#11744893	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#90718
commutator	C₃×C₄×C₁₉	C₂×C₄
Frattini	C₂×C₄	C₂×D₅₇
Fitting	C₃×C₄⋊C₄×C₁₉	C₂
socle, prime radical	C₂²×C₃×C₁₉	D₄
cosocle	C₂×C₃×C₄×C₁₉	C₂²
hypercenter	C₄⋊C₄	D₅₇
hypocenter	C₃×C₁₉	#103
LCS	G ▷ C₃×C₄×C₁₉ ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
9. Dic₁₁₄	C₄	semidirect
34. C₃×C₁₉	#103	semidirect
48. C₁₉	#810	semidirect
71. C₃	#10597267	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₁₄	2
C₃×C₄⋊C₄×C₁₉	2
C₂×C₃⋊(C₁₉⋊C₈)	2
#10597267	3
#810	19