Subgroups — #14269030

Order 1824.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	#11744885	C₂	1	2	yes	maximal
3	#10597293	—	3	1	no	maximal, Hall
4	C₃×Q₈×C₁₉	—	2	2	no	—
5	C₂×C₃×C₄×C₁₉	C₄	1	2	yes	—
6	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₃⋊(C₁₉⋊C₈)	—	2	2	no	—
8	C₂×Q₈×C₁₉	D₃	1	1	yes	characteristic
9	#64520	—	3	2	no	—
10	C₂²×C₃×C₁₉	C₂×C₄	1	1	yes	characteristic
11	C₃×C₄×C₁₉	—	2	2	no	—
12	C₃×C₄×C₁₉	D₄	1	2	yes	—
13	Q₈×C₁₉	—	2	2	no	—
14	C₂×C₄×C₁₉	Dic₃	1	2	yes	—
15	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
16	C₁₉⋊C₈	—	6	2	no	—
17	C₂×C₃×C₁₉	—	2	1	no	—
18	C₂×C₃×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
19	#836	—	19	1	no	maximal, Hall
20	C₂²×C₁₉	C₂×Dic₃	1	1	yes	characteristic
21	C₄×C₁₉	—	2	2	no	—
22	C₄×C₁₉	#67	1	2	yes	—
23	C₃×C₁₉	#101	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×Q₈	D₁₉	1	1	yes	characteristic
25	#208	—	19	2	no	—
26	C₂×C₁₉	—	2	1	no	—
27	C₂×C₁₉	#217	1	1	yes	characteristic
28	#101	—	57	1	no	Sylow
29	C₃×Q₈	—	2	2	no	—
30	C₂×C₃×C₄	Dic₁₉	1	2	yes	—
31	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
32	C₃⋊C₈	—	38	2	no	—
33	C₁₉	#836	1	1	yes	characteristic, complemented, Sylow
34	C₂×Q₈	D₅₇	1	1	yes	characteristic
35	M₁₆	—	57	2	no	—
36	C₂²×C₃	C₂×Dic₁₉	1	1	yes	characteristic
37	C₃×C₄	—	2	2	no	—
38	C₃×C₄	C₂²⋊D₁₉	1	2	yes	—
39	Q₈	—	2	2	no	—
40	C₂×C₄	Dic₅₇	1	2	yes	—
41	C₂×C₄	C₂×D₅₇	1	1	yes	characteristic
42	C₈	—	114	2	no	—
43	C₂×C₃	—	2	1	no	—
44	C₂×C₃	C₂²⋊Dic₁₉	1	1	yes	characteristic
45	C₂²	C₂×Dic₅₇	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	#90718	1	2	yes	—
48	C₃	#10597293	1	1	yes	characteristic, complemented, Sylow
49	C₂	—	2	1	no	—
50	C₂	#11744894	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11744894
commutator, prime radical	C₂²×C₃×C₁₉	C₂×C₄
Frattini	C₂×C₄	C₂×D₅₇
Fitting	C₂×C₃×Q₈×C₁₉	C₂
socle	C₂×C₃×C₁₉	C₂²⋊C₄
cosocle	C₂×C₃×C₄×C₁₉	C₂²
hypercenter	C₂×Q₈	D₅₇
hypocenter	C₃×C₁₉	#101
LCS	G ▷ C₂²×C₃×C₁₉ ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
23. C₃×C₁₉	#101	semidirect
33. C₁₉	#836	semidirect
48. C₃	#10597293	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×Q₈×C₁₉	2
#11744885	2
#10597293	3
#836	19