Subgroups — #14269707

Order 1824.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₁₄	C₂	1	2	yes	maximal
2	C₃×C₄²×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₅₇	C₂	1	4	yes	maximal
4	#10597315	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₁₉	C₂²	1	2	yes	—
7	C₂×Dic₅₇	C₂²	1	4	yes	—
8	Dic₁₁₄	—	2	4	no	—
9	C₂×Dic₃₈	—	3	2	no	—
10	C₄²×C₁₉	D₃	1	1	yes	characteristic
11	C₄⋊Dic₁₉	—	3	4	no	—
12	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
13	C₃×C₄×C₁₉	D₄	1	2	yes	—
14	C₃×C₄×C₁₉	Q₈	1	4	yes	complemented
15	Dic₅₇	—	2	4	no	—
16	C₂×C₄×C₁₉	C₂×D₃	1	2	yes	—
17	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
18	C₂×Dic₁₉	—	3	4	no	—
19	Dic₃₈	—	6	4	no	—
20	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
21	C₂×C₃×C₁₉	C₂×Q₈	1	2	yes	—
22	#869	—	19	1	no	maximal, Hall
23	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
24	C₄×C₁₉	Dic₆	1	4	yes	complemented
25	C₄×C₁₉	D₁₂	1	2	yes	—
26	Dic₁₉	—	6	4	no	—
27	C₃×C₁₉	C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
28	C₂×Dic₆	—	19	2	no	—
29	C₃×C₄²	D₁₉	1	1	yes	characteristic
30	C₄⋊Dic₃	—	19	4	no	—
31	C₂×C₁₉	C₂×Dic₆	1	2	yes	—
32	C₂×C₁₉	C₂×D₁₂	1	1	yes	characteristic
33	C₄⋊Q₈	—	57	1	no	Sylow
34	C₂×C₃×C₄	C₂×D₁₉	1	2	yes	—
35	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
36	C₂×Dic₃	—	19	4	no	—
37	Dic₆	—	38	4	no	—
38	C₁₉	#869	1	1	yes	characteristic, complemented, Sylow
39	C₂×Q₈	—	57	2	no	—
40	C₄⋊C₄	—	57	4	no	—
41	C₄²	D₅₇	1	1	yes	characteristic
42	C₂²×C₃	C₂²×D₁₉	1	1	yes	characteristic
43	C₃×C₄	Dic₃₈	1	4	yes	complemented
44	C₃×C₄	D₇₆	1	2	yes	—
45	Dic₃	—	38	4	no	—
46	Q₈	—	114	4	no	—
47	C₂×C₄	—	57	4	no	—
48	C₂×C₄	C₂×D₅₇	1	2	yes	—
49	C₂×C₄	C₂×D₅₇	1	1	yes	characteristic
50	C₂×C₃	C₂×Dic₃₈	1	2	yes	—
51	C₂×C₃	C₂×D₇₆	1	1	yes	characteristic
52	C₂²	C₂²×D₅₇	1	1	yes	characteristic
53	C₄	—	114	4	no	—
54	C₄	Dic₁₁₄	1	4	yes	complemented
55	C₄	D₂₂₈	1	2	yes	—
56	C₃	#10597315	1	1	yes	characteristic, complemented, Sylow
57	C₂	C₂×Dic₁₁₄	1	2	yes	—
58	C₂	C₂×D₂₂₈	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₅₇
commutator, socle, prime radical, cosocle	C₂²×C₃×C₁₉	C₂³
Fitting	C₃×C₄²×C₁₉	C₂
hypercenter	C₄²	D₅₇
hypocenter	C₃×C₁₉	C₄⋊Q₈
LCS	G ▷ C₂²×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂² ◁ C₄²

Complements

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

N	H ≅ G/N	type
14. C₃×C₄×C₁₉	Q₈	semidirect
24. C₄×C₁₉	Dic₆	semidirect
27. C₃×C₁₉	C₄⋊Q₈	semidirect
38. C₁₉	#869	semidirect
43. C₃×C₄	Dic₃₈	semidirect
54. C₄	Dic₁₁₄	semidirect
56. C₃	#10597315	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×C₄²×C₁₉	2
C₄⋊Dic₅₇	2
#10597315	3
#869	19