Subgroups — #14269248

Order 1824.

136 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	C₂×C₁₉×Dic₆	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×Dic₁₉	C₂	1	1	yes	maximal, characteristic
4	Dic₁₉⋊Dic₃	C₂	1	4	yes	maximal
5	#10597390	—	3	1	no	maximal, Hall
6	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×Dic₅₇	C₂²	1	2	yes	—
8	Dic₁₁₄	—	2	2	no	—
9	C₂×Dic₃×C₁₉	C₂²	1	2	yes	—
10	C₁₉×Dic₆	—	2	2	no	—
11	C₂×C₃×Dic₁₉	C₂²	1	2	yes	—
12	C₂×Q₈×C₁₉	—	3	1	no	—
13	C₂×Dic₃₈	—	3	1	no	—
14	Dic₁₉⋊C₄	—	3	4	no	—
15	C₄×Dic₁₉	D₃	1	1	yes	characteristic
16	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
17	C₃×C₄×C₁₉	D₄	1	2	yes	—
18	Dic₅₇	—	2	2	no	—
19	C₃×Dic₁₉	Q₈	1	4	yes	complemented
20	Dic₃×C₁₉	—	2	2	no	—
21	Q₈×C₁₉	—	6	2	no	—
22	C₂×C₄×C₁₉	—	3	2	no	—
23	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
24	C₂×Dic₁₉	—	3	2	no	—
25	C₂×Dic₁₉	C₂×D₃	1	2	yes	—
26	Dic₃₈	—	6	2	no	—
27	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
28	C₂×C₃×C₁₉	C₂×Q₈	1	2	yes	—
29	#869	—	19	1	no	maximal, Hall
30	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
31	C₄×C₁₉	—	6	2	no	—
32	C₄×C₁₉	D₁₂	1	2	yes	—
33	Dic₁₉	—	6	2	no	—
34	Dic₁₉	Dic₆	1	4	yes	complemented
35	C₃×C₁₉	C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
36	C₂×Dic₆	—	19	1	no	—
37	C₂×Dic₆	D₁₉	1	1	yes	characteristic
38	C₃×C₄²	—	19	1	no	—
39	C₄⋊Dic₃	—	19	4	no	—
40	C₂×C₁₉	C₂×Dic₆	1	2	yes	—
41	C₂×C₁₉	C₂×D₁₂	1	1	yes	characteristic
42	C₄⋊Q₈	—	57	1	no	Sylow
43	C₂×C₃×C₄	—	19	2	no	—
44	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
45	C₂×Dic₃	—	19	2	no	—
46	C₂×Dic₃	C₂×D₁₉	1	2	yes	—
47	Dic₆	—	2	2	no	—
48	Dic₆	—	38	2	no	—
49	C₁₉	#869	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₈	—	3	1	no	—
51	C₂×Q₈	—	57	1	no	—
52	C₄⋊C₄	—	57	4	no	—
53	C₄²	—	19	1	no	—
54	C₂²×C₃	C₂²×D₁₉	1	1	yes	characteristic
55	C₃×C₄	—	19	4	no	—
56	C₃×C₄	C₂²⋊D₁₉	1	2	yes	—
57	Dic₃	—	2	2	no	—
58	Dic₃	—	38	2	no	—
59	Q₈	—	6	2	no	—
60	Q₈	—	114	2	no	—
61	C₂×C₄	—	3	2	no	—
62	C₂×C₄	—	19	2	no	—
63	C₂×C₄	—	57	2	no	—
64	C₂×C₄	D₃×D₁₉	1	1	yes	characteristic
65	C₂×C₃	Q₈×D₁₉	1	2	yes	—
66	C₂×C₃	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
67	C₂²	C₂×D₃×D₁₉	1	1	yes	characteristic
68	C₄	—	6	2	no	—
69	C₄	—	19	4	no	—
70	C₄	—	114	2	no	—
71	C₄	#90697	1	2	yes	—
72	C₃	#10597390	1	1	yes	characteristic, complemented, Sylow
73	C₂	Dic₆×D₁₉	1	2	yes	—
74	C₂	C₂×#90697	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×D₃×D₁₉
commutator, socle, prime radical, cosocle	C₂²×C₃×C₁₉	C₂³
Fitting	C₂×C₃×C₄×C₁₉	C₂²
hypercenter	C₂×C₄	D₃×D₁₉
hypocenter	C₃×C₁₉	C₄⋊Q₈
LCS	G ▷ C₂²×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
19. C₃×Dic₁₉	Q₈	semidirect
34. Dic₁₉	Dic₆	semidirect
35. C₃×C₁₉	C₄⋊Q₈	semidirect
49. C₁₉	#869	semidirect
72. C₃	#10597390	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
C₂×C₁₉×Dic₆	2
C₃×C₄×Dic₁₉	2
Dic₁₉⋊Dic₃	2
#10597390	3
#869	19