Subgroups — #14269242

Order 1824.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×Dic₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Dic₃₈	C₂	1	1	yes	maximal, characteristic
3	C₄×Dic₅₇	C₂	1	1	yes	maximal, characteristic
4	#11744835	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	C₂×Dic₃×C₁₉	C₂²	1	2	yes	—
9	C₁₉×Dic₆	—	2	2	no	—
10	C₂×C₃×Dic₁₉	C₂²	1	2	yes	—
11	C₃×Dic₃₈	—	2	2	no	—
12	C₂×Q₈×C₁₉	—	3	1	no	—
13	C₂×Dic₃₈	D₃	1	1	yes	characteristic
14	Dic₁₉⋊C₄	—	3	4	no	—
15	C₄×Dic₁₉	—	3	1	no	—
16	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
17	C₃×C₄×C₁₉	D₄	1	2	yes	—
18	Dic₅₇	Q₈	1	4	yes	complemented
19	C₃×Dic₁₉	—	2	2	no	—
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	—	2	2	no	—
27	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
28	C₂×C₃×C₁₉	C₂×Q₈	1	2	yes	—
29	#944	—	19	1	no	maximal, Hall
30	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
31	C₄×C₁₉	—	6	2	no	—
32	C₄×C₁₉	#67	1	2	yes	—
33	Dic₁₉	—	2	2	no	—
34	Dic₁₉	—	3	4	no	—
35	C₃×C₁₉	C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×Q₈	—	19	1	no	—
37	C₂×Dic₆	D₁₉	1	1	yes	characteristic
38	Dic₃⋊C₄	—	19	4	no	—
39	C₄×Dic₃	—	19	1	no	—
40	C₂×C₁₉	D₃×Q₈	1	2	yes	—
41	C₂×C₁₉	C₂×#67	1	1	yes	characteristic
42	C₄⋊Q₈	—	57	1	no	Sylow
43	C₃×Q₈	—	38	2	no	—
44	C₂×C₃×C₄	—	19	2	no	—
45	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
46	C₂×Dic₃	—	19	2	no	—
47	C₂×Dic₃	C₂×D₁₉	1	2	yes	—
48	Dic₆	—	2	2	no	—
49	C₁₉	#944	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₈	—	3	1	no	—
51	C₂×Q₈	—	19	1	no	—
52	C₄⋊C₄	—	57	4	no	—
53	C₄²	—	57	1	no	—
54	C₂²×C₃	C₂²×D₁₉	1	1	yes	characteristic
55	C₃×C₄	—	38	2	no	—
56	C₃×C₄	C₂²⋊D₁₉	1	2	yes	—
57	Dic₃	—	2	2	no	—
58	Dic₃	—	19	4	no	—
59	Q₈	—	6	2	no	—
60	Q₈	—	38	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	—	38	2	no	—
70	C₄	—	57	4	no	—
71	C₄	#90695	1	2	yes	—
72	C₃	#10597390	1	1	yes	characteristic, complemented, Sylow
73	C₂	D₅₇⋊Q₈	1	2	yes	—
74	C₂	C₂×#90695	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
18. Dic₅₇	Q₈	semidirect
35. C₃×C₁₉	C₄⋊Q₈	semidirect
49. C₁₉	#944	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×C₁₉×Dic₆	2
C₂×C₃×Dic₃₈	2
C₄×Dic₅₇	2
#11744835	2
#10597390	3
#944	19