Subgroups — #14269713

Order 1824.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₂₈	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₁₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#11744889	C₂	1	4	yes	maximal, complemented
5	#10597321	—	3	1	no	maximal, Hall
6	C₂²×D₅₇	C₂²	1	2	yes	—
7	C₂×C₃×C₄×C₁₉	C₂²	1	2	yes	—
8	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×Dic₅₇	C₂²	1	2	yes	—
10	D₂₂₈	—	2	2	no	—
11	Dic₁₁₄	—	2	2	no	—
12	C₂×D₇₆	—	3	1	no	—
13	C₂×Dic₃₈	—	3	1	no	—
14	C₄²×C₁₉	D₃	1	1	yes	characteristic, complemented
15	(C₂×D₁₉)⋊C₄	—	3	4	no	—
16	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
17	C₂×D₅₇	—	2	2	no	—
18	C₂×D₅₇	—	2	4	no	—
19	C₃×C₄×C₁₉	—	2	2	no	—
20	C₃×C₄×C₁₉	D₄	1	2	yes	—
21	Dic₅₇	—	2	2	no	—
22	C₂²×D₁₉	—	3	2	no	—
23	C₂×C₄×C₁₉	C₂×D₃	1	2	yes	—
24	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
25	C₂×Dic₁₉	—	3	2	no	—
26	D₇₆	—	6	2	no	—
27	Dic₃₈	—	6	2	no	—
28	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
29	C₂×C₃×C₁₉	#41	1	2	yes	—
30	D₅₇	—	4	2	no	—
31	#875	—	19	1	no	maximal, Hall
32	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
33	C₂×D₁₉	—	6	2	no	—
34	C₂×D₁₉	—	6	4	no	—
35	C₄×C₁₉	—	2	2	no	—
36	C₄×C₁₉	D₁₂	1	2	yes	—
37	Dic₁₉	—	6	2	no	—
38	C₃×C₁₉	#124	1	1	yes	characteristic, complemented, Hall
39	C₂×D₁₂	—	19	1	no	—
40	C₂×Dic₆	—	19	1	no	—
41	C₃×C₄²	D₁₉	1	1	yes	characteristic, complemented
42	(C₂×D₃)⋊C₄	—	19	4	no	—
43	C₂×C₁₉	C₂×D₁₂	1	1	yes	characteristic
44	C₂×C₁₉	#235	1	2	yes	—
45	D₁₉	—	12	2	no	—
46	#124	—	57	1	no	Sylow
47	C₂²×D₃	—	19	2	no	—
48	C₂×C₃×C₄	C₂×D₁₉	1	2	yes	—
49	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
50	C₂×Dic₃	—	19	2	no	—
51	D₁₂	—	38	2	no	—
52	Dic₆	—	38	2	no	—
53	C₁₉	#875	1	1	yes	characteristic, complemented, Sylow
54	C₂×Q₈	—	57	1	no	—
55	C₂×D₄	—	57	1	no	—
56	C₂²⋊C₄	—	57	4	no	—
57	C₄²	D₅₇	1	1	yes	characteristic, complemented
58	C₂²×C₃	C₂²×D₁₉	1	1	yes	characteristic
59	C₂×D₃	—	38	2	no	—
60	C₂×D₃	—	38	4	no	—
61	C₃×C₄	—	2	2	no	—
62	C₃×C₄	D₇₆	1	2	yes	—
63	Dic₃	—	38	2	no	—
64	C₂³	—	57	2	no	—
65	Q₈	—	114	2	no	—
66	D₄	—	114	2	no	—
67	C₂×C₄	—	57	2	no	—
68	C₂×C₄	C₂×D₅₇	1	2	yes	—
69	C₂×C₄	C₂×D₅₇	1	1	yes	characteristic
70	C₂×C₃	C₂×D₇₆	1	1	yes	characteristic
71	C₂×C₃	#64541	1	2	yes	—
72	D₃	—	76	2	no	—
73	C₂²	—	114	2	no	—
74	C₂²	—	114	4	no	—
75	C₂²	C₂²×D₅₇	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	114	2	no	—
78	C₄	D₂₂₈	1	2	yes	—
79	C₃	#10597321	1	1	yes	characteristic, complemented, Sylow
80	C₂	—	228	2	no	—
81	C₂	C₂×D₂₂₈	1	1	yes	characteristic
82	C₂	#11744985	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₅₇
commutator, socle, cosocle	C₂²×C₃×C₁₉	C₂³
Fitting	C₃×C₄²×C₁₉	C₂
prime radical	C₂×D₂₂₈	C₂
hypercenter	C₄²	D₅₇
hypocenter	C₃×C₁₉	#124
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
2. C₂×Dic₁₁₄	C₂	semidirect
3. C₃×C₄²×C₁₉	C₂	semidirect
4. #11744889	C₂	semidirect
14. C₄²×C₁₉	D₃	semidirect
38. C₃×C₁₉	#124	semidirect
41. C₃×C₄²	D₁₉	semidirect
53. C₁₉	#875	semidirect
57. C₄²	D₅₇	semidirect
79. C₃	#10597321	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₂₂₈	2
C₂×Dic₁₁₄	2
C₃×C₄²×C₁₉	2
#11744889	2
#10597321	3
#875	19