Subgroups — #14269017

Order 1824.

92 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	C₃×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#11744885	C₂	1	1	yes	maximal, characteristic, complemented
4	#10597280	—	3	1	no	maximal, Hall
5	C₂²×D₅₇	C₄	1	2	yes	—
6	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	D₂₂₈	—	2	1	no	—
8	D₂₂₈	—	2	1	no	—
9	C₃×C₈×C₁₉	—	2	1	no	—
10	C₃⋊(C₁₉⋊C₈)	—	2	1	no	—
11	C₂×D₇₆	—	3	1	no	—
12	M₁₆×C₁₉	D₃	1	1	yes	characteristic, complemented
13	#64520	—	3	1	no	—
14	C₂²×C₃×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂×D₅₇	—	2	2	no	—
16	C₂×D₅₇	—	4	2	no	—
17	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
18	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
19	C₂²×D₁₉	—	3	2	no	—
20	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
21	D₇₆	—	6	1	no	—
22	D₇₆	—	6	1	no	—
23	C₈×C₁₉	—	2	1	no	—
24	C₁₉⋊C₈	—	6	1	no	—
25	C₂×C₃×C₁₉	—	2	1	no	—
26	C₂×C₃×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
27	D₅₇	—	4	2	no	—
28	#823	—	19	1	no	maximal, Hall
29	C₂²×C₁₉	C₄×D₃	1	1	yes	characteristic
30	C₂×D₁₉	—	6	2	no	—
31	C₂×D₁₉	—	12	2	no	—
32	C₄×C₁₉	D₁₂	1	1	yes	characteristic
33	C₄×C₁₉	#67	1	1	yes	characteristic
34	C₃×C₁₉	#100	1	1	yes	characteristic, complemented, Hall
35	C₂×D₁₂	—	19	1	no	—
36	C₃×M₁₆	D₁₉	1	1	yes	characteristic, complemented
37	#208	—	19	1	no	—
38	C₂×C₁₉	—	2	1	no	—
39	C₂×C₁₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
40	D₁₉	—	12	2	no	—
41	#100	—	57	1	no	Sylow
42	C₂²×D₃	—	19	2	no	—
43	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
44	D₁₂	—	38	1	no	—
45	D₁₂	—	38	1	no	—
46	C₃×C₈	—	2	1	no	—
47	C₃⋊C₈	—	38	1	no	—
48	C₁₉	#823	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₄	—	57	1	no	—
50	M₁₆	—	57	1	no	—
51	M₁₆	D₅₇	1	1	yes	characteristic, complemented
52	C₂²×C₃	C₄×D₁₉	1	1	yes	characteristic
53	C₂×D₃	—	38	2	no	—
54	C₂×D₃	—	76	2	no	—
55	C₃×C₄	D₇₆	1	1	yes	characteristic
56	C₃×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
57	C₂³	—	57	2	no	—
58	D₄	—	114	1	no	—
59	D₄	—	114	1	no	—
60	C₂×C₄	C₂×D₅₇	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	114	1	no	—
63	C₂×C₃	—	2	1	no	—
64	C₂×C₃	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
65	D₃	—	76	2	no	—
66	C₂²	—	114	2	no	—
67	C₂²	—	228	2	no	—
68	C₂²	C₄×D₅₇	1	1	yes	characteristic
69	C₄	D₂₂₈	1	1	yes	characteristic
70	C₄	#90718	1	1	yes	characteristic
71	C₃	#10597280	1	1	yes	characteristic, complemented, Sylow
72	C₂	—	2	1	no	—
73	C₂	—	228	2	no	—
74	C₂	#11744889	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11744889
commutator	C₂²×C₃×C₁₉	C₂×C₄
Frattini	C₂×C₄	C₂×D₅₇
Fitting	C₃×M₁₆×C₁₉	C₂
socle	C₂×C₃×C₁₉	C₂²⋊C₄
prime radical	C₂×D₂₂₈	C₂
cosocle	C₂×C₃×C₄×C₁₉	C₂²
hypercenter	M₁₆	D₅₇
hypocenter	C₃×C₁₉	#100
LCS	G ▷ C₂²×C₃×C₁₉ ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×M₁₆×C₁₉	C₂	semidirect
3. #11744885	C₂	semidirect
12. M₁₆×C₁₉	D₃	semidirect
34. C₃×C₁₉	#100	semidirect
36. C₃×M₁₆	D₁₉	semidirect
48. C₁₉	#823	semidirect
51. M₁₆	D₅₇	semidirect
71. C₃	#10597280	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
C₃×M₁₆×C₁₉	2
#11744885	2
#10597280	3
#823	19