Subgroups — #14561671

Order 2432.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926921	C₂	1	1	yes	maximal, characteristic
2	#11926365	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#364	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₅₂	—	2	1	no	—
5	C₂×D₁₅₂	—	2	1	no	—
6	#10597320	C₄	1	2	yes	—
7	C₁₉×M₃₂	—	2	1	no	—
8	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	#10597269	—	2	1	no	—
10	C₂×D₇₆	—	2	2	no	—
11	C₂×D₇₆	—	4	2	no	—
12	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
13	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
14	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
15	D₁₅₂	—	4	1	no	—
16	D₁₅₂	—	4	1	no	—
17	D₁₅₂	—	4	1	no	—
18	D₁₅₂	—	4	1	no	—
19	C₁₆×C₁₉	—	4	1	no	—
20	C₁₉⋊C₁₆	—	4	1	no	—
21	C₂²×D₁₉	—	4	2	no	—
22	C₂×C₄×C₁₉	—	2	1	no	—
23	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
24	D₇₆	—	4	2	no	—
25	D₇₆	—	4	2	no	—
26	D₇₆	—	8	4	no	—
27	C₈×C₁₉	D₈	1	1	yes	characteristic
28	C₈×C₁₉	D₈	1	1	yes	characteristic
29	C₈×C₁₉	SD₁₆	1	1	yes	characteristic
30	C₈×C₁₉	SD₁₆	1	1	yes	characteristic
31	#1357	—	19	1	no	maximal, Sylow
32	C₂²×C₁₉	#100	1	1	yes	characteristic
33	C₂×D₁₉	—	8	4	no	—
34	C₂×D₁₉	—	8	2	no	—
35	C₄×C₁₉	—	2	2	no	—
36	C₄×C₁₉	#102	1	1	yes	characteristic
37	C₄×C₁₉	#102	1	1	yes	characteristic
38	#493	—	19	1	no	—
39	#364	—	19	1	no	—
40	#364	D₁₉	1	1	yes	characteristic, complemented
41	C₂×C₁₉	—	2	1	no	—
42	C₂×C₁₉	#331	1	1	yes	characteristic
43	D₁₉	—	16	2	no	—
44	C₂×D₈	—	38	1	no	—
45	C₂×D₈	—	38	1	no	—
46	#127	—	19	2	no	—
47	M₃₂	—	2	1	no	—
48	M₃₂	—	38	1	no	—
49	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
50	C₁₉	#1357	1	1	yes	characteristic, complemented, Sylow
51	C₂×D₄	—	38	2	no	—
52	C₂×D₄	—	76	2	no	—
53	D₈	—	76	1	no	—
54	D₈	—	76	1	no	—
55	D₈	—	76	1	no	—
56	D₈	—	76	1	no	—
57	C₂×C₈	D₇₆	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
59	C₄²	C₄×D₁₉	1	1	yes	characteristic
60	C₁₆	—	4	1	no	—
61	C₁₆	—	76	1	no	—
62	C₂³	—	76	2	no	—
63	D₄	—	76	2	no	—
64	D₄	—	76	2	no	—
65	D₄	—	152	4	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
68	C₈	#64516	1	1	yes	characteristic
69	C₈	D₁₅₂	1	1	yes	characteristic
70	C₈	#64525	1	1	yes	characteristic
71	C₈	#64527	1	1	yes	characteristic
72	C₂²	—	152	4	no	—
73	C₂²	—	152	2	no	—
74	C₂²	#10597280	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	#10597266	1	1	yes	characteristic
77	C₄	#10597278	1	1	yes	characteristic
78	C₂	—	2	1	no	—
79	C₂	—	304	2	no	—
80	C₂	#11926287	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11926287
commutator	C₄²×C₁₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₁₉
Fitting	C₁₉×#364	C₂
socle	C₂×C₁₉	#331
prime radical	#11926921	C₂
cosocle	C₄×C₈×C₁₉	C₂²
hypercenter	#364	D₁₉
hypocenter	C₁₉	#1357
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
2. #11926365	C₂	semidirect
3. C₁₉×#364	C₂	semidirect
40. #364	D₁₉	semidirect
50. C₁₉	#1357	semidirect

Maximal subgroups

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

subgroup	index
#11926921	2
#11926365	2
C₁₉×#364	2
#1357	19