Subgroups — #14561607

Order 2432.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926662	C₂	1	1	yes	maximal, characteristic
2	C₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#364	C₂	1	1	yes	maximal, characteristic, complemented
4	#10597350	C₄	1	1	yes	characteristic
5	#10597347	—	2	1	no	—
6	C₁₉×M₃₂	—	2	1	no	—
7	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	#10597276	C₄	1	1	yes	characteristic
9	#10597262	—	2	1	no	—
10	C₄×C₁₉⋊C₈	—	2	1	no	—
11	#64541	—	2	1	no	—
12	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
14	C₄²×C₁₉	D₄	1	1	yes	characteristic
15	#64520	—	2	1	no	—
16	C₂×C₁₉⋊C₈	—	2	2	no	—
17	Dic₇₆	C₈	1	1	yes	characteristic, complemented
18	D₁₅₂	C₈	1	1	yes	characteristic, complemented
19	#64516	—	2	1	no	—
20	#64515	—	4	1	no	—
21	C₈×D₁₉	—	4	1	no	—
22	C₁₆×C₁₉	—	4	1	no	—
23	C₂×C₄×C₁₉	—	2	1	no	—
24	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²⋊D₁₉	—	4	1	no	—
26	D₇₆	—	2	1	no	—
27	C₄×D₁₉	—	4	1	no	—
28	Dic₃₈	—	2	1	no	—
29	C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
30	C₈×C₁₉	M₁₆	1	1	yes	characteristic
31	C₈×C₁₉	D₈	1	1	yes	characteristic
32	C₈×C₁₉	SD₁₆	1	1	yes	characteristic
33	C₁₉⋊C₈	—	2	4	no	—
34	C₁₉⋊C₈	—	4	1	no	—
35	#1335	—	19	1	no	maximal, Sylow
36	C₂²×C₁₉	#104	1	1	yes	characteristic
37	C₂×D₁₉	—	4	1	no	—
38	C₄×C₁₉	—	2	2	no	—
39	C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
40	C₄×C₁₉	#102	1	1	yes	characteristic
41	Dic₁₉	—	4	1	no	—
42	#443	—	19	1	no	—
43	#364	D₁₉	1	1	yes	characteristic, complemented
44	C₈²	—	19	1	no	—
45	C₂×C₁₉	—	2	1	no	—
46	C₂×C₁₉	D₄⋊C₈	1	1	yes	characteristic
47	D₁₉	—	8	1	no	—
48	#135	—	19	1	no	—
49	#131	—	38	1	no	—
50	M₃₂	—	2	1	no	—
51	#108	—	19	1	no	—
52	#104	—	38	1	no	—
53	C₄×C₈	—	38	1	no	—
54	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
55	C₁₉	#1335	1	1	yes	characteristic, complemented, Sylow
56	#41	—	38	1	no	—
57	Q₁₆	—	19	1	no	—
58	SD₁₆	—	38	1	no	—
59	D₈	—	19	1	no	—
60	M₁₆	—	38	1	no	—
61	M₁₆	—	76	1	no	—
62	C₂×C₈	—	38	2	no	—
63	C₂×C₈	—	76	1	no	—
64	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
65	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
66	C₄²	D₇₆	1	1	yes	characteristic
67	C₁₆	—	4	1	no	—
68	Q₈	—	38	1	no	—
69	D₄	—	38	1	no	—
70	D₄	—	76	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	76	1	no	—
73	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
74	C₈	—	38	4	no	—
75	C₈	—	76	1	no	—
76	C₈	C₈×D₁₉	1	1	yes	characteristic
77	C₈	#64515	1	1	yes	characteristic
78	C₈	#64525	1	1	yes	characteristic
79	C₈	#64527	1	1	yes	characteristic
80	C₂²	—	76	1	no	—
81	C₂²	#10597282	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	76	1	no	—
84	C₄	#10597266	1	1	yes	characteristic
85	C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	152	1	no	—
88	C₂	#11926271	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#64525
commutator	C₈×C₁₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₉
Fitting	C₁₉×#364	C₂
socle	C₂×C₁₉	D₄⋊C₈
prime radical	#10597350	C₄
cosocle	C₄×C₈×C₁₉	C₂²
hypercenter	#364	D₁₉
hypocenter	C₁₉	#1335
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
2. C₈×C₁₉⋊C₈	C₂	semidirect
3. C₁₉×#364	C₂	semidirect
17. Dic₇₆	C₈	semidirect
18. D₁₅₂	C₈	semidirect
43. #364	D₁₉	semidirect
55. C₁₉	#1335	semidirect

Maximal subgroups

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

subgroup	index
#11926662	2
C₈×C₁₉⋊C₈	2
C₁₉×#364	2
#1335	19