Subgroups — #14565430

Order 2432.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597276	C₂	1	2	yes	maximal
2	#11926374	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₉×M₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
5	C₂×#64520	—	2	2	no	—
6	C₁₉×M₃₂	C₄	1	4	yes	—
7	C₂×C₁₆×C₁₉	C₂²	1	2	yes	—
8	#10597276	—	2	2	no	—
9	#10597276	C₂²	1	4	yes	—
10	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
11	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
13	C₂×C₈×C₁₉	Q₈	1	2	yes	—
14	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
15	#64520	—	2	4	no	—
16	#64520	—	4	2	no	—
17	C₂×C₁₉⋊C₈	—	4	2	no	—
18	C₁₆×C₁₉	C₂×C₄	1	4	yes	—
19	C₂³×C₁₉	Q₁₆	1	1	yes	characteristic
20	C₂×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
21	C₂×C₄×C₁₉	D₈	1	2	yes	—
22	C₂×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
23	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
24	C₈×C₁₉	C₄⋊C₄	1	2	yes	—
25	C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
26	C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
27	C₁₉⋊C₈	—	4	4	no	—
28	#2161	—	19	1	no	maximal, Sylow
29	C₂²×C₁₉	—	4	1	no	—
30	C₂²×C₁₉	#107	1	2	yes	—
31	C₂²×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
32	C₄×C₁₉	#107	1	2	yes	—
33	C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
35	C₂×M₃₂	D₁₉	1	1	yes	characteristic
36	C₂×#108	—	19	2	no	—
37	#368	—	19	4	no	—
38	C₂×C₁₉	—	2	2	no	—
39	C₂×C₁₉	—	2	1	no	—
40	C₂×C₁₉	C₂×#107	1	1	yes	characteristic
41	C₂×M₁₆	—	38	2	no	—
42	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
43	M₃₂	Dic₁₉	1	4	yes	—
44	C₂×C₁₆	C₂×D₁₉	1	2	yes	—
45	#108	—	19	4	no	—
46	#108	—	38	2	no	—
47	C₁₉	#2161	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₄	D₇₆	1	1	yes	characteristic
49	M₁₆	—	38	4	no	—
50	M₁₆	—	76	2	no	—
51	C₂×C₈	—	76	2	no	—
52	C₂×C₈	Dic₃₈	1	2	yes	—
53	C₂×C₈	D₇₆	1	1	yes	characteristic
54	C₂×C₈	C₂×Dic₁₉	1	2	yes	—
55	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
56	C₁₆	C₂×Dic₁₉	1	4	yes	—
57	C₂³	Dic₇₆	1	1	yes	characteristic
58	C₂×C₄	D₁₅₂	1	2	yes	—
59	C₂×C₄	Dic₇₆	1	1	yes	characteristic
60	C₂×C₄	C₄⋊Dic₁₉	1	2	yes	—
61	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
62	C₈	—	76	4	no	—
63	C₈	C₄⋊Dic₁₉	1	2	yes	—
64	C₈	C₂×Dic₃₈	1	1	yes	characteristic
65	C₈	C₂²×Dic₁₉	1	1	yes	characteristic
66	C₂²	—	4	1	no	—
67	C₂²	#10597275	1	2	yes	—
68	C₂²	C₂×Dic₇₆	1	1	yes	characteristic
69	C₄	#10597275	1	2	yes	—
70	C₄	C₂×D₁₅₂	1	1	yes	characteristic
71	C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
72	C₂	—	2	2	no	—
73	C₂	—	2	1	no	—
74	C₂	C₂×#10597275	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₁₅₂
commutator	C₈×C₁₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₂×C₁₉×M₃₂	C₂
socle	C₂×C₁₉	C₂×#107
prime radical	C₂³×C₁₉	Q₁₆
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	C₂×M₃₂	D₁₉
hypocenter	C₁₉	#2161
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
2. #11926374	C₂	semidirect
47. C₁₉	#2161	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597276	2
#11926374	2
C₂×C₁₉×M₃₂	2
#2161	19