Subgroups — C₂×#10597292 #11926535

Order 1216.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#10597292	C₂	1	4	yes	maximal, direct product factor
5	C₂×Q₈×C₁₉	—	2	2	no	—
6	C₂×Q₈×C₁₉	—	2	1	no	—
7	C₂×Q₈×C₁₉	C₄	1	4	yes	complemented
8	C₂×Q₈×C₁₉	C₂²	1	2	yes	—
9	C₂²×C₄×C₁₉	—	2	1	no	—
10	C₂²×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×Dic₁₉	—	2	1	no	—
12	C₄⋊Dic₁₉	—	2	1	no	—
13	C₄⋊Dic₁₉	C₂²	1	2	yes	—
14	C₂×C₁₉⋊C₈	—	2	2	no	—
15	C₂×C₁₉⋊C₈	C₂²	1	2	yes	—
16	C₂³×C₁₉	D₄	1	1	yes	characteristic
17	Q₈×C₁₉	—	2	4	no	—
18	Q₈×C₁₉	—	2	2	no	—
19	Q₈×C₁₉	C₂×C₄	1	4	yes	complemented
20	C₂×C₄×C₁₉	—	2	4	no	—
21	C₂×C₄×C₁₉	—	2	2	no	—
22	C₂×C₄×C₁₉	C₂×C₄	1	2	yes	—
23	C₂×C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₄×C₁₉	D₄	1	2	yes	—
25	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂×Dic₁₉	—	2	2	no	—
27	C₂×Dic₁₉	—	4	2	no	—
28	C₁₉⋊C₈	—	2	2	no	—
29	C₂²×C₁₉	C₂²⋊C₄	1	2	yes	—
30	C₂²×C₁₉	SD₁₆	1	2	yes	—
31	C₂²×C₁₉	Q₁₆	1	2	yes	—
32	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
33	C₄×C₁₉	—	2	4	no	—
34	C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
35	C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
36	C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
37	Dic₁₉	—	4	2	no	—
38	C₂×#103	—	19	1	no	maximal, Sylow
39	C₂×C₁₉	#103	1	4	yes	complemented
40	C₂×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
41	C₂×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
42	C₂×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
43	C₂²×Q₈	D₁₉	1	1	yes	characteristic
44	C₂²×C₈	—	19	1	no	—
45	C₂×C₄⋊C₄	—	19	1	no	—
46	#103	—	19	4	no	—
47	C₁₉	C₂×#103	1	1	yes	characteristic, complemented, Sylow
48	C₂×Q₈	—	2	2	no	—
49	C₂×Q₈	—	2	1	no	—
50	C₂×Q₈	Dic₁₉	1	4	yes	complemented
51	C₂×Q₈	C₂×D₁₉	1	2	yes	—
52	C₂²×C₄	—	2	1	no	—
53	C₂²×C₄	—	38	1	no	—
54	C₂²×C₄	C₂×D₁₉	1	1	yes	characteristic
55	C₂×C₈	—	19	2	no	—
56	C₂×C₈	—	38	2	no	—
57	C₄⋊C₄	—	19	2	no	—
58	C₄⋊C₄	—	38	1	no	—
59	C₂³	C₂²⋊D₁₉	1	1	yes	characteristic
60	Q₈	—	2	4	no	—
61	Q₈	—	2	2	no	—
62	Q₈	C₂×Dic₁₉	1	4	yes	complemented
63	C₂×C₄	—	2	4	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	38	2	no	—
66	C₂×C₄	—	76	2	no	—
67	C₂×C₄	C₂×Dic₁₉	1	2	yes	—
68	C₂×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
69	C₂×C₄	C₂²⋊D₁₉	1	2	yes	—
70	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
71	C₈	—	38	2	no	—
72	C₂²	#64527	1	2	yes	—
73	C₂²	#64528	1	2	yes	—
74	C₂²	C₂²⋊Dic₁₉	1	2	yes	—
75	C₂²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
76	C₄	—	2	4	no	—
77	C₄	—	76	2	no	—
78	C₄	C₂²⋊Dic₁₉	1	2	yes	—
79	C₄	C₂²×Dic₁₉	1	1	yes	characteristic
80	C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
81	C₂	#10597292	1	4	yes	direct product factor
82	C₂	C₂×#64527	1	1	yes	characteristic
83	C₂	C₂×#64528	1	1	yes	characteristic
84	C₂	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₁₉
commutator	C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₉
Fitting	C₂²×Q₈×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	D₄
cosocle	C₂×C₄×C₁₉	C₂³
hypercenter	C₂²×Q₈	D₁₉
hypocenter	C₁₉	C₂×#103
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
4. #10597292	C₂	direct (N × H)
7. C₂×Q₈×C₁₉	C₄	semidirect
19. Q₈×C₁₉	C₂×C₄	semidirect
39. C₂×C₁₉	#103	semidirect
47. C₁₉	C₂×#103	semidirect
50. C₂×Q₈	Dic₁₉	semidirect
62. Q₈	C₂×Dic₁₉	semidirect
81. C₂	#10597292	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Q₈×C₁₉	2
C₂×C₄⋊Dic₁₉	2
C₂²×C₁₉⋊C₈	2
#10597292	2
C₂×#103	19

Subgroups — C2×#10597292 #11926535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10597292 #11926535