Subgroups — #11926554

Order 1216.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₃₈	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
3	#10597372	C₂	1	1	yes	maximal, characteristic
4	#10597273	C₂	1	4	yes	maximal, complemented
5	C₂²×C₄×C₁₉	C₂²	1	1	yes	characteristic
6	C₂²×Dic₁₉	—	2	1	no	—
7	C₂×Dic₃₈	—	2	1	no	—
8	C₂×Dic₃₈	—	2	2	no	—
9	C₂×Dic₃₈	C₄	1	4	yes	complemented
10	C₂×Dic₃₈	C₂²	1	2	yes	—
11	M₁₆×C₁₉	—	2	2	no	—
12	C₂×C₈×C₁₉	C₂²	1	2	yes	—
13	C₂²⋊Dic₁₉	—	2	1	no	—
14	C₄⋊Dic₁₉	C₂²	1	2	yes	—
15	C₄×Dic₁₉	—	2	1	no	—
16	C₂³×C₁₉	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₉	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₁₉	D₄	1	1	yes	characteristic
19	C₂×C₄×C₁₉	D₄	1	2	yes	—
20	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₂×Dic₁₉	—	2	4	no	—
22	C₂×Dic₁₉	—	2	2	no	—
23	C₂×Dic₁₉	—	2	2	no	—
24	Dic₃₈	—	2	4	no	—
25	Dic₃₈	—	2	2	no	—
26	Dic₃₈	C₂×C₄	1	4	yes	—
27	C₈×C₁₉	—	2	2	no	—
28	C₂²×C₁₉	—	2	2	no	—
29	C₂²×C₁₉	C₂²⋊C₄	1	2	yes	—
30	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
31	C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
32	C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
33	C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
34	Dic₁₉	—	2	4	no	—
35	Dic₁₉	—	4	2	no	—
36	#419	—	19	1	no	maximal, Sylow
37	C₂×C₁₉	—	2	2	no	—
38	C₂×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
39	C₂×C₁₉	#137	1	2	yes	—
40	C₂²×Q₈	—	19	1	no	—
41	C₂×M₁₆	D₁₉	1	1	yes	characteristic
42	#117	—	19	1	no	—
43	#103	—	19	4	no	—
44	C₁₉	#419	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₈	—	19	4	no	—
46	C₂×Q₈	—	19	2	no	—
47	C₂×Q₈	—	38	1	no	—
48	C₂×Q₈	—	38	2	no	—
49	C₂²×C₄	—	38	1	no	—
50	C₂²×C₄	C₂×D₁₉	1	1	yes	characteristic
51	M₁₆	—	2	2	no	—
52	C₂×C₈	C₂×D₁₉	1	2	yes	—
53	C₄⋊C₄	—	19	2	no	—
54	C₂²⋊C₄	—	38	1	no	—
55	C₄²	—	38	1	no	—
56	C₂³	D₇₆	1	1	yes	characteristic
57	Q₈	—	19	4	no	—
58	Q₈	—	38	4	no	—
59	Q₈	—	38	2	no	—
60	C₂×C₄	—	38	4	no	—
61	C₂×C₄	—	38	2	no	—
62	C₂×C₄	—	38	2	no	—
63	C₂×C₄	C₄×D₁₉	1	2	yes	—
64	C₂×C₄	D₇₆	1	1	yes	characteristic
65	C₂×C₄	C₂²⋊D₁₉	1	2	yes	—
66	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
67	C₈	—	2	2	no	—
68	C₂²	—	2	2	no	—
69	C₂²	(C₂×D₁₉)⋊C₄	1	2	yes	—
70	C₂²	C₂×D₇₆	1	1	yes	characteristic
71	C₄	—	38	4	no	—
72	C₄	—	76	2	no	—
73	C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
74	C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
75	C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
76	C₂	—	2	2	no	—
77	C₂	#10597355	1	2	yes	—
78	C₂	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₇₆
commutator	C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₉
Fitting	C₂×M₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂×D₄
prime radical	C₂³×C₁₉	D₄
cosocle	C₂×C₄×C₁₉	C₂³
hypercenter	C₂×M₁₆	D₁₉
hypocenter	C₁₉	#419
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
4. #10597273	C₂	semidirect
9. C₂×Dic₃₈	C₄	semidirect
44. C₁₉	#419	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Dic₃₈	2
C₂×M₁₆×C₁₉	2
#10597372	2
#10597273	2
#419	19