Subgroups — #11926672

Order 1216.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#97	C₂	1	1	yes	maximal, characteristic
3	#10597272	C₂	1	1	yes	maximal, characteristic
4	Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
5	Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
7	C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₃₈	C₄	1	1	yes	characteristic
9	C₂×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₉	C₄	1	1	yes	characteristic
13	Dic₁₉⋊C₄	C₄	1	1	yes	characteristic
14	Dic₁₉⋊C₄	C₄	1	1	yes	characteristic
15	C₄×Dic₁₉	C₂²	1	1	yes	characteristic
16	C₄×Dic₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×Dic₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂×Dic₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×Dic₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂×Dic₁₉	C₂×C₄	1	1	yes	characteristic
26	Dic₃₈	—	2	2	no	—
27	C₈×C₁₉	—	2	1	no	—
28	C₈×C₁₉	Q₈	1	2	yes	complemented
29	C₁₉⋊C₈	—	2	1	no	—
30	C₁₉⋊C₈	—	2	1	no	—
31	C₂²×C₁₉	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₁₉	—	2	1	no	—
33	C₄×C₁₉	—	2	1	no	—
34	C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
35	C₄×C₁₉	#41	1	1	yes	characteristic
36	Dic₁₉	—	2	1	no	—
37	Dic₁₉	—	2	1	no	—
38	Dic₁₉	—	2	1	no	—
39	Dic₁₉	M₁₆	1	2	yes	—
40	#446	—	19	1	no	maximal, Sylow
41	C₂×C₁₉	C₄×Q₈	1	1	yes	characteristic
42	C₂×C₁₉	C₂×M₁₆	1	1	yes	characteristic
43	C₂×C₁₉	#131	1	1	yes	characteristic
44	C₄×Q₈	—	19	1	no	—
45	C₄⋊C₈	—	19	1	no	—
46	C₄⋊C₈	—	19	1	no	—
47	C₄⋊C₈	—	19	1	no	—
48	#97	—	19	1	no	—
49	#97	D₁₉	1	1	yes	characteristic
50	C₄×C₈	—	19	1	no	—
51	C₁₉	#446	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₈	—	19	1	no	—
53	C₂×C₈	—	19	1	no	—
54	C₂×C₈	—	19	1	no	—
55	C₂×C₈	C₂×D₁₉	1	1	yes	characteristic
56	C₂×C₈	C₂×D₁₉	1	1	yes	characteristic
57	C₄⋊C₄	—	19	1	no	—
58	C₄⋊C₄	—	19	1	no	—
59	C₄⋊C₄	—	19	1	no	—
60	C₄²	—	19	1	no	—
61	C₄²	—	19	1	no	—
62	C₄²	C₂×D₁₉	1	1	yes	characteristic
63	Q₈	—	38	2	no	—
64	C₂×C₄	—	19	1	no	—
65	C₂×C₄	—	19	1	no	—
66	C₂×C₄	—	19	1	no	—
67	C₂×C₄	—	19	1	no	—
68	C₂×C₄	C₄×D₁₉	1	1	yes	characteristic
69	C₂×C₄	C₄×D₁₉	1	1	yes	characteristic
70	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
71	C₈	—	2	1	no	—
72	C₈	—	38	1	no	—
73	C₈	—	38	1	no	—
74	C₈	Dic₃₈	1	2	yes	complemented
75	C₂²	C₂×C₄×D₁₉	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	2	1	no	—
78	C₄	—	19	2	no	—
79	C₄	—	38	1	no	—
80	C₄	—	38	1	no	—
81	C₄	—	38	1	no	—
82	C₄	C₂×Dic₃₈	1	1	yes	characteristic
83	C₄	#64541	1	1	yes	characteristic
84	C₂	C₄×Dic₃₈	1	1	yes	characteristic
85	C₂	M₁₆×D₁₉	1	1	yes	characteristic
86	C₂	#10597353	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₁₉
commutator, socle, prime radical	C₂²×C₁₉	C₂²×C₄
Fitting	C₁₉×#97	C₂
cosocle	C₂×C₄×C₁₉	C₂³
hypercenter	#97	D₁₉
hypocenter	C₁₉	#446
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #97

Complements

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

N	H ≅ G/N	type
28. C₈×C₁₉	Q₈	semidirect
51. C₁₉	#446	semidirect
74. C₈	Dic₃₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₃₈	2
C₁₉×#97	2
#10597272	2
Dic₁₉⋊C₈	2
C₈×Dic₁₉	2
C₄⋊(C₁₉⋊C₈)	2
#446	19