Subgroups — #11926754

Order 1216.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#64528	C₂	1	2	yes	maximal
3	#10597315	C₂	1	1	yes	maximal, characteristic
4	#10597267	C₂	1	2	yes	maximal
5	C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×Dic₃₈	C₂²	1	2	yes	—
8	C₄⋊C₄×C₁₉	—	2	1	no	—
9	C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₄²×C₁₉	—	2	1	no	—
11	C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	#64528	—	2	4	no	—
13	C₄⋊Dic₁₉	—	2	1	no	—
14	C₄⋊Dic₁₉	—	2	1	no	—
15	C₂×C₁₉⋊C₈	C₂²	1	2	yes	—
16	Q₈×C₁₉	—	2	1	no	—
17	Q₈×C₁₉	D₄	1	2	yes	—
18	C₂×C₄×C₁₉	—	2	1	no	—
19	C₂×C₄×C₁₉	—	2	1	no	—
20	C₂×C₄×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	C₂×Dic₁₉	—	2	2	no	—
24	Dic₃₈	—	2	2	no	—
25	Dic₃₈	—	2	2	no	—
26	C₁₉⋊C₈	—	2	2	no	—
27	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
28	C₄×C₁₉	—	2	2	no	—
29	C₄×C₁₉	—	2	1	no	—
30	C₄×C₁₉	—	4	1	no	—
31	C₄×C₁₉	Q₁₆	1	2	yes	complemented
32	C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
33	C₄×C₁₉	#41	1	1	yes	characteristic
34	Dic₁₉	—	4	2	no	—
35	#462	—	19	1	no	maximal, Sylow
36	C₂×C₁₉	#121	1	1	yes	characteristic
37	C₂×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
38	C₂×C₁₉	#137	1	1	yes	characteristic
39	C₂×Q₁₆	—	19	2	no	—
40	C₄⋊Q₈	—	19	1	no	—
41	C₄×Q₈	D₁₉	1	1	yes	characteristic
42	C₄⋊C₈	—	19	1	no	—
43	#103	—	19	2	no	—
44	C₁₉	#462	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₈	—	19	2	no	—
46	C₂×Q₈	C₂×D₁₉	1	1	yes	characteristic
47	Q₁₆	—	38	4	no	—
48	C₂×C₈	—	19	2	no	—
49	C₄⋊C₄	—	2	1	no	—
50	C₄⋊C₄	—	38	1	no	—
51	C₄⋊C₄	—	38	1	no	—
52	C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
53	C₄²	—	2	1	no	—
54	C₄²	C₂×D₁₉	1	1	yes	characteristic
55	Q₈	—	2	1	no	—
56	Q₈	—	38	2	no	—
57	Q₈	—	38	2	no	—
58	Q₈	D₇₆	1	2	yes	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	38	2	no	—
62	C₂×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
63	C₂×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
64	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
65	C₈	—	38	2	no	—
66	C₂²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
67	C₄	—	2	2	no	—
68	C₄	—	2	1	no	—
69	C₄	—	4	1	no	—
70	C₄	—	76	2	no	—
71	C₄	#64528	1	2	yes	complemented
72	C₄	C₂×D₇₆	1	1	yes	characteristic
73	C₄	#64541	1	1	yes	characteristic
74	C₂	#10597376	1	1	yes	characteristic
75	C₂	C₂×#64528	1	1	yes	characteristic
76	C₂	#10597397	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₉
Fitting	C₄×Q₈×C₁₉	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₄
hypercenter	C₄×Q₈	D₁₉
hypocenter	C₁₉	#462
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
31. C₄×C₁₉	Q₁₆	semidirect
44. C₁₉	#462	semidirect
71. C₄	#64528	semidirect

Maximal subgroups

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

subgroup	index
C₄×Q₈×C₁₉	2
C₂×#64528	2
#10597315	2
#10597267	2
C₄⋊(C₁₉⋊C₈)	2
#462	19