Subgroups — #11926799

Order 1216.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#10597392	C₂	1	2	yes	maximal
3	C₂×#64515	C₂	1	1	yes	maximal, characteristic
4	#10597292	C₂	1	2	yes	maximal, complemented
5	#10597274	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₁₉	C₂²	1	2	yes	—
7	C₂×C₄×D₁₉	C₂²	1	1	yes	characteristic
8	Q₁₆×C₁₉	—	2	2	no	—
9	C₂×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	(C₂×D₁₉)⋊C₄	—	2	2	no	—
11	C₄⋊Dic₁₉	C₂²	1	2	yes	—
12	Dic₁₉⋊C₄	—	2	2	no	—
13	C₂×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	#64515	—	2	2	no	—
15	C₂²×D₁₉	D₄	1	1	yes	characteristic
16	Q₈×C₁₉	—	2	2	no	—
17	Q₈×C₁₉	—	2	2	no	—
18	C₂×C₄×C₁₉	—	2	2	no	—
19	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
20	C₂×Dic₁₉	—	2	2	no	—
21	C₂×Dic₁₉	D₄	1	1	yes	characteristic
22	C₄×D₁₉	—	2	1	no	—
23	C₄×D₁₉	—	2	1	no	—
24	C₈×C₁₉	D₄	1	2	yes	—
25	C₁₉⋊C₈	—	2	1	no	—
26	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
27	C₂×D₁₉	—	2	1	no	—
28	C₂×D₁₉	—	2	2	no	—
29	C₄×C₁₉	—	4	2	no	—
30	C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
31	C₄×C₁₉	#41	1	1	yes	characteristic
32	Dic₁₉	—	2	1	no	—
33	Dic₁₉	—	4	2	no	—
34	#470	—	19	1	no	maximal, Sylow
35	C₂×C₁₉	#121	1	1	yes	characteristic
36	C₂×C₁₉	#137	1	2	yes	—
37	D₁₉	—	4	1	no	—
38	C₂×Q₁₆	D₁₉	1	1	yes	characteristic, complemented
39	C₂×M₁₆	—	19	1	no	—
40	C₂²⋊Q₈	—	19	2	no	—
41	#106	—	19	1	no	—
42	#103	—	19	2	no	—
43	C₁₉	#470	1	1	yes	characteristic, complemented, Sylow
44	C₂×Q₈	C₂×D₁₉	1	2	yes	—
45	C₂²×C₄	—	19	1	no	—
46	Q₁₆	—	2	2	no	—
47	M₁₆	—	38	2	no	—
48	C₂×C₈	—	19	1	no	—
49	C₂×C₈	C₂×D₁₉	1	1	yes	characteristic
50	C₄⋊C₄	—	19	2	no	—
51	C₄⋊C₄	—	38	2	no	—
52	C₂²⋊C₄	—	38	2	no	—
53	C₂³	—	19	1	no	—
54	Q₈	—	2	2	no	—
55	Q₈	—	2	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	19	1	no	—
58	C₂×C₄	—	38	1	no	—
59	C₂×C₄	—	38	1	no	—
60	C₂×C₄	—	38	2	no	—
61	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
62	C₈	—	38	1	no	—
63	C₈	C₂²⋊D₁₉	1	2	yes	—
64	C₂²	—	38	1	no	—
65	C₂²	—	38	2	no	—
66	C₂²	D₄×D₁₉	1	1	yes	characteristic
67	C₄	—	4	2	no	—
68	C₄	—	38	1	no	—
69	C₄	—	76	2	no	—
70	C₄	#64543	1	1	yes	characteristic
71	C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
72	C₂	—	76	1	no	—
73	C₂	#10597364	1	2	yes	—
74	C₂	#10597384	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₉
Fitting	C₂×Q₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂×D₄
prime radical	C₂²×D₁₉	D₄
hypercenter	C₂×Q₁₆	D₁₉
hypocenter	C₁₉	#470
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×Q₁₆×C₁₉	C₂	semidirect
4. #10597292	C₂	semidirect
5. #10597274	C₂	semidirect
38. C₂×Q₁₆	D₁₉	semidirect
43. C₁₉	#470	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×C₁₉	2
#10597392	2
C₂×#64515	2
#10597292	2
#10597274	2
#470	19