Subgroups — C₂²×#64526 #11927317

Order 1216.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#64526	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁴×C₁₉	—	2	1	no	—
6	C₂×D₄×C₁₉	—	2	3	no	—
7	C₂×D₄×C₁₉	C₂²	1	6	yes	—
8	C₂²×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₁₉	—	2	1	no	—
10	C₂×Dic₃₈	—	2	3	no	—
11	C₂×Dic₃₈	C₂²	1	6	yes	complemented
12	#64526	C₂²	1	16	yes	direct product factor
13	C₂×C₁₉⋊C₈	C₂²	1	6	yes	complemented
14	C₂³×C₁₉	—	2	6	no	—
15	C₂³×C₁₉	—	4	4	no	—
16	C₂³×C₁₉	D₄	1	1	yes	characteristic
17	D₄×C₁₉	—	2	6	no	—
18	D₄×C₁₉	C₂³	1	4	yes	—
19	C₂×C₄×C₁₉	D₄	1	3	yes	—
20	C₂×C₄×C₁₉	C₂³	1	3	yes	—
21	C₂×Dic₁₉	—	2	6	no	—
22	Dic₃₈	—	2	6	no	—
23	Dic₃₈	C₂³	1	4	yes	complemented
24	C₁₉⋊C₈	C₂³	1	4	yes	complemented
25	C₂²×C₁₉	—	2	4	no	—
26	C₂²×C₁₉	—	4	12	no	—
27	C₂²×C₁₉	SD₁₆	1	4	yes	complemented
28	C₂²×C₁₉	C₂×D₄	1	3	yes	—
29	C₄×C₁₉	C₂×D₄	1	3	yes	—
30	C₄×C₁₉	C₂⁴	1	1	yes	characteristic
31	Dic₁₉	—	2	4	no	—
32	C₂²×SD₁₆	—	19	1	no	maximal, Sylow
33	C₂×C₁₉	—	4	4	no	—
34	C₂×C₁₉	C₂×SD₁₆	1	6	yes	complemented
35	C₂×C₁₉	C₂²×D₄	1	1	yes	characteristic
36	C₂²×Q₈	—	19	1	no	—
37	C₂²×D₄	D₁₉	1	1	yes	characteristic
38	C₂×SD₁₆	—	19	12	no	—
39	C₂²×C₈	—	19	1	no	—
40	C₁₉	C₂²×SD₁₆	1	1	yes	characteristic, complemented, Sylow
41	C₂⁴	—	2	1	no	—
42	C₂×Q₈	—	19	6	no	—
43	C₂×Q₈	—	38	3	no	—
44	C₂×D₄	—	2	3	no	—
45	C₂×D₄	C₂×D₁₉	1	6	yes	—
46	C₂²×C₄	—	38	1	no	—
47	C₂²×C₄	C₂×D₁₉	1	1	yes	characteristic
48	SD₁₆	—	19	16	no	—
49	C₂×C₈	—	19	6	no	—
50	C₂³	—	2	6	no	—
51	C₂³	—	4	4	no	—
52	C₂³	C₂²⋊D₁₉	1	1	yes	characteristic
53	Q₈	—	19	4	no	—
54	Q₈	—	38	6	no	—
55	D₄	—	2	6	no	—
56	D₄	C₂²×D₁₉	1	4	yes	—
57	C₂×C₄	—	38	6	no	—
58	C₂×C₄	C₂²⋊D₁₉	1	3	yes	—
59	C₂×C₄	C₂²×D₁₉	1	3	yes	—
60	C₈	—	19	4	no	—
61	C₂²	—	2	4	no	—
62	C₂²	—	4	12	no	—
63	C₂²	#64526	1	4	yes	direct product factor
64	C₂²	C₂×C₂²⋊D₁₉	1	3	yes	—
65	C₄	—	38	4	no	—
66	C₄	C₂×C₂²⋊D₁₉	1	3	yes	—
67	C₄	C₂³×D₁₉	1	1	yes	characteristic
68	C₂	—	4	4	no	—
69	C₂	C₂×#64526	1	6	yes	direct product factor
70	C₂	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₁₉
commutator, cosocle	C₄×C₁₉	C₂⁴
Frattini	C₄	C₂³×D₁₉
Fitting, prime radical	C₂²×D₄×C₁₉	C₂
socle	C₂³×C₁₉	D₄
hypercenter	C₂²×D₄	D₁₉
hypocenter	C₁₉	C₂²×SD₁₆
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₃₈	C₂	semidirect
3. C₂×#64526	C₂	direct (N × H)
4. C₂²×C₁₉⋊C₈	C₂	semidirect
11. C₂×Dic₃₈	C₂²	semidirect
12. #64526	C₂²	direct (N × H)
13. C₂×C₁₉⋊C₈	C₂²	semidirect
23. Dic₃₈	C₂³	semidirect
24. C₁₉⋊C₈	C₂³	semidirect
27. C₂²×C₁₉	SD₁₆	semidirect
34. C₂×C₁₉	C₂×SD₁₆	semidirect
40. C₁₉	C₂²×SD₁₆	semidirect
63. C₂²	#64526	direct (N × H)
69. C₂	C₂×#64526	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×D₄×C₁₉	2
C₂²×Dic₃₈	2
C₂×#64526	2
C₂²×C₁₉⋊C₈	2
C₂²×SD₁₆	19

Subgroups — C22×#64526 #11927317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#64526 #11927317