Subgroups — C₂×#90698 #11744948

Order 912.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₅₇	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₃×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×Dic₁₉	C₂	1	1	yes	maximal, characteristic
4	#90698	C₂	1	4	yes	maximal, direct product factor
5	C₂×Dic₃₈	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₁₉	C₂²	1	1	yes	characteristic
7	Dic₅₇	C₂²	1	2	yes	—
8	C₃×Dic₁₉	C₂²	1	2	yes	—
9	Dic₃×C₁₉	C₂²	1	2	yes	—
10	C₂×C₄×C₁₉	—	3	1	no	—
11	C₂×Dic₁₉	—	3	1	no	—
12	C₂×Dic₁₉	D₃	1	1	yes	characteristic
13	Dic₃₈	—	3	4	no	—
14	C₂×C₃×C₁₉	Q₈	1	2	yes	complemented
15	C₂×C₃×C₁₉	C₂³	1	1	yes	characteristic
16	C₂²×C₁₉	C₂×D₃	1	1	yes	characteristic
17	C₄×C₁₉	—	3	2	no	—
18	Dic₁₉	—	3	2	no	—
19	Dic₁₉	C₂×D₃	1	2	yes	—
20	C₃×C₁₉	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
21	C₂×Dic₆	—	19	1	no	maximal, Hall
22	C₂×C₁₉	Dic₆	1	2	yes	complemented
23	C₂×C₁₉	C₂²×D₃	1	1	yes	characteristic
24	C₂×C₃×C₄	—	19	1	no	—
25	C₂×Dic₃	—	19	1	no	—
26	C₂×Dic₃	D₁₉	1	1	yes	characteristic
27	Dic₆	—	19	4	no	—
28	C₁₉	C₂×Dic₆	1	1	yes	characteristic, complemented, Sylow
29	C₂×Q₈	—	57	1	no	Sylow
30	C₂²×C₃	C₂×D₁₉	1	1	yes	characteristic
31	C₃×C₄	—	19	2	no	—
32	Dic₃	—	19	2	no	—
33	Dic₃	C₂×D₁₉	1	2	yes	—
34	Q₈	—	57	4	no	—
35	C₂×C₄	—	3	1	no	—
36	C₂×C₄	—	19	1	no	—
37	C₂×C₄	—	57	1	no	—
38	C₂×C₃	Dic₃₈	1	2	yes	complemented
39	C₂×C₃	C₂²×D₁₉	1	1	yes	characteristic
40	C₂²	D₃×D₁₉	1	1	yes	characteristic
41	C₄	—	3	2	no	—
42	C₄	—	19	2	no	—
43	C₄	—	57	2	no	—
44	C₃	C₂×Dic₃₈	1	1	yes	characteristic, complemented, Sylow
45	C₂	#90698	1	2	yes	direct product factor
46	C₂	C₂×D₃×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₃×D₁₉
commutator, cosocle	C₂×C₃×C₁₉	C₂³
Frattini	C₂	C₂×D₃×D₁₉
Fitting, socle, prime radical	C₂²×C₃×C₁₉	C₂²
hypocenter	C₃×C₁₉	C₂×Q₈
LCS	G ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
4. #90698	C₂	direct (N × H)
14. C₂×C₃×C₁₉	Q₈	semidirect
20. C₃×C₁₉	C₂×Q₈	semidirect
22. C₂×C₁₉	Dic₆	semidirect
28. C₁₉	C₂×Dic₆	semidirect
38. C₂×C₃	Dic₃₈	semidirect
44. C₃	C₂×Dic₃₈	semidirect
45. C₂	#90698	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Dic₅₇	2
C₂×Dic₃×C₁₉	2
C₂×C₃×Dic₁₉	2
#90698	2
C₂×Dic₃₈	3
C₂×Dic₆	19

Subgroups — C2×#90698 #11744948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#90698 #11744948