Subgroups — C₂×#11758298 #14520220

Order 1968.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×Dic₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#11758298	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₂²⋊D₄₁	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₄₁	C₂²	1	1	yes	characteristic
7	C₂×D₁₂₃	—	2	2	no	—
8	C₂×D₁₂₃	C₂²	1	2	yes	complemented
9	C₂×D₃×C₄₁	—	2	2	no	—
10	C₂×D₃×C₄₁	C₂²	1	2	yes	complemented
11	C₃×Dic₄₁	C₂²	1	2	yes	complemented
12	C₂³×C₄₁	—	3	1	no	—
13	C₂²×D₄₁	—	3	1	no	—
14	C₂²⋊D₄₁	—	3	4	no	—
15	C₂×Dic₄₁	D₃	1	1	yes	characteristic, complemented
16	C₂×C₃×C₄₁	D₄	1	2	yes	complemented
17	C₂×C₃×C₄₁	C₂³	1	1	yes	characteristic
18	D₁₂₃	—	2	2	no	—
19	D₃×C₄₁	—	2	2	no	—
20	C₂²×C₄₁	—	3	2	no	—
21	C₂²×C₄₁	—	6	2	no	—
22	C₂²×C₄₁	C₂×D₃	1	1	yes	characteristic
23	C₂×D₄₁	—	3	2	no	—
24	C₂×D₄₁	—	6	2	no	—
25	Dic₄₁	C₂×D₃	1	2	yes	complemented
26	C₃×C₄₁	C₂×D₄	1	1	yes	characteristic, complemented, Hall
27	C₂×C₄₁	—	6	2	no	—
28	C₂×C₄₁	D₁₂	1	2	yes	complemented
29	C₂×C₄₁	C₂²×D₃	1	1	yes	characteristic
30	D₄₁	—	6	2	no	—
31	C₂×D₁₂	—	41	1	no	maximal, Hall
32	C₄₁	C₂×D₁₂	1	1	yes	characteristic, complemented, Sylow
33	C₂²×D₃	—	41	1	no	—
34	C₂²×D₃	D₄₁	1	1	yes	characteristic, complemented
35	C₂×C₃×C₄	—	41	1	no	—
36	D₁₂	—	41	4	no	—
37	C₂×D₄	—	123	1	no	Sylow
38	C₂²×C₃	C₂×D₄₁	1	1	yes	characteristic
39	C₂×D₃	—	2	2	no	—
40	C₂×D₃	—	41	2	no	—
41	C₂×D₃	—	82	2	no	—
42	C₂×D₃	C₂×D₄₁	1	2	yes	complemented
43	C₃×C₄	—	41	2	no	—
44	C₂³	—	3	1	no	—
45	C₂³	—	123	1	no	—
46	D₄	—	123	4	no	—
47	C₂×C₄	—	41	1	no	—
48	C₂×C₃	C₂²⋊D₄₁	1	2	yes	complemented
49	C₂×C₃	C₂²×D₄₁	1	1	yes	characteristic
50	D₃	—	2	2	no	—
51	D₃	—	82	2	no	—
52	C₂²	—	3	2	no	—
53	C₂²	—	6	2	no	—
54	C₂²	—	123	2	no	—
55	C₂²	—	246	2	no	—
56	C₂²	D₃×D₄₁	1	1	yes	characteristic
57	C₄	—	41	2	no	—
58	C₃	C₂×C₂²⋊D₄₁	1	1	yes	characteristic, complemented, Sylow
59	C₂	—	6	2	no	—
60	C₂	—	246	2	no	—
61	C₂	#11758298	1	2	yes	direct product factor
62	C₂	C₂×D₃×D₄₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₃×D₄₁
commutator, cosocle	C₂×C₃×C₄₁	C₂³
Frattini	C₂	C₂×D₃×D₄₁
Fitting, socle	C₂²×C₃×C₄₁	C₂²
hypocenter	C₃×C₄₁	C₂×D₄
LCS	G ▷ C₂×C₃×C₄₁ ▷ C₃×C₄₁
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂²×D₁₂₃	C₂	semidirect
2. C₂²×D₃×C₄₁	C₂	semidirect
3. C₂×C₃×Dic₄₁	C₂	semidirect
4. #11758298	C₂	direct (N × H)
8. C₂×D₁₂₃	C₂²	semidirect
10. C₂×D₃×C₄₁	C₂²	semidirect
11. C₃×Dic₄₁	C₂²	semidirect
15. C₂×Dic₄₁	D₃	semidirect
16. C₂×C₃×C₄₁	D₄	semidirect
25. Dic₄₁	C₂×D₃	semidirect
26. C₃×C₄₁	C₂×D₄	semidirect
28. C₂×C₄₁	D₁₂	semidirect
32. C₄₁	C₂×D₁₂	semidirect
34. C₂²×D₃	D₄₁	semidirect
42. C₂×D₃	C₂×D₄₁	semidirect
48. C₂×C₃	C₂²⋊D₄₁	semidirect
58. C₃	C₂×C₂²⋊D₄₁	semidirect
61. C₂	#11758298	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×D₁₂₃	2
C₂²×D₃×C₄₁	2
C₂×C₃×Dic₄₁	2
#11758298	2
C₂×C₂²⋊D₄₁	3
C₂×D₁₂	41

Subgroups — C2×#11758298 #14520220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11758298 #14520220