Subgroups — C₂×#11745160 #14271578

Order 1856.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic
2	#11745160	C₂	1	4	yes	maximal, direct product factor
3	C₂×#90768	C₂	1	2	yes	maximal, complemented
4	C₂²×C₄×C₂₉	C₄	1	1	yes	characteristic
5	C₂×C₈×C₂₉	C₄	1	1	yes	characteristic
6	C₂×C₈×C₂₉	C₄	1	2	yes	—
7	C₂×C₈×C₂₉	C₂²	1	2	yes	—
8	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
9	#90768	C₂²	1	4	yes	complemented
10	C₂³×C₂₉	C₈	1	1	yes	characteristic
11	C₂×C₄×C₂₉	C₈	1	2	yes	—
12	C₂×C₄×C₂₉	C₈	1	1	yes	characteristic
13	C₂×C₄×C₂₉	C₂×C₄	1	2	yes	—
14	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₈×C₂₉	C₂×C₄	1	2	yes	—
16	C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₈×C₂₉	C₂³	1	1	yes	characteristic
18	C₂²×C₂₉	—	2	2	no	—
19	C₂²×C₂₉	C₂×C₈	1	2	yes	—
20	C₂²×C₂₉	C₂×C₈	1	1	yes	characteristic
21	C₄×C₂₉	C₂×C₈	1	2	yes	—
22	C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
23	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
24	C₂×M₃₂	—	29	1	no	maximal, Sylow
25	C₂×C₂₉	—	2	2	no	—
26	C₂×C₂₉	M₃₂	1	2	yes	complemented
27	C₂×C₂₉	C₂²×C₈	1	1	yes	characteristic
28	C₂²×C₈	D₂₉	1	1	yes	characteristic
29	M₃₂	—	29	4	no	—
30	C₂×C₁₆	—	29	2	no	—
31	C₂₉	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
32	C₂²×C₄	Dic₂₉	1	1	yes	characteristic
33	C₂×C₈	Dic₂₉	1	1	yes	characteristic
34	C₂×C₈	Dic₂₉	1	2	yes	—
35	C₂×C₈	C₂×D₂₉	1	2	yes	—
36	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
37	C₁₆	—	29	4	no	—
38	C₂³	#6597	1	1	yes	characteristic
39	C₂×C₄	#6597	1	2	yes	—
40	C₂×C₄	#6597	1	1	yes	characteristic
41	C₂×C₄	C₂×Dic₂₉	1	2	yes	—
42	C₂×C₄	C₂×Dic₂₉	1	1	yes	characteristic
43	C₈	C₂×Dic₂₉	1	2	yes	—
44	C₈	C₂×Dic₂₉	1	1	yes	characteristic
45	C₈	C₂²×D₂₉	1	1	yes	characteristic
46	C₂²	—	2	2	no	—
47	C₂²	C₂×#6597	1	2	yes	—
48	C₂²	C₂×#6597	1	1	yes	characteristic
49	C₄	C₂×#6597	1	2	yes	—
50	C₄	C₂×#6597	1	1	yes	characteristic
51	C₄	C₂²×Dic₂₉	1	1	yes	characteristic
52	C₂	—	2	2	no	—
53	C₂	#11745160	1	2	yes	direct product factor
54	C₂	C₂²×#6597	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₂₉
commutator	C₂×C₂₉	C₂²×C₈
Frattini	C₈	C₂²×D₂₉
Fitting	C₂²×C₈×C₂₉	C₂
socle	C₂²×C₂₉	C₂×C₈
prime radical	C₂³×C₂₉	C₈
cosocle	C₈×C₂₉	C₂³
hypercenter	C₂²×C₈	D₂₉
hypocenter	C₂₉	C₂×M₃₂
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #11745160	C₂	direct (N × H)
3. C₂×#90768	C₂	semidirect
9. #90768	C₂²	semidirect
26. C₂×C₂₉	M₃₂	semidirect
31. C₂₉	C₂×M₃₂	semidirect
53. C₂	#11745160	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×C₈×C₂₉	2
#11745160	2
C₂×#90768	2
C₂×M₃₂	29

Subgroups — C2×#11745160 #14271578

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11745160 #14271578