Subgroups — C₂×#11745236 #14271703

Order 1856.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₁₆	C₂	1	6	yes	maximal, complemented
2	C₂×C₄²×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#11745236	C₂	1	8	yes	maximal, direct product factor
4	C₂³×D₂₉	C₂²	1	4	yes	—
5	C₂²×C₄×C₂₉	C₂²	1	3	yes	—
6	C₂×D₁₁₆	—	2	24	no	—
7	C₂×D₁₁₆	C₂²	1	24	yes	complemented
8	C₄²×C₂₉	C₂²	1	4	yes	complemented
9	C₂³×C₂₉	C₂³	1	1	yes	characteristic
10	C₂²×D₂₉	—	2	24	no	—
11	C₂²×D₂₉	C₂³	1	8	yes	—
12	C₂×C₄×C₂₉	D₄	1	12	yes	complemented
13	C₂×C₄×C₂₉	C₂³	1	6	yes	—
14	D₁₁₆	—	2	48	no	—
15	C₂²×C₂₉	C₂×D₄	1	6	yes	—
16	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
17	C₂×D₂₉	—	2	24	no	—
18	C₂×D₂₉	—	4	16	no	—
19	C₄×C₂₉	C₂×D₄	1	12	yes	complemented
20	C₂×#127	—	29	1	no	maximal, Sylow
21	C₂×C₂₉	#127	1	4	yes	complemented
22	C₂×C₂₉	C₂²×D₄	1	3	yes	—
23	D₂₉	—	4	8	no	—
24	C₂²×D₄	—	29	6	no	—
25	#127	—	29	8	no	—
26	C₂×C₄²	D₂₉	1	1	yes	characteristic, complemented
27	C₂₉	C₂×#127	1	1	yes	characteristic, complemented, Sylow
28	C₂⁴	—	29	4	no	—
29	C₂×D₄	—	29	24	no	—
30	C₂×D₄	—	58	24	no	—
31	C₂²×C₄	C₂×D₂₉	1	3	yes	—
32	C₄²	C₂×D₂₉	1	4	yes	complemented
33	C₂³	—	29	8	no	—
34	C₂³	—	58	24	no	—
35	C₂³	C₂²×D₂₉	1	1	yes	characteristic
36	D₄	—	58	48	no	—
37	C₂×C₄	D₁₁₆	1	12	yes	complemented
38	C₂×C₄	C₂²×D₂₉	1	6	yes	—
39	C₂²	—	58	24	no	—
40	C₂²	—	116	16	no	—
41	C₂²	C₂×D₁₁₆	1	6	yes	—
42	C₂²	C₂³×D₂₉	1	1	yes	characteristic
43	C₄	C₂×D₁₁₆	1	12	yes	complemented
44	C₂	—	116	8	no	—
45	C₂	#11745236	1	4	yes	direct product factor
46	C₂	C₂²×D₁₁₆	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₂₉
commutator, cosocle	C₂²×C₂₉	C₂⁴
Frattini	C₂²	C₂³×D₂₉
Fitting	C₂×C₄²×C₂₉	C₂
socle	C₂³×C₂₉	C₂³
hypercenter	C₂×C₄²	D₂₉
hypocenter	C₂₉	C₂×#127
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂²×D₁₁₆	C₂	semidirect
2. C₂×C₄²×C₂₉	C₂	semidirect
3. #11745236	C₂	direct (N × H)
7. C₂×D₁₁₆	C₂²	semidirect
8. C₄²×C₂₉	C₂²	semidirect
12. C₂×C₄×C₂₉	D₄	semidirect
19. C₄×C₂₉	C₂×D₄	semidirect
21. C₂×C₂₉	#127	semidirect
26. C₂×C₄²	D₂₉	semidirect
27. C₂₉	C₂×#127	semidirect
32. C₄²	C₂×D₂₉	semidirect
37. C₂×C₄	D₁₁₆	semidirect
43. C₄	C₂×D₁₁₆	semidirect
45. C₂	#11745236	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×D₁₁₆	2
C₂×C₄²×C₂₉	2
#11745236	2
C₂×#127	29

Subgroups — C2×#11745236 #14271703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11745236 #14271703