Subgroups — C₂×#11745231 #14271707

Order 1856.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₅₈	C₂	1	2	yes	maximal
2	C₂×C₄²×C₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₂₉	C₂	1	4	yes	maximal
4	#11745231	C₂	1	8	yes	maximal, direct product factor
5	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₂₉	C₂²	1	2	yes	—
7	C₂²×Dic₂₉	C₂²	1	4	yes	—
8	C₂×Dic₅₈	—	2	8	no	—
9	C₂×Dic₅₈	C₂²	1	8	yes	—
10	C₄²×C₂₉	C₂²	1	4	yes	—
11	C₄⋊Dic₂₉	C₂²	1	16	yes	—
12	C₂³×C₂₉	C₂³	1	1	yes	characteristic
13	C₂×C₄×C₂₉	D₄	1	4	yes	—
14	C₂×C₄×C₂₉	Q₈	1	8	yes	complemented
15	C₂×C₄×C₂₉	C₂³	1	2	yes	—
16	C₂×C₄×C₂₉	C₂³	1	4	yes	—
17	C₂×Dic₂₉	—	2	8	no	—
18	C₂×Dic₂₉	C₂³	1	8	yes	—
19	Dic₅₈	—	2	16	no	—
20	C₂²×C₂₉	C₂×D₄	1	2	yes	—
21	C₂²×C₂₉	C₂×Q₈	1	4	yes	—
22	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
23	C₄×C₂₉	C₂×D₄	1	4	yes	—
24	C₄×C₂₉	C₂×Q₈	1	8	yes	complemented
25	Dic₂₉	—	2	8	no	—
26	C₂×C₄⋊Q₈	—	29	1	no	maximal, Sylow
27	C₂×C₂₉	C₄⋊Q₈	1	4	yes	complemented
28	C₂×C₂₉	C₂²×D₄	1	1	yes	characteristic
29	C₂×C₂₉	C₂²×Q₈	1	2	yes	—
30	C₂²×Q₈	—	29	2	no	—
31	C₄⋊Q₈	—	29	8	no	—
32	C₂×C₄⋊C₄	—	29	4	no	—
33	C₂×C₄²	D₂₉	1	1	yes	characteristic
34	C₂₉	C₂×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
35	C₂×Q₈	—	29	8	no	—
36	C₂×Q₈	—	58	8	no	—
37	C₂²×C₄	—	29	4	no	—
38	C₂²×C₄	C₂×D₂₉	1	2	yes	—
39	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
40	C₄⋊C₄	—	29	16	no	—
41	C₄²	C₂×D₂₉	1	4	yes	—
42	C₂³	C₂²×D₂₉	1	1	yes	characteristic
43	Q₈	—	58	16	no	—
44	C₂×C₄	—	29	8	no	—
45	C₂×C₄	—	58	8	no	—
46	C₂×C₄	Dic₅₈	1	8	yes	complemented
47	C₂×C₄	D₁₁₆	1	4	yes	—
48	C₂×C₄	C₂²×D₂₉	1	4	yes	—
49	C₂×C₄	C₂²×D₂₉	1	2	yes	—
50	C₂²	C₂×Dic₅₈	1	4	yes	—
51	C₂²	C₂×D₁₁₆	1	2	yes	—
52	C₂²	C₂³×D₂₉	1	1	yes	characteristic
53	C₄	—	58	8	no	—
54	C₄	C₂×Dic₅₈	1	8	yes	complemented
55	C₄	C₂×D₁₁₆	1	4	yes	—
56	C₂	#11745231	1	4	yes	direct product factor
57	C₂	C₂²×Dic₅₈	1	2	yes	—
58	C₂	C₂²×D₁₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₂₉
commutator, cosocle	C₂²×C₂₉	C₂⁴
Frattini	C₂²	C₂³×D₂₉
Fitting	C₂×C₄²×C₂₉	C₂
socle, prime radical	C₂³×C₂₉	C₂³
hypercenter	C₂×C₄²	D₂₉
hypocenter	C₂₉	C₂×C₄⋊Q₈
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
4. #11745231	C₂	direct (N × H)
14. C₂×C₄×C₂₉	Q₈	semidirect
24. C₄×C₂₉	C₂×Q₈	semidirect
27. C₂×C₂₉	C₄⋊Q₈	semidirect
34. C₂₉	C₂×C₄⋊Q₈	semidirect
46. C₂×C₄	Dic₅₈	semidirect
54. C₄	C₂×Dic₅₈	semidirect
56. C₂	#11745231	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×Dic₅₈	2
C₂×C₄²×C₂₉	2
C₂×C₄⋊Dic₂₉	2
#11745231	2
C₂×C₄⋊Q₈	29

Subgroups — C2×#11745231 #14271707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11745231 #14271707