Subgroups — C₂×C₄×Dic₅₈ #14271628

Order 1856.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₅₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄²×C₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#90779	C₂	1	2	yes	maximal
5	C₂×C₄×Dic₂₉	C₂	1	2	yes	maximal
6	C₄×Dic₅₈	C₂	1	8	yes	maximal, direct product factor
7	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
9	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
10	C₂²×Dic₂₉	C₂²	1	2	yes	—
11	C₂²×Dic₂₉	C₂²	1	2	yes	—
12	C₂×Dic₅₈	C₄	1	8	yes	direct product factor
13	C₂×Dic₅₈	C₂²	1	4	yes	—
14	C₄²×C₂₉	C₂²	1	4	yes	—
15	C₄⋊Dic₂₉	C₂²	1	4	yes	—
16	#90779	C₂²	1	8	yes	—
17	C₄×Dic₂₉	C₂²	1	8	yes	—
18	C₂³×C₂₉	C₂³	1	1	yes	characteristic
19	C₂×C₄×C₂₉	—	2	2	no	—
20	C₂×C₄×C₂₉	C₂×C₄	1	4	yes	—
21	C₂×C₄×C₂₉	Q₈	1	4	yes	complemented
22	C₂×C₄×C₂₉	C₂³	1	2	yes	—
23	C₂×C₄×C₂₉	C₂³	1	2	yes	—
24	C₂×C₄×C₂₉	C₂³	1	2	yes	—
25	C₂×Dic₂₉	—	2	4	no	—
26	C₂×Dic₂₉	C₂×C₄	1	8	yes	—
27	C₂×Dic₂₉	C₂³	1	4	yes	—
28	C₂×Dic₂₉	C₂³	1	4	yes	—
29	Dic₅₈	C₂×C₄	1	16	yes	direct product factor
30	C₂²×C₂₉	C₂²×C₄	1	2	yes	—
31	C₂²×C₂₉	C₂×Q₈	1	2	yes	—
32	C₂²×C₂₉	#41	1	2	yes	—
33	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
34	C₄×C₂₉	—	2	2	no	—
35	C₄×C₂₉	C₂²×C₄	1	4	yes	—
36	C₄×C₂₉	C₂×Q₈	1	4	yes	complemented
37	Dic₂₉	—	2	4	no	—
38	Dic₂₉	C₂²×C₄	1	8	yes	—
39	C₂×C₄×Q₈	—	29	1	no	maximal, Sylow
40	C₂×C₂₉	C₄×Q₈	1	4	yes	complemented
41	C₂×C₂₉	C₂³×C₄	1	1	yes	characteristic
42	C₂×C₂₉	C₂²×Q₈	1	1	yes	characteristic
43	C₂×C₂₉	C₂×#41	1	1	yes	characteristic
44	C₂²×Q₈	—	29	1	no	—
45	C₄×Q₈	—	29	8	no	—
46	C₂×C₄⋊C₄	—	29	2	no	—
47	C₂×C₄⋊C₄	—	29	1	no	—
48	C₂×C₄²	—	29	2	no	—
49	C₂×C₄²	D₂₉	1	1	yes	characteristic
50	C₂₉	C₂×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
51	C₂×Q₈	—	29	8	no	—
52	C₂×Q₈	—	29	4	no	—
53	C₂²×C₄	—	29	2	no	—
54	C₂²×C₄	—	29	2	no	—
55	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
56	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
57	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
58	C₄⋊C₄	—	29	8	no	—
59	C₄⋊C₄	—	29	4	no	—
60	C₄²	—	29	8	no	—
61	C₄²	C₂×D₂₉	1	4	yes	—
62	C₂³	C₂²×D₂₉	1	1	yes	characteristic
63	Q₈	—	29	16	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	29	8	no	—
66	C₂×C₄	—	29	4	no	—
67	C₂×C₄	—	29	4	no	—
68	C₂×C₄	—	58	4	no	—
69	C₂×C₄	Dic₅₈	1	4	yes	direct product factor
70	C₂×C₄	C₄×D₂₉	1	4	yes	—
71	C₂×C₄	C₂²×D₂₉	1	2	yes	—
72	C₂×C₄	C₂²×D₂₉	1	2	yes	—
73	C₂×C₄	C₂²×D₂₉	1	2	yes	—
74	C₂²	C₂×Dic₅₈	1	2	yes	—
75	C₂²	C₂×C₄×D₂₉	1	2	yes	—
76	C₂²	#90805	1	2	yes	—
77	C₂²	C₂³×D₂₉	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	29	8	no	—
80	C₄	—	58	4	no	—
81	C₄	C₂×Dic₅₈	1	4	yes	direct product factor
82	C₄	C₂×C₄×D₂₉	1	4	yes	—
83	C₂	C₄×Dic₅₈	1	4	yes	direct product factor
84	C₂	C₂²×Dic₅₈	1	1	yes	characteristic
85	C₂	C₂²×C₄×D₂₉	1	1	yes	characteristic
86	C₂	C₂×#90805	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₂₉
commutator	C₂×C₂₉	C₂³×C₄
Frattini	C₂²	C₂³×D₂₉
Fitting	C₂×C₄²×C₂₉	C₂
socle, prime radical	C₂³×C₂₉	C₂³
cosocle	C₂²×C₂₉	C₂⁴
hypercenter	C₂×C₄²	D₂₉
hypocenter	C₂₉	C₂×C₄×Q₈
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
6. C₄×Dic₅₈	C₂	direct (N × H)
12. C₂×Dic₅₈	C₄	direct (N × H)
21. C₂×C₄×C₂₉	Q₈	semidirect
29. Dic₅₈	C₂×C₄	direct (N × H)
36. C₄×C₂₉	C₂×Q₈	semidirect
40. C₂×C₂₉	C₄×Q₈	semidirect
50. C₂₉	C₂×C₄×Q₈	semidirect
69. C₂×C₄	Dic₅₈	direct (N × H)
81. C₄	C₂×Dic₅₈	direct (N × H)
83. C₂	C₄×Dic₅₈	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
C₂×#90779	2
C₂×C₄×Dic₂₉	2
C₄×Dic₅₈	2
C₂×C₄×Q₈	29

Subgroups — C2×C4×Dic58 #14271628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×Dic₅₈ #14271628