Subgroups — #14271968

Order 1856.

268 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745364	C₂	1	2	yes	maximal, complemented
2	C₂₉×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	#11745270	C₂	1	6	yes	maximal, complemented
4	#11745266	C₂	1	3	yes	maximal, complemented
5	C₂×D₂₃₂	C₂	1	3	yes	maximal, complemented
6	#41×C₂₉	C₂²	1	1	yes	characteristic
7	#90809	—	2	2	no	—
8	D₄×D₂₉	—	2	6	no	—
9	#90805	C₂²	1	6	yes	complemented
10	C₂×D₁₁₆	C₂²	1	6	yes	complemented
11	M₁₆×C₂₉	C₂²	1	3	yes	complemented
12	C₂×C₈×C₂₉	C₂²	1	3	yes	complemented
13	Dic₁₁₆	C₂²	1	1	yes	characteristic, complemented
14	D₂₃₂	C₂²	1	3	yes	complemented
15	D₂₃₂	C₂²	1	6	yes	complemented
16	#90773	C₂²	1	6	yes	complemented
17	C₂²×D₂₉	—	2	6	no	—
18	Q₈×C₂₉	D₄	1	1	yes	characteristic
19	D₄×C₂₉	D₄	1	3	yes	—
20	C₂×C₄×C₂₉	C₂³	1	3	yes	—
21	C₂²⋊D₂₉	—	2	6	no	—
22	D₁₁₆	—	2	6	no	—
23	D₁₁₆	C₂³	1	6	yes	—
24	C₄×D₂₉	—	2	6	no	—
25	Dic₅₈	C₂³	1	2	yes	—
26	C₈×C₂₉	C₂³	1	3	yes	—
27	C₈×C₂₉	C₂³	1	1	yes	characteristic
28	C₂²×C₂₉	C₂×D₄	1	3	yes	—
29	C₂×D₂₉	—	2	6	no	—
30	C₂×D₂₉	—	8	6	no	—
31	C₄×C₂₉	C₂×D₄	1	3	yes	—
32	C₄×C₂₉	C₂⁴	1	1	yes	characteristic
33	Dic₂₉	—	2	2	no	—
34	#576	—	29	1	no	maximal, Sylow
35	C₂×C₂₉	—	2	3	no	—
36	C₂×C₂₉	C₂²×D₄	1	1	yes	characteristic
37	D₂₉	—	4	6	no	—
38	H(5,𝔽₂)	—	29	2	no	—
39	AGL(1,ℤ/8)	—	29	6	no	—
40	#135	—	29	3	no	—
41	C₂×D₈	—	29	3	no	—
42	#131	D₂₉	1	1	yes	characteristic, complemented
43	C₂₉	#576	1	1	yes	characteristic, complemented, Sylow
44	#41	—	29	6	no	—
45	#41	—	58	2	no	—
46	#41	C₂×D₂₉	1	1	yes	characteristic
47	C₂×D₄	—	29	6	no	—
48	C₂×D₄	—	58	6	no	—
49	Q₁₆	—	29	1	no	—
50	SD₁₆	—	29	6	no	—
51	D₈	—	29	3	no	—
52	D₈	—	29	6	no	—
53	M₁₆	C₂×D₂₉	1	3	yes	complemented
54	C₂×C₈	C₂×D₂₉	1	3	yes	complemented
55	C₂³	—	58	6	no	—
56	Q₈	—	29	2	no	—
57	Q₈	D₁₁₆	1	1	yes	characteristic
58	D₄	—	29	6	no	—
59	D₄	—	58	6	no	—
60	D₄	—	58	6	no	—
61	D₄	D₁₁₆	1	3	yes	—
62	C₂×C₄	—	58	6	no	—
63	C₂×C₄	C₂²×D₂₉	1	3	yes	—
64	C₈	C₂²×D₂₉	1	1	yes	characteristic
65	C₈	C₂²×D₂₉	1	3	yes	—
66	C₂²	—	58	6	no	—
67	C₂²	—	232	6	no	—
68	C₂²	C₂×D₁₁₆	1	3	yes	—
69	C₄	—	58	2	no	—
70	C₄	C₂×D₁₁₆	1	3	yes	—
71	C₄	C₂³×D₂₉	1	1	yes	characteristic
72	C₂	—	2	3	no	—
73	C₂	—	116	6	no	—
74	C₂	C₂²×D₁₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₁₁₆
commutator, cosocle	C₄×C₂₉	C₂⁴
Frattini	C₄	C₂³×D₂₉
Fitting	C₂₉×#131	C₂
socle	C₂×C₂₉	C₂²×D₄
hypercenter	#131	D₂₉
hypocenter	C₂₉	#576
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ #41 ◁ #131

Complements

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

N	H ≅ G/N	type
1. #11745364	C₂	semidirect
2. C₂₉×#131	C₂	semidirect
3. #11745270	C₂	semidirect
4. #11745266	C₂	semidirect
5. C₂×D₂₃₂	C₂	semidirect
9. #90805	C₂²	semidirect
10. C₂×D₁₁₆	C₂²	semidirect
11. M₁₆×C₂₉	C₂²	semidirect
12. C₂×C₈×C₂₉	C₂²	semidirect
13. Dic₁₁₆	C₂²	semidirect
14. D₂₃₂	C₂²	semidirect
15. D₂₃₂	C₂²	semidirect
16. #90773	C₂²	semidirect
42. #131	D₂₉	semidirect
43. C₂₉	#576	semidirect
53. M₁₆	C₂×D₂₉	semidirect
54. C₂×C₈	C₂×D₂₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#11745364	2
C₂₉×#131	2
#11745270	2
#11745266	2
C₂×D₂₃₂	2
#576	29