Subgroups — #14270974

Order 1856.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745266	C₂	1	1	yes	maximal, characteristic
2	C₂₉×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#11745165	C₂	1	1	yes	maximal, characteristic, complemented
4	#90805	—	2	1	no	—
5	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	C₄⋊Dic₂₉	—	2	1	no	—
7	Dic₁₁₆	C₄	1	1	yes	characteristic, complemented
8	D₂₃₂	C₄	1	1	yes	characteristic, complemented
9	#90773	—	2	1	no	—
10	C₁₆×C₂₉	—	2	1	no	—
11	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
12	C₂²⋊D₂₉	—	4	1	no	—
13	C₂×Dic₂₉	—	4	1	no	—
14	D₁₁₆	—	2	1	no	—
15	C₄×D₂₉	—	4	1	no	—
16	Dic₅₈	—	2	1	no	—
17	C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₈×C₂₉	D₄	1	1	yes	characteristic
19	C₂²×C₂₉	D₈	1	1	yes	characteristic
20	C₂×D₂₉	—	4	1	no	—
21	C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₂₉	SD₁₆	1	1	yes	characteristic
23	Dic₂₉	—	4	1	no	—
24	Dic₂₉	—	8	1	no	—
25	#360	—	29	1	no	maximal, Sylow
26	C₂×C₂₉	—	2	1	no	—
27	C₂×C₂₉	#102	1	1	yes	characteristic
28	D₂₉	—	8	1	no	—
29	#135	—	29	1	no	—
30	M₃₂	D₂₉	1	1	yes	characteristic, complemented
31	#106	—	29	1	no	—
32	C₂₉	#360	1	1	yes	characteristic, complemented, Sylow
33	#41	—	58	1	no	—
34	Q₁₆	—	29	1	no	—
35	SD₁₆	—	58	1	no	—
36	D₈	—	29	1	no	—
37	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
38	C₄⋊C₄	—	58	1	no	—
39	C₁₆	—	2	1	no	—
40	Q₈	—	58	1	no	—
41	D₄	—	58	1	no	—
42	D₄	—	116	1	no	—
43	C₂×C₄	—	116	1	no	—
44	C₂×C₄	—	116	1	no	—
45	C₂×C₄	D₁₁₆	1	1	yes	characteristic
46	C₈	C₄×D₂₉	1	1	yes	characteristic
47	C₈	C₂²⋊D₂₉	1	1	yes	characteristic
48	C₂²	—	116	1	no	—
49	C₂²	D₂₃₂	1	1	yes	characteristic
50	C₄	—	116	1	no	—
51	C₄	—	232	1	no	—
52	C₄	#90773	1	1	yes	characteristic
53	C₄	#90781	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	232	1	no	—
56	C₂	#11745169	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11745169
commutator	C₈×C₂₉	C₂×C₄
Frattini	C₂×C₈	C₂×D₂₉
Fitting	C₂₉×M₃₂	C₂
socle	C₂×C₂₉	#102
prime radical	#11745266	C₂
cosocle	C₂×C₈×C₂₉	C₂²
hypercenter	M₃₂	D₂₉
hypocenter	C₂₉	#360
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. C₂₉×M₃₂	C₂	semidirect
3. #11745165	C₂	semidirect
7. Dic₁₁₆	C₄	semidirect
8. D₂₃₂	C₄	semidirect
30. M₃₂	D₂₉	semidirect
32. C₂₉	#360	semidirect

Maximal subgroups

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

subgroup	index
#11745266	2
C₂₉×M₃₂	2
#11745165	2
#360	29