Subgroups — #14271595

Order 1856.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745266	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₂₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745148	C₂	1	2	yes	maximal, complemented
5	D₄₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	#90805	—	2	2	no	—
7	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
8	Dic₁₁₆	C₂²	1	2	yes	—
9	D₂₃₂	C₂²	1	2	yes	—
10	#90773	—	2	2	no	—
11	C₁₆×C₂₉	C₂²	1	1	yes	characteristic
12	C₁₆×C₂₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
14	C₂²⋊D₂₉	—	4	2	no	—
15	D₁₁₆	—	2	2	no	—
16	C₄×D₂₉	—	4	2	no	—
17	Dic₅₈	—	2	2	no	—
18	C₈×C₂₉	D₄	1	1	yes	characteristic
19	C₈×C₂₉	C₂³	1	1	yes	characteristic
20	C₂²×C₂₉	D₈	1	1	yes	characteristic
21	C₂×D₂₉	—	4	2	no	—
22	C₄×C₂₉	D₈	1	1	yes	characteristic
23	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
24	Dic₂₉	—	4	2	no	—
25	#508	—	29	1	no	maximal, Sylow
26	C₂×C₂₉	—	2	1	no	—
27	C₂×C₂₉	C₂×D₈	1	1	yes	characteristic
28	D₂₉	—	8	2	no	—
29	#135	—	29	2	no	—
30	Q₃₂	—	29	1	no	—
31	SD₃₂	—	29	2	no	—
32	D₁₆	—	29	1	no	—
33	C₂×C₁₆	D₂₉	1	1	yes	characteristic, complemented
34	C₂₉	#508	1	1	yes	characteristic, complemented, Sylow
35	#41	—	58	2	no	—
36	Q₁₆	—	29	2	no	—
37	SD₁₆	—	58	2	no	—
38	D₈	—	29	2	no	—
39	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
40	C₁₆	C₂×D₂₉	1	1	yes	characteristic
41	C₁₆	C₂×D₂₉	1	1	yes	characteristic
42	Q₈	—	58	2	no	—
43	D₄	—	58	2	no	—
44	D₄	—	116	2	no	—
45	C₂×C₄	—	116	2	no	—
46	C₂×C₄	D₁₁₆	1	1	yes	characteristic
47	C₈	D₁₁₆	1	1	yes	characteristic
48	C₈	C₂²×D₂₉	1	1	yes	characteristic
49	C₂²	—	116	2	no	—
50	C₂²	D₂₃₂	1	1	yes	characteristic
51	C₄	—	116	2	no	—
52	C₄	D₂₃₂	1	1	yes	characteristic
53	C₄	C₂×D₁₁₆	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	232	2	no	—
56	C₂	C₂×D₂₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₂₃₂
commutator, cosocle	C₈×C₂₉	C₂³
Frattini	C₈	C₂²×D₂₉
Fitting	C₂×C₁₆×C₂₉	C₂
socle	C₂×C₂₉	C₂×D₈
hypercenter	C₂×C₁₆	D₂₉
hypocenter	C₂₉	#508
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. #11745266	C₂	semidirect
2. C₂×C₁₆×C₂₉	C₂	semidirect
3. Dic₂₃₂	C₂	semidirect
4. #11745148	C₂	semidirect
5. D₄₆₄	C₂	semidirect
33. C₂×C₁₆	D₂₉	semidirect
34. C₂₉	#508	semidirect

Maximal subgroups

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

subgroup	index
#11745266	2
C₂×C₁₆×C₂₉	2
Dic₂₃₂	2
#11745148	2
D₄₆₄	2
#508	29