Subgroups — #14270920

Order 1856.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
2	#11745288	C₂	1	2	yes	maximal
3	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
4	M₁₆×C₂₉	—	2	2	no	—
5	C₂×C₈×C₂₉	C₄	1	2	yes	complemented
6	C₂²⋊Dic₂₉	—	2	2	no	—
7	C₄⋊Dic₂₉	—	2	2	no	—
8	C₄×Dic₂₉	C₄	1	4	yes	complemented
9	C₂³×C₂₉	D₄	1	1	yes	characteristic
10	C₂×C₄×C₂₉	C₂×C₄	1	2	yes	—
11	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₂₉	D₄	1	2	yes	—
13	C₂×C₄×C₂₉	Q₈	1	1	yes	characteristic
14	C₂×Dic₂₉	—	2	4	no	—
15	C₈×C₂₉	—	2	2	no	—
16	C₂²×C₂₉	—	4	1	no	—
17	C₂²×C₂₉	C₂²⋊C₄	1	2	yes	—
18	C₂²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
19	C₄×C₂₉	C₄²	1	1	yes	characteristic
20	C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₂₉	C₄⋊C₄	1	2	yes	—
22	Dic₂₉	—	4	4	no	—
23	H(3,ℤ/4)	—	29	1	no	maximal, Sylow
24	C₂×C₂₉	—	2	2	no	—
25	C₂×C₂₉	—	2	1	no	—
26	C₂×C₂₉	#95	1	1	yes	characteristic
27	C₂×M₁₆	D₂₉	1	1	yes	characteristic
28	#117	—	29	2	no	—
29	C₂₉	H(3,ℤ/4)	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
31	M₁₆	—	2	2	no	—
32	C₂×C₈	Dic₂₉	1	2	yes	complemented
33	C₄⋊C₄	—	58	2	no	—
34	C₂²⋊C₄	—	58	2	no	—
35	C₄²	—	29	4	no	—
36	C₂³	D₁₁₆	1	1	yes	characteristic
37	C₂×C₄	—	58	4	no	—
38	C₂×C₄	Dic₅₈	1	1	yes	characteristic
39	C₂×C₄	C₄×D₂₉	1	2	yes	—
40	C₂×C₄	C₂×Dic₂₉	1	1	yes	characteristic
41	C₂×C₄	C₂²⋊D₂₉	1	2	yes	—
42	C₈	—	2	2	no	—
43	C₂²	—	4	1	no	—
44	C₂²	C₄⋊Dic₂₉	1	1	yes	characteristic
45	C₂²	#90781	1	2	yes	—
46	C₄	—	116	4	no	—
47	C₄	C₄×Dic₂₉	1	1	yes	characteristic
48	C₄	#90779	1	2	yes	—
49	C₄	C₂²⋊Dic₂₉	1	1	yes	characteristic
50	C₂	—	2	2	no	—
51	C₂	—	2	1	no	—
52	C₂	#11745179	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×Dic₂₉
commutator	C₄×C₂₉	C₄²
Frattini	C₂²×C₄	C₂×D₂₉
Fitting	C₂×M₁₆×C₂₉	C₂
socle	C₂×C₂₉	#95
prime radical	C₂³×C₂₉	D₄
cosocle	C₂²×C₄×C₂₉	C₂²
hypercenter	C₂×M₁₆	D₂₉
hypocenter	C₂₉	H(3,ℤ/4)
LCS	G ▷ C₄×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
5. C₂×C₈×C₂₉	C₄	semidirect
8. C₄×Dic₂₉	C₄	semidirect
29. C₂₉	H(3,ℤ/4)	semidirect
32. C₂×C₈	Dic₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×C₂₉	2
#11745288	2
H(3,ℤ/4)	29