Subgroups — #14271560

Order 1856.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745250	C₂	1	2	yes	maximal
2	C₂₉×#106	C₂	1	1	yes	maximal, characteristic
3	#11745165	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₂₉	C₂	1	1	yes	maximal, characteristic
5	#11745156	C₂	1	2	yes	maximal
6	C₂×Dic₅₈	—	2	2	no	—
7	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
8	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
9	C₄⋊Dic₂₉	C₂²	1	2	yes	—
10	#90779	—	2	2	no	—
11	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
12	C₂×#6597	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₂₉	—	2	2	no	—
14	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
15	C₂×Dic₂₉	—	2	2	no	—
16	C₂×Dic₂₉	D₄	1	2	yes	—
17	Dic₅₈	—	4	4	no	—
18	C₈×C₂₉	Q₈	1	2	yes	complemented
19	#6597	Q₈	1	2	yes	complemented
20	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
21	C₄×C₂₉	—	4	2	no	—
22	C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
24	Dic₂₉	—	4	2	no	—
25	Dic₂₉	SD₁₆	1	4	yes	—
26	#498	—	29	1	no	maximal, Sylow
27	C₂×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
28	C₂×C₂₉	C₂×SD₁₆	1	2	yes	—
29	C₄⋊Q₈	—	29	2	no	—
30	#106	—	29	1	no	—
31	#106	—	29	2	no	—
32	#106	D₂₉	1	1	yes	characteristic
33	C₄×C₈	—	29	1	no	—
34	C₂₉	#498	1	1	yes	characteristic, complemented, Sylow
35	C₂×Q₈	—	58	2	no	—
36	C₂×C₈	—	29	1	no	—
37	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
38	C₄⋊C₄	—	29	2	no	—
39	C₄⋊C₄	—	58	2	no	—
40	C₄⋊C₄	C₂×D₂₉	1	2	yes	—
41	C₄²	—	29	1	no	—
42	Q₈	—	116	4	no	—
43	C₂×C₄	—	2	2	no	—
44	C₂×C₄	—	29	2	no	—
45	C₂×C₄	—	58	2	no	—
46	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
47	C₈	—	29	2	no	—
48	C₈	Dic₅₈	1	2	yes	complemented
49	C₂²	D₄×D₂₉	1	1	yes	characteristic
50	C₄	—	4	2	no	—
51	C₄	—	29	4	no	—
52	C₄	—	116	2	no	—
53	C₄	C₂×Dic₅₈	1	1	yes	characteristic
54	C₄	Q₈×D₂₉	1	1	yes	characteristic
55	C₂	#11745250	1	1	yes	characteristic
56	C₂	SD₁₆×D₂₉	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₂₉
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×#106	C₂
socle, prime radical	C₂²×C₂₉	C₂×D₄
hypercenter	#106	D₂₉
hypocenter	C₂₉	#498
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
18. C₈×C₂₉	Q₈	semidirect
19. #6597	Q₈	semidirect
34. C₂₉	#498	semidirect
48. C₈	Dic₅₈	semidirect

Maximal subgroups

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

subgroup	index
#11745250	2
C₂₉×#106	2
#11745165	2
C₈×Dic₂₉	2
#11745156	2
#498	29