Subgroups — #14271275

Order 1856.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈×C₂₉	C₂	1	1	yes	maximal, characteristic
2	D₄×Dic₂₉	C₂	1	2	yes	maximal, complemented
3	#11745180	C₂	1	2	yes	maximal, complemented
4	#11745165	C₂	1	1	yes	maximal, characteristic, complemented
5	#11745163	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×C₂₉	C₂²	1	2	yes	—
7	C₂²×Dic₂₉	—	2	2	no	—
8	D₈×C₂₉	C₄	1	4	yes	complemented
9	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
10	C₂²⋊Dic₂₉	—	2	2	no	—
11	C₄⋊Dic₂₉	C₂²	1	2	yes	—
12	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
13	C₂×#6597	C₂²	1	1	yes	characteristic
14	C₂³×C₂₉	—	2	2	no	—
15	D₄×C₂₉	—	2	2	no	—
16	D₄×C₂₉	C₂×C₄	1	4	yes	complemented
17	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
18	C₂×Dic₂₉	—	2	2	no	—
19	C₂×Dic₂₉	—	4	4	no	—
20	C₂×Dic₂₉	D₄	1	2	yes	—
21	C₈×C₂₉	C₂×C₄	1	2	yes	complemented
22	#6597	—	2	1	no	—
23	C₂²×C₂₉	—	2	4	no	—
24	C₂²×C₂₉	—	4	2	no	—
25	C₂²×C₂₉	—	4	2	no	—
26	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
27	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
28	C₄×C₂₉	#41	1	1	yes	characteristic
29	Dic₂₉	—	2	2	no	—
30	Dic₂₉	—	4	2	no	—
31	#442	—	29	1	no	maximal, Sylow
32	C₂×C₂₉	—	4	4	no	—
33	C₂×C₂₉	C₄×D₄	1	1	yes	characteristic
34	C₂×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
35	C₂×D₈	D₂₉	1	1	yes	characteristic
36	C₄×D₄	—	29	2	no	—
37	#106	—	29	1	no	—
38	#102	—	29	2	no	—
39	#97	—	29	1	no	—
40	C₂₉	#442	1	1	yes	characteristic, complemented, Sylow
41	C₂×D₄	C₂×D₂₉	1	2	yes	—
42	C₂²×C₄	—	58	2	no	—
43	D₈	Dic₂₉	1	4	yes	complemented
44	C₂×C₈	—	29	1	no	—
45	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
46	C₄⋊C₄	—	29	2	no	—
47	C₂²⋊C₄	—	58	2	no	—
48	C₄²	—	29	1	no	—
49	C₂³	—	2	2	no	—
50	D₄	—	2	2	no	—
51	D₄	C₂×Dic₂₉	1	4	yes	complemented
52	C₂×C₄	—	29	2	no	—
53	C₂×C₄	—	58	2	no	—
54	C₂×C₄	—	116	4	no	—
55	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
56	C₈	—	58	1	no	—
57	C₈	C₂×Dic₂₉	1	2	yes	complemented
58	C₂²	—	2	4	no	—
59	C₂²	—	4	2	no	—
60	C₂²	—	4	2	no	—
61	C₂²	D₄×D₂₉	1	1	yes	characteristic
62	C₄	—	58	2	no	—
63	C₄	—	116	2	no	—
64	C₄	#90807	1	1	yes	characteristic
65	C₄	C₂²×Dic₂₉	1	1	yes	characteristic
66	C₂	—	4	4	no	—
67	C₂	#11745273	1	2	yes	—
68	C₂	D₄×Dic₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₉
commutator	C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₉
Fitting, prime radical	C₂×D₈×C₂₉	C₂
socle	C₂²×C₂₉	C₂×D₄
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	C₂×D₈	D₂₉
hypocenter	C₂₉	#442
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
2. D₄×Dic₂₉	C₂	semidirect
3. #11745180	C₂	semidirect
4. #11745165	C₂	semidirect
5. #11745163	C₂	semidirect
8. D₈×C₂₉	C₄	semidirect
16. D₄×C₂₉	C₂×C₄	semidirect
21. C₈×C₂₉	C₂×C₄	semidirect
40. C₂₉	#442	semidirect
43. D₈	Dic₂₉	semidirect
51. D₄	C₂×Dic₂₉	semidirect
57. C₈	C₂×Dic₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₈×C₂₉	2
D₄×Dic₂₉	2
#11745180	2
#11745165	2
#11745163	2
#442	29