Subgroups — #14271459

Order 1856.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745231	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₅₈	C₂	1	1	yes	maximal, characteristic
3	C₂₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#11745166	C₂	1	2	yes	maximal
5	#11745164	C₂	1	2	yes	maximal
6	C₂×Dic₅₈	—	2	1	no	—
7	C₂×Dic₅₈	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₂₉	C₂²	1	2	yes	—
9	C₄²×C₂₉	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₂₉	—	2	1	no	—
11	C₄⋊Dic₂₉	C₂²	1	2	yes	—
12	C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
13	#90779	—	2	1	no	—
14	C₄×Dic₂₉	—	2	1	no	—
15	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
16	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
17	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
18	C₂×Dic₂₉	—	2	1	no	—
19	C₂×Dic₂₉	—	2	1	no	—
20	C₂×Dic₂₉	—	2	2	no	—
21	Dic₅₈	—	2	1	no	—
22	Dic₅₈	—	4	2	no	—
23	Dic₅₈	Q₈	1	2	yes	complemented
24	C₈×C₂₉	—	2	2	no	—
25	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
26	C₄×C₂₉	—	2	1	no	—
27	C₄×C₂₉	Q₁₆	1	2	yes	—
28	C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
29	C₄×C₂₉	#41	1	1	yes	characteristic
30	Dic₂₉	—	2	2	no	—
31	Dic₂₉	—	4	2	no	—
32	Dic₂₉	—	4	1	no	—
33	#477	—	29	1	no	maximal, Sylow
34	C₂×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
35	C₂×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
36	C₂×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
37	C₄⋊Q₈	—	29	1	no	—
38	C₄×Q₈	—	29	1	no	—
39	#107	—	29	2	no	—
40	C₄⋊C₈	D₂₉	1	1	yes	characteristic
41	#103	—	29	2	no	—
42	C₂₉	#477	1	1	yes	characteristic, complemented, Sylow
43	C₂×Q₈	—	29	1	no	—
44	C₂×Q₈	—	58	1	no	—
45	C₂×C₈	C₂×D₂₉	1	2	yes	—
46	C₄⋊C₄	—	29	2	no	—
47	C₄⋊C₄	—	29	1	no	—
48	C₄⋊C₄	—	58	1	no	—
49	C₄⋊C₄	—	58	1	no	—
50	C₄²	—	58	1	no	—
51	C₄²	C₂×D₂₉	1	1	yes	characteristic
52	Q₈	—	29	2	no	—
53	Q₈	—	58	1	no	—
54	Q₈	—	116	2	no	—
55	C₂×C₄	—	58	1	no	—
56	C₂×C₄	—	58	1	no	—
57	C₂×C₄	—	58	2	no	—
58	C₂×C₄	D₁₁₆	1	1	yes	characteristic
59	C₂×C₄	D₁₁₆	1	1	yes	characteristic
60	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
61	C₈	—	2	2	no	—
62	C₂²	C₂×D₁₁₆	1	1	yes	characteristic
63	C₄	—	2	1	no	—
64	C₄	—	58	2	no	—
65	C₄	—	116	2	no	—
66	C₄	—	116	1	no	—
67	C₄	Dic₁₁₆	1	2	yes	—
68	C₄	#90807	1	1	yes	characteristic
69	C₄	Q₈×D₂₉	1	1	yes	characteristic
70	C₂	#11745259	1	1	yes	characteristic
71	C₂	C₂×Dic₁₁₆	1	1	yes	characteristic
72	C₂	#11745270	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₁₆
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×C₄⋊C₈	C₂
socle, prime radical	C₂²×C₂₉	C₂×D₄
hypercenter	C₄⋊C₈	D₂₉
hypocenter	C₂₉	#477
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
23. Dic₅₈	Q₈	semidirect
42. C₂₉	#477	semidirect

Maximal subgroups

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

subgroup	index
#11745231	2
C₄×Dic₅₈	2
C₂₉×C₄⋊C₈	2
#11745166	2
#11745164	2
#477	29