Subgroups — #14271510

Order 1856.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745236	C₂	1	1	yes	maximal, characteristic
2	#11745231	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745169	C₂	1	4	yes	maximal, complemented
5	C₂×D₁₁₆	—	2	1	no	—
6	C₂×D₁₁₆	—	2	1	no	—
7	C₂×D₁₁₆	C₂²	1	2	yes	—
8	C₂×Dic₅₈	—	2	1	no	—
9	C₂×C₈×C₂₉	C₂²	1	2	yes	—
10	C₄²×C₂₉	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₂₉	—	2	1	no	—
12	C₄⋊Dic₂₉	C₂²	1	2	yes	—
13	C₂²×D₂₉	—	2	2	no	—
14	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
15	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
16	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
17	C₂×Dic₂₉	—	2	2	no	—
18	D₁₁₆	—	2	4	no	—
19	D₁₁₆	—	4	2	no	—
20	D₁₁₆	—	4	2	no	—
21	Dic₅₈	—	4	2	no	—
22	C₈×C₂₉	—	2	2	no	—
23	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
24	C₂×D₂₉	—	4	2	no	—
25	C₂×D₂₉	—	4	2	no	—
26	C₂×D₂₉	—	4	2	no	—
27	C₄×C₂₉	D₈	1	2	yes	—
28	C₄×C₂₉	SD₁₆	1	2	yes	—
29	C₄×C₂₉	#41	1	2	yes	—
30	Dic₂₉	—	4	2	no	—
31	#486	—	29	1	no	maximal, Sylow
32	C₂×C₂₉	#124	1	1	yes	characteristic
33	C₂×C₂₉	C₂×D₈	1	1	yes	characteristic
34	C₂×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
35	D₂₉	—	8	2	no	—
36	C₄⋊Q₈	—	29	1	no	—
37	#127	—	29	1	no	—
38	#102	—	29	4	no	—
39	C₄×C₈	D₂₉	1	1	yes	characteristic, complemented
40	C₂₉	#486	1	1	yes	characteristic, complemented, Sylow
41	C₂×Q₈	—	58	1	no	—
42	C₂×D₄	—	29	2	no	—
43	C₂×D₄	—	58	1	no	—
44	C₂×D₄	—	58	1	no	—
45	C₂×C₈	C₂×D₂₉	1	2	yes	—
46	C₄⋊C₄	—	29	2	no	—
47	C₄⋊C₄	—	58	1	no	—
48	C₄²	C₂×D₂₉	1	1	yes	characteristic
49	C₂³	—	58	2	no	—
50	Q₈	—	116	2	no	—
51	D₄	—	58	4	no	—
52	D₄	—	116	2	no	—
53	D₄	—	116	2	no	—
54	C₂×C₄	—	58	2	no	—
55	C₂×C₄	D₁₁₆	1	1	yes	characteristic
56	C₂×C₄	D₁₁₆	1	1	yes	characteristic
57	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
58	C₈	—	2	2	no	—
59	C₂²	—	116	2	no	—
60	C₂²	—	116	2	no	—
61	C₂²	—	116	2	no	—
62	C₂²	C₂×D₁₁₆	1	1	yes	characteristic
63	C₄	—	116	2	no	—
64	C₄	#90773	1	2	yes	—
65	C₄	D₂₃₂	1	2	yes	—
66	C₄	#90805	1	2	yes	—
67	C₂	—	232	2	no	—
68	C₂	#11745237	1	1	yes	characteristic
69	C₂	C₂×#90773	1	1	yes	characteristic
70	C₂	C₂×D₂₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₁₆
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₄×C₈×C₂₉	C₂
socle	C₂²×C₂₉	C₂×D₄
prime radical	#11745236	C₂
hypercenter	C₄×C₈	D₂₉
hypocenter	C₂₉	#486
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
2. #11745231	C₂	semidirect
3. C₄×C₈×C₂₉	C₂	semidirect
4. #11745169	C₂	semidirect
39. C₄×C₈	D₂₉	semidirect
40. C₂₉	#486	semidirect

Maximal subgroups

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

subgroup	index
#11745236	2
#11745231	2
C₄×C₈×C₂₉	2
#11745169	2
#486	29