Subgroups — #14271557

Order 1856.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₁₆	C₂	1	2	yes	maximal, complemented
2	C₂×#90773	C₂	1	2	yes	maximal
3	#11745237	C₂	1	1	yes	maximal, characteristic
4	#11745231	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₁₆	C₂²	1	1	yes	characteristic
7	C₂×Dic₅₈	C₂²	1	2	yes	—
8	C₂×Dic₅₈	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₂₉	C₂²	1	2	yes	—
10	C₄²×C₂₉	C₂²	1	1	yes	characteristic
11	#90781	—	2	2	no	—
12	C₄⋊Dic₂₉	—	2	2	no	—
13	Dic₁₁₆	—	2	4	no	—
14	#90773	—	2	4	no	—
15	C₂²×D₂₉	—	2	1	no	—
16	C₂×C₄×C₂₉	D₄	1	2	yes	—
17	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
18	C₂×Dic₂₉	—	2	2	no	—
19	C₂×Dic₂₉	—	2	1	no	—
20	D₁₁₆	—	2	2	no	—
21	Dic₅₈	—	2	2	no	—
22	Dic₅₈	—	2	2	no	—
23	Dic₅₈	—	2	2	no	—
24	C₈×C₂₉	D₄	1	4	yes	—
25	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
26	C₂×D₂₉	—	4	1	no	—
27	C₂×D₂₉	—	4	2	no	—
28	C₄×C₂₉	—	2	2	no	—
29	C₄×C₂₉	C₂×D₄	1	2	yes	—
30	Dic₂₉	—	4	2	no	—
31	Dic₂₉	—	4	1	no	—
32	#497	—	29	1	no	maximal, Sylow
33	C₂×C₂₉	#127	1	1	yes	characteristic
34	C₂×C₂₉	#137	1	2	yes	—
35	D₂₉	—	8	1	no	—
36	C₂×Q₁₆	—	29	2	no	—
37	C₂×SD₁₆	—	29	2	no	—
38	C₄⋊Q₈	—	29	1	no	—
39	#124	—	29	1	no	—
40	#97	D₂₉	1	1	yes	characteristic, complemented
41	C₂₉	#497	1	1	yes	characteristic, complemented, Sylow
42	C₂×Q₈	—	29	1	no	—
43	C₂×Q₈	—	29	2	no	—
44	C₂×D₄	—	29	1	no	—
45	Q₁₆	—	58	4	no	—
46	SD₁₆	—	58	4	no	—
47	C₂×C₈	C₂×D₂₉	1	2	yes	—
48	C₄⋊C₄	—	58	2	no	—
49	C₂²⋊C₄	—	58	2	no	—
50	C₄²	C₂×D₂₉	1	1	yes	characteristic
51	C₂³	—	58	1	no	—
52	Q₈	—	58	2	no	—
53	Q₈	—	58	2	no	—
54	Q₈	—	58	2	no	—
55	D₄	—	58	2	no	—
56	C₂×C₄	—	58	1	no	—
57	C₂×C₄	—	58	2	no	—
58	C₂×C₄	D₁₁₆	1	2	yes	—
59	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
60	C₈	D₁₁₆	1	4	yes	—
61	C₂²	—	116	1	no	—
62	C₂²	—	116	2	no	—
63	C₂²	C₂×D₁₁₆	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	116	1	no	—
66	C₄	—	116	2	no	—
67	C₄	C₂×D₁₁₆	1	2	yes	—
68	C₂	—	232	1	no	—
69	C₂	#11745236	1	1	yes	characteristic
70	C₂	#11745271	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₁₆
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×#97	C₂
socle	C₂²×C₂₉	C₂×D₄
prime radical	C₂×D₁₁₆	C₂²
hypercenter	#97	D₂₉
hypocenter	C₂₉	#497
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₁₁₆	C₂	semidirect
4. #11745231	C₂	semidirect
5. C₂₉×#97	C₂	semidirect
40. #97	D₂₉	semidirect
41. C₂₉	#497	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₁₆	2
C₂×#90773	2
#11745237	2
#11745231	2
C₂₉×#97	2
#497	29