Subgroups — #14272129

Order 1856.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745345	C₂	1	1	yes	maximal, characteristic
2	C₂×D₂₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	M₁₆×D₂₉	C₂	1	1	yes	maximal, characteristic
4	#11745208	C₂	1	2	yes	maximal, complemented
5	C₈×#1181	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
7	C₂²⋊#1181	C₄	1	2	yes	—
8	C₂×#6599	C₄	1	2	yes	complemented
9	C₄⋊#1181	C₄	1	2	yes	—
10	C₄×#1181	C₂²	1	2	yes	—
11	D₂₉⋊C₈	C₄	1	2	yes	complemented
12	D₂₉⋊C₈	C₂²	1	1	yes	characteristic
13	D₂₉⋊C₈	C₂²	1	1	yes	characteristic
14	M₁₆×C₂₉	C₄	1	1	yes	characteristic, complemented
15	#90777	C₄	1	1	yes	characteristic, complemented
16	#90772	C₄	1	2	yes	complemented
17	C₈×D₂₉	C₂²	1	2	yes	—
18	C₂²×D₂₉	C₂×C₄	1	1	yes	characteristic
19	C₂×#1181	C₂×C₄	1	4	yes	—
20	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₂₉	C₂×C₄	1	1	yes	characteristic
22	C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
23	C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
24	C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
25	C₄×D₂₉	C₂³	1	1	yes	characteristic
26	#6599	C₂×C₄	1	2	yes	—
27	#6599	C₂×C₄	1	2	yes	—
28	C₈×C₂₉	C₂×C₄	1	2	yes	—
29	#6597	C₂×C₄	1	2	yes	—
30	C₂²×C₂₉	C₄²	1	1	yes	characteristic
31	C₂×D₂₉	—	2	2	no	—
32	C₂×D₂₉	C₄²	1	1	yes	characteristic
33	C₂×D₂₉	C₂²×C₄	1	1	yes	characteristic
34	#1181	—	2	4	no	—
35	C₄×C₂₉	C₄²	1	1	yes	characteristic
36	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
37	Dic₂₉	C₄²	1	1	yes	characteristic
38	Dic₂₉	C₂²×C₄	1	1	yes	characteristic
39	#405	—	29	1	no	maximal, Sylow
40	C₂×C₂₉	—	2	1	no	—
41	C₂×C₂₉	C₂×C₄²	1	1	yes	characteristic
42	D₂₉	—	2	1	no	—
43	D₂₉	#131	1	2	yes	—
44	C₂×M₁₆	—	29	1	no	—
45	C₂²×C₈	—	29	1	no	—
46	#117	—	29	1	no	—
47	#97	—	29	2	no	—
48	C₄×C₈	—	29	2	no	—
49	C₂₉	#405	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₄	—	29	1	no	—
51	M₁₆	—	29	1	no	—
52	M₁₆	—	29	2	no	—
53	M₁₆	#1181	1	1	yes	characteristic, complemented
54	C₂×C₈	—	29	1	no	—
55	C₂×C₈	—	29	1	no	—
56	C₂×C₈	—	29	2	no	—
57	C₂×C₈	—	29	2	no	—
58	C₂×C₈	—	29	2	no	—
59	C₄⋊C₄	—	29	2	no	—
60	C₂²⋊C₄	—	29	2	no	—
61	C₄²	—	29	2	no	—
62	C₂³	—	29	1	no	—
63	C₂×C₄	—	29	1	no	—
64	C₂×C₄	—	29	1	no	—
65	C₂×C₄	—	29	1	no	—
66	C₂×C₄	—	29	1	no	—
67	C₂×C₄	—	29	1	no	—
68	C₂×C₄	—	29	4	no	—
69	C₂×C₄	C₂×#1181	1	1	yes	characteristic
70	C₈	—	29	2	no	—
71	C₈	—	29	2	no	—
72	C₈	—	29	2	no	—
73	C₈	C₂×#1181	1	2	yes	—
74	C₂²	—	29	1	no	—
75	C₂²	—	29	1	no	—
76	C₂²	—	58	2	no	—
77	C₂²	C₄×#1181	1	1	yes	characteristic
78	C₄	—	29	1	no	—
79	C₄	—	29	1	no	—
80	C₄	—	58	4	no	—
81	C₄	C₄×#1181	1	1	yes	characteristic
82	C₄	C₂²×#1181	1	1	yes	characteristic
83	C₂	—	2	1	no	—
84	C₂	—	29	2	no	—
85	C₂	—	58	1	no	—
86	C₂	C₂×C₄×#1181	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×#1181
commutator, socle	C₂×C₂₉	C₂×C₄²
Fitting	M₁₆×C₂₉	C₄
prime radical	C₂²×D₂₉	C₂×C₄
cosocle	C₄×D₂₉	C₂³
hypercenter	M₁₆	#1181
hypocenter	C₂₉	#405
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
4. #11745208	C₂	semidirect
5. C₈×#1181	C₂	semidirect
8. C₂×#6599	C₄	semidirect
11. D₂₉⋊C₈	C₄	semidirect
14. M₁₆×C₂₉	C₄	semidirect
15. #90777	C₄	semidirect
16. #90772	C₄	semidirect
49. C₂₉	#405	semidirect
53. M₁₆	#1181	semidirect

Maximal subgroups

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

subgroup	index
#11745345	2
C₂×D₂₉⋊C₈	2
M₁₆×D₂₉	2
#11745208	2
C₈×#1181	2
#405	29