Subgroups — #14272038

Order 1856.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₉⋊M₁₆	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	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
5	#90800	—	2	1	no	—
6	C₂×#6599	—	2	1	no	—
7	#90796	C₄	1	2	yes	—
8	D₂₉⋊C₈	—	2	1	no	—
9	D₂₉⋊C₈	—	2	1	no	—
10	D₂₉⋊C₈	C₄	1	2	yes	—
11	M₁₆×C₂₉	C₄	1	1	yes	characteristic
12	#90777	C₄	1	1	yes	characteristic
13	#90772	—	2	1	no	—
14	C₈×D₂₉	—	2	1	no	—
15	C₂²×D₂₉	Q₈	1	1	yes	characteristic
16	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₂₉	D₄	1	1	yes	characteristic
18	C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
19	C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
20	C₄×D₂₉	D₄	1	1	yes	characteristic
21	C₄×D₂₉	D₄	1	1	yes	characteristic
22	#6599	—	2	2	no	—
23	#6599	—	2	2	no	—
24	C₈×C₂₉	—	2	1	no	—
25	#6597	—	2	1	no	—
26	C₂²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
27	C₂×D₂₉	—	2	2	no	—
28	C₂×D₂₉	C₄⋊C₄	1	1	yes	characteristic
29	C₂×D₂₉	C₄⋊C₄	1	1	yes	characteristic
30	C₄×C₂₉	C₄²	1	1	yes	characteristic
31	C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
32	Dic₂₉	C₂²⋊C₄	1	1	yes	characteristic
33	Dic₂₉	C₂²⋊C₄	1	1	yes	characteristic
34	#341	—	29	1	no	maximal, Sylow
35	C₂×C₂₉	—	2	1	no	—
36	C₂×C₂₉	#95	1	1	yes	characteristic
37	D₂₉	—	2	1	no	—
38	D₂₉	#108	1	2	yes	—
39	C₂×M₁₆	—	29	1	no	—
40	C₂×M₁₆	—	29	1	no	—
41	C₂²×C₈	—	29	1	no	—
42	C₂₉	#341	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₄	—	29	1	no	—
44	M₁₆	—	29	2	no	—
45	M₁₆	—	29	1	no	—
46	M₁₆	—	58	1	no	—
47	M₁₆	—	58	1	no	—
48	M₁₆	#1181	1	1	yes	characteristic
49	C₂×C₈	—	29	2	no	—
50	C₂×C₈	—	58	1	no	—
51	C₂×C₈	—	58	1	no	—
52	C₂×C₈	—	58	1	no	—
53	C₂×C₈	—	58	1	no	—
54	C₂³	—	29	1	no	—
55	C₂×C₄	—	29	1	no	—
56	C₂×C₄	—	29	1	no	—
57	C₂×C₄	—	29	1	no	—
58	C₂×C₄	—	29	1	no	—
59	C₂×C₄	—	29	1	no	—
60	C₂×C₄	C₂×#1181	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	58	2	no	—
63	C₈	—	58	2	no	—
64	C₈	—	58	1	no	—
65	C₂²	—	29	1	no	—
66	C₂²	—	29	1	no	—
67	C₂²	—	58	2	no	—
68	C₂²	C₄⋊#1181	1	1	yes	characteristic
69	C₄	—	29	1	no	—
70	C₄	—	29	1	no	—
71	C₄	C₄×#1181	1	1	yes	characteristic
72	C₄	C₂²⋊#1181	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	—	29	2	no	—
75	C₂	—	58	1	no	—
76	C₂	(C₂×#1181)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#1181
commutator	C₄×C₂₉	C₄²
Frattini	C₂×C₄	C₂×#1181
Fitting	M₁₆×C₂₉	C₄
socle	C₂×C₂₉	#95
prime radical	C₂²×D₂₉	Q₈
cosocle	C₂×C₄×D₂₉	C₂²
hypercenter	M₁₆	#1181
hypocenter	C₂₉	#341
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
42. C₂₉	#341	semidirect

Maximal subgroups

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

subgroup	index
D₂₉⋊M₁₆	2
C₂×D₂₉⋊C₈	2
M₁₆×D₂₉	2
#341	29