Subgroups — #14272178

Order 1856.

102 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×#90796	C₂	1	1	yes	maximal, characteristic
3	M₁₆×D₂₉	C₂	1	1	yes	maximal, characteristic
4	#11745212	C₂	1	2	yes	maximal, complemented
5	#11745211	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
7	#90800	—	2	1	no	—
8	C₂×#6599	—	2	1	no	—
9	#90796	—	2	1	no	—
10	#90796	C₂²	1	2	yes	—
11	#90796	C₂²	1	1	yes	characteristic
12	#90796	C₂²	1	1	yes	characteristic
13	D₂₉⋊C₈	—	2	1	no	—
14	M₁₆×C₂₉	C₄	1	1	yes	characteristic
15	#90777	C₄	1	1	yes	characteristic
16	#90772	C₄	1	2	yes	—
17	C₈×D₂₉	C₂²	1	2	yes	—
18	C₂²×D₂₉	Q₈	1	1	yes	characteristic
19	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₂₉	D₄	1	1	yes	characteristic
21	C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
22	C₄×D₂₉	D₄	1	1	yes	characteristic
23	C₄×D₂₉	Q₈	1	1	yes	characteristic
24	C₄×D₂₉	C₂³	1	1	yes	characteristic
25	#6599	—	2	1	no	—
26	#6599	—	2	1	no	—
27	#6599	—	2	2	no	—
28	C₈×C₂₉	C₂×C₄	1	2	yes	—
29	#6597	C₂×C₄	1	2	yes	—
30	C₂²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
31	C₂×D₂₉	—	4	1	no	—
32	C₂×D₂₉	C₄⋊C₄	1	1	yes	characteristic
33	C₂×D₂₉	C₂×Q₈	1	1	yes	characteristic
34	C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
35	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
36	Dic₂₉	C₄⋊C₄	1	1	yes	characteristic
37	Dic₂₉	C₂×D₄	1	1	yes	characteristic
38	#430	—	29	1	no	maximal, Sylow
39	C₂×C₂₉	—	2	1	no	—
40	C₂×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
41	D₂₉	—	2	1	no	—
42	D₂₉	—	2	1	no	—
43	C₂×M₁₆	—	29	1	no	—
44	C₂×M₁₆	—	29	1	no	—
45	C₂×M₁₆	—	29	1	no	—
46	#108	—	29	2	no	—
47	#108	—	29	2	no	—
48	C₂₉	#430	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₄	—	29	1	no	—
50	M₁₆	—	29	1	no	—
51	M₁₆	—	29	2	no	—
52	M₁₆	—	29	1	no	—
53	M₁₆	—	29	2	no	—
54	M₁₆	—	29	1	no	—
55	M₁₆	—	58	1	no	—
56	M₁₆	—	58	1	no	—
57	M₁₆	#1181	1	1	yes	characteristic
58	C₂×C₈	—	29	2	no	—
59	C₂×C₈	—	58	1	no	—
60	C₂×C₈	—	58	1	no	—
61	C₂³	—	29	1	no	—
62	C₂×C₄	—	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	C₂×#1181	1	1	yes	characteristic
68	C₈	—	29	2	no	—
69	C₈	—	58	1	no	—
70	C₈	—	58	1	no	—
71	C₈	—	58	2	no	—
72	C₈	C₂×#1181	1	2	yes	—
73	C₂²	—	29	1	no	—
74	C₂²	—	29	1	no	—
75	C₂²	—	116	1	no	—
76	C₂²	C₄⋊#1181	1	1	yes	characteristic
77	C₄	—	29	1	no	—
78	C₄	—	29	1	no	—
79	C₄	C₄⋊#1181	1	1	yes	characteristic
80	C₄	C₂²×#1181	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	—	58	1	no	—
83	C₂	—	58	1	no	—
84	C₂	C₂×C₄⋊#1181	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₄⋊#1181
commutator	C₄×C₂₉	C₂²×C₄
Frattini	C₄	C₂²×#1181
Fitting	M₁₆×C₂₉	C₄
socle	C₂×C₂₉	C₂×C₄⋊C₄
prime radical	C₂²×D₂₉	Q₈
cosocle	C₄×D₂₉	C₂³
hypercenter	M₁₆	#1181
hypocenter	C₂₉	#430
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
4. #11745212	C₂	semidirect
5. #11745211	C₂	semidirect
48. C₂₉	#430	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×#90796	2
M₁₆×D₂₉	2
#11745212	2
#11745211	2
#430	29