Subgroups — #16834644

Order 3712.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₉⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#14272091	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271596	C₂	1	1	yes	maximal, characteristic
4	#11745281	—	2	1	no	—
5	#11745212	—	2	1	no	—
6	C₂₉×Q₃₂	C₄	1	1	yes	characteristic
7	#11745176	—	2	1	no	—
8	D₄₆₄	C₄	1	1	yes	characteristic
9	C₁₆×D₂₉	C₂²	1	1	yes	characteristic
10	#11745144	—	2	1	no	—
11	#90809	—	4	1	no	—
12	#90796	—	4	1	no	—
13	Q₁₆×C₂₉	—	2	1	no	—
14	#90784	—	4	1	no	—
15	D₂₃₂	—	2	1	no	—
16	C₈×D₂₉	D₄	1	1	yes	characteristic
17	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
18	#90768	D₄	1	1	yes	characteristic
19	Q₈×C₂₉	—	4	1	no	—
20	D₁₁₆	—	4	1	no	—
21	D₁₁₆	—	8	1	no	—
22	C₄×D₂₉	—	8	1	no	—
23	C₄×D₂₉	D₈	1	1	yes	characteristic
24	#6599	—	8	1	no	—
25	C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
26	#6597	SD₁₆	1	1	yes	characteristic
27	#1417	—	29	1	no	maximal, Sylow
28	C₂×D₂₉	—	8	1	no	—
29	C₂×D₂₉	SD₃₂	1	1	yes	characteristic
30	C₄×C₂₉	—	8	1	no	—
31	C₄×C₂₉	#102	1	1	yes	characteristic
32	Dic₂₉	D₁₆	1	1	yes	characteristic
33	#508	—	29	1	no	—
34	C₂×C₃₂	—	29	1	no	—
35	#368	—	29	1	no	—
36	C₂×C₂₉	#357	1	1	yes	characteristic
37	D₂₉	—	2	1	no	—
38	D₂₉	—	16	1	no	—
39	#135	—	58	1	no	—
40	Q₃₂	#1181	1	1	yes	characteristic
41	SD₃₂	—	58	1	no	—
42	D₁₆	—	29	1	no	—
43	C₂×C₁₆	—	29	1	no	—
44	#108	—	58	1	no	—
45	C₃₂	—	58	1	no	—
46	C₂₉	#1417	1	1	yes	characteristic, complemented, Sylow
47	#41	—	116	1	no	—
48	Q₁₆	—	2	1	no	—
49	SD₁₆	—	116	1	no	—
50	D₈	—	58	1	no	—
51	M₁₆	—	116	1	no	—
52	C₂×C₈	—	29	1	no	—
53	C₁₆	—	29	1	no	—
54	C₁₆	C₂×#1181	1	1	yes	characteristic
55	Q₈	—	4	1	no	—
56	D₄	—	116	1	no	—
57	D₄	—	232	1	no	—
58	C₂×C₄	—	29	1	no	—
59	C₂×C₄	—	232	1	no	—
60	C₈	—	29	1	no	—
61	C₈	—	232	1	no	—
62	C₈	C₂²⋊#1181	1	1	yes	characteristic
63	C₂²	—	29	1	no	—
64	C₂²	—	232	1	no	—
65	C₄	—	8	1	no	—
66	C₄	—	29	1	no	—
67	C₄	#11745223	1	1	yes	characteristic
68	C₂	—	58	1	no	—
69	C₂	—	464	1	no	—
70	C₂	#14272075	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14272075
commutator	C₁₆×C₂₉	C₂×C₄
Frattini	C₁₆	C₂×#1181
Fitting	C₂₉×Q₃₂	C₄
socle	C₂×C₂₉	#357
prime radical	#14271596	C₂
cosocle	C₁₆×D₂₉	C₂²
hypercenter	Q₃₂	#1181
hypocenter	C₂₉	#1417
LCS	G ▷ C₁₆×C₂₉ ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
1. D₂₉⋊C₃₂	C₂	semidirect
2. #14272091	C₂	semidirect
46. C₂₉	#1417	semidirect

Maximal subgroups

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

subgroup	index
D₂₉⋊C₃₂	2
#14272091	2
#14271596	2
#1417	29