Subgroups — #16817678

Order 3712.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271595	C₂	1	1	yes	maximal, characteristic
2	#14270997	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#367	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745266	—	2	1	no	—
5	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
6	C₂₉×#107	—	2	1	no	—
7	Dic₂₃₂	C₄	1	1	yes	characteristic, complemented
8	#11745148	—	2	1	no	—
9	D₄₆₄	C₄	1	1	yes	characteristic, complemented
10	#11745142	—	2	1	no	—
11	#90805	—	4	1	no	—
12	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
13	C₄⋊C₄×C₂₉	—	4	1	no	—
14	Dic₁₁₆	—	2	1	no	—
15	D₂₃₂	—	2	1	no	—
16	#90773	—	4	1	no	—
17	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₂₉	D₄	1	1	yes	characteristic
19	C₂×C₄×C₂₉	—	8	1	no	—
20	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
21	C₂²⋊D₂₉	—	8	1	no	—
22	D₁₁₆	—	4	1	no	—
23	C₄×D₂₉	—	8	1	no	—
24	Dic₅₈	—	4	1	no	—
25	C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₂₉	SD₁₆	1	1	yes	characteristic
27	#1418	—	29	1	no	maximal, Sylow
28	C₂²×C₂₉	D₁₆	1	1	yes	characteristic
29	C₂×D₂₉	—	8	1	no	—
30	C₄×C₂₉	—	16	1	no	—
31	C₄×C₂₉	#102	1	1	yes	characteristic
32	C₄×C₂₉	SD₃₂	1	1	yes	characteristic
33	Dic₂₉	—	8	1	no	—
34	#508	—	29	1	no	—
35	M₆₄	—	29	1	no	—
36	#367	D₂₉	1	1	yes	characteristic, complemented
37	C₂×C₂₉	—	2	1	no	—
38	C₂×C₂₉	#357	1	1	yes	characteristic
39	D₂₉	—	16	1	no	—
40	#135	—	58	1	no	—
41	Q₃₂	—	29	1	no	—
42	SD₃₂	—	58	1	no	—
43	D₁₆	—	29	1	no	—
44	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
45	#107	—	2	1	no	—
46	C₃₂	—	58	1	no	—
47	C₂₉	#1418	1	1	yes	characteristic, complemented, Sylow
48	#41	—	116	1	no	—
49	Q₁₆	—	58	1	no	—
50	SD₁₆	—	116	1	no	—
51	D₈	—	58	1	no	—
52	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
53	C₄⋊C₄	—	4	1	no	—
54	C₁₆	C₄×D₂₉	1	1	yes	characteristic
55	C₁₆	D₁₁₆	1	1	yes	characteristic
56	Q₈	—	116	1	no	—
57	D₄	—	116	1	no	—
58	D₄	—	232	1	no	—
59	C₂×C₄	—	8	1	no	—
60	C₂×C₄	—	232	1	no	—
61	C₂×C₄	#90782	1	1	yes	characteristic
62	C₈	#90781	1	1	yes	characteristic
63	C₈	#90784	1	1	yes	characteristic
64	C₂²	—	232	1	no	—
65	C₂²	#11745174	1	1	yes	characteristic
66	C₄	—	16	1	no	—
67	C₄	—	232	1	no	—
68	C₄	#11745157	1	1	yes	characteristic
69	C₄	#11745176	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	464	1	no	—
72	C₂	#14270963	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14270963
commutator	C₁₆×C₂₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₉
Fitting	C₂₉×#367	C₂
socle	C₂×C₂₉	#357
prime radical	#14271595	C₂
cosocle	C₂×C₁₆×C₂₉	C₂²
hypercenter	#367	D₂₉
hypocenter	C₂₉	#1418
LCS	G ▷ C₁₆×C₂₉ ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #367

Complements

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

N	H ≅ G/N	type
2. #14270997	C₂	semidirect
3. C₂₉×#367	C₂	semidirect
7. Dic₂₃₂	C₄	semidirect
9. D₄₆₄	C₄	semidirect
36. #367	D₂₉	semidirect
47. C₂₉	#1418	semidirect

Maximal subgroups

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

subgroup	index
#14271595	2
#14270997	2
C₂₉×#367	2
#1418	29