Subgroups — #16817669

Order 3712.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₆₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#11745142	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#366	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₃₂	—	2	1	no	—
5	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
6	C₂₉×#107	—	2	1	no	—
7	D₄₆₄	—	2	1	no	—
8	D₄₆₄	C₄	1	2	yes	complemented
9	#11745142	—	2	1	no	—
10	C₂×D₁₁₆	—	4	1	no	—
11	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
12	C₄⋊C₄×C₂₉	—	4	1	no	—
13	D₂₃₂	—	2	2	no	—
14	D₂₃₂	—	4	1	no	—
15	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₂₉	D₄	1	1	yes	characteristic
17	C₂²×D₂₉	—	8	1	no	—
18	C₂×C₄×C₂₉	—	8	1	no	—
19	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
20	D₁₁₆	—	4	2	no	—
21	D₁₁₆	—	8	1	no	—
22	C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₂₉	SD₁₆	1	1	yes	characteristic
24	#1415	—	29	1	no	maximal, Sylow
25	C₂²×C₂₉	D₁₆	1	1	yes	characteristic
26	C₂×D₂₉	—	8	2	no	—
27	C₂×D₂₉	—	16	1	no	—
28	C₂×D₂₉	—	16	1	no	—
29	C₄×C₂₉	—	16	1	no	—
30	C₄×C₂₉	#102	1	1	yes	characteristic
31	C₄×C₂₉	SD₃₂	1	1	yes	characteristic
32	C₂×D₁₆	—	29	1	no	—
33	C₂×C₃₂	—	29	1	no	—
34	#366	D₂₉	1	1	yes	characteristic, complemented
35	C₂×C₂₉	#357	1	1	yes	characteristic
36	C₂×C₂₉	D₃₂	1	1	yes	characteristic
37	C₂×C₂₉	SD₆₄	1	1	yes	characteristic
38	D₂₉	—	16	2	no	—
39	C₂×D₈	—	58	1	no	—
40	D₁₆	—	29	2	no	—
41	D₁₆	—	58	1	no	—
42	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
43	#107	—	2	1	no	—
44	C₃₂	—	58	1	no	—
45	C₂₉	#1415	1	1	yes	characteristic, complemented, Sylow
46	C₂×D₄	—	116	1	no	—
47	D₈	—	58	2	no	—
48	D₈	—	116	1	no	—
49	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
50	C₄⋊C₄	—	4	1	no	—
51	C₁₆	C₄×D₂₉	1	1	yes	characteristic
52	C₁₆	D₁₁₆	1	1	yes	characteristic
53	C₂³	—	232	1	no	—
54	D₄	—	116	2	no	—
55	D₄	—	232	1	no	—
56	C₂×C₄	—	8	1	no	—
57	C₂×C₄	#90782	1	1	yes	characteristic
58	C₈	#90781	1	1	yes	characteristic
59	C₈	#90784	1	1	yes	characteristic
60	C₂²	—	464	1	no	—
61	C₂²	—	464	1	no	—
62	C₂²	—	232	2	no	—
63	C₂²	#11745174	1	1	yes	characteristic
64	C₄	—	16	1	no	—
65	C₄	#11745157	1	1	yes	characteristic
66	C₄	#11745176	1	1	yes	characteristic
67	C₂	—	464	2	no	—
68	C₂	#14270963	1	1	yes	characteristic
69	C₂	#14270998	1	1	yes	characteristic
70	C₂	#14271000	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11745174
commutator	C₁₆×C₂₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₉
Fitting	C₂₉×#366	C₂
socle	C₂²×C₂₉	D₁₆
prime radical	C₂×D₄₆₄	C₂
cosocle	C₂×C₁₆×C₂₉	C₂²
hypercenter	#366	D₂₉
hypocenter	C₂₉	#1415
LCS	G ▷ C₁₆×C₂₉ ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
2. C₂×#11745142	C₂	semidirect
3. C₂₉×#366	C₂	semidirect
8. D₄₆₄	C₄	semidirect
34. #366	D₂₉	semidirect
45. C₂₉	#1415	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄₆₄	2
C₂×#11745142	2
C₂₉×#366	2
#1415	29