Subgroups — #16817683

Order 3712.

78 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	#14270993	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₃₂	—	2	1	no	—
5	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
6	#11745167	—	2	1	no	—
7	D₄₆₄	—	2	1	no	—
8	D₄₆₄	C₄	1	2	yes	—
9	C₂₉×C₃₂	—	2	1	no	—
10	C₂×D₁₁₆	—	4	1	no	—
11	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
12	#90777	—	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	D₈	1	1	yes	characteristic
19	D₁₁₆	—	4	2	no	—
20	D₁₁₆	—	8	1	no	—
21	C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₂₉	SD₁₆	1	1	yes	characteristic
23	#6597	—	8	1	no	—
24	#1419	—	29	1	no	maximal, Sylow
25	C₂²×C₂₉	SD₃₂	1	1	yes	characteristic
26	C₂×D₂₉	—	8	2	no	—
27	C₂×D₂₉	—	16	2	no	—
28	C₄×C₂₉	#102	1	1	yes	characteristic
29	C₄×C₂₉	D₁₆	1	1	yes	characteristic
30	C₂×D₁₆	—	29	1	no	—
31	M₆₄	D₂₉	1	1	yes	characteristic, complemented
32	#368	—	29	1	no	—
33	C₂×C₂₉	—	2	1	no	—
34	C₂×C₂₉	#357	1	1	yes	characteristic
35	D₂₉	—	16	2	no	—
36	C₂×D₈	—	58	1	no	—
37	D₁₆	—	29	2	no	—
38	D₁₆	—	58	1	no	—
39	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
40	#108	—	58	1	no	—
41	C₃₂	—	2	1	no	—
42	C₂₉	#1419	1	1	yes	characteristic, complemented, Sylow
43	C₂×D₄	—	116	1	no	—
44	D₈	—	58	2	no	—
45	D₈	—	116	1	no	—
46	M₁₆	—	116	1	no	—
47	C₂×C₈	D₁₁₆	1	1	yes	characteristic
48	C₁₆	C₄×D₂₉	1	1	yes	characteristic
49	C₁₆	C₂²⋊D₂₉	1	1	yes	characteristic
50	C₂³	—	232	1	no	—
51	D₄	—	116	2	no	—
52	D₄	—	232	1	no	—
53	C₂×C₄	D₂₃₂	1	1	yes	characteristic
54	C₈	—	232	1	no	—
55	C₈	#90773	1	1	yes	characteristic
56	C₈	#90781	1	1	yes	characteristic
57	C₂²	—	464	2	no	—
58	C₂²	—	232	2	no	—
59	C₂²	#11745148	1	1	yes	characteristic
60	C₄	D₄₆₄	1	1	yes	characteristic
61	C₄	#11745169	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	464	2	no	—
64	C₂	#14270965	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14270965
commutator	C₁₆×C₂₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₉
Fitting	C₂₉×M₆₄	C₂
socle	C₂×C₂₉	#357
prime radical	C₂×D₄₆₄	C₂
cosocle	C₂×C₁₆×C₂₉	C₂²
hypercenter	M₆₄	D₂₉
hypocenter	C₂₉	#1419
LCS	G ▷ C₁₆×C₂₉ ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
2. #14270993	C₂	semidirect
3. C₂₉×M₆₄	C₂	semidirect
31. M₆₄	D₂₉	semidirect
42. C₂₉	#1419	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
#14270993	2
C₂₉×M₆₄	2
#1419	29