Subgroups — #16817674

Order 3712.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₃₂	C₂	1	1	yes	maximal, characteristic
2	#14270989	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₁₆	—	2	1	no	—
5	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
6	#11745166	—	2	1	no	—
7	Dic₂₃₂	—	2	1	no	—
8	Dic₂₃₂	C₄	1	2	yes	complemented
9	C₂₉×C₃₂	—	2	1	no	—
10	C₂×Dic₅₈	—	4	1	no	—
11	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
12	C₄⋊Dic₂₉	—	4	1	no	—
13	Dic₁₁₆	—	2	2	no	—
14	Dic₁₁₆	—	4	1	no	—
15	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₂₉	D₄	1	1	yes	characteristic
17	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
18	C₂×Dic₂₉	—	8	1	no	—
19	C₂×Dic₂₉	—	8	1	no	—
20	Dic₅₈	—	4	2	no	—
21	Dic₅₈	—	8	1	no	—
22	C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₂₉	SD₁₆	1	1	yes	characteristic
24	#1416	—	29	1	no	maximal, Sylow
25	C₂²×C₂₉	D₁₆	1	1	yes	characteristic
26	C₄×C₂₉	#102	1	1	yes	characteristic
27	C₄×C₂₉	SD₃₂	1	1	yes	characteristic
28	Dic₂₉	—	8	2	no	—
29	Dic₂₉	—	16	1	no	—
30	C₂×Q₃₂	—	29	1	no	—
31	C₂×C₃₂	D₂₉	1	1	yes	characteristic
32	#366	—	29	1	no	—
33	C₂×C₂₉	#357	1	1	yes	characteristic
34	C₂×C₂₉	SD₆₄	1	1	yes	characteristic
35	C₂×C₂₉	Q₆₄	1	1	yes	characteristic
36	C₂×Q₁₆	—	58	1	no	—
37	Q₃₂	—	29	2	no	—
38	Q₃₂	—	58	1	no	—
39	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
40	#107	—	58	1	no	—
41	C₃₂	—	2	1	no	—
42	C₂₉	#1416	1	1	yes	characteristic, complemented, Sylow
43	C₂×Q₈	—	116	1	no	—
44	Q₁₆	—	58	2	no	—
45	Q₁₆	—	116	1	no	—
46	C₂×C₈	D₁₁₆	1	1	yes	characteristic
47	C₄⋊C₄	—	116	1	no	—
48	C₁₆	C₄×D₂₉	1	1	yes	characteristic
49	C₁₆	C₂²⋊D₂₉	1	1	yes	characteristic
50	Q₈	—	116	2	no	—
51	Q₈	—	232	1	no	—
52	C₂×C₄	—	232	1	no	—
53	C₂×C₄	—	232	1	no	—
54	C₂×C₄	D₂₃₂	1	1	yes	characteristic
55	C₈	#90773	1	1	yes	characteristic
56	C₈	#90781	1	1	yes	characteristic
57	C₂²	D₄₆₄	1	1	yes	characteristic
58	C₄	—	464	1	no	—
59	C₄	—	232	2	no	—
60	C₄	#11745148	1	1	yes	characteristic
61	C₄	#11745169	1	1	yes	characteristic
62	C₂	#14270965	1	1	yes	characteristic
63	C₂	#14271002	1	1	yes	characteristic
64	C₂	Dic₄₆₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄₆₄
commutator	C₁₆×C₂₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₉
Fitting	C₂×C₂₉×C₃₂	C₂
socle, prime radical	C₂²×C₂₉	D₁₆
cosocle	C₂×C₁₆×C₂₉	C₂²
hypercenter	C₂×C₃₂	D₂₉
hypocenter	C₂₉	#1416
LCS	G ▷ C₁₆×C₂₉ ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
8. Dic₂₃₂	C₄	semidirect
42. C₂₉	#1416	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₂₃₂	2
#14270989	2
C₂×C₂₉×C₃₂	2
#1416	29