Subgroups — #16821801

Order 3712.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271595	C₂	1	2	yes	maximal, complemented
2	Dic₄₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271002	C₂	1	2	yes	maximal, complemented
4	D₉₂₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₉×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745266	—	2	2	no	—
7	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
8	Dic₂₃₂	C₂²	1	2	yes	—
9	#11745148	—	2	2	no	—
10	D₄₆₄	C₂²	1	2	yes	—
11	C₂₉×C₃₂	C₂²	1	1	yes	characteristic
12	C₂₉×C₃₂	C₂²	1	1	yes	characteristic
13	#90805	—	4	2	no	—
14	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
15	Dic₁₁₆	—	2	2	no	—
16	D₂₃₂	—	2	2	no	—
17	#90773	—	4	2	no	—
18	C₁₆×C₂₉	D₄	1	1	yes	characteristic
19	C₁₆×C₂₉	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
21	C₂²⋊D₂₉	—	8	2	no	—
22	D₁₁₆	—	4	2	no	—
23	C₄×D₂₉	—	8	2	no	—
24	Dic₅₈	—	4	2	no	—
25	C₈×C₂₉	D₈	1	1	yes	characteristic
26	C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
27	#2262	—	29	1	no	maximal, Sylow
28	C₂²×C₂₉	D₁₆	1	1	yes	characteristic
29	C₂×D₂₉	—	8	2	no	—
30	C₄×C₂₉	D₁₆	1	1	yes	characteristic
31	C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
32	Dic₂₉	—	8	2	no	—
33	#508	—	29	2	no	—
34	Q₆₄	—	29	1	no	—
35	SD₆₄	—	29	2	no	—
36	D₃₂	—	29	1	no	—
37	C₂×C₃₂	D₂₉	1	1	yes	characteristic, complemented
38	C₂×C₂₉	—	2	1	no	—
39	C₂×C₂₉	C₂×D₁₆	1	1	yes	characteristic
40	D₂₉	—	16	2	no	—
41	#135	—	58	2	no	—
42	Q₃₂	—	29	2	no	—
43	SD₃₂	—	58	2	no	—
44	D₁₆	—	29	2	no	—
45	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
46	C₃₂	C₂×D₂₉	1	1	yes	characteristic
47	C₃₂	C₂×D₂₉	1	1	yes	characteristic
48	C₂₉	#2262	1	1	yes	characteristic, complemented, Sylow
49	#41	—	116	2	no	—
50	Q₁₆	—	58	2	no	—
51	SD₁₆	—	116	2	no	—
52	D₈	—	58	2	no	—
53	C₂×C₈	D₁₁₆	1	1	yes	characteristic
54	C₁₆	D₁₁₆	1	1	yes	characteristic
55	C₁₆	C₂²×D₂₉	1	1	yes	characteristic
56	Q₈	—	116	2	no	—
57	D₄	—	116	2	no	—
58	D₄	—	232	2	no	—
59	C₂×C₄	—	232	2	no	—
60	C₂×C₄	D₂₃₂	1	1	yes	characteristic
61	C₈	D₂₃₂	1	1	yes	characteristic
62	C₈	C₂×D₁₁₆	1	1	yes	characteristic
63	C₂²	—	232	2	no	—
64	C₂²	D₄₆₄	1	1	yes	characteristic
65	C₄	—	232	2	no	—
66	C₄	D₄₆₄	1	1	yes	characteristic
67	C₄	C₂×D₂₃₂	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	464	2	no	—
70	C₂	C₂×D₄₆₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄₆₄
commutator, cosocle	C₁₆×C₂₉	C₂³
Frattini	C₁₆	C₂²×D₂₉
Fitting	C₂×C₂₉×C₃₂	C₂
socle	C₂×C₂₉	C₂×D₁₆
hypercenter	C₂×C₃₂	D₂₉
hypocenter	C₂₉	#2262
LCS	G ▷ C₁₆×C₂₉ ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. #14271595	C₂	semidirect
2. Dic₄₆₄	C₂	semidirect
3. #14271002	C₂	semidirect
4. D₉₂₈	C₂	semidirect
5. C₂×C₂₉×C₃₂	C₂	semidirect
37. C₂×C₃₂	D₂₉	semidirect
48. C₂₉	#2262	semidirect

Maximal subgroups

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

subgroup	index
#14271595	2
Dic₄₆₄	2
#14271002	2
D₉₂₈	2
C₂×C₂₉×C₃₂	2
#2262	29