Subgroups — #16821802

Order 3712.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271596	C₂	1	2	yes	maximal, complemented
2	#14271000	C₂	1	2	yes	maximal, complemented
3	D₉₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₂×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745281	—	2	2	no	—
7	C₂₉×Q₃₂	C₂²	1	2	yes	—
8	#11745176	—	2	2	no	—
9	D₄₆₄	C₂²	1	2	yes	—
10	C₁₆×D₂₉	C₂²	1	1	yes	characteristic
11	C₂₉×C₃₂	C₂²	1	1	yes	characteristic
12	#11745142	C₂²	1	1	yes	characteristic
13	#90809	—	4	2	no	—
14	Q₁₆×C₂₉	—	2	2	no	—
15	#90784	—	4	2	no	—
16	D₂₃₂	—	2	2	no	—
17	C₈×D₂₉	D₄	1	1	yes	characteristic
18	C₁₆×C₂₉	C₂³	1	1	yes	characteristic
19	#90768	D₄	1	1	yes	characteristic
20	Q₈×C₂₉	—	4	2	no	—
21	D₁₁₆	—	4	2	no	—
22	D₁₁₆	—	8	2	no	—
23	C₄×D₂₉	—	8	2	no	—
24	C₄×D₂₉	D₈	1	1	yes	characteristic
25	C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
26	#6597	D₈	1	1	yes	characteristic
27	#2262	—	29	1	no	maximal, Sylow
28	C₂×D₂₉	—	8	2	no	—
29	C₂×D₂₉	D₁₆	1	1	yes	characteristic
30	C₄×C₂₉	—	8	2	no	—
31	C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
32	Dic₂₉	D₁₆	1	1	yes	characteristic
33	#508	—	29	2	no	—
34	Q₆₄	D₂₉	1	1	yes	characteristic, complemented
35	SD₆₄	—	29	2	no	—
36	D₃₂	—	29	1	no	—
37	C₂×C₃₂	—	29	1	no	—
38	C₂×C₂₉	C₂×D₁₆	1	1	yes	characteristic
39	D₂₉	—	2	1	no	—
40	D₂₉	—	16	2	no	—
41	#135	—	58	2	no	—
42	Q₃₂	C₂×D₂₉	1	2	yes	—
43	SD₃₂	—	58	2	no	—
44	D₁₆	—	29	2	no	—
45	C₂×C₁₆	—	29	1	no	—
46	C₃₂	—	29	1	no	—
47	C₃₂	C₂×D₂₉	1	1	yes	characteristic
48	C₂₉	#2262	1	1	yes	characteristic, complemented, Sylow
49	#41	—	116	2	no	—
50	Q₁₆	—	2	2	no	—
51	SD₁₆	—	116	2	no	—
52	D₈	—	58	2	no	—
53	C₂×C₈	—	29	1	no	—
54	C₁₆	—	29	1	no	—
55	C₁₆	C₂²×D₂₉	1	1	yes	characteristic
56	Q₈	—	4	2	no	—
57	D₄	—	116	2	no	—
58	D₄	—	232	2	no	—
59	C₂×C₄	—	29	1	no	—
60	C₂×C₄	—	232	2	no	—
61	C₈	—	29	1	no	—
62	C₈	D₄×D₂₉	1	1	yes	characteristic
63	C₂²	—	29	1	no	—
64	C₂²	—	232	2	no	—
65	C₄	—	8	2	no	—
66	C₄	—	29	1	no	—
67	C₄	D₈×D₂₉	1	1	yes	characteristic
68	C₂	—	58	1	no	—
69	C₂	—	464	2	no	—
70	C₂	D₁₆×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₂₉
commutator, cosocle	C₁₆×C₂₉	C₂³
Frattini	C₁₆	C₂²×D₂₉
Fitting	C₂₉×Q₆₄	C₂
socle	C₂×C₂₉	C₂×D₁₆
hypercenter	Q₆₄	D₂₉
hypocenter	C₂₉	#2262
LCS	G ▷ C₁₆×C₂₉ ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
1. #14271596	C₂	semidirect
2. #14271000	C₂	semidirect
3. D₉₂₈	C₂	semidirect
4. C₃₂×D₂₉	C₂	semidirect
5. C₂₉×Q₆₄	C₂	semidirect
34. Q₆₄	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
#14271596	2
#14271000	2
D₉₂₈	2
C₃₂×D₂₉	2
C₂₉×Q₆₄	2
#2262	29