Subgroups — #16817675

Order 3712.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271595	C₂	1	1	yes	maximal, characteristic
2	C₂×#11745142	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#368	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745266	—	2	1	no	—
5	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
6	C₂₉×#108	—	2	1	no	—
7	Dic₂₃₂	C₄	1	1	yes	characteristic
8	#11745148	—	2	1	no	—
9	D₄₆₄	C₄	1	1	yes	characteristic
10	#11745142	—	2	1	no	—
11	#90805	—	4	1	no	—
12	M₁₆×C₂₉	—	4	1	no	—
13	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
14	Dic₁₁₆	—	2	1	no	—
15	D₂₃₂	—	2	1	no	—
16	#90773	—	4	1	no	—
17	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₂₉	D₄	1	1	yes	characteristic
19	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
20	C₂²⋊D₂₉	—	8	1	no	—
21	D₁₁₆	—	4	1	no	—
22	C₄×D₂₉	—	8	1	no	—
23	Dic₅₈	—	4	1	no	—
24	C₈×C₂₉	—	8	1	no	—
25	C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₂₉	SD₁₆	1	1	yes	characteristic
27	#1417	—	29	1	no	maximal, Sylow
28	C₂²×C₂₉	SD₃₂	1	1	yes	characteristic
29	C₂×D₂₉	—	8	1	no	—
30	C₄×C₂₉	#102	1	1	yes	characteristic
31	C₄×C₂₉	D₁₆	1	1	yes	characteristic
32	Dic₂₉	—	8	1	no	—
33	#508	—	29	1	no	—
34	C₂×C₃₂	—	29	1	no	—
35	#368	D₂₉	1	1	yes	characteristic, complemented
36	C₂×C₂₉	—	2	1	no	—
37	C₂×C₂₉	#357	1	1	yes	characteristic
38	D₂₉	—	16	1	no	—
39	#135	—	58	1	no	—
40	Q₃₂	—	29	1	no	—
41	SD₃₂	—	58	1	no	—
42	D₁₆	—	29	1	no	—
43	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
44	#108	—	2	1	no	—
45	C₃₂	—	58	1	no	—
46	C₂₉	#1417	1	1	yes	characteristic, complemented, Sylow
47	#41	—	116	1	no	—
48	Q₁₆	—	58	1	no	—
49	SD₁₆	—	116	1	no	—
50	D₈	—	58	1	no	—
51	M₁₆	—	4	1	no	—
52	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
53	C₁₆	C₄×D₂₉	1	1	yes	characteristic
54	C₁₆	D₁₁₆	1	1	yes	characteristic
55	Q₈	—	116	1	no	—
56	D₄	—	116	1	no	—
57	D₄	—	232	1	no	—
58	C₂×C₄	—	232	1	no	—
59	C₂×C₄	#90782	1	1	yes	characteristic
60	C₈	—	8	1	no	—
61	C₈	#90781	1	1	yes	characteristic
62	C₈	#90784	1	1	yes	characteristic
63	C₂²	—	232	1	no	—
64	C₂²	#11745176	1	1	yes	characteristic
65	C₄	—	232	1	no	—
66	C₄	#11745157	1	1	yes	characteristic
67	C₄	#11745174	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	464	1	no	—
70	C₂	#14270963	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11745174
commutator	C₁₆×C₂₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₉
Fitting	C₂₉×#368	C₂
socle	C₂×C₂₉	#357
prime radical	#14271595	C₂
cosocle	C₂×C₁₆×C₂₉	C₂²
hypercenter	#368	D₂₉
hypocenter	C₂₉	#1417
LCS	G ▷ C₁₆×C₂₉ ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
2. C₂×#11745142	C₂	semidirect
3. C₂₉×#368	C₂	semidirect
35. #368	D₂₉	semidirect
46. C₂₉	#1417	semidirect

Maximal subgroups

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

subgroup	index
#14271595	2
C₂×#11745142	2
C₂₉×#368	2
#1417	29