Subgroups — #16817684

Order 3712.

70 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	#14270997	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#368	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₁₆	—	2	1	no	—
5	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
6	C₂₉×#108	—	2	1	no	—
7	Dic₂₃₂	—	2	1	no	—
8	Dic₂₃₂	C₄	1	2	yes	—
9	#11745142	—	2	1	no	—
10	C₂×Dic₅₈	—	4	1	no	—
11	M₁₆×C₂₉	—	4	1	no	—
12	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
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	Dic₅₈	—	4	2	no	—
20	Dic₅₈	—	8	1	no	—
21	C₈×C₂₉	—	8	1	no	—
22	C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₂₉	SD₁₆	1	1	yes	characteristic
24	#1420	—	29	1	no	maximal, Sylow
25	C₂²×C₂₉	SD₃₂	1	1	yes	characteristic
26	C₄×C₂₉	#102	1	1	yes	characteristic
27	C₄×C₂₉	D₁₆	1	1	yes	characteristic
28	Dic₂₉	—	8	2	no	—
29	C₂×Q₃₂	—	29	1	no	—
30	M₆₄	—	29	1	no	—
31	#368	D₂₉	1	1	yes	characteristic
32	C₂×C₂₉	—	2	1	no	—
33	C₂×C₂₉	#357	1	1	yes	characteristic
34	C₂×Q₁₆	—	58	1	no	—
35	Q₃₂	—	29	2	no	—
36	Q₃₂	—	58	1	no	—
37	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
38	#108	—	2	1	no	—
39	C₃₂	—	58	1	no	—
40	C₂₉	#1420	1	1	yes	characteristic, complemented, Sylow
41	C₂×Q₈	—	116	1	no	—
42	Q₁₆	—	58	2	no	—
43	Q₁₆	—	116	1	no	—
44	M₁₆	—	4	1	no	—
45	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
46	C₁₆	C₄×D₂₉	1	1	yes	characteristic
47	C₁₆	D₁₁₆	1	1	yes	characteristic
48	Q₈	—	116	2	no	—
49	Q₈	—	232	1	no	—
50	C₂×C₄	—	232	1	no	—
51	C₂×C₄	#90782	1	1	yes	characteristic
52	C₈	—	8	1	no	—
53	C₈	#90781	1	1	yes	characteristic
54	C₈	#90784	1	1	yes	characteristic
55	C₂²	#11745176	1	1	yes	characteristic
56	C₄	—	232	2	no	—
57	C₄	#11745157	1	1	yes	characteristic
58	C₄	#11745174	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	#14270963	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14270963
commutator	C₁₆×C₂₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₉
Fitting	C₂₉×#368	C₂
socle	C₂×C₂₉	#357
prime radical	C₂²×C₂₉	SD₃₂
cosocle	C₂×C₁₆×C₂₉	C₂²
hypercenter	#368	D₂₉
hypocenter	C₂₉	#1420
LCS	G ▷ C₁₆×C₂₉ ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
40. C₂₉	#1420	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
#14270997	2
C₂₉×#368	2
#1420	29