Subgroups — #16817561

Order 3712.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#90768	C₂	1	1	yes	maximal, characteristic
2	C₈×#6597	C₂	1	1	yes	maximal, characteristic
3	C₂₉×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₆×C₂₉	—	2	1	no	—
5	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	C₂×#90768	—	2	1	no	—
7	C₄×#6597	C₄	1	1	yes	characteristic
8	C₄×#6597	C₄	1	1	yes	characteristic
9	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
10	C₂×C₈×C₂₉	Q₈	1	1	yes	characteristic
11	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
12	C₂×#6597	—	2	1	no	—
13	C₂×#6597	C₈	1	1	yes	characteristic
14	C₂×#6597	C₈	1	1	yes	characteristic
15	C₁₆×C₂₉	—	4	1	no	—
16	#90768	—	4	1	no	—
17	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
19	C₂×C₄×C₂₉	M₁₆	1	1	yes	characteristic
20	C₈×C₂₉	—	2	1	no	—
21	C₈×C₂₉	D₈	1	1	yes	characteristic
22	C₈×C₂₉	Q₁₆	1	1	yes	characteristic
23	#6597	—	2	2	no	—
24	#6597	—	2	1	no	—
25	#6597	C₁₆	1	2	yes	complemented
26	#1370	—	29	1	no	maximal, Sylow
27	C₂²×C₂₉	C₄⋊C₈	1	1	yes	characteristic
28	C₄×C₂₉	—	2	1	no	—
29	C₄×C₂₉	#107	1	1	yes	characteristic
30	C₄×C₂₉	#108	1	1	yes	characteristic
31	C₄×C₂₉	C₂×C₁₆	1	1	yes	characteristic
32	C₄×C₂₉	M₃₂	1	1	yes	characteristic
33	C₄⋊C₁₆	—	29	1	no	—
34	C₄⋊C₁₆	D₂₉	1	1	yes	characteristic
35	C₈²	—	29	1	no	—
36	C₂×C₂₉	#335	1	1	yes	characteristic
37	C₂×C₂₉	C₄⋊C₁₆	1	1	yes	characteristic
38	C₂×C₂₉	#364	1	1	yes	characteristic
39	C₂×C₁₆	—	2	1	no	—
40	C₂×C₁₆	—	58	1	no	—
41	C₄×C₈	—	29	1	no	—
42	C₄×C₈	—	29	1	no	—
43	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
44	C₂₉	#1370	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₈	—	29	1	no	—
46	C₂×C₈	—	29	1	no	—
47	C₂×C₈	—	58	1	no	—
48	C₂×C₈	Dic₅₈	1	1	yes	characteristic
49	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
50	C₄²	C₄×D₂₉	1	1	yes	characteristic
51	C₁₆	—	4	1	no	—
52	C₁₆	—	116	1	no	—
53	C₂×C₄	C₈×D₂₉	1	1	yes	characteristic
54	C₂×C₄	#90772	1	1	yes	characteristic
55	C₂×C₄	#90779	1	1	yes	characteristic
56	C₈	—	2	1	no	—
57	C₈	—	29	2	no	—
58	C₈	—	58	2	no	—
59	C₈	—	58	1	no	—
60	C₈	#90782	1	1	yes	characteristic
61	C₈	#90785	1	1	yes	characteristic
62	C₂²	#11745162	1	1	yes	characteristic
63	C₄	—	2	1	no	—
64	C₄	C₁₆×D₂₉	1	1	yes	characteristic
65	C₄	#11745146	1	1	yes	characteristic
66	C₄	#11745155	1	1	yes	characteristic
67	C₄	#11745170	1	1	yes	characteristic
68	C₂	#14270915	1	1	yes	characteristic
69	C₂	#14270981	1	1	yes	characteristic
70	C₂	#14270983	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₂₉
commutator	C₄×C₂₉	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₂₉
Fitting	C₂₉×C₄⋊C₁₆	C₂
socle, prime radical	C₂²×C₂₉	C₄⋊C₈
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	C₄⋊C₁₆	D₂₉
hypocenter	C₂₉	#1370
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
25. #6597	C₁₆	semidirect
44. C₂₉	#1370	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#90768	2
C₈×#6597	2
C₂₉×C₄⋊C₁₆	2
#1370	29