Subgroups — #16834518

Order 3712.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272024	C₂	1	1	yes	maximal, characteristic
2	#14272024	C₂	1	1	yes	maximal, characteristic
3	#14270938	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#6599	—	2	1	no	—
5	C₄⋊#6599	—	2	1	no	—
6	C₂×C₁₆×C₂₉	C₄	1	1	yes	characteristic
7	C₈×Dic₂₉	C₂²	1	1	yes	characteristic
8	C₂×#90768	C₄	1	1	yes	characteristic
9	C₂×#6599	—	4	1	no	—
10	C₂×#6599	—	4	1	no	—
11	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
12	C₄×Dic₂₉	D₄	1	1	yes	characteristic
13	C₂×#6597	Q₈	1	1	yes	characteristic
14	C₁₆×C₂₉	—	2	1	no	—
15	#90768	C₈	1	2	yes	complemented
16	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
17	C₂×Dic₂₉	SD₁₆	1	1	yes	characteristic
18	C₂×Dic₂₉	SD₁₆	1	1	yes	characteristic
19	#6599	—	8	1	no	—
20	#6599	—	8	1	no	—
21	C₈×C₂₉	C₂×C₈	1	1	yes	characteristic
22	C₈×C₂₉	M₁₆	1	1	yes	characteristic
23	#6597	—	2	1	no	—
24	#1368	—	29	1	no	maximal, Sylow
25	C₂²×C₂₉	#106	1	1	yes	characteristic
26	C₄×C₂₉	C₄⋊C₈	1	1	yes	characteristic
27	C₄×C₂₉	#108	1	1	yes	characteristic
28	Dic₂₉	—	2	1	no	—
29	Dic₂₉	—	2	1	no	—
30	#346	—	29	1	no	—
31	#334	—	29	1	no	—
32	#334	—	29	1	no	—
33	C₂×C₂₉	#334	1	1	yes	characteristic
34	C₂×C₂₉	#365	1	1	yes	characteristic
35	C₂×C₂₉	#365	1	1	yes	characteristic
36	C₂×C₁₆	—	29	1	no	—
37	C₂×C₁₆	#1181	1	1	yes	characteristic
38	C₄⋊C₈	—	58	1	no	—
39	C₄⋊C₈	—	58	1	no	—
40	C₄×C₈	—	29	1	no	—
41	C₂₉	#1368	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₈	—	29	1	no	—
43	C₂×C₈	—	116	1	no	—
44	C₂×C₈	—	116	1	no	—
45	C₂×C₈	C₂×#1181	1	1	yes	characteristic
46	C₄²	—	29	1	no	—
47	C₁₆	—	2	1	no	—
48	C₁₆	—	29	2	no	—
49	C₂×C₄	—	29	1	no	—
50	C₂×C₄	—	29	1	no	—
51	C₂×C₄	C₄⋊#1181	1	1	yes	characteristic
52	C₈	—	58	1	no	—
53	C₈	—	232	1	no	—
54	C₈	—	232	1	no	—
55	C₈	D₂₉⋊C₈	1	1	yes	characteristic
56	C₈	#90800	1	1	yes	characteristic
57	C₂²	#11745209	1	1	yes	characteristic
58	C₄	—	58	1	no	—
59	C₄	—	58	1	no	—
60	C₄	#11745212	1	1	yes	characteristic
61	C₄	#11745220	1	1	yes	characteristic
62	C₂	#14272025	1	1	yes	characteristic
63	C₂	#14272087	1	1	yes	characteristic
64	C₂	#14272088	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11745209
commutator	C₈×C₂₉	C₂×C₈
Frattini	C₂×C₈	C₂×#1181
Fitting	C₂×C₁₆×C₂₉	C₄
socle, prime radical	C₂²×C₂₉	#106
cosocle	C₈×Dic₂₉	C₂²
hypercenter	C₂×C₁₆	#1181
hypocenter	C₂₉	#1368
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
15. #90768	C₈	semidirect
41. C₂₉	#1368	semidirect

Maximal subgroups

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

subgroup	index
#14272024	2
#14270938	2
#1368	29