Subgroups — C₄⋊#11745142 #16817688

Order 3712.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745142	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₂₉	C₄	1	1	yes	characteristic
4	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
5	C₄×C₈×C₂₉	C₄	1	1	yes	characteristic
6	#11745142	—	2	2	no	—
7	C₂×C₈×C₂₉	C₈	1	1	yes	characteristic
8	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₂₉	C₈	1	1	yes	characteristic
10	C₁₆×C₂₉	—	2	1	no	—
11	C₁₆×C₂₉	D₄	1	1	yes	characteristic
12	C₁₆×C₂₉	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₂₉	C₁₆	1	1	yes	characteristic
14	C₂×C₄×C₂₉	C₁₆	1	1	yes	characteristic
15	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
16	C₈×C₂₉	—	2	1	no	—
17	C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₂₉	M₁₆	1	1	yes	characteristic
19	C₄⋊C₃₂	—	29	1	no	maximal, Sylow
20	C₂²×C₂₉	C₂×C₁₆	1	1	yes	characteristic
21	C₄×C₂₉	—	2	1	no	—
22	C₄×C₂₉	C₃₂	1	2	yes	complemented
23	C₄×C₂₉	C₄⋊C₈	1	1	yes	characteristic
24	C₄×C₂₉	M₃₂	1	1	yes	characteristic
25	C₂×C₃₂	—	29	2	no	—
26	C₄×C₁₆	D₂₉	1	1	yes	characteristic
27	C₂×C₂₉	C₄⋊C₁₆	1	1	yes	characteristic
28	C₂×C₂₉	C₂×C₃₂	1	1	yes	characteristic
29	C₂×C₂₉	M₆₄	1	1	yes	characteristic
30	C₂×C₁₆	Dic₂₉	1	1	yes	characteristic
31	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
32	C₄×C₈	Dic₂₉	1	1	yes	characteristic
33	C₃₂	—	58	2	no	—
34	C₂₉	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₈	#6597	1	1	yes	characteristic
36	C₂×C₈	C₂×Dic₂₉	1	1	yes	characteristic
37	C₄²	#6597	1	1	yes	characteristic
38	C₁₆	—	2	1	no	—
39	C₁₆	Dic₅₈	1	1	yes	characteristic
40	C₁₆	D₁₁₆	1	1	yes	characteristic
41	C₂×C₄	#90768	1	1	yes	characteristic
42	C₂×C₄	#90768	1	1	yes	characteristic
43	C₂×C₄	C₂×#6597	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	#90777	1	1	yes	characteristic
46	C₈	C₄⋊Dic₂₉	1	1	yes	characteristic
47	C₂²	C₂×#90768	1	1	yes	characteristic
48	C₄	—	2	1	no	—
49	C₄	#11745142	1	2	yes	complemented
50	C₄	C₄⋊#6597	1	1	yes	characteristic
51	C₄	#11745160	1	1	yes	characteristic
52	C₂	C₄⋊#90768	1	1	yes	characteristic
53	C₂	C₂×#11745142	1	1	yes	characteristic
54	C₂	#14270997	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×D₂₉
commutator	C₂×C₂₉	C₂×C₃₂
Fitting	C₄×C₁₆×C₂₉	C₂
socle, prime radical	C₂²×C₂₉	C₂×C₁₆
cosocle	C₂×C₁₆×C₂₉	C₂²
hypercenter	C₄×C₁₆	D₂₉
hypocenter	C₂₉	C₄⋊C₃₂
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
22. C₄×C₂₉	C₃₂	semidirect
34. C₂₉	C₄⋊C₃₂	semidirect
49. C₄	#11745142	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745142	2
C₄×C₁₆×C₂₉	2
C₄⋊C₃₂	29

Subgroups — C4⋊#11745142 #16817688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊#11745142 #16817688