Subgroups — C₄⋊#88034 #13113032

Order 1664.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#88034	C₂	1	2	yes	maximal
3	C₂×C₁₃×C₁₆	C₄	1	1	yes	characteristic
4	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
5	C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
6	#88034	—	2	2	no	—
7	C₂×C₈×C₁₃	C₈	1	1	yes	characteristic
8	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₁₃	C₈	1	1	yes	characteristic
10	C₁₃×C₁₆	—	2	1	no	—
11	C₁₃×C₁₆	D₄	1	1	yes	characteristic
12	C₁₃×C₁₆	Q₈	1	1	yes	characteristic
13	C₄⋊C₃₂	—	13	1	no	maximal, Sylow
14	C₂×C₄×C₁₃	C₁₆	1	1	yes	characteristic
15	C₂×C₄×C₁₃	C₁₆	1	1	yes	characteristic
16	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
17	C₈×C₁₃	—	2	1	no	—
18	C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
19	C₈×C₁₃	M₁₆	1	1	yes	characteristic
20	C₂×C₃₂	—	13	2	no	—
21	C₄×C₁₆	D₁₃	1	1	yes	characteristic
22	C₂²×C₁₃	C₂×C₁₆	1	1	yes	characteristic
23	C₄×C₁₃	—	2	1	no	—
24	C₄×C₁₃	C₃₂	1	2	yes	complemented
25	C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
26	C₄×C₁₃	M₃₂	1	1	yes	characteristic
27	C₂×C₁₆	Dic₁₃	1	1	yes	characteristic
28	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
29	C₄×C₈	Dic₁₃	1	1	yes	characteristic
30	C₃₂	—	26	2	no	—
31	C₂×C₁₃	C₄⋊C₁₆	1	1	yes	characteristic
32	C₂×C₁₃	C₂×C₃₂	1	1	yes	characteristic
33	C₂×C₁₃	M₆₄	1	1	yes	characteristic
34	C₂×C₈	#1055	1	1	yes	characteristic
35	C₂×C₈	C₂×Dic₁₃	1	1	yes	characteristic
36	C₄²	#1055	1	1	yes	characteristic
37	C₁₆	—	2	1	no	—
38	C₁₆	Dic₂₆	1	1	yes	characteristic
39	C₁₆	D₅₂	1	1	yes	characteristic
40	C₁₃	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₄	#6090	1	1	yes	characteristic
42	C₂×C₄	#6090	1	1	yes	characteristic
43	C₂×C₄	C₂×#1055	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	#6099	1	1	yes	characteristic
46	C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
47	C₂²	C₂×#6090	1	1	yes	characteristic
48	C₄	—	2	1	no	—
49	C₄	#88034	1	2	yes	complemented
50	C₄	C₄⋊#1055	1	1	yes	characteristic
51	C₄	#88052	1	1	yes	characteristic
52	C₂	C₄⋊#6090	1	1	yes	characteristic
53	C₂	C₂×#88034	1	1	yes	characteristic
54	C₂	#11718091	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×D₁₃
commutator	C₂×C₁₃	C₂×C₃₂
Fitting	C₄×C₁₃×C₁₆	C₂
socle, prime radical	C₂²×C₁₃	C₂×C₁₆
cosocle	C₂×C₁₃×C₁₆	C₂²
hypercenter	C₄×C₁₆	D₁₃
hypocenter	C₁₃	C₄⋊C₃₂
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
24. C₄×C₁₃	C₃₂	semidirect
40. C₁₃	C₄⋊C₃₂	semidirect
49. C₄	#88034	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₃×C₁₆	2
C₂×#88034	2
C₄⋊C₃₂	13

Subgroups — C4⋊#88034 #13113032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊#88034 #13113032