Subgroups — C₄⋊#16814669 #28412401

Order 14656.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16814669	C₂	1	2	yes	maximal
2	C₄×#14270080	C₂	1	1	yes	maximal, characteristic
3	#16814669	—	2	2	no	—
4	C₂×#14270080	C₄	1	1	yes	characteristic
5	C₂×#14270080	C₂²	1	1	yes	characteristic
6	C₄²×C₂₂₉	C₄	1	1	yes	characteristic
7	#14270080	—	2	1	no	—
8	#14270080	D₄	1	1	yes	characteristic
9	#14270080	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₂₂₉	C₈	1	1	yes	characteristic
11	C₂×C₄×C₂₂₉	C₈	1	1	yes	characteristic
12	C₂×C₄×C₂₂₉	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₂₂₉	C₂×C₈	1	1	yes	characteristic
14	C₄×C₂₂₉	—	2	1	no	—
15	C₄×C₂₂₉	C₁₆	1	2	yes	complemented
16	C₄×C₂₂₉	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₂₂₉	M₁₆	1	1	yes	characteristic
18	C₂×C₂₂₉	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₂₂₉	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₂₂₉	M₃₂	1	1	yes	characteristic
21	C₂₂₉	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄⋊C₁₆	—	229	1	no	maximal, Sylow
23	C₂×C₁₆	—	229	2	no	—
24	C₄×C₈	—	229	1	no	—
25	C₂×C₈	—	229	1	no	—
26	C₂×C₈	—	229	1	no	—
27	C₄²	#11745021	1	1	yes	characteristic
28	C₁₆	—	458	2	no	—
29	C₂×C₄	#14270087	1	1	yes	characteristic
30	C₂×C₄	#14270087	1	1	yes	characteristic
31	C₂×C₄	C₂×#11745021	1	1	yes	characteristic
32	C₈	—	458	1	no	—
33	C₈	—	229	1	no	—
34	C₈	—	229	1	no	—
35	C₂²	C₂×#14270087	1	1	yes	characteristic
36	C₄	—	2	1	no	—
37	C₄	#16814669	1	2	yes	complemented
38	C₄	C₄⋊#11745021	1	1	yes	characteristic
39	C₄	#16814676	1	1	yes	characteristic
40	C₂	C₄⋊#14270087	1	1	yes	characteristic
41	C₂	C₂×#16814669	1	1	yes	characteristic
42	C₂	#20301062	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#11745021
commutator	C₂×C₂₂₉	C₂×C₁₆
Fitting	C₄²×C₂₂₉	C₄
socle, prime radical	C₂²×C₂₂₉	C₂×C₈
cosocle	C₂×#14270080	C₂²
hypercenter	C₄²	#11745021
hypocenter	C₂₂₉	C₄⋊C₁₆
LCS	G ▷ C₂×C₂₂₉ ▷ C₂₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
15. C₄×C₂₂₉	C₁₆	semidirect
21. C₂₂₉	C₄⋊C₁₆	semidirect
37. C₄	#16814669	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16814669	2
C₄×#14270080	2
C₄⋊C₁₆	229

Subgroups — C4⋊#16814669 #28412401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊#16814669 #28412401