Subgroups — #28412349

Order 14656.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20301067	C₂	1	2	yes	maximal
2	C₂×#16814649	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#11745021	—	2	2	no	—
4	C₂²⋊#11745021	—	2	2	no	—
5	C₄×#11745021	C₄	1	4	yes	complemented
6	C₂×C₄×D₂₂₉	C₂²	1	1	yes	characteristic
7	#16814649	—	2	2	no	—
8	C₂×#14270080	C₄	1	1	yes	characteristic, complemented
9	C₂×C₈×C₂₂₉	C₄	1	1	yes	characteristic, complemented
10	C₂×#11745021	—	2	4	no	—
11	C₂²×D₂₂₉	D₄	1	1	yes	characteristic
12	C₂×Dic₂₂₉	Q₈	1	1	yes	characteristic
13	C₄×D₂₂₉	C₂×C₄	1	2	yes	—
14	C₄×D₂₂₉	D₄	1	2	yes	—
15	#14270080	—	2	1	no	—
16	C₂×C₄×C₂₂₉	C₂×C₄	1	1	yes	characteristic
17	C₈×C₂₂₉	—	2	1	no	—
18	C₂²×C₂₂₉	C₄⋊C₄	1	1	yes	characteristic
19	C₂×D₂₂₉	—	4	1	no	—
20	C₂×D₂₂₉	C₂²⋊C₄	1	2	yes	—
21	#11745021	—	4	4	no	—
22	C₄×C₂₂₉	C₄²	1	1	yes	characteristic
23	C₄×C₂₂₉	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₂₂₉	C₄⋊C₄	1	2	yes	—
25	C₂×C₂₂₉	—	2	1	no	—
26	C₂×C₂₂₉	#95	1	1	yes	characteristic
27	D₂₂₉	—	2	2	no	—
28	C₂₂₉	H(3,ℤ/4)	1	1	yes	characteristic, complemented, Sylow
29	H(3,ℤ/4)	—	229	1	no	maximal, Sylow
30	C₂×M₁₆	—	229	1	no	—
31	#117	—	229	2	no	—
32	C₂²×C₄	—	229	1	no	—
33	M₁₆	—	458	2	no	—
34	C₂×C₈	—	229	1	no	—
35	C₂×C₈	#11745021	1	1	yes	characteristic, complemented
36	C₄⋊C₄	—	458	2	no	—
37	C₂²⋊C₄	—	458	2	no	—
38	C₄²	—	229	4	no	—
39	C₂³	—	229	1	no	—
40	C₂×C₄	—	458	4	no	—
41	C₂×C₄	—	229	1	no	—
42	C₂×C₄	—	229	2	no	—
43	C₂×C₄	—	229	2	no	—
44	C₂×C₄	C₂×#11745021	1	1	yes	characteristic
45	C₈	—	2	1	no	—
46	C₈	—	458	1	no	—
47	C₂²	—	916	1	no	—
48	C₂²	—	229	2	no	—
49	C₂²	C₄⋊#11745021	1	1	yes	characteristic
50	C₄	—	916	4	no	—
51	C₄	—	229	2	no	—
52	C₄	C₄×#11745021	1	1	yes	characteristic
53	C₄	C₂²⋊#11745021	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	458	2	no	—
56	C₂	(C₂×#11745021)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×#11745021
commutator	C₄×C₂₂₉	C₄²
Frattini	C₂×C₄	C₂×#11745021
Fitting	C₂×C₈×C₂₂₉	C₄
socle	C₂×C₂₂₉	#95
prime radical	C₂²×D₂₂₉	D₄
cosocle	C₂×C₄×D₂₂₉	C₂²
hypercenter	C₂×C₈	#11745021
hypocenter	C₂₂₉	H(3,ℤ/4)
LCS	G ▷ C₄×C₂₂₉ ▷ C₂₂₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
5. C₄×#11745021	C₄	semidirect
8. C₂×#14270080	C₄	semidirect
9. C₂×C₈×C₂₂₉	C₄	semidirect
28. C₂₂₉	H(3,ℤ/4)	semidirect
35. C₂×C₈	#11745021	semidirect

Maximal subgroups

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

subgroup	index
#20301067	2
C₂×#16814649	2
H(3,ℤ/4)	229